Is Cetacean Intelligence Special? New Perspectives
on the Debate
Departamento de Fisica Fundamental, Facultad de Ciencias de la UNED, Paseo Senda del Rey No. 9,
28040 Madrid, Spain; firstname.lastname@example.org
Received: 28 June 2017; Accepted: 2 September 2017; Published: 13 October 2017
In recent years, the interpretation of our observations of animal behaviour, in particular
that of cetaceans, has captured a substantial amount of attention in the scientiﬁc community.
The traditional view that supports a special intellectual status for this mammalian order has fallen
under signiﬁcant scrutiny, in large part due to problems of how to deﬁne and test the cognitive
performance of animals. This paper presents evidence supporting complex cognition in cetaceans
obtained using the recently developed intelligence and embodiment hypothesis. This hypothesis is
based on evolutionary neuroscience and postulates the existence of a common information-processing
principle associated with nervous systems that evolved naturally and serves as the foundation from
which intelligence can emerge. This theoretical framework explaining animal intelligence in neural
computational terms is supported using a new mathematical model. Two pathways leading to
higher levels of intelligence in animals are identiﬁed, each reﬂecting a trade-off either in energetic
requirements or the number of neurons used. A description of the evolutionary pathway that led
to increased cognitive capacities in cetacean brains is detailed and evidence supporting complex
cognition in cetaceans is presented. This paper also provides an interpretation of the adaptive function
of cetacean neuronal traits.
brain representations; intelligence; cetaceans; neural connectivity; energetic requirements
Cetaceans (whales, dolphins, and porpoises) are marine mammals that resulted from the
re-adaptation to the aquatic environment by terrestrial species. This evolutionary process of
re-adaptation was accompanied by extreme anatomical and physiological changes in the brain that
resulted in the most successful mammalian colonization of the aquatic environment. Cetaceans possess
not only extremely large and convoluted brains that set them apart from most other mammals but
also many other neurological features, such as a high glia-to-neuron ratio, reduction of the olfactory
system, or a cytoarchitectural organization of the cerebral cortex that does not resemble that of
terrestrial mammals [
] Among the toothed whales (Odontocetes), one family, the Delphinidae or
dolphins, evolved not only a relatively large size of the cortex but also a new and highly sophisticated
sonar system for underwater orientation and navigation. For example, the encephalization quotient
(a relative brain size measure) of the bottlenose dolphin (Tursiop truncatus) is greater compared to all
non-human primates.In the Physeteridae (another toothed whale family), which comprises the sperm
whale (Physeter macrocephalus), adult males can attain a brain mass of up to 9200 g [
the absolute brain size of the biggest member of the family Delphinidae, that is, the killer whale
(Orcinus orca), is more similar to that of the sperm whale than has previously been recognized [
which leads to both of them being classed as the animals having the largest brains in absolute terms.
Undoubtedly, cetacean’s brains harbor many mysteries, including why they evolved a cortex that
is less highly laminated and in general much thinner than the neocortex of primates, the ability to
Entropy 2017,19, 543; doi:10.3390/e19100543 www.mdpi.com/journal/entropy
Entropy 2017,19, 543 2 of 35
sleep with one cerebral hemisphere at a time [
], or simply which evolutionary strategies were
used to cope with the network scaling costs of an increased brain size. The current understanding
of how brain anatomy and physiology relate to animal behavior is still so incomplete that in spite
of the fact that several hypotheses have been proposed for most of the neuronal traits [
], it is
difﬁcult to comprehend what their adaptive function might have been [
]. Thus, the interpretation
of the evolutionary and functional signiﬁcance of such specializations has long been a challenge to
neurobiologists. For example, the development of this high encephalization level of dolphins and
other toothed whales has been correlated with social competition [
], water temperature during
the Eocene-Oligocene transition period [
], enhanced auditory processing [
], and audiomotor
Perhaps the largest challenge is to determine how these various specializations of the cetacean
brain relate to intelligence. The large size of the cetacean brain and their reported behaviors have
been popularly accepted as being indicative of high levels of intelligence. However, from the scientiﬁc
community’s viewpoint, the interpretation of behavioral observations in cetaceans and especially
whether there is real support (or not) for a special intellectual status for this mammalian order has
generated a substantial amount of controversy [2,18–23].
Historically, humans have tended to undervalue the cognitive capacities of animals (e.g., their
exceptional sensory skills), over-evaluating at the same time our problem-solving ability, our capacity
to modify our environment, and our ability to communicate with one another. For example, the notion
that only humans can remember speciﬁc episodes of their life or the image of man as the only toolmaker
were destroyed by the ﬁndings that some crows and chimpanzees also use and manufacture tools, and
more recently, other species such as elephants or cetaceans have been found to do so [
]. Thus, ideas
about what marks the boundary between human and nonhuman intelligence have undergone repeated
revision. Certainly, the accurate assessment of animal intelligence requires evaluating cognitive
functioning against simpler accounts and, at the same time, requires determining the conditions that
maximally elicit the animal’s cognitive capacity [
], for example, most reptiles, perform much better
in learning tasks if they are given warmth, rather than food, as a reward. Similarly, chimpanzees are
better at learning human sign language than spoken language partly because they naturally use their
hands to gesture and also because their vocal tract does not allow them to produce well-formed speech
]. These goals are especially important in the case of cetaceans not only because of the
clearly perceptible logistical difﬁculties of studying them but also because there is a compelling need
to relate these supposed differences in animal intelligence to brain properties and to understand them
in neural-computational terms .
In this paper, attention is placed on presenting an analysis of the cognitive capacities of cetaceans
from the perspective of the intelligence and embodiment hypothesis [
]. In doing so, the goal
is to reveal further insights that are of relevance to the current debate on cetacean intelligence.
The hypothesis postulates the existence of a common information-processing principle that is being
exploited in naturally evolved nervous systems, and that this serves as the founding pillar of
intelligence. A mathematical model that is suited for making quantitative predictions about the
cognitive capacities of species for comparative purposes is also provided. As the order Cetacea is a
very diverse group [
], and due to the aforementioned reasons, little is currently known about the
intelligence of most cetaceans [
]; hence, it is important to emphasize that the focus of the present study
is primarily on large-brained cetacean species and/or those species with brains of comparable size
to terrestrial species on which there are sufﬁcient neurophysiological statistics and also documented
behavioural evidence of their overall cognitive sophistication. Furthermore, the principal conclusions
derived from this study must be interpreted according to the premises of the scientiﬁc method, that
is, as predictions resulting from the extension of the mathematical model and a hypothesis that must
subsequently be veriﬁed or refuted by future studies.
Entropy 2017,19, 543 3 of 35
2. Materials and Methods
2.1. Hypothesis Background
The intelligence and embodiment hypothesis [
] subscribes to the idea of cognition as
an evolutionary adaptational redeployment of movement control [
]. This term is used to express,
from an evolutionary perspective the idea that the extensive neuronal machinery developed to
control animal movement was expanded to control new brain structures instead of muscles (Figure 1).
Speciﬁcally, discrete bodies of neuronal tissue speciﬁcally evolved to exploit the pre-existing neuronal
muscle-control mechanism but instead of conferring motility, these new brain structures would carry
out a type of information processing that is currently denoted as cognition. This information-processing
principle common to the nervous systems that evolved in nature is postulated to be the basis for
the emergence of intelligence. Furthermore, the hypothesis associates this information-processing
principle to the cortex and its homologues (i.e., functionally similar cerebral structures in other
species), in other words, the neurobiological structures that emerged as a result of the aforementioned
evolutionary adaptational redeployment of movement control. Particularly, in the insect’s brain the
mushroom body (a sensory associative brain center) is the homologue structure of the cerebral cortex
in mammals [
]. The amphibian dorsal pallium is the most likely homologue of the mammalian
cortex and is a bi-laminar structure. Similarly, in bird and reptile brains, the dorsal ventricular ridge
is a cerebral structure with gross differences in morphology (i.e., forming nuclei instead of layers)
compared to the mammalian cortex but fullﬁlling similar functions [13,33,34].
From a computational point of view the hypothesis describes this information-processing principle
in terms of combinatorial operations that are carried out over brain representations. This computational
mechanism is denoted as movement primitives to emphasize the fact that is inherited from primitive
animals as a result of the phylogenetic conservation principle. These movement primitives are
postulated as the underlying substrate that is common to any cognitive function. They are proposed
to put forward for consideration the idea of an information-processing mechanism that is designed
to combine sensorimotor representations into rule-conforming higher-order brain representations.
Such high-order or more complex representations are postulated to be the basis for context-independent
representations in a hierarchically organized information-processing system.
A cognitive architecture is deﬁned to capture the aforementioned principles, and also some aspects
of the structural (e.g., physiologic) and functional (e.g., dynamic) characteristics of these cerebral
structures with a certain level of abstraction. The cognitive architecture consists of a hierarchical
symbol-based architecture of varying size and complexity to account for certain neurobiological
differences between species, where the symbols act as the embodiment of brain representations.
These hierarchical symbol-based structures are used to account for certain neurobiological differences
between species, and especially to model the fact that progressive functional abstraction over network
depth is a fundamental feature of brains [
]. Speciﬁcally, in spite of the fact that recurrent connectivity
is a fundamental feature of brain’s structural networks, cortical functional networks display a global
hierarchical organization. In other words, information representation in the brain demonstrates a
hierarchical structure [
]. Brain representations are assumed to be physically encoded by neuron
assemblies (i.e., as states of attractor networks). In other words, a piece of information is represented
as the simultaneous activity of a group of neurons [
]. It is important to note that nervous systems
are physical devices that are conﬁgured in such a way that their states represent the external world,
the body and, in some instances, parts of the nervous system itself, but the whole concept is that their
physical state transitions execute computations [
]. Furthermore, the interactions between symbols in
the cognitive architecture are grounded in the concept of movement primitives. Speciﬁcally, they are
modeled in terms of permutations operations between symbols.
Entropy 2017,19, 543 4 of 35
Graphical synthesis of the essential components of the Intelligence and embodiment
]. This hypothesis postulates the existence of a common information-processing
principle being exploited by the nervous systems that evolved from nature as the basis for the
emergence of intelligence. The hypothesis subscribes to the idea of cognition as an evolutionary
adaptational redeployment of movement control [
]. Speciﬁcally, discrete bodies of neuronal tissue
speciﬁcally evolved to exploit the pre-existing neuronal muscle-control mechanism but instead of
conferring motility, these new brain structures would carry out a type of information processing that
is currently denoted as cognition. This information-processing principle common to the nervous
systems that evolved in nature is postulated to be the basis for the emergence of intelligence.
Furthermore, the hypothesis associates this information-processing principle to the cerebral cortex and
its homologues (i.e., functionally similar cerebral structures in other species). A cognitive architecture
is deﬁned to capture the aforementioned principles, and also the structural (e.g., physiologic) and
functional (e.g., dynamic) characteristics of these cerebral structures with a certain level of abstraction.
The cognitive architecture consists of a hierarchical symbol-based architecture of varying size and
complexity, where the symbols act as the embodiment of brain representations. These hierarchical
symbol-based structures are used to model the fact that progressive functional abstraction over
network depth is a fundamental feature of brains [
]. Brain representations are assumed to
be physically encoded by neuron assemblies [
]. The interactions between symbols in the cognitive
architecture are grounded in the concept of movement primitives. This qualiﬁer is used to emphasize
the fact that is inherited from primitive animals as a result of the phylogenetic conservation principle.
This computational mechanism models the evolutionary adaptational redeployment of movement
control. Furthermore, these movement primitives are postulated as the underlying substrate that
is common to any cognitive function. The hypothesis is accompanied with a mathematical model
grounded in statistical mechanics that is used to analyze the information-processing capacities of the
described architecture. In summary, the hypothesis provides some answers to the efﬁciency of the
brain’s computations and to the quantitative discontinuities in the cognitive capacities across species,
simultaneously explaining the similarities in the intelligence levels that are observed.
Entropy 2017,19, 543 5 of 35
Moreover, the hypothesis is accompanied with a mathematical model that is used to analyze
the information-processing capacities of the described architecture with the overall goal of checking
whether an animal’s intelligence can be explained as an emergent phenomenon that results from
the interaction of a large number of brain representations (i.e., neuron assemblies) grounded on the
hypothesized principles. In other words, how neurobiological differences in the cerebral structures that
appeared as a result of the evolutionary redeployment of movement control might explain differences
in the cognitive capacities across species. The main innovative contribution of the mathematical
model is the analysis of a cognitive architecture in terms of its free energy and entropy using a
statistical mechanics formulation. In summary, although the hypothesis is not intended to fully explain
cognition, it provides some answers with regards to the efﬁciency of the brain’s computations and to
the quantitative discontinuities in the cognitive capacities across species, simultaneously explaining
the similarities in the intelligence levels that are observed.
2.2. Statistical Mechanics
The aim of this discipline of theoretical Physics [
] is to bridge the gap between the microscopic
and macroscopic worlds [
]. Its ﬁrst step consists in stating hypotheses about the microscopic behavior
of the constituents (e.g., atoms, molecules, particles, or neuron assemblies in the present study) of
a macroscopic system. The objective is then the prediction of macroscopic properties, which can be
measured in experiments. Furthermore, the quantities which are of interest in statistical mechanics
are the averaged values of the observables. The macroscopic system under study in this case is the
brain, speciﬁcally the cerebral cortex and its homologues, and the macroscopic property under study
is intelligence. Exactly, intelligence is interpreted as an emergent phenomenon that results from the
microscopic interactions of millions of neurons (i.e., neuron assemblies) grounded in the concept of
movement primitives. Furthermore, neurons are considered information-processing elements that
receive, process, store, and communicate information to other neurons being this fact independent
of its morphology. Entropy is used as an approximative measure of intelligence. This concept
was originally developed by physicists in the context of equilibrium thermodynamics and later
introduced into information theory. There are two distinct but related interpretations of entropy the
ﬁrst based on information content (Information Theory) and the second based on degree of disorder
(Thermodynamics), here the former is used. Intuitively, as higher is the information-content of the
cerebral structures modeled as higher will be the degree of intelligence that can be associated to them.
The free energy is used as an approximate measure of energetic requirements (i.e., metabolic costs)
incurred by cognitive operations in the aforementioned structures due to its relationship with the work
theorem in Physics.
2.3. The Principal Actor of Energy Consumption in the Brain
Previous studies focused on the metabolic budget of the brain had overestimated the energy cost
of action potentials in mammalian neurons. Action potentials within mammalian neurons are more
energetically efﬁcient than previously assumed. A recent work [
] updates those previous estimations
of energy use associated with neural computation in the cerebral cortex and cerebellum demonstrating
that the principal actor of energy consumption in the brain is synaptic transmission. Therefore, neural
connectivity can be assumed as the principal factor considered in the energetic requirements of the
cerebral cortex and its homologues given that the higher the number of synapses contained in those
cerebral structures the higher the associated metabolic costs will be. Furthermore, a higher number of
synapses (in absolute terms) may be the result of a higher number of synapses per neuron, a larger
number of neurons, or a combination of those two facts.
2.4. Neurophysiologic Indicators of Neural Connectivity
The qualiﬁer connectivity between brain representations used by the model must be interpreted
as mainly involving both the neurophysiologic concept of local and non-local connectivity. Local
Entropy 2017,19, 543 6 of 35
connectivity is related to the connectivity between neighbouring neurons encoding and processing
similar representations and is provided by axon collaterals of neurons. Non-local connectivity, consists
of the main axon and its ramiﬁcations (axonal branches) to more remote neurons, and involves
representations created from associative links between distant groups of neurons encoding different
pieces of information (e.g., information coming from different sensory modalities). However, it is
important to note that the total number of synapses that are present in the cerebral cortex and its
homologues constitutes the primarily physiological indicator of neural connectivity. A higher number
of synapses (in absolute terms) in these structures may be the result of a higher number of synapses
per neuron, a larger number of neurons, or a combination of both. The cortex of mammals ranges from
millions to billions of neurons, whereas the number of synapses per neuron ranges from hundreds to
]. Thus, it can be reasonably assumed that the strongest contribution in the resulting
product is predominantly due to the total amount of neurons.
Moreover, it is important to emphasize that the ability to perform associations constitutes
an important resource for intelligent behavior. Accordingly, higher levels of connectivity are also
expected to correlate with increased ratios of cortical white matter over gray matter because, as stated
before, most of the white matter ﬁbers are used to create associative links between different cortical
]. The gyriﬁcation index is a quantitative calculation of the degree of folding of the cerebral
cortex. This parameter is strongly linked to the properties of the white matter (e.g., strongly connected
cortical regions tend to face one another within gyri [
]). More highly folded cortices are those
that have more neurons connected through the white matter [
]. Thus, gyriﬁcation index can also
be considered as an indicator of neural connectivity. Finally, higher ratios of glial cells to neurons are
also expected to correlate with higher levels of neural connectivity. The ratio of glial cells to neurons
does not increase with the brain size, but instead increases with decreasing neuronal density [
Taking into consideration that neuronal density correlates with the inverse of neuronal size [
(measured in terms of the soma size, dendritic and axonal arborizations volume), it can be deduced
that glia–neuron ratio correlates with the size of the dendritic arborizations and length of axons since
the size of individual cell bodies changes relatively little (compared to the changes in the volume of
arborizations) as brain size goes up [
]. Further arguments under this view come from past studies
that suggested that the interspeciﬁc variation in the neocortical glia–neuron ratio correlated with the
size of the dendritic tree and the length of the axons because the increased scale of these structures
would require a larger number of astrocytes (i.e., one of the major glial cells) to regulate the glucose
uptake and more oligodendrocytes (i.e., another type of glial cell) to actively synthesize the myelin for
long-range projecting axons ﬁbers .
2.5. An Extension of the Mathematical Model of the Hypothesis
The cognitive architecture [
] models with a certain level of abstraction the patterns of functional
connectivity that are observed between regions of the cerebral cortex and its homologues. It is
important to emphasize that the constraints imposed by the structural connectivity in the functional
interactions cause that the topological parameters are generally conserved between structural and
functional networks [
]. These patterns of functional connectivity are characterized by displaying
a certain degree of randomness. This peculiarity is modelled by the randomness associated to the
symbolic structures, i.e., the connectivity between symbols and the number of information processing
levels are random variables. Thus, the size and complexity of the cerebral structures that are modelled
is abstractly represented in terms of the number of symbols and their connectivity through the
hierarchical symbolic structures deﬁned by the cognitive architecture.
Taking into consideration that a larger number of neurons correlates with a larger number of
brain representations (i.e., more neurons provide more resources to store more information), and also
that a higher connectivity between brain representations correlates, from the physiological point of
view, with a higher number of synapses, and thus with a higher neural connectivity, it can be deduced
that the number of symbols provides a reasonable estimate of the descriptive power of a symbolic
Entropy 2017,19, 543 7 of 35
structure and therefore of the underlying cognitive power of the cerebral structures that are modelled.
It is important to emphasize again that symbols act as embodiments of brain representations, and
brain representations correspond to the simultaneously activity of a group of neurons (i.e., the states of
In the following, the focus is put on the calculation of a mathematical expression for the number
of symbols implemented by the symbolic structures (in terms of its structural parameters) under the
assumption that the content of higher-order symbols (i.e., symbols close to the root node of the symbolic
structures) is built from lower-order symbols (i.e., symbols belonging to lower information-processing
levels). It is important to note that the content of higher-order brain representations (i.e., semantic
representations) includes sensorimotor representations [
]. In other words, sensory and motor
information is activated whenever a higher-order brain representation (e.g., a semantic representation)
is accessed since the content of higher-order representations includes perception and action information
representations (i.e., lower-order representations).
Without a loss of generality let us suppose a tree-like structure (see Figure 2). The structure is
levels where the branching factor associated to each level is indicated by the variable
. The circular arrows represent the combinatorial operations that model how brain
representations (i.e., symbols in the cognitive architecture) are combined according to the hypothesis.
More speciﬁcally, the circular arrows represent permutations operations carried out over the nodes
of the structure. Furthermore, each of the circular arrows is affecting the corresponding set of nodes
involved in the combinatorial operations. The goal here is to calculate as a function of the parameters
(levels of the structure) and the branching factors
, the number of possible symbol
conﬁgurations that can be attained by a structure of this kind as a result of the combinatorial operations
described before. To this end, the calculation is done iteratively expressing at each iteration step the
calculation recursively in terms of the calculation carried out in the previous step. More speciﬁcally,
the calculation starts with a structure containing just the root node, and thereby only one possible
), afterwards a structure with the root node plus nodes (i.e., a structure with
just one level and with a branching factor equal to
) leading to a number of conﬁgurations equal to
m1! (iteration R1), and so forth:
R1=m1!=Γ(m1+1) = Γ(m1+1)R0
Entropy 2017,19, 543 8 of 35
General example of the Cayley-like structures used by the cognitive architecture of the
intelligence and embodiment hypothesis [
]. It is important to remember that the branching factor
associated to each level is ﬁxed for all the nodes belonging to that level and represented by the variables
, for instance, the branching factor of level 1 is represented by the variable
the branching factor associated to the second level of the structure by
and so forth. The circular
arrows are used to represent the combinatorial operations described in the model.
Thus, for a generic structure of depth equal to
and branching factors
. . .
of possible conﬁgurations reads:
R(k,m1,m2,m3, . . . , mk) =
correspond to the branching factor associated to level
(see Figure 2), where
. As can be deduced, the function that expresses the number of possible conﬁgurations in
terms of the structural parameters
(depth of the structures) and (branching factors). The randomness
associated to the branching factors and the depth of the structures is encapsulated in two random
and the function expressing the
number of conﬁgurations becomes a random function that reads:
R(k,m) = Γ(m+1)Γ(m+1)mΓ(m+1)m2···Γ(m+1)mk−1
The random function
provides the number of conﬁgurations that can be supported by
any instance of the cognitive architecture, which is expressed in terms of the Euler gamma function
Γ(m) = R+∞
. To extract the typical behavior of the system, i.e., the average number of
symbols implemented by the cognitive architecture, the expectation of this random function, i.e.,
quenched averages in statistical mechanics terminology, must be calculated:
R(µk,µm) = R(k,m)=∑
Entropy 2017,19, 543 9 of 35
In expression (4) the operator
is used to express the expectation of the random function.
is representing the joint probability distribution of the random variables
(information-processing levels) and
(connectivity between brain representations). It is assumed that
the random variables
are independent. Furthermore, limit Gaussian probability distributions
are assumed for
respectively. Speciﬁcally, Dirac delta functions are used simulating the
concentration of the probability mass around the mean of the Gaussian distribution. These assumptions
permit to capture the essence of the processes being modeled allowing at the same time a considerable
simpliﬁcation of the calculation:
P(m,k) = P(m)P(k)
Thus, the expectation of the random function R(k,m)ﬁnally reads:
R(µk,µm) = R(k,m)=∑
In order to justify this approximation, it is important to note that the random variable
the depth of the structures (i.e., the number of information processing levels) that correlate to the
number of physical laminae (i.e., layers, and/or nuclei) associated to the cerebral structures postulated
by the hypothesis. This value is practically constant for each species. For example, in terrestrial
mammals, the cerebral cortex is typically a six-layered structure, although in certain regions it is difﬁcult
to appreciate the characteristics of this layered pattern, or it is poorly developed [
the typical laminar organisation of the mammalian cortex (or the dorsal pallium in amphibians) is
not as obvious in bird or reptile DVR since it is mainly a nuclear structure (i.e., large clusters of very
densely packed neurons), although these nuclear clusters of neurons are homologous to lamina-speciﬁc
populations of the mammalian cerebral cortex [
]. Furthermore, the characteristic laminar
organisation that is seen in the cerebral cortex of mammals is also observed in the DVR’s principal
sensory zones [
]. Pigeons, for instance, have at least six distinct visual areas within their DVR,
whereas turtles and lizards only possess between one and three [
]. In other words, the avian DVR
contains more subdivisions than the DVR of reptiles. Many of these DVR subdivisions (i.e., clusters) are
arranged like the layers of an onion, or geological strata, and connected by relatively short axons that
course at right angles to those laminae [
]. According to the hypothesis [
], the number of clusters of
densely packed neurons (or nuclei) correlates to the depth of the information-processing hierarchy.
Similarly, to justify the use of a limit Gaussian probability distribution with respect to the
(i.e., connectivity between brain representations) studies concerning the functional
networks of the brain carried out in humans as well as in other mammalian species [
] revealed the
These studies demonstrated that the pattern of functional connectivity between cortical areas
was consistent with a small-world network architecture. This is of particular interest since this
architecture is mainly characterized by being modular and hierarchical. Furthermore, these
studies also revealed that as a result of the constraints imposed by the structural connectivity in
Entropy 2017,19, 543 10 of 35
the functional interactions, the topological parameters are generally conserved between structural
and functional networks.
The patterns of functional connectivity between cortical regions undergo spontaneous ﬂuctuations
and are highly responsive to perturbations (i.e., sensory input or cognitive tasks) on a timescale
of hundreds of milliseconds. However, these rapid reconﬁgurations do not affect the stability
of global topological characteristics. In other words, on longer timescales of seconds to minutes
(i.e., in equilibrium from a statistical mechanics point of view), correlations between spontaneous
ﬂuctuations in brain activity form functional networks that are particularly robust.
Physical Interpretation of Equation R(µk,µm)
The principal characteristic of the function
is that it is a monotonically increasing
function. Thus, for any two arbitrary points in the averaged variable
(i.e., average number
of information-processing levels), for example
, the expression
holds for all values of
(i.e., the average connectivity between brain
representations). Similarly, choosing two arbitrary points in the averaged variable
, for example,
for all values of
. In turn, combining
the joint graph of entropy and free energy of Figure 3with the properties of the function
following statements can be inferred:
If the average connectivity between symbols is ﬁxed to any given value, for example,
then increasing the average number of information processing levels
not only increases the average number of symbols encoded, i.e.,
but also the associated entropy values
. It is important to remember that
if the connectivity is ﬁxed, then the differences in the information-content in the structures varies
exponentially when different numbers of information-processing levels are considered .
Similarly, if the average number of information processing levels
is ﬁxed to
then if the average connectivity
is increased, for example, from
then the average number of symbols encoded and the associated entropy values also increases,
. However, in this case the values of
the free energy (in absolute value) are also higher (i.e., |F(µk1,µm2)|>|F(µk1,µm1)|).
Higher entropy values are always linked to structures encoding a higher number of symbols
independently of the parameterization of
. For example, if
. Similarly, if
, if the average connectivity
is ﬁxed to any particular value, for example,
, there always exists a value for the average connectivity
, such as
the values that are reached by the entropy function in these points, i.e.,
respectively, that is identical (or very close because the entropy is an integer function),
, then the following inequalities hold:
. In other words, the average number of representations is higher
for the point in the space of parameters with the highest number of information-processing levels,
) in this case, but at the same time the values of the free energy are lower compared
to the point in the space of parameters with a lower number of information-processing levels but
a higher average connectivity, i.e., (µk1,µm2).
Entropy 2017,19, 543 11 of 35
Graphical illustration of the study’s results. The top-left ﬁgure shows that higher levels
of intelligence require more neurons in the cerebral cortex and its homologues, but also lead to
unavoidable growth of the energetic requirements. The ﬁgure on the right shows two routes to attain
higher levels of intelligence, each of them reﬂecting a trade-off between energetic requirements and the
number of neurons used. Animal intelligence is explained by increased neural connectivity, a deeper
information-processing hierarchy, or a combination of these in the cerebral structures postulated by the
hypothesis as responsible of intelligence.
To interpret these mathematical properties, it is important to emphasize that a concrete
parameterization of the average connectivity
and the average number of information processing
mapped to the graphs of entropy and free energy of Figure 3quantitatively represents the
average information content and associated metabolic costs, respectively, that are incurred by the
cognitive operations that take place in the cerebral cortex or in its homologues.
The ﬁrst statement suggests that for similar values of the average neural connectivity, those
cerebral structures possessing a deeper information-processing hierarchy have the potential to encode
a higher number of brain representations (e.g.,
for any value of
). Similarly, with respect to the second statement, considering cerebral structures with an
identical number of information-processing levels, encoding a higher number of brain representations
is also possible for those structures possessing a higher neural connectivity but at the cost of supporting
increased metabolic costs. In both cases, encoding a higher number of brain representations is not
possible without increasing the number of neurons recruited to encode such representations, which
requires cerebral structures with a larger number of neurons and thereby with an implicit increase
on the associated metabolic costs. The third statement suggests that higher levels of intelligence are
associated to those cerebral structures encoding a higher number of brain representations. In other
words, the number of neurons in the cerebral structures deﬁned by the hypothesis correlates with
the expected levels of intelligence (e.g., a larger range and versatility of behaviours and cognitive
abilities). This result seems to corroborate the general assumption in neuroscience that associates
Entropy 2017,19, 543 12 of 35
brains possessing a larger number of neurons with better cognitive functioning and/or behavioural
ﬂexibility of some kind (i.e., higher levels of intelligence).
However, this preliminary conclusion must be analyzed with a greater detail in light of the fact
that is strongly linked to the implications derived from the interpretation of the fourth statement.
More speciﬁcally, the last statement suggests the existence of two pathways to reach similar levels of
intelligence, the ﬁrst possibility (implicitly evidenced in the ﬁrst statement) requires a larger number
of neurons because it involves cerebral structures with a higher number of information-processing
levels but at relatively lower metabolic costs when compared to the second possibility (remember
). In contrast, the second possibility
(evidenced in the second statement), needs an increased average neural connectivity in the cerebral
structures that are studied but requires a fewer number of neurons when compared to the ﬁrst
possibility (remember that
), although at the cost of a substantial increase in the associated metabolic costs when
compared to the ﬁrst possibility.
Of particular interest is the fact that the number of neurons needed implicitly increase when
considering higher values of the average neural connectivity, cerebral structures with a deeper
information-processing hierarchy or a combination of those two facts. This is due to the procedure
that is used to encode brain representations according to the hypothesis (based on the concept of
movement primitives). For example, when increasing the connectivity between representations at
any generic level of the hierarchy, the number of possibilities (i.e., the number of combinations) to
generate higher-order representations at the upper levels of the hierarchy automatically increase and
thus, the number of neurons required for their codiﬁcation. In turn, this explanation also arises for
the other possibility offered by the model, because to the extent the depth of the hierarchy increases
(i.e., the successive stages of information processing), the amount of higher-order representations also
increases and therefore the number of neurons needed to encode such representations.
In summary, the theoretical evidence presented before put forward not only the importance of
the absolute number of neurons in the cerebral structures postulated by the hypothesis as a proxy for
intelligence but especially the primary role of neural connectivity with regards to intelligence and
cognitive capacities in general.
3.1. An Equation Relating Intelligence, Energetic Requirements, and Neuron Numbers
The most important aspects of the intelligence and embodiment hypothesis (see Section 2.1) are
synthesized in a space of cognitive architecture complexity that is deﬁned by the average number
of information-processing levels (
) and the average connectivity between symbols (
symbols act as embodiments of brain representations. Brain representations are assumed to be
physically the states of attractor networks. In other words, a piece of information is represented as
the simultaneous activity of a group of neurons. The average number of information processing
levels is hypothesized to be a function of the density of neurons and the number of physical laminae
(i.e., layers, and/or nuclei) that are present in the cerebral structures postulated by the hypothesis as
mainly responsible of intelligence in macroscopic moving animals. The main innovative contribution
of the mathematical model of the hypothesis is the analysis of the cognitive architecture in terms of
its free energy and entropy, macroscopic magnitudes that are derived using a statistical mechanics
formulation. The expectation of the entropy is used as an approximated measure to the concept of
intelligence, whereas the expectation of the free energy is used to analyze the computational properties
that emerge at a macroscopic scale as a result of the deﬁned interactions between brain representations,
providing, at the same time, a quantitative measure of the metabolic costs incurred by cognitive
operations in the cerebral structures studied. Both functions are expressed in terms of the parameters
of the model, i.e., the variables µk, and µm.
Entropy 2017,19, 543 13 of 35
Equation (7) (see also Section 2.5) provides an estimation of the average number of brain
representations that are used by the cognitive operations that take place in the cerebral cortex and
its homologues. This equation is obtained under the assumption that sensory and motor systems
are directly modulated by higher-order processing [
]. In other words, sensory and motor
information is activated whenever a higher-order brain representation (e.g., a semantic representation)
is accessed since the content of higher-order representations includes perception and action information
representations (i.e., lower-order representations).
R(µk,µm) = Γ(µm+1)
Taking into consideration the fact that brain representations are assumed to be physically encoded
by neuron assemblies (i.e., as states of attractor networks), Equation (7) provides a quantitative
estimation on the number of neurons used. Thus, using a concrete parameterization of the averaged
the equation allows to associate any value of the entropy (i.e., intelligence)
and free energy (i.e., metabolic costs) functions with the expected number of brain representations
(i.e., neuron numbers) needed to reach those points (see Figure 3and also the supporting information
in the suplement). In other words, it permits quantitatively to relate intelligence, brain energetic
requirements, and neuron numbers.
3.2. The Limiting Factors of Intelligence: Neuron Numbers and Energetic Requirements
Higher levels of intelligence are explained as a result of an increased connectivity between
brain representations, a deeper information processing hierarchy, or a combination of those two facts.
In any of those cases, increasing the intelligence levels is always accompanied by an increase in
the number of brain representations but also in the associated metabolic costs (i.e., higher levels of
intelligence always require higher energetic requirements). Thus, higher levels of intelligence cannot
be achieved without implicitly increasing the absolute number of neurons in the cerebral cortex and
its homologues. Correspondingly, higher levels of intelligence are not possible without the existence
of higher metabolic costs in the cerebral cortex and its homologues (Figure 3). This result provides
a theoretical justiﬁcation to the general assumption in neuroscience that associates brains possessing
a larger number of neurons with better cognitive functioning and/or behavioral ﬂexibility. In addition,
it supports the belief that brain size cannot be increased indeﬁnitely due to metabolic considerations.
For example, from an evolutionary neuroscience perspective several studies have correlated increases
in relative brain size with changes in diet, size of other organs, or neural rate of energy consumption to
make those large brains possible [9,13,65].
This result appears also to corroborate previously formulated hypotheses from studies of social
]. Particularly, they had hypothesized that within a given taxonomic group, larger
animals always have larger brains and that these additional neurons may well provide more computing
power. This argument follows even if one accepts the argument that larger bodies require more
neurons to control them, since the number of neurons not dedicated to muscular control or sensory
processing is almost certainly larger in larger brains and these extra neurons may permit more complex
]. As a matter of fact, the largest species of ants, bees, and wasps tend to have the most
complex social instincts; rats (Rattus norvegicus) tend to perform better than mice (Mus musculus) in
learning tasks, i.e., 15 million cortical neurons against 4 million cortical neurons; ravens (Corvus corax)
learn better than small corvids like jackdaws (Corvus monedula), i.e., 1204 million of pallium neurons
against 492 millions; and large parrots seem smarter than parakeets, e.g., 850 million of pallium
neurons in the grey parrot (Psittacula erithacus) against 575 millions pallium neurons in the alexandrine
parakeet (Psittacula eupatria) [13,67].
It is important to remark that the adult vertebrate brain is divisible into telencephalon,
diencephalon, mesencepahlon, and rhombencephalon, where the telencephalon and diencephalon
are collectively referred as the forebrain. The qualiﬁer pallium is used in anatomy to denote the most
Entropy 2017,19, 543 14 of 35
dorsal part of the telencephalon which in birds includes the DVR as well as other cerebral structures
(e.g., the hyperpallium or wulst). Similarly, in mammals the pallium includes the cerebral cortex, and
other cerebral structures like the claustrum or the hippocampal formation just to mention a few .
3.3. Two Routes for the Attainment of Higher Levels of Intelligence
The interpretation of the mathematical model (see Section 2.5) implies the existence of two
pathways to reach similar levels of intelligence, each of them showing the existence of a trade-off
between the energetic requirements and the number of neurons used (Figure 3). Speciﬁcally, the ﬁrst
pathway (Route 1) of considering cerebral structures with a deeper information-processing hierarchy
achieves higher levels of intelligence at relatively lower metabolic costs but at the price of requiring a
larger number of neurons when compared to the second possibility. In contrast, the second pathway
(Route 2) characterized by the existence of cerebral structures with higher levels of neural connectivity
requires fewer neurons compared to the former but at the cost of a substantial increase in the
associated metabolic costs. From a physiologic point of view both routes are linked to an increase in
encephalization since they implicitly require an increase in neuron numbers and/or neural connectivity,
thus leading to an overall increase in the volume of gray matter (i.e., the neuronal cell bodies, their
dendrites and the local ramiﬁcation of axons plus glial cells and blood vessels) and/or an increase in
the volume of white matter (i.e., mostly the bundles of axons that run a long distance).
The existence of a trade-off between energetic requirements and the number of neurons used in
given pathways, seen as an increase in cognitive capacities following the natural evolution of brains,
might help to explain the evolutionary changes in both brain region size and structure occurring across
vertebrate species. Clearly, brain region size and structure can differ in a variety of ways, and different
types of changes have different consequences for brain function [
]. Furthermore, changes in brain
region size and/or structure are implicitly linked to changes in overall brain size. In particular, it is
plausible to hypothesize that the observed differences (or non-uniformity) in the cytoarchitecture of
the mammalian cerebral cortex—demonstrating modiﬁcations linked to the evolution of this cerebral
structure (e.g., changes in size and/or structure)—are driven by the interplay between these two
pathways. For example, the area considered unique to the primate brain, albeit controversial, is the
prefrontal cortex which lies rostral to the premotor cortex.
Non-primate mammals do have a prefrontal cortex, but it consists of only two major regions
rather than the three found in primates [
]. The two prefrontal regions shared with primates are
ﬁrstly, the orbital prefrontal region and second, the anterior cingulate cortex. The third prefrontal
region that is unique to primates is the lateral (or granular) prefrontal cortex. This region consists
of an additional granular layer connected to part of the prefrontal cortex [
]. This add-on suggests
an increase in the number of information-processing levels of the brain according to the theoretical
model (i.e., the ﬁrst route) with the resulting entropy increase. What is more, the small-celled granular
layer that characterises the lateral prefrontal cortex in primates is missing in most other mammals [
This fact is of particular interest because there is ample behavioural evidence documenting overall
cognitive sophistication in primates.
In addition, the prefrontal cortex is an area of upmost importance for human evolution because
it mediates complex behaviours such as planning, working memory, memory for serial order and
temporal information, aspects of language, and social information processing [
], thus making it
the principal actor behind human intelligence. The human prefrontal cortex is approximately twice
as large as predicted on the basis of the size of the rest of the brain. It averages approximately
12.7% of total brain volume, compared with an average of 10.3% for the great apes (i.e., chimpanzees,
gorillas, and orangutans) [
]. Similarly, the volume of the non-prefrontal cerebral in humans is, on
average, 3.7 times larger than that of chimpanzees (Pan paniscus and Pan troglodytes) but the prefrontal
regions are, on average, 4.9 times larger [
]. Furthermore, humans appear to have substantially more
convoluted cortex (i.e., higher values of the gyriﬁcation index) in the prefrontal regions [68,70].
Entropy 2017,19, 543 15 of 35
Surprisingly, when compared against other primates, the volume of prefrontal white matter
is disproportionately larger in humans [
]. More speciﬁcally, when comparing humans against
chimpanzees, prefrontal gray matter volumes were, on average, 4.8 times larger in humans, whereas
nonprefrontal gray volumes were 4.2 times larger. By contrast, prefrontal white matter volumes
were, an average, of 5.0 times larger in humans, whereas nonprefrontal white volumes averaged
only 3.3 times larger [
]. In other words, the differences in humans appeared to demonstrate a bias
toward the growth of white matter rather than gray matter. These data appear to suggest an increase
in average connectivity (e.g., higher white matter versus gray matter ratios, and higher cortical folding
in this area) accompanied with a moderate increase in neuron numbers in the human prefrontal cortex
with respect to other cortical regions, but most notably, substantially higher numbers when compared
to the great apes. Thus, it is plausible to hypothesize that the evolution of the prefrontal areas in the
hominid lineage is the result of the interplay between the routes derived from the theoretical model, in
particular, to the pathway evidencing a strong inﬂuence of neural connectivity on cognitive capacities.
The pictures on the left and right side of the ﬁgure show how the mathematical model and
the physiological parameters of the brain correspond (reprinted with kind permission of Springer [
], and the Nature Publishing Group [
]). Regarding the picture of the raven at the bottom,
the high intelligence in animals with small brains, such as corvid birds, is explained in terms
of the ﬁrst route which regards how nature evolved brains to increase their cognitive capacities:
A deeper information-processing hierarchy combined, in this case, with an extremely reduced average
connectivity to mitigate the cost of requiring larger number of neurons. From a neurophysiologic point
of view this results from higher packing of neurons, which also results in a reduced overall connectivity
(shorter interneuronal distances). The dorsal ventricular ridge, especially that of corvids, owls, and
parrots (all exceptionally intelligent birds), is particularly more developed in birds when compared to
reptiles. This indicates a higher number of neurons compared to other birds and reptiles. Indeed, it has
been recently shown that large-brained parrots and corvids have forebrain neuron numbers equal or
greater than primates with much larger brains as a result of the extremely high packing densities of
their brains .
Entropy 2017,19, 543 16 of 35
In summary, although the level of hierarchy for birds, amphibians and mammals is agreed upon
in neuroscience [
], the exact number of information-processing levels that can be associated with
a particular brain is still unclear. Bearing this fact in mind, the existence of these pathways has also
helped to clarify the difﬁculties encountered in trying to explain the complex cognitive behaviours
documented across different vertebrates species that have substantially different physiological
characteristics in their brains (e.g., animals with high intelligence but relatively small brains like
corvid birds, see Figure 4). Thus, differences in intelligence are predominantly explained in terms of
the absolute number of neurons, and the average number of synapses per neuron that are present in
the cerebral cortex and its homologues.
3.4. The Primary Role of Connectivity in Intelligence
Intelligence is not only a result of a higher number of neurons in the cerebral cortex and its
homologues but is also the result of the interplay between the absolute number of neurons in these
structures and their connectivity (i.e., local and non-local connectivity). A brain that in absolute terms
has a lower number of neurons in the cerebral structures studied might have the potential to exhibit
similar or higher levels of intelligence with respect to a brain that has a higher number of neurons if
the former possesses a higher average neural connectivity and is able to sustain the higher associated
metabolic costs (see Figure 3).
For example, two recent studies of the cellular composition of both the brain of the African elephant
and those of great apes have shown that the African elephant (Loxodonta africana) contains 257,000 million
neurons, whereas the brain of the gorila (Gorilla gorilla) and the orangutan (Pongo pygmaeus) contain
respectively 29,300 and 28,500 million neurons [
]. In contrast, the elephant cerebral cortex, which has
twice the mass of the human cerebral cortex, holds only 5600 million neurons, about one-third of the
number of neurons found in the human cerebral cortex. Furthermore, the cortex of the gorilla and the
orangutan hold respectively 9100 and 8900 million neurons, whereas for the cortex of chimpanzees
(Pan troglodytes), the authors provide an estimation of 9000 million neurons, values that surpass the
number of neurons found in the cortex of the elephant.
Moreover, with regards to neural connectivity, the average number of dendritic spines per
neuron can be used as an approximate measure of the average number of synapses per neuron
(e.g., each spine can have one, two, three, or even zero synapses). Using a Golgi quantiﬁcation
Jacobs et al. 
reported an average number of 2693 basilar dendritic spines per neuron
for pyramidal neurons in layer III of the frontal cortex of elephants, whereas they reported a value
of 2018 spines for the occipital cortex. Surprisingly, these values are almost one order of magnitude
higher than those found in the cerebral cortex of chimpanzees when using an identical quantiﬁcation
technique. Speciﬁcally, an average of 401 spines per neuron (basilar dendritic spines) were reported
for the typical layer III pyramidal neuron in the frontal cortex of chimpanzees, and 169 spines for
the occipital cortex [
]. Furthermore, the remaining neural connectivity indicators (i.e., cortical
gyriﬁcation index, white matter versus gray matter ratio, and cortical glia–neuron ratio), including
the energetic requirements of the brain, are higher in elephants compared to those found in great
apes (see Table 1). Differences in intelligence between the great apes and elephants have not yet been
sufﬁciently tested, however, these data are of particular interest given the lower number of neurons
found in the cerebral cortex of elephants when compared to great apes, especially as both species
are cognitively sophisticated and possess an extensive cognitive repertoire [24,76]. Perhaps, the most
surprising cognitive ability in elephants, which appear to be somewhat unique among non-human
species, is their reaction to disabled and deceased conspeciﬁcs: they exhibit behaviours that are
characteristic of the theory of mind phenomena (i.e., the ability to understand another individual’s
mental state and take it into account with regards to one’s own behaviour). In summary, these data
appear to corroborate the existence of increased cortical connectivity in the elephant brain compared
to great apes, therefore, increasing the likelihood of the formulated prediction.
Entropy 2017,19, 543 17 of 35
Finally, to complement the aforementioned connectivity data, a quantitative Golgi study
performed in humans (Homo sapiens ) to study the dendritic and spine variation of the cerebral
cortex reported an average number of 1377 basilar dendritic spines per neuron [
] for area 10 (frontal
cortex). In other words, a value very close to that reported for humans in the study of
Bianchi et al. 
(i.e., approximately 1340 basilar dendritic spines), but lower than those found for the elephant.
In particular, the study of Jacobs et al.
reported that in the elephant frontal cortex, basilar dendrites
exhibited a 63.6% higher number of spines per neuron than in humans, whereas in the elephant
occipital cortex, basilar dendrites exhibited a 52.3% higher number of spines per neuron than in
humans. Similarly, as in the case of the chimpanzee, the rest of the neural connectivity indicators,
including the energetic requirements of the brain, are higher in elephants compared to humans.
However, it is important to note two facts: the cerebral cortex of the elephant lacks granular layer IV
(i.e., a lower number of information-processing levels compared to humans and great apes) [
and the human cerebral cortex contains approximately three times the number of neurons of the
elephant’s cortex (see Table 1). Both these facts clearly mark the differences in intelligence that have
The above image highlights the current available statistics for the cerebral cortex
of cognitive sophisticated terrestrial mammal species as well as several species of cetaceans
). The table on top of the figure provides estimations of different
physiological parameter for the brains of great apes, humans, and African elephants. The table on
the bottom provides identical estimations for the brain of several cetacean species. The lack of
neurophysiological data for cetacean species reﬂects the logistical difﬁculties that are associated with
the study of cetaceans (e.g., obtaining materials that are in sufﬁciently good condition for histological
analysis is known to be purely opportunistic).
Primates and the African Elephant Orangutan Gorilla Chimpanzee Human Elephant
Cortical Gyriﬁcation Index 2.29 2.07 2.19 2.57 3.89
Cortical Surface (cm2) 530 2275 6300
Cortical Glia–neuron ratio 0.98 c1.21 c1.2 c1.68–1.78 4.7
Cortical White matter-Gray matter ratio 0.488 0.618 0.617 0.71 0.78
Cortical Neuron Number (millions) 8900 9100 9000 16,300 5600
Brain weight (g) 370 509.2 420 1500 4783
Basal Metabolic Rate (kcal/day) 569.1 581.9 1400 65,000
Brain Metabolic Rate (kcal/day) 63 77 280 1200 a
Cetaceans Harbor Bottlenose Pilot Killer Minke
Porpoise Dolphin Whale Whale Whale
Cortical Gyriﬁcation Index 5.63 5.70
Cortical Surface (cm2) 3745 5800 13,629 5900
Cortical Glia–neuron ratio 2.34 2–3.1 3.41 d7.67
Cortical White matter-Gray matter ratio 0.66 0.76 0.74
Cortical Neuron Number (millions) 14,900 37,200 d12,800
Brain weight (g) 540 1550 2679 6622 2228
Basal Metabolic Rate (kcal/day) 2389 9000–10,000 40,000 90,000–110,000
Brain Metabolic Rate (kcal/day) 48 b429–477 800 b1800–2200 b
97.5 % of the neurons of the African elephant brain are located in the cerebellum;
The ratio of brain
to basal body metabolism for those species not listed in the study of Mink [
] has been calculated using
the lower bound provided by the author for the vertebrate brain (i.e., 2% of the body basal metabolic rate);
The glial-neuron ratio for the great apes correspond to the prefrontal cortex;
These values correspond to the
long-ﬁnned pilot whale (Globicephala melas).
From a behavioral perspective, there have been extensive studies of cognitive capabilities
of captive bottlenose dolphins (Tursiops truncatus) demonstrating their sophisticated cognitive
]. These various studies illustrate impressive learning capacities and behavioral
ﬂexibility in dolphins. For example, (just to mention a few) dolphins can reliably understand indicatives
cues provided by a human informant such as pointing an object, or gazing the particular sample
Entropy 2017,19, 543 18 of 35
object with a turn of the head. Dolphins can understand spontaneously the use of pointing gestures
substituted for symbolic gestures in language-like tasks. Additionally, dolphins can spontaneously
produce pointing (using rostrum and body alignment) to communicate desired objects to a human
observer, and appear to understand that the human observer must be present and attending to
the pointing dolphin for communication to be effective. Dolphins have demonstrated rapid and
spontaneous vocal imitation, vocal learning, and the ability to develop learned associations between
temporally paired elements in the absence of explicit training. Furthermore, ﬁeld studies of social
complexity in bottlenose dolphins in the wild in Shark Bay (Australia) revealed a society of great
size with complex social relationships including nested alliances, afﬁliative behaviors, and individual
foraging specializations and tool use [14,25].
Moreover, recent ﬁeld studies have evidenced complex cognitive abilities in large-brained
delphinids-like killer whales (Orcinus orca): a special type of cooperative hunting in which the animals
work together to create waves to displace penguins and seals on ice ﬂoes [
], evidence for vocal
], and observational evidence for imitation and teaching, such as intentional stranding on
beaches to catch pinnipeds [
]. These ﬁeld studies have evidenced not only that cultural transmission
is important for killer whales but also that the complex and stable vocal and behavioral cultures of
sympatric groups appear to have no parallel outside humans and represent an independent evolution
of cultural faculties .
Data on mysticete (baleen whales) behavior are much more limited than for odontocetes (toothed
whales). The available information suggests that social communication and structure are often complex
in mysticetes [
], and include long-term social bonds, long-range communication, cooperative hunting,
cultural traditions, and ﬁssion-fusion like social behavior [
]. These behaviors are observed in some
large-brained odontocetes like the Sperm whale (Physeter macrocephalus) and primates, and are considered
cognitively demanding [
]. For instance, the discovery of complex learned songs, i.e., structured
sequences of vocalizations that cycle with a period of 5–25 min and clever ﬁsh corralling strategy
techniques, including the use of bubble clouds to encircle prey, the production of loud feeding calls
and the waving of their large pectoral ﬂippers as a feeding tactic [
] certainly suggest that humpback
whales (Megaptera novaeangliae) are quite intelligent [
]. Furthermore, to date, the social calling
repertoire of humpback whales has received considerably less attention than either the song or foraging
calls. Social calls are deﬁned as phonations that do not possess the rhythmic or continuous patterning
of song [
]. A recent study on the vocal repertoire and social calling behavior of the Southeast Alaska
humpback whale has evidenced a more varied and diverse repertoire of social vocalizations than
has previously been documented, identifying variability in the vocal behavior as a function of the
social-spatial context .
The support for cognitive sophistication in humpback whales, and its tremendous behavioral
ﬂexibility come also from recent reports of whale watchers who observed, on several occasions,
groups of humpbacks whales attempting to help a member of another species. Examples include
a group of humpback whales intervening when a pod of killer whales was in the process of trying to
separate a grey whale’s calf from its mother or humpback whales rescuing a seal from killer whales
in the Antarctic. These observations have been corroborated by a recent study [
] that investigated
humpback whales interfering with attacking killer whales. The authors concluded that these behaviors,
even if unintentional, might be the focus of future research into possible genetic or cultural drivers of
interspeciﬁc altruism. To date, altruism among cetaceans has been attributed almost exclusively to
smaller odontocetes [
]. For example, some odontocetes species are famously known for coming to
the aid of threatened or injured conspeciﬁcs, as well as other species, including humans [
these behaviors have also been reported for killer whales and sperm whales .
Having said this, it is important to emphasize that the interpretation of the cognitive capacities of
cetaceans has been a subject of active discussion over the past decade. For example, cetacean’s modest
use of tools when compared to those of primates. The fact that a greater proportion of cetacean’s
cerebral cortex when compared to great apes and other mammals of similar brain sizes is occupied by
Entropy 2017,19, 543 19 of 35
white matter rather than by gray matter (where neuronal computation occurs), and particularly an
unfavourable combination of high interneuronal distance plus low axonal conduction velocity has lead
to the scientiﬁc judgement that cetacean’s brains have less computational power [
]. Further it
has lead to the belief that there is not a single behavioral achievement that has not also been shown in
several other species [
]. This has increased the reluctance of one part of the scientiﬁc community
to believe that cetaceans’ large brain is related to intelligence or any special intellectual capacities.
This controversy has increased even further as a result of a recent study that showed that large and
highly convoluted brains, such as the elephant brain, are not necessarily composed of an enormously
large number of cortical neurons .
However, concerning the assumption that cetacean’s brains have less computational power,
the study by Dicke and Roth[
] identiﬁes the principal factors determining general information
processing capacity in the brain, and thus intelligence among mammals, as a combination of the
number of cortical neurons, the number of cortical synapses, and processing speed. Addressing these
in turn, ﬁrstly, it is important to note that processing speed provides a necessary but not sufﬁcient
condition for intelligence [
]. For instance, Sheppard and Vernon [
] compiled results from
172 studies on processing speed and intelligence in humans that involved more than 53,500 participants.
They concluded that although the understanding of differences in mental speed may be essential to an
improved understanding of intelligence, these differences do not provide a full account of differences
in intelligence. Secondly, with regards to the total number of cortical neurons, the present study
showed that intelligence is not only a result of a higher number of neurons in the cerebral cortex
and its homologues but that it is also the result of the interplay between the absolute number of
neurons in these structures and their connectivity (see Section 3.4). Surprisingly, Mortensen et al.
using modern unbiased stereological methods [
], recently found that the number of neurons in the
cerebral cortex of long-ﬁnned pilot whales (Globicephala melas)—a delphinid with an average brain
mass of 3500 g—was 37,200 million. This is a ﬁgure that is beyond the number of cortical neurons
reported for the human brain [104,105].
Furthermore, Dicke and Roth [
] initially explored whether the number of synapses (i.e., neural
connectivity) in the cerebral cortex is potentially of importance to the cortical information processing
capacity, however this factor is ﬁnally rejected on two assumptions: that it is compensated for by
a decrease in NPD and that the number of cortical synapses per neuron is approximately constant
throughout mammals. Nevertheless, recent studies on the morphology, regional dendritic and spine
variation in the cerebral cortex of several mammal species have revealed substantial differences in the
average number of dendritic spines per cortical neuron. This is found not only between species, but is
also true when different areas of the cerebral cortex are sampled [
]. Once again, it is important
to bear in mind that dendritic spines can be used as a proxy for the number of synapses. Thus, one
cannot assume that the increase in the number of synapses in large-brained animals is compensated
for by a decrease in NPD, as has been suggested for the cetacean’s brain. This is especially relevant
when considering the major role played by the total number of synapses (i.e., a major indicator of
neural connectivity) as an important neurobiological structure that determines intelligence, according
to the results presented earlier (see Section 3). The importance of neural connectivity as a major
neurobiological structure governing intelligence may be further elicited by the comparison of extreme
cases, such as a comparison between the brain of one of the greatest intellectual giants of recorded
history, Albert Einstein, and control groups. The study of Witelson et al.
found that brain length,
height, the size of the corpus callosum, and measurements of the frontal and temporal lobes did not
differ between Einstein and the control subjects. Furthermore, the limited data on Einstein’s brain do
not point to a difference in the number of neurons throughout the depth of the cortex in the frontal or
temporal lobes. In contrast, in the parietal lobes, Witelson et al.
found quantitative differences
such as an increased expansion of the inferior parietal region, suggesting a difference in the ratio
of glial cells relative to neurons in the left parietal cortex. In other words, according to the results
presented herein, they were observing increased neural connectivity in the region when compared to
Entropy 2017,19, 543 20 of 35
control subjects. This region is a secondary association area that provides cross-modal associations
among visual, somatosensory, and auditory stimuli. For example, visuospatial cognition, mathematical
thought, and imagery of movement are strongly dependent on this region. Admitting to the fact that
the ability to perform associations constitutes an important resource for intelligent behaviour, higher
neural connectivity (i.e., a higher connectivity between brain representations) in a deeper associative
area may be of particular importance for abstract thinking, and thus for intelligence.
The number of computations within a given timeframe that can be supported by neural tissue
is dependent on, amongst other things, absolute brain size, the number and size of the neurons, and
the number of connections among neurons. The energy available for neural processing, which is
affected by the speciﬁc metabolic rate, is also an important variable in determining computational
]. For example, two brains with similar neurophysiologic characteristics, i.e., a similar
number of neurons and neural connectivity, may exhibit substantial differences in the number of
computations they are able to perform per unit of time as a result of differences in the metabolic
turnover of their brains. This fact is particularly interesting, especially when taking into consideration
that bottlenose dolphins (and other cetaceans) have a higher basal metabolic rate than terrestrial
mammals of the same size and they consume oxygen at a rate that is greater than that documented for
both humans and elephants [65,108,109].
According to Dicke and Roth [
], processing speed depends on interneuronal distance, axonal
conduction velocity, and synaptic transmission speed. Interneuronal distance is determined by neuron
packing density (NPD hereafter), and in large-brained animals such as cetaceans and elephants there
exists an unfavourable combination of high interneuronal distance plus low axonal conduction velocity,
which strongly impairs their neuronal information processing capacity. However, it is important to note
that rapid hard-wired connections are present in the brains of cetaceans. For instance,
De Graaf 
reported the existence of large diameter myelinated axons in the nervous system of toothed whales.
These large axons are reported in the auditory system, visual system, and even in the nervus terminalis.
Such rapid connections might explain, for example, why the evoked potentials in the dolphin’s central
nervous system have shorter latencies (i.e., faster conduction times) compared to similarly sized human
]. In experiments involving a cognitive processing paradigm and phonatory response times
(i.e, the time from information reception, processing, and voluntary acoustic response), dolphins were
faster than in humans in the majority of instances. Surprisingly, dolphins were able to select individual
responses in the aforementioned paradigm in as little as 20 ms (i.e., faster than in humans) .
Further arguments falling under this umbrella can be found in the work of Wang et al.
who showed that from shrews to whales, the composition of white matter shifts from compact,
slow-conducting, and energetically expensive unmyelinated axons to large, fast-conducting, and
energetically inexpensive myelinated axons. The fastest axons have conduction times of 1–5 ms across
the cerebral cortex and below 1 ms from the eye to the brain. More speciﬁcally,
Wang et al. 
analyzed specimens from 14 species (including the great apes) whose brain volumes span nearly ﬁve
orders of magnitude, starting right down with the shrew (Cryptotis parvus; brain weight 120 mg) and all
the way up to the Humpback whale (Megaptera novaeangliae; brain weight 7.5 kg). These authors found
very large axons in all cetaceans brains (Phocoena phocoena, the harbour porpoise; Stenella coeruleoalba,
the striped dolphin; Tursiop truncatus, the bottlenose dolphin; and Megaptera novaeangliae, the humpback
whale) as well as in the remainder of the species analyzed. In larger brains, they found a clear
tendency for axons to be wider in diameter and greater myelination. It is important to note that in
addition to myelination, axon diameter also affects conduction times in vertebrates axons, and both
factors (increased myelination and diameter) increase axonal volume. Furthermore, the existence of
subpopulations of exceptionally wide axons with submillisecond conduction times appears to be a
recurring theme in large brains. Similarly, large myelinated axons also constituted a small fraction of
the total number present in white matter, suggesting they compose highly specialised highways of
Entropy 2017,19, 543 21 of 35
With respect to synaptic transmission speed, this parameter is assumed to be constant among
mammals, occurring at synapses requiring the release of neurotransmitters from a presynaptic neuron
and their detection by a postsynaptic nerve cell. Glutamate is the main excitatory neurotransmitter
in the mammalian brain. After it is released, glutamate is promptly removed from the synapse
by uptake into an adjacent astrocyte (the other major cell type in the brain). There, glutamate
is converted to glutamine before being returned to the neuron and recycled [
]. The energy
needed to process glutamate is provided by glycolysis (i.e., a molecule of glucose is degraded in
a series of enzyme-catalyzed reactions to yield two molecules of pyruvate), using glucose obtained
from blood and, during sudden increases in activity, from a glycogen store (i.e., a polymer storage
form of glucose) in astrocytes through glycogenolysis (i.e., catabolic pathway to convert glycogen to
glucose). Of particular importance is the fact that there are large difference in both the rates of glucose
consumption as well as the total amount of glucose consumption when these processes (i.e., glycolysis
and glycogenolysis) follow aerobic or anaerobic pathways. Under anaerobic conditions, consumption
rates are considerably higher than under aerobic conditions .
The baseline metabolic rate of large-brained mammals is very high. The energy needed is supplied
by glucose oxidation and the brain vasculature is precisely organized to meet the accompanying
ongoing oxygen demands. However, changes in activity associated with activation (e.g., echolocation
in odontocetes), despite only requiring a small and brief increment in energy expenditure, occur in
the span of milliseconds. The brain vasculature simply cannot respond quickly enough to meet these
energy requirements in a timely fashion, thus causing it to resort to glycolysis, or even to glycogenolysis
in extreme cases [
]. This is of particular importance when the speed of information processing in
the brain is of the essence, i.e., when the brain has to process information from the highly sophisticated
echolocation system of odontocetes (echolocating animals emit trains of clicks to detect a target); not
forgetting that the speed of sound in water is approximately four times faster than air.
Although glycolysis and glycogenolysis yield less energy overall, they produce this energy faster
than glucose oxidation. It is now generally accepted that the metabolic needs of active neural tissue
are met, at least partially, by anaerobic glucose metabolism occurring in the astrocytes. Astrocytes can
oxidise fatty acids in another energy-yielding pathway that frequently occurs in the mitochondrion.
The four-step process called
oxidation leads to acetyl-CoA, a molecule that is also an intermediate
product used for energy production through the citric acid cycle during glucose oxidation. Importantly,
astrocytes are more resilient to hypoxia (low oxygen conditions) compared to neurons [115–119].
Cetaceans possess a number of adaptations that aid diving, including increased myoglobin levels
(i.e., an oxygen-storing and iron-carrying protein found in the muscles of all mammals); increased
blood volume; and a higher concentration of hemoglobin than in terrestrial mammals [
dive limits are also dictated by rates of oxygen consumption, which is of particular relevance when
discussing a very oxygen-sensitive organ like the brain. In other words, in addition to the primary
source of neural energy substrate, which is the direct entry of glucose into neurons, there is evidence
that a second source of energy is provided by the entry of glucose into astrocytes. Thus, it is plausible
to hypothesize that a faster synaptic transmission speed is possible in the cerebral cortex of cetaceans
compared to terrestrial mammals as their metabolism may have evolved to rely more on anaerobic
glucose metabolism, especially during periods of increased energy requirements and/or under oxygen
deprived conditions (i.e., diving conditions) [
]. For example, the dolphin lineage showed positive
for the inheritance of genes involved in the metabolism of glucose and lipids, as well as faster
rates of evolution in genes expressed in the mitochondria, both of which indicate an evolution in
energy metabolism [
]. Further arguments supporting this perspective come from the work of
Williams et al. 
who studied the physiology of the bottlenose dolphin during exercise (i.e., animals
either pushing against a load cell or swimming next to a boat). Surprisingly, the authors found that the
dolphins’ behaviour, dynamic metabolic scope and level of maximal oxygen consumption fell short
of those reported for elite terrestrial athletes such as the horse and the dog (i.e., animals with smaller
brains in absolute terms). This suggests that a swimming dolphin may rely on metabolic pathways or
Entropy 2017,19, 543 22 of 35
oxygen reserves (e.g., large oxygen reserves in the lungs, blood or muscle) that were not identiﬁed by
conventional evaluation methods. In other words, the study documented evidence of the possibility
that marine mammals might rely on anaerobic metabolism, at least during high work loads. Moreover,
the work of
Ridgway et al. 
using functional imaging to study the metabolism of the brain of the
bottlenose dolphin concluded that there may be more advantages to the unihemispheric physiology
observed in the dolphin brain than just its ability to have slow brain waves in one hemisphere while
maintaining the ability to swim and remain alert in the other. Speciﬁcally, the ability to partially ‘shut
down’ or at least reduce oxygen and glucose consumption in a major portion of the dolphin’s large
and active brain—evidence of the use of alternative metabolic pathways
—may be an
advantage to a dolphin making repetitive, prolonged feeding dives .
Finally, with respect to the behavioural data, it is important to note that the intelligence of most
cetaceans is currently unknown despite the large body of older or more recent studies that have shown
the complex cognitive abilities of cetaceans. Currently, available data has led to much debate and
controversy within the scientiﬁc community, but as yet no clear consensus has been reached. One of
many possible factors causing this may be the logistical difﬁculties that are associated with the study
of cetaceans; these difﬁculties often give rise to incomplete information that lacks important details
for analytical purposes. Another factor, if not the major factor, is the intrinsic difﬁculty of deﬁning
and testing the cognitive performance of animals, and thus reaching a consensus on how to interpret
the gathered data. Indeed, the development of truly rigorous comparative tests through which the
intelligence of members of distantly related taxa, such as corvid birds, primates and cetaceans can be
tested whilst ensuring they are under same conditions [
] still remains a challenge to comparative
psychologists. Hence, the discussion presented hereafter must be interpreted according to the premises
of the scientiﬁc method, namely, as predictions of the hypothesis that should subsequently be veriﬁed
or refuted by future studies, once more data becomes available.
4.1. Implications for Cetacean Cognition
The ﬁrst important implication of this study was to show that a brain which in absolute terms has
a lower number of neurons in the cerebral structures considered might have the potential to exhibit
similar or higher levels of intelligence with respect to a brain that has a higher number of neurons.
This is always possible if the former possesses a higher average neural connectivity and is able to
sustain the higher associated metabolic costs. The second important implication was to show that
higher levels of intelligence are not possible without implicitly increasing the number of neurons in
the cerebral cortex and its homologues. The increase in neuron numbers is always accompanied by
unavoidable growth of the associated energetic requirements, but imposing, at the same time, a limit
due to metabolic considerations. Thus, animals possessing a large number of neurons in the cerebral
structures postulated by the hypothesis have the potential for displaying higher levels of intelligence
(i.e., a larger range and versatility of behaviors and cognitive abilities).
However, the most important result of the present study is to show from the perspective of the
] the existence of two routes to augment intelligence each of them evidencing the speciﬁc
manifestation of a trade-off between metabolic necessities and the unavoidable requirement on neuron
numbers. For the ﬁrst route, the attainment of higher levels of intelligence evidenced the existence of
cerebral structures (i.e., the cortex and its homologues) with a deeper information-processing hierarchy
that required a higher growth on neuron numbers compared to the second route, but at relatively
lower metabolic costs. In contrast, the second route evoked by the existence of cerebral structures
with higher levels of neural connectivity, the attainement of higher levels of intelligence was possible
with a more moderate growth on neuron numbers compared with the ﬁrst route but at the cost of
a substantial (or faster) increase in the associated metabolic costs.
The order Cetacea comprises highly diversiﬁed species distributed into two suborders:
the Mysticeti (baleen whales) and the Odontoceti (toothed whales). The suborder Odontoceti contains
72 species of toothed whales, dolphins, and porpoises, distributed into four families. In general,
Entropy 2017,19, 543 23 of 35
cetaceans possess large brains when compared to terrestrial mammals, both in absolute and relative
terms. Their brains also have much lower neuronal density, but at the same time, higher ratios of
glial cells to neurons, and greater proportion of cortical white matter versus gray matter [
Furthermore, one of the most fascinating characteristics of their brains is the high degree of cortical
gyriﬁcation and the resulting neocortical surface area. Therefore, in spite of the fact that recent studies
have revealed great diversity amongst the brains found across this order (e.g., differences in brain
parts, as well as body and brain measurements) [
], based on available data it is plausible to argue
that, generally speaking, their brains appear to have followed the second pathway (Route 2), presented
by the mathematical model being used to support the hypothesis exploring how brains evolved
naturally and the causes of increased cognitive capacities. More speciﬁcally, if the assumption being
made is that the depth of the information-processing hierarchy in the cerebral cortex of cetaceans is
lower when compared to most of the intelligent terrestrial mammals species, then those defending
complex cognition in cetaceans would need to demonstrate the existence of a higher neural connectivity
(and thus higher metabolic costs), but, at the same time, a comparable (or higher) number of neurons
in their cortices when compared to terrestrial mammal species for which there is enough documented
evidence (besides humans) for their overall cognitive superiority, for example the great apes.
Having said this, in contrasting the data provided in Table 1, it is possible to deduce that all
the neurophysiologic indicators of neural connectivity are higher for the cetacean species that were
selected when compared to primates. For example, the highest gyriﬁcation index in primates is on
par with humans with a value of 2.57, whereas the average value in cetaceans is 5.43 (i.e., the most
gyrencephalic mammals). In primates, the highest ratios of white matter to cortical gray matter, and
glial cells to neurons, also correspond to humans. When comparing the glia–neuron ratio in the cerebral
cortex of the bottlenose dolphin with that of humans (two brains of similar size), a ratio of 2–3.1/1
against 1.68–1.78/1 is obtained. Similarly, the ratio between cortical white matter and gray matter
in the bottlenose dolphin is approximately 0.76, whilst this ratio is 0.71 in humans [
when comparing the glia–neuron ratio in the cerebral cortex of the harbour porpoise with that of the
gorilla (both brains of similar size), a ratio of 2.34/1 against 1.21/1 is obtained, respectively. Similarly,
the ratio between cortical white matter and gray matter in the harbour porpoise is approximately 0.66,
while this ratio is approximately 0.62 in gorillas. Finally, comparing the available neurophysiologic
indicators of neural connectivity for the killer whale with those of the African Elephant (the only
terrestrial mammal with a comparable absolute brain size) it can be deduced that indicators such as the
gyriﬁcation index and the cortical surface area are higher in the killer whale. In particular, their cortex
is extremely convoluted and thin which results in an expansion of the surface area by approximately
. This means that this animal has a cerebral cortex with the highest gyriﬁcation index
reported thus far (i.e., 5.70).
Increased neural connectivity is implicitly linked to the existence of a higher number of synapses
but also a larger number of neurons (second route). Thus, higher metabolic costs are expected in
cetaceans’ brains compared to primates and terrestrial mammals possessing brains of a similar size.
The energetic requirements of the brain of the bottlenose dolphin and humans can be calculated
using a past study which relates the basal body (or resting) metabolic rate (RMR hereafter) to brain
metabolism in vertebrates [
]. The measured resting metabolic rate for captive bottlenose dolphins
(Tursiops truncatus) is within the range of 8000–9000 kcal/day [
], whereas the RMR for an adult human
(Homo sapiens) is approximately 1400 kcal/day [
]. For the bottlenose dolphin, 4.77 % of the RMR
is dedicated to its brain’s metabolism, which produces a value within the range of 429–477 kcal/day.
Similarly, for humans, the energetic requirements of the brain account for 20% of the RMR, leading to
280 kcal/day for the human brain. Hence, according to these data, the energetic requirements of the
brain of the bottlenose dolphin are higher when compared to those of the human brain (considered
the most intelligent organism in the animal kingdom by far, and the only primate with a comparable
brain size). Furthermore, the energetic requirements of the brain of the killer whale (see Table 1) are
Entropy 2017,19, 543 24 of 35
also higher compared to those of the elephant—within the range 1800–2200 kcal/day compared to
1200 kcal/day for the elephant brain.
However, it is important to note that for reliable comparisons the energetic requirements calculated
above must refer to the cerebral cortex and not to the entire brain (e.g., 97.5% of the neurons of the
elephant are located in the cerebellum [
]). The energetic requirements of the cerebral cortex can be
estimated whenever the absolute number of neurons, the total number of cortical neurons, and the
ratio of brain to basal body metabolism (e.g, 13.14 % of the RMR for the chimpanzee brain) are available
for a given species. The total number of neurons in the elephant brains is 257,000 millions [
in human and chimpanzee brains these numbers stand at approximately 86,000, and 27,900 million
neurons respectively [
]. For these species, the aforementioned neuron numbers (see also Table 1)
were obtained using an identical quantiﬁcation technique, that is, the isotropic fractionator [
which produces (in combination with the data on the brain to body basal metabolic ratio of the study
Mink et al. 
) an energetic requirement of approximately 53 kcal/day for the cerebral cortex of
the human brain, 26 kcal/day for the cerebral cortex of the elephant, and 22 kcal/day for the cerebral
cortex of the chimpanzee (
). These data, although approximative, appear to corroborate
the prediction that higher levels of intelligence are not possible without higher energetic requirements
in the cerebral cortex and its homologues (see Section 3.2). Speciﬁcally, the higher levels of intelligence
observed in humans compared to chimpanzees and elephants are evidenced by the higher metabolic
requirements of the cerebral cortex. Furthermore, the similarity of the values obtained for the energetic
requirements of the cortices of chimpanzees and elephants appear to suggest the existence of comparable
levels of intelligence, in spite of the substantial differences in cortical neuron numbers.
The total number of synapses in the cerebral cortex are correlated to the brain’s metabolic costs,
however, the principal contribution to the resulting energetic requirements of the brain was due to the
total number of neurons (see Section 2.4). Thus, it is reasonable to expect a large number of neurons in
the cerebral cortex of the bottlenose dolphin and the killer whale, perhaps comparable to the neuronal
numbers found for great apes, and/or a higher average number of synapses per neuron compared to
great apes. Unfortunately, the neocortical neuron number (or the absolute neuronal numbers) of the
bottlenose dolphin is unknown. Similarly, data on neuronal numbers and/or the dendritic system
in the cerebral cortex of killer whales are not currently available. However, a Mysticeti such as the
minke whale (Balaenoptera acutorostrata) has a higher number of cortical neurons compared to great
] (see also Table 1). Moreover, using a Golgi quantitative methodology, the average number
of dendritic spines (both basilar and apical dendrites) in the visual and motor cortices of the minke
whale was found to be approximately 2436 and 2814 respectively for a typical pyramidal neuron [
It is important to remember that dendritic spine counts are used as an approximate measure (or proxy)
to the number of synapses per neuron.
Average values of 169 and 166 spines were found in the visual and motor cortices of the
chimpanzee using an identical quantitative technique, although these values are not directly
comparable because of the fact that only basilar dendrites are reported in the quantiﬁcation study of
the primates [
]. To roughly calculate the number of spines per neuron (basilar and apical dendritic
spines) in the chimpanzee brain, one needs to multiply these numbers by the dendritic trees count that
is reported by the authors (see Table 2 in [
]). This produces an average number of 723 and 745 spines
in the visual and motor cortices respectively. These values, although approximative, are more than
three times lower compared to those found for the minke whale in the same areas, thus providing at
least a preliminary comparison among these two species.
Furthermore, using stereology quantiﬁcation techniques [
], it was shown that odontocetes
such as the long-ﬁnned pilot whale (Globicephala melas), or the harbour porpoise (Phocoena phocoena)
have an unexpectedly high number of cortical neurons [
]. Figures for harbour porpoises
approach the lowest cortical neuron number found in humans [
], and long-ﬁnned pilot whales
possessing the highest number of cortical neurons of any species studied so far, including humans [
Of particular interest is the study by Kazu et al.
which predicted that the large cerebral cortex
Entropy 2017,19, 543 25 of 35
of cetaceans will have fewer neurons than the human cerebral cortex. For the bottlenose dolphin,
they predicted numbers close to 1750 million cortical neurons. These predictions for other delphinid
such as the pilot whale (Globicephala macrorhynchus) and phocoenidae the harbour porpoise (477 g of brain
mass) translated into values of 3010 and 1127 million cortical neurons respectively. Furthermore, recent
studies have hypothesized that the larger absolute number of neurons in the human cerebral cortex
(but not in the whole brain) is correlated with the superior cognitive abilities of humans compared to
elephants and other large-brained mammals [
]. For example, Herculano-Houzel
that even the cerebral cortex of the largest whales might be composed of only a fraction of the
average 16,300 million neurons found in the human cerebral cortex. In fact, both Kazu et al.
do not agree with the aforementioned results concerning the neuronal
numbers found in the cerebral cortex of the harbour porpoise and the minke whale, [
that the neuron numbers obtained might be over-estimations of the real values due to undersampling
problems associated with the stereology quantiﬁcation technique.
Having said this, it is important to highlight that modern unbiased stereology techniques make
use of efﬁcient sampling techniques [
], therefore even when accounting for the existence of errors,
it is unlikely that variance errors that are of the magnitude needed to explain the discrepancies obtained
between the predictions of Kazu et al.
and the neuronal numbers found by Wallöe et al.
Mortensen et al.
would have been made; this is especially so for the study by Mortensen et al.
which used a meaningful sample of specimens (i.e.,
10). Furthermore, according to the results
of the theoretical model, these data do not falsify, but rather reﬁne the aforementioned hypotheses
concerning the levels of intelligence that would be expected for a species based on the cortical neuron
], as a larger absolute number of neurons in the cerebral cortex is a necessary but not
a sufﬁcient condition for exhibiting higher levels of intelligence. For example, as previously evidenced
in the differences found in cortical neuronal numbers between the chimpanzee and the elephant, in
spite of a similarity in the energetic requirements of their cortices.
In summary, it has been possible to demonstrate the following for the cetacean species listed in
Table 1: all the indicators of neural connectivity are higher compared to great apes; cortical neuronal
numbers are comparable with those of great apes; the energetic requirements of the brain are also
higher compared to the brains of similarly sized cognitively sophisticated terrestrial mammal species
such as the great apes and the elephant. In accepting the strong inﬂuence of neural connectivity on
cognitive capacities—e.g., doubling the average connectivity between brain representations may lead
to a substantial increase of the entropy values of one order of magnitude or higher depending on the
average number of information-processing levels contemplated—and reviewing the behavioural
data presented earlier, it is plausible to conclude that the brains of cetaceans primarily reﬂect
the second pathway (Route 2). Thus, within the debate on the complexity of cetacean cognition,
the author defends the position that there is evidence of complex cognition as the second pathway
is an evolutionary adaption that has lent itself to increased cognitive capacities. Furthermore, data
from future studies may conﬁrm the existence of an unexpectedly large number of neurons in the
cerebral cortex of the bottlenose dolphin (Tursiops truncatus), and particularly, in other large-brained
cetaceans such as killer whales (Orcinus orca), humpback whales (Megaptera novaeangliae), or sperm
whales (Physeter macrocephalus), which would conﬁrm predictions made using the theoretical and
mathematical models, which together point to the possibility of the existence of levels of intelligence
in these mammals that go beyond what has previously been hypothesized.
However, it is also important to emphasize that the conclusions obtained may vary to the extent
that new data becomes available from studies using novel quantiﬁcation techniques, especially those
related to brain energetics, since current data are currently very scarce and relatively out-dated.
However, the theoretical results used to reach such conclusions shall not vary.
Entropy 2017,19, 543 26 of 35
4.2. Brain Evolution: The Loss of Layer IV in the Cerebral Cortex
One of the most intriguing neuronal traits of cetaceans is the lack (or underdevelopment) of
layer IV in their cerebral cortex. The laminar organization of the cetacean cerebral cortex has been
considered a heterotypical formation resulting from a reduction in the number of cortical layers.
Currently, it is generally accepted that the common ancestor of all cetaceans possessed layer IV granule
]. The loss of the granule cells in layer IV in cetaceans has been regarded a rare derived trait
in which layer II has undergone a secondary transformation speciﬁc to the cetaceans. This secondary
transformation has been correlated with the shift of the orphaned terminations of the speciﬁc thalamic
afferents (originally terminating in layer IV) back to layers I and II, thus allowing more neurons in
layer II to persist .
One of the principal theoretical results inferred from Equation (7) was to show the existence of
two routes for the attainment of higher levels of intelligence. Particularly, an increase in intelligence
was possible with a more economical but inevitable increase on the total neuron numbers if the
depth of the information-processing hierarchy was reduced, although at the cost of increasing the
average neural connectivity (i.e., increased local and non-local connectivity), and thus leading to
a substantial (or faster) increase in the associated metabolic costs. Therefore, the loss of layer IV
in the cerebral cortex of cetaceans may be interpreted as an evolutionary modiﬁcation representing
a solution to the need of increasing cognitive abilities in a brain previously adapted to the aquatic
environment. In other words, the heterotypical agranularity of the cetacean cerebral cortex (i.e., the lack
or underdevelopment of layer IV) is hypothesized to be the result of the causal linkage between two
ecological pressures, ﬁrstly the readaptation to the aquatic environment, especially to the progressive
adquisition of endurance underwater without breathing, and later to the cooling of water temperatures
during the Eocene-Oligocene transition period [
] both leading to an overall increase of the glial
cells, secondly the response to selective pressures for increasing cognitive skills principally driven
by social demands [
] that were responsible of the encephalization spurts observed in this lineage
(see Section 4.3 for further details).
It is important to note that from a physiological point of view, a fewer number of cortical layers
permits that the radially coursing dendrites and axons of neurons have more room to pass between the
neocortical cell bodies. In other words, more space becomes available in the neuropil if the number of
neurons and especially the average cortical connectivity need to be increased, something impractical
for the six layered pattern of the ancestral cetacean neocortex, when a greater proportion of the neuropil
was already occupied by glial processes, and especially by the faster increase on the cortical neuron
numbers required, as suggested by Equation (7). Furthermore, it can be argued that the unavoidable
increase in neuron numbers, needed to augment their cognitive capacities, was absorbed mainly by its
cortical densely populated layer II, and also by layer I since is far more cellular and thick than in most
terrestrial species .
Moreover, evolutionary modiﬁcations have always been made within the context of the
organization and architecture already in place and computational solutions invented by nature may be
well neither optimal nor predictable from generally accepted human assumptions [
]. According to
the model the cost incurred by this evolutionary modiﬁcation resulted in a substantial increase of the
associated brain metabolic costs, however, the energetic costs of maintaining an enlarged brain were
possible, probably, because of their dietary quality (i.e., the energetic and nutrient density of their diet)
accompanied by an increase in basal metabolic rate and/or efﬁciency of metabolism to accomodate
expanded energy demands. For instance, the dolphin lineage showed faster rates of evolution in genes
expressed in the mitochondria, the source of aerobic metabolism suggesting the increased need to
provide additional energy to such a large organ. Furthermore, of all terrestrial and aquatic animals
tested, only primates and cetaceans have red blood cells that are extraordinarily permeable to glucose
(large brains require readily available blood glucose in order to function) [65,130].
Entropy 2017,19, 543 27 of 35
Terrestrial Mammals Lacking Internal Granular Layer IV in the Cerebral Cortex
From a cytoachitecture point of view the cerebral cortex of terrestrial mammals, such as elephants,
or hippopotamids, also lack granular layer IV. This fact is of particular interest because the closest
phylogenetic relatives to elephants are sirenians [
] whose order includes two extant families
Dugondidae (dugongs) and Trichechidae (manatees), and both species possess a fully developed cortex
(i.e., the six characteristic layers of the cerebral cortex are present). However, it has recently been
shown that elephants had an aquatic ancestor .
One of the adaptations seen in diving marine mammals is the presence of higher concentrations
of myoglobin in muscles when compared to terrestrial mammals. What is more, those that dive
regularly, e.g., sperm whales, have the highest concentrations. Indeed, sperm whales are better than
any other animal at staying underwater for long periods without having to take air (e.g., they can stay
underwater for approximately 73 min at a time [
]). Diving mammals have higher concentrations
of this protein, but according to Mirceta et al.
they also exhibit an adaptation: the surface of
this oxygen-binding protein possesses a net surface charge causing it to repel itself more strongly,
thus enabling deep diving animals to pack their myoglobin into even higher concentrations (proteins
tend to stick together at high concentrations impairing their function). Furthermore, it appears
that myoglobin with the aforementioned molecular signature is a clear sign of a diving lifestyle.
Increased myoglobin net surface charge was observed in lineages of expert divers like cetaceans
and pinnipeds, to name a few). However, it did not occur in a common ancestor of whales or their
closest living relatives, the semiaquatic hippopotamuses, which implies a low degree of aquatic
specialization in their last common ancestor. Surprisingly, they found that terrestrial mammals like
elephants and hyraxes descend from ancestors with the aforementioned adaptation of myoglobin
(i.e., the protein has a net surface charge), suggesting that they have aquatic ancestors. Thus, the lack
or underdevelopment of layer IV in the cerebral cortex of the elephant together with their resulting
cognitive capacities (remember that elephants have a complex social structure and sophisticated
cognitive abilities) is also explained in terms of the second pathway and how the selective advantages
and natural evolution led to an increase in cognitive capacities. Speciﬁcally, as the result of selective
pressures for increasing cognitive abilities driven by the social demands of a brain ancestrally adapted
to the aquatic environment. It is important to note that the cerebral cortex of the elephant also possess
a high glia-to-neuron ratio (see Table 1).
A similar conclusion cannot be drawn to explain the agranularity of the cerebral cortex of
hippopotamids, ﬁrstly because there is not enough physiological data about its cerebral cortex at this
time (e.g., glial-to-neuron ratio, neuron numbers and white matter to gray matter ratio), but primarily
because of the fact that there is a large ghost lineage (i.e, missing fossils inferred from the phylogeny
throughout signiﬁcant periods of history) between the family Hippopotamidae and the base of the order
]. Thus, as a consequence of the uncertainity surrounding the exact closest fossil relatives
for hippopotamids, it is not clear whether their most recent common ancestor was terrestrial, aquatic
4.3. Brain Evolution: Large Brains, Thinner Cortices, and an Extreme Gyrencephaly
The large brain of cetaceans, and the combination of extreme cortical surface area together
with a narrow cortical width put forward a unique underlying cerebral cortex organization scheme
that has been the focal point of longstanding and unresolved controversy about the computational
capacities (and resulting intelligence) of the cetacean brain [
]. It has been recently shown that the most
encephalized mammals were odontocetes, not primates as traditionally believed. Speciﬁcally, the rate
of increase in encephalization along the terminal Homo lineage is exceeded by three primate and four
cetacean branches, with the terminal Tursiops truncatus branch (i.e., bottlenose dolphins) having the
highest rate .
Entropy 2017,19, 543 28 of 35
These data are of particular interest, ﬁrstly, because from an evolutionary perspective, whenever
evolution increased absolute brain size, it has apparently done so mainly by increasing neuron
number, not neuron size [
]. Secondly, because the focus on explanatory theories about brain
evolution, the discussion has currently shifted to theories proposing social beneﬁts of enhanced
]. In other words, the spurts in brain enlargement in cetacean and hominid lineages
are principally explained in response to the especially challenging demands of a complex social life of
constant competition and cooperation with others in the social group [14,133,134].
Thus, the large size of the cetacean brain, and especially the intriguing cortical organization
scheme based on an extreme gyrencephaly are explained in terms of the second route derived from
the theoretical model which regards how nature evolved brains to increase their cognitive capacities.
From a physiologic point of view both routes leads to an increase in encephalization because of the
need of increased neuron numbers. Particularly, the second route is implicitly linked to an overall
increase in the volume of white matter as a result of the postulated increase in the average connectivity
that happened as the result of the two selective pressures mentioned before. Therefore, the evolutionary
process favoured the extreme gyriﬁcation that is observed in the cetacean brain since highly folded
cortices are those that have more neurons connected through the white matter [
] (i.e., a higher
non-local connectivity), which leads to a thinner cortex because it offers less mechanical resistance
to folding, but at the same time leading to the remarkable large brains that are currently observed in
Many researchers have attempted to specify what marks the intellectual divide between species,
especially between human and nonhuman intelligence. Clearly, the role of human intelligence in
the domination of other species appears to be obvious, and perhaps this fact is one of the reasons
that could explain why the notion of an evolutionary scale with humans at the top is still popularly
held. However, researchers have tended to under-evaluate the cognitive capacities of other animals,
for example, because of the difﬁculty in providing animals with task instructions, which one can quite
easily do with humans [
]; our bias is to present animals with tasks that are convenient to the human
sensory, response, and motivational systems. In the case of cetaceans, there are also obvious logistical
difﬁculties associated with their study. From a broader perspective, an extensive amount of positive
research ﬁndings in the ﬁeld of animal intelligence have suggested that many of the special capacities
that have been attributed to humans might be more quantitative than qualitative [
]. Thus, ideas
about what marks the boundary between human and nonhuman intelligence have undergone repeated
revision and will continue to do so in the near future (Figure 5). Most notably, the cognitive capacities
and intelligence of cetaceans have most likely been one of the research subjects that have been highly
debated in recent years. The present study is expected to provide plausible evidence not only to respect
the position of defending the potential of cetaceans for complex cognition but also to stimulate more
focused studies that could support or refute the concepts that are presented throughout this paper,
possibly narrowing the existing boundary between human and nonhuman intelligence.
Entropy 2017,19, 543 29 of 35
Graphical illustration of the study’s implications. The exact number of information-processing
levels that can be associated with a particular brain is still unclear. Furthermore, the cortical neuron
numbers in most of the large-brained cetacean species is not currently known. Recent studies have
hypothesized that the larger absolute number of neurons in the human cerebral cortex (but not in
the whole brain) is correlated with the superior cognitive abilities of humans compared to elephants
and other large-brained mammals [
]. Furthermore, it has been suggested that the cerebral
cortex of the largest whales might be composed of only a fraction of the average 16,300 million neurons
found in the human cerebral cortex. Surprisingly, it has also been shown by another study that
long-ﬁnned pilot whales (Globicephala melas) possess the highest number of cortical cells of any specie
studied so far, including humans [
]. A larger absolute number of neurons in the cerebral cortex is a
necessary but not a sufﬁcient condition for exhibiting superior cognitive abilities or higher levels of
intelligence. However, if future studies conﬁrm the existence of unexpected large number of neurons in
the cerebral cortex of the bottlenose dolphin (Tursiops truncatus), and particularly, in other large-brained
cetaceans such as killer whales (Orcinus orca), humpback whales (Megaptera novaeangliae), or sperm
whales (Physeter macrocephalus), the predictions made by the model would suggest the possibility
of the existence of levels of intelligence in these animals that might go beyond what has previously
Supplementary Materials: Supporting data information are available online at www.mdpi.com/1099-4300/19/
The author would like to thank the University of Massachussets, Amherts (UMASS) to give
time for the writing part of this paper during a postdoctoral research position at the College of Information and
Computer Sciences (CICS) concerning a personal and previous research not covered by the funds of CICS, and
especially to Kerry Shaw (the director of External Relations and Communications at CICS) for her valued help
in the proof reading of some important parts of the manuscript. The author furthermore thanks Angel Acebes
Vindel for his help on questions concerning the anatomy and physiology of the vertebrate’s brain, Nina Eriksen
for providing important information on stereology techniques, Patrick Hof for the pictures of the brain of the
Humpback whale, Ciro Romero Manrique de Lara for the illustration of the Phylogenetic tree, and Constatine
Alexander for the picture of the Humpback whale breaching off the coast of Juneau (Alaska).
Conﬂicts of Interest: The author declares no conﬂict of interest.
Entropy 2017,19, 543 30 of 35
The following abbreviations are used in this manuscript:
RMR Resting Metabolic Rate
DVR Dorsal Ventricular Ridge
NPD Neuron Packing Density
Butti, C.; Raghanti, M.A.; Sherwood, C.C.; Hof, P.R. The neocortex of cetaceans: Cytoarchitecture and
comparison with other aquatic and terrestrial species. Ann. N. Y. Acad. Sci. 2011,1225, 7–58.
Manger, P.R. An examination of cetacean brain structure with a novel hypothesis correlating thermogenesis
to the evolution of a big brain. Biol. Rev. 2006,81, 293–338.
Eriksen, N.; Pakkenberg, B. Total neocortical cell number in the Mysticete brain. Anat. Rec.
Hof, P.R.; Van Der Gucht, E. Structure of the cerebral cortex of the Humpback whale, Megaptera Novaeangliae
(Cetacean, Mysticety, Balaenopteridae). Anat. Rec. A 2007,290, 1–31.
Kojima, T. On the brain of the sperm whale (Physeter catodon L.). Sci. Rep. Whales Res. Inst. Tokyo
Ridgway, S.H.; Hanson, A.C. Sperm Whales and Killer Whales with the Largest Brain of All Toothed Whales
Show Extreme Differences in Cerebellum. Brain Behav. Evol. 2014,83, 266–274.
Lyamin, O.I, Manger, P.R.; Ridgway, S.H.; Mukhameov, L.M.; Siegel, J.M. Cetacean sleep: An unusual form
of mammalian sleep. Neurosci. Biobehav. Rev. 2008,32, 1451–1484.
Ridgway, S.H. The central nervous system of the bottlenose dolphin. In The Bottlenose Dolphin; Leatherwood, S.,
Reeves, R.R., Eds.; Academic Press: New York, NY, USA, 1990; pp. 69–97.
Isler, K.; van Schaik, P. Metabolic costs of brain size evolution. Biol. Lett.
,2, 557–560, doi:10.1098/rsbl.2006.0538.
Mota, B.; Herculano-Houzel, S. How the cortex gets its folds and inside-out connectivity-driven model for
the scaling of mammalian cortical folding. Front. Neuroanat. 2012, doi:10.3389/fnana.2012.00003.
Prothero, J.W.; Sundsten, J.W. Folding of the cerebral cortex in mammals. Brain Behav. Evol.
Herculano-Houzel, S. Not All Brains Are Made the Same: New Views on Brain Scaling in Evolution.
Brain Behav. Evol. 2011,78, 22–36.
13. Striedter, G.F. Principles of Brain Evolution; Sinauer Associates: Sunderland, MA, USA, 2005.
Connor, R.C. Dolphin social intelligence: Complex alliance relationships in bottlenose dolphins and
a consideration of selective environments for extreme brain size evolution in mammals. Philos. Trans. R.
Soc. B 2007,362, 587–602.
15. Oelschläger, H.H.A.; Kemp, B. Ontogenesis of the sperm whale brain. J. Comp. Neurol. 1998,399, 210–228.
Ridgway, S.H.; Au, W.W.L. Hearing and echolocation: Dolphin. In Elsevier’s Encyclopedia of Neuroscience,
2nd ed.; Adelman, G., Smith, B.H., Eds.; Elsevier: New York, NY, USA, 1999; pp. 858–862.
Oelschläger, H.H.A.; Oelschläger, J. Brain. In Encyclopedia of Marine Mammals; Wursig, B., Thewissen, J.G.M.,
Eds.; Academic Press: San Diego, CA, USA, 2008; pp. 134–149.
18. Güntürkun, O. Is dolphin cognition special? Brain Behav. Evol. 2014, doi:10.1159/00357551.
Huggenberger, S. The size and complexity of dolphin brains a paradox? J. Mar. Biol. Assoc. UK
Manger, P.R. Questioning the interpretation of behavioral observations of cetaceans: Is there really support
for a special intellectual status for this mammalian order? Neuroscience 2013,250, 664–696.
21. Marino, L. Dolphin cognition. Curr. Biol. 2004,14, R910–R911.
Marino, L.; Butti, C.; Connor, R.C.; Fordyce, R.E.; Herman, L.M.; Hof, P.R.; Lefevre, L.; Lusseau, D.;
McCowan, B.; Nimchincky, E.A.; et al. A claim in search of evidence: Reply to Manger’s thermogenesis
hypothesis of cetacean brain structure. Biol. Rev. Camb. Philos. 2008,83, 417–440.
Patzke, N.; Spocter, M.A.; Karlsson, K.A.; Bertelsen, M.F.; Haagensen, M.; Chawana, R.; Streicher, S.;
Kaswera, C.; Gilissen, E.; Alagaili, A.N.; et al. In contrast to many other mammals, cetaceans have relatively
small hippocampi that appear to lack adult neurogenesis. Brain Struct. Funct. 2013,220, 361–383.
Hart, B.L.; Hart, L.A.; Pinter-Wollman, N.; Large brains and cognition: Where do elephants ﬁt in?
Neurosci. Biobehav. R. 2008,32, 86–98.
Entropy 2017,19, 543 31 of 35
Mann, J.; Patterson, E.M. Tool use by aquatic animals. Philos. Trans. R. Soc. B
Zentall, T.R. Animal intelligence. In The Cambridge Handbook of Intelligence; Sternberg, R.J., Kaufman, S.B.,
Eds.; Cambridge University Press: Cambridge, UK, 2011; pp. 309–327.
Chittka, L.; Rossiter, S.J.; Skorupski, P.; Fernando, C. What is comparable in comparative cognition?
Philos. Trans. R. Soc. B 2012,367, 2677–2685.
Chinea, A.; Korutcheva, E. Intelligence and embodiment: A statistical mechanics approach. Neural Netw.
Ridgway, S.H.; Carln, P.C.; Van Alstyne, K.R.; Hanson, A.C.; Tarpley, R.J. Comparison of Dolphins’ Body and
Brain Measurements with Four other Groups of Cetaceans Reveals Great Diversity. Brain Behav. Evol.
Mortensen, H.S.; Pakkenberg, B.; Dam, M.; Dietz, R.; Sonne, C.; Mikkelsen, B.; Eriksen, N. Quantitative
relationships in delphinid neocortex. Front. Neuroanat. 2014,8, 132.
Hecht-Nielsen, R. Confabulation Theory: The Mechanism of Thought; Springer: Berlin/Heidelberg, Germany, 2007.
Tomer, R.; Denes, A.S.; Tessmar-Raible, K.; Arendt, D. Proﬁling by image registration reveals common origin
of annelid mushroom bodies and vertebrate pallium. Cell 2010,142, 800–809.
Dugas-Ford, J.; Rowell, J.J.; Ragsdale, C.W. Cell-type homologies and the origins of the neocortex. Proc. Natl.
Acad. Sci. USA 2012,109, 16974–16979.
Karten, H.J. Vertebrate brains and evolutionary connectomics: On the origins of the mammalian ‘neocortex’.
Philos. Trans. R. Soc. B 2015,370, 60.
Taylor, P.; Hobbs, J.N.; Burroni, J.; Siegelmann, H. The global landscape of cognition:hierarchical aggregation
as an organizational principle of human cortical networks and functions. Sci. Rep. 2015,5, 18112.
Calabrese, A.; Woolley, S.M.N. Coding principles in the avian brain. Proc. Natl. Acad. Sci. USA
Felleman, D.J.; Van Essen, D.C. Distributed hierarchical processing in the primate cerebral cortex.
Cereb. Cortex 1991,1, doi:10.1093/cercor/1.1.1.
Salazar, R.F.; Dotson, N.M.; Bressler, S.L.; Gray, C.M. Content Speciﬁc Fronto-Parietal Synchronization during
Visual Working Memory. Science 2012,338, 1097–1100.
39. Churchland, P.; Sejnowski, T. The Computational Brain; MIT Press: Cambridge, MA, USA, 1992.
40. Chandler, D. Introduction to Modern Statistical Mechanics; Oxford University Press: Oxford, UK, 1987.
41. Reichl, L.E. A Modern Course in Statistical Physics; Wiley: New York, NY, USA, 1998.
Hermann, C. Statistical Physics (Including Applications to Condensed Matter); Springer: New York, NY, USA, 2005.
Howarth, C.; Gleeson, P.; Attwell, D. Updated energy budgets for neural computation in the neocortex and
cerebellum. J. Cerebr. Blood Flow Metab. 2012,32, 1222–1232.
Bianchi, S.; Stimpson, C.D.; Bauernfeind, A.L.; Schapiro, S.J.; Baze, W.B.; McArthur, M.J.; Bronson, E.; Hopkins,
W.D.; Semendeferi, K.; Jacobs, B.; et al. Dendritic morphology of pyramidal neurons in the chimpanzee
neocortex: Regional specializations and comparison to humans. Cereb. Cortex 2013,23, 2429–2436.
Butti, C.; Janeway, C.M.; Townshend, C.; Wicinski, B.A.; Reidenberg, J.S.; Ridgway, S.H.; Sherwood, C.C.;
Hof, P.R.; Jacobs, B. The neocortex of cetartiodactyls: I. A comparative Golgi analysis of neuronal morphology
in the bottlenose dolphin (Tursiops truncatus), the minke whale (Balaenoptera acutorostrata), and the humpback
whale (Megaptera novaeangliae). Brain Struct. Funct. 2015,220, 3339–3368.
Jacobs, B.; Schall, M.; Prather, M.; Kapler, E.; Driscoll, L.; Baca, S.; Jacobs, J.; Ford, K.; Wainwright, M.;
Treml, M. Regional dendritic and spine variation in human cerebral cortex: A quantitative golgi study.
Cereb. Cortex 2001,11, 558–571.
Jacobs, B.; Harland, T.; Kennedy, D.; Schall, M.; Wicinski, B.; Butti, C.; Hof, P.R.; Sherwood, C.C.; Manger, P.R.
The neocortex of cetartiodactyls. II. Neuronal morphology of the visual and motor cortices in the giraffe
(Giraffa camelopardalis). Brain Struct. Funct. 2015,220, 2851–2872.
Nieuwenhuys, R.; Ten Donkelaar, H.J.; Nicholson, C. The Central Nervous System of Vertebrates; Springer:
Berlin, Germany, 1998; Volume 3.
Van Essen, D.C. A tension-based theory of morphogenesis and compact wiring in the central nervous system.
Nature 1997,385, 313–318.
Harrison, K.H.; Hof, P.; Wang, S.S.H. Scaling laws in the mammalian neocortex: Does form provides clues to
function?. J. Neurocytol. 2002,31, 289–298.
Entropy 2017,19, 543 32 of 35
Ventura-Antunes, L.; Mota, B.; Herculano-Houzel, S. Different scaling of white matter volume, cortical connectivity,
and gyrification across rodent and primate brains. Front. Neuroanat. 2013,7, doi:10.3389/fnana.2013.00003.
Herculano-Houzel, S.; Manger, P.R.; Kaas, J.H. Brain scaling in mammalian evolution as a consequence of
concerted and mosaic changes in number of neurons and average neuronal size. Front. Neuroanat.
Goodman, M.; Sterner, K.N.; Islam, M.; Uddin, M.; Sherwood, C.C.; Hof, P.R.; Hou, Z.C.; Lipovich, L.; Jia, H.;
Grossman, L.I.; et al. Phylogenetic analyses reveal convergent patterns of adaptive evolution in elephants
and human ancestries. Proc. Natl. Acad. Sci. USA 2009,106, 20824–20829.
Bullmore, E.; Sporns, O. Complex brain networks: Graph theoretical analysis of structural and functional
systems. Nat. Rev. Neurosci. 2009,10, 186–198.
Bedny, M.; Caramazza, A. Perception, action, and word meanings in the human brain: The case from action
verbs. Ann. N. Y. Acad. Sci. 2011,1224, 81–95.
Pullvermüller, F.; Huss, M.; Kheriff, F.; Moscoso del Prado Martin, F.; Hauk. O. Motor cortex maps
articulatory features of speech sounds. Proc. Natl. Acad. Sci. USA 2006,103, 7865–7870.
Pullvermüller, F. Semantic embodiment, disembodiment or misembodiment? In search of meaning in
modules and neuron circuits. Brain Lang. 2013,127, 86–103.
Herculano-Houzel, S.; Collins, C.E.; Wong, P.; Kaas, J.H. The basic nonuniformity of the cerebral cortex.
Proc. Natl. Acad. Sci. USA 2010,105, 12593–12598.
Nieuwenhuys, R.; Voogd, J.; Van Huijzen, C. The Human Central Nervous System; Springer: Berlin/Heidelberg,
Wang, Y.; Brzozowska-Prechtl, A.; Karten, H.J. Laminar and columnar auditory cortex in avian brain.
Proc. Natl. Acad. Sci. USA 2010,107, 12676–12681.
Ahumada-Galleguillos, P.; Fernandez, M.; Marin, G.J.; Letelier, J.C.; Mpodozis, J. Anatomical Organization
of the Visual Dorsal Ventricular Ridge in the Chick (Gallus gallus): Layers and Columns in the Avian Pallium.
J. Comp. Neurol. 2015,406, 329–345.
Husband, S.A.; Shimizu, T. Efferent projections of the ectostriatum in the pigeon Columba livia.J. Comp. Neurol.
Ulinsky, P. Dorsal Ventricular Ridge: A Treatise on Forebrain Organization in Reptiles and Birds; Wiley: New York,
NY, USA, 1983
Manger, P.R.; Slutsky, D.A.; Molnar, Z. Visual subdivisions of the dorsal ventricular ridge of the iguana
(Iguana iguana) as determined by electrophysiologic mapping. J. Comp. Neurol. 2002,453, 226–246.
McGowen, M.R.; Grossman, L.I.; Wildman, D.E. Dolphin genome provides evidence for adaptive evolution
of nervous system genes and molecular rate slowdown. Philos. Trans. R. Soc. B 2012,279, 3643–3651.
Byrne, R.W.; Whiten, A. Machiavellian Intelligence: Social Expertise and the Evolution of the Intellect in Monkeys,
Apes and Humans; Oxford University Press: Oxford, UK, 1988.
Olkowicz, S.; Kocourek, M.; Lucan, R.K.; Portes, M.; Fitch, W.T.; Herculano-Houzel, S.; Nemec, P. Birds have
primate-like numbers of neurons in the forebrain. Proc. Natl. Acad. Sci. USA 2016,113, 7255–7260.
Schoenemann, P.T.; Sheehan, M.J.; Glotzer, D.L. Prefrontal white matter volume is disproportionately larger
in humans than in other primates. Nat. Rev. Neurosci. 2005,8, 242–252.
Schoenemann, P.T. Evolution of the size and functional areas of the human brain. Annu. Rev. Anthropol.
Rilling, J.K.; Insel, T.R. The primate neocortex in comparative perspective using magnetic resonance imaging.
J. Hum. Evol. 1999,37, 191–223.
Jacobs, B.; Lubs, J.; Hannan, M.; Anderson, K.; Butti, C.; Sherwood, C.C.; Hof, P.R.; Manger, P.R. Neuronal
morphology in the African elephant (Loxodonta africana) neocortex. Brain Struct. Funct. 2011,215, 273–298.
72. Douglas-Fields, R. Map the other brain. Nature 2013,501, 25–26.
Herculano-Houzel, S.; Kaas, J.H. Gorilla and orangutan brains conform to the primate cellular scaling rules:
implications for human evolution. Brain Behav. Evol. 2011,77, 33–44.
Herculano-Houzel, S.; Avelino-de-Souza, K.; Neves, K.; Porfírio, J.; Messeder, D.; Mattos Feijó, L.; Maldonado, J.;
Manger, P. The elephant brain in numbers. Front. Neuroanat. 2014,8, doi:10.3389/fnana.2014.00046.
Bianchi, S.; Stimpson, C.D.; Duka, T.; Larsen, M.D.; Janssen, W.G.M.; Collins, Z.; Bauernfeind, A.L.;
Schapiro, S.J.; Baze, W.B, McArthur, M.J.; et al. Synaptogenesis and development of pyramidal neuron
dendritic morphology in the chimpanzee neocortex resembles humans. Proc. Natl. Acad. Sci. USA
Entropy 2017,19, 543 33 of 35
Tomasello, M.; Call, J. The Gestural Communication of Apes and Monkeys; Lawrence Erlbaum Associates:
Mahwah, NJ, USA, 2007.
Costa, D.P.; Williams, T.M. Marine Mammals Energetics. In The Biology of Marine Mammals; Reynold, J.,
Twiss, J., Eds.; The Smithsonian Institution Press: Washington, DC, USA, 2000; pp. 176–211.
Hakeem, A.Y.; Hof, P.R.; Sherwood, C.C.; Switzer, R.C.; Rasmussen, L.R.L.; Allman, J.M. Brain of the
African elephant (Loxodonta africana): Neuroanatomy from magnetic resonance images. Anat. Rec.
79. Hof, P.R.; Chanis, R.; Marino, L. Cortical Complexity in Cetacean Brains. Anat. Rec. 2005,287, 1142–1152.
McKay, G.M. Behavior and Ecology of the Asiatic Elephant in Southeastern Ceylon; Smithsonian Institution,
Government Printing Ofﬁce: Washington, DC, USA, 1973.
Manger, P.R.; Prowse, M.; Haagensen, M.; Hemingway, J. A quantitative analysis of neocortical gyrencephaly
in African elephants (Loxodonta Africana) and six species of cetaceans: comparisons to other mammals.
J. Comp. Neurol. 2012,520, 2430–2439.
Mink, J.W.; Blumenschine, R.J.; Adams, D.B. Ratio of central nervous system to body metabolism in
vertebrates: Its constancy and functional basis. Am. J. Physiol. 1981,241, 203–212.
Leonard, W.R.; Snodgrass, J.J.; Robertson, M.L. Effects of brain evolution on human nutrition and metabolism.
Annu. Rev. Nutr. 2007,27, 311–327.
Lockyer, C. All creatures great and smaller: A study in cetacean life history energetics. J. Mar. Biol. Assoc. UK
Sherwood, C.C.; Stimpson, C.D.; Raghanti, M.A.; Wildman, D.E.; Uddin, M.; Grossman, L.I.; Goodman, M.;
Redmond, J.C.; Bonar, C.J.; Erwin, J.M. Evolution of increased glia-neuron ratios in the human frontal cortex.
Proc. Natl. Acad. Sci. USA 2006,103, 13606–13611.
86. Herman, L.M. Body and self in dolphins. Conscious. Cogn. 2012,21, 526–545.
Xitco, J.M.; Gory, J.D.; Kuczaj, S.A.Spontaneous pointing by bottlenose dolphins (Tursiops truncatus).
Anim. Cogn. 2001,4, 115–123.
Visser, I.N.; Smith, T.G.; Bullock, I.D.; Green, G.D.; Carlsson, O.G.L.; Imberti, S. Antartica peninsula killer
whales (Orcinus orca) hunt seals and penguin on ﬂoating ice. Mar. Mamm. Sci. 2008,24, 225–234.
Foote, A.D.; Grifﬁn, R.M.; Howitt, D.; Larsson, L.; Miller, P.J.O.; Hoelzel, A.R. Killer whales are capable of
vocal learning. Biol. Lett. 2006,2, 509–512.
Baird, R.W. The killer whale: Foraging specializations and group hunting. In Cetacean Societies: Field Studies
of Dolphins and Whales; Mann, J., Conno, R.C., Tyack, P.L., Whitehead, H., Eds.; University of Chicago Press:
Chicago, IL, USA, 2000.
Whitehead, H.; Rendell, L. The Cultural Lives of Whales and Dolphins; University of Chicago Press: Chicago,
IL, USA, 2015.
Montgomery, S.H.; Geisler, J.H.; McGowen, M.R.; Fox, C.; Marino, L.; Gatesy, J. The Evolutionary History of
Cetacean Brain and Body Size. Evolution 2013,67, 3339–3353.
Sharpe, F.S.; Szabo, A.S.; Pack, A.; Nahmens, J. The social structure of bubble net feeding whales in SE Alaska.
In Proceedings of the 20th Biennal Conference on the Biology of Marine Mammals, Dunedin, New Zealand,
9 December 2013.
Stimpert, A.K.; Au, W.W.; Parks, S.E.; Hurst, T.; Wiley, D.N. Common humpback whale (Megaptera novaeangliae)
sound types for passive acoustic monitoring. J. Acoust. Soc. Am. 2011,129, 476–482.
Fournet, M.; Szabo, A. Vocal repertoire of southeast Alaska humpback whales (Megaptera novaeangliae).
J. Acoust. Soc. Am. 2013,134, 3988-3988.
Pitman, R.L, Deecke, V.B.; Gabriele, C.M.; Srinivasan, M.; Black, N.; Denkinger, J.; Durban, J.W.;
Mathews, E.A.; Matkin, D.R.; Neilson, J.L.; et al. Humpback whales interfering when mammal-eating
killer whales attack other species: Mobbing behavior and interspeciﬁc altruism? Mar. Mamm. Sci.
Whitehead, H. Sperm Whales: Social Evolution in the Ocean; University of Chicago Press: Chicago, IL, USA, 2003.
98. Roth, G.; Dicke, U. Evolution of the brain and intelligence. Trends Cogn. Sci. 2005,9, 250–257.
Dicke, U.; Roth, G. Neuronal Factors Determining High Intelligence. Philos. Trans. R. Soc. Lond. B
Nettelbeck, T. Basic processes of intelligence. In The Cambridge Handbook of Intelligence; Sternberg, R.J.,
Kaufman, S.B., Eds.; Cambridge University Press: Cambridge, UK, 2011; pp. 371–388.
Entropy 2017,19, 543 34 of 35
Nettelbeck, T.; Wilson, C. A cross-sequential analysis of developmental differences in speed of visual
information processing. J. Exp. Child Psychol. 1985,40, doi:10.1016/0022-0965(85)90063-3.
Sheppard, L.D.; Vernon, P.A. Intelligence and speed of information-processing: A review of 50 years of
research. Personal. Individ. Differ. 2008,44, 535–551.
Howard, C.V.; Reid, M.G. Unbiased Stereology: Three-Dimensional Measurement in Microscopy; BIOS: Oxford,
UK, 1998, ISBN 1-85996-071-5.
Azevedo, F.A.C.; Carvalho, L.R.B.; Grinberg, L.T.; Farfel, J.M.; Ferretti, R.E.L.; Leite, R.E.P.; Filho, W.J.;
Lent, R.; Herculano-Houzel, S. Equal Numbers of Neuronal and Nonneuronal Cells Make the Human Brain
an Isometrically Scaled-up Primate Brain. J. Comp. Neurol. 2009,513, 532–541.
Pakkenberg, B.; Gundersen, H.J. Neocortical neuron number in humans: Effect of sex and age. J. Comp. Neurol.
106. Witelson, S.F.; Kigar, D.L.; Harvey, T. The exceptional brain of Albert Einstein. Lancet 1999,353, 2149–2153.
107. Chittka, L.; Niven, J. Are bigger brains better? Curr. Biol. 2009,19, R995–R1008.
Irving, L.; Scholander, P.F.; Grinnell, S.W. The respiration of the porpoise, Tursiops truncatus. J. Cell.
Comp. Physiol. 1941,17, 145–168.
Hampton, I.F.G.; Whittow, G.C.; Szekercezes, J.; Rutherford, S. Heat transfer and body temperature in the
Atlantic bottlenosed dolphin, Tursiops truncatus.Int. J. Biometeorol. 1971,15, 247–253.
De Graaf, A.S. Anatomical Aspects of the Cetacean Brain Stem; Von Gorcum: Assen, The Netherlands, 1967;
Ridgway, S.H.; Bullock, T.H.; Carder, T.A.; Seeley, R.L.; Woods, D.; Galanbos, R. Auditory brainstem response
in dolphins. Proc. Natl. Acad. Sci. USA 1981,78, 943–1947.
Ridgway, S.H. Neural time and movement time in choice of whistle or pulse burst responses to different
auditory stimuli by dolphins. J. Acoust. Soc. Am. 2011,129, 1073–1080.
Wang, S.S.H.; Shultz, J.R.; Burish, M.J.; Harrison, K.H.; Hof, P.R.; Towns, L.C.; Wagers, M.W.; Wyatt, K.D.
Functional trade-offs in white matter axonal scaling. J. Neurosci. 2008,28, 4047–4056.
Gusnard, D.A.; Raichle, M.E. Searching for a Baseline: Functional Imaging and the Resting Human Bran.
Nat. Rev. Neurosci. 2001,2, 685–694.
Nelson, D.L.; Cox, M.M. Lehninger Principles of Biochemistry, 6th ed.; Macmillan Learning Publishers: London,
Belanger, M.; Allaman, I.; Magistretti, P. Brain Energy Metabolism: Focus on Astrocyte-Neuron Metabolism
Cooperation. Cell 2011,14, doi:10.1016/j.cmet.2011.08.016.
Pellerin, L.; Magistretti, P.J. Food for Thought: Challenging the Dogmas. J. Cereb. Blood Flow Metab.
Pellerin, L.; Magistretti, P.J. Neuroenergetics: Calling up astrocytes to satisfy hungry neurons. Neuroscientist
Pellerin, L.; Bouzier-Store, A.K.; Aubert, A.; Serres, S.; Merle, M.; Costalat, R.; Magistretti, P.J. Activity-dependent
regulation of energy metabolism by astrocytes: An update. Glia 2007,55, 1251–1262.
Marino, L.; Sol, D.; Toren, K.; Lefebvre, L. Does Diving Limit rain Size in Cetaceans? Mar. Mamm. Sci.
Ridgway, S.H.; Houser, D.; Finneran, J.J.; Carder, D.A.; Keogh, M.; Van Bonn, W.; Smith, C.R.; Scadeng, M.;
Mattrey, R.; Hoh, C. Functional Imaging of Dolphin Brain Metabolism and Blood Flow. J. Exp. Biol.
Williams, T.M.; Friedl, W.A.; Haun, J.E. The physiology of bottlenose dolphins (Tursiops truncatus): Heart
rate, metabolic rate and plasma kactate concentrations during exercise. J. Exp. Biol. 1993,179, 31–46.
Wyss, M.T.; Jolivet, R.; Buck, A.; Magistretti, P.J.; Weber, B. In Vivo Evidence for Lactate as a Neuronal Energy
Source. J. Neurosci. 2011,31, 7477–7485.
Herculano-Houzel, S.; Lent. R. Isotropic fractionator: A simple, rapid method for the quantiﬁcation of total
cell and neuron numbers in the brain. J. Neurosci. 2005,25, 2518–2521.
Gundersen, H.J.; Jensen, E.B. The Efﬁciency of systematic sampling in stereology and its prediction. J. Microsc.
Gundersen, H.J.; Jensen, E.B.; Kiêu, K.; Nielsen, J. The Efﬁciency of systematic sampling in stereology
reconsidered. J. Microsc. 1999,193, 199–211.
Entropy 2017,19, 543 35 of 35
Wallöe, S.; Eriksen, N.; Dabelsteen, T. Pakkenberg, B. A Neurological comparative study of the harp seal
(Pagophylus groenlandicus) and harbour porpoise (Phocoena phocoena). Anat. Rec. 2010,293, 2129–2135.
Kazu, R.S.; Maldonado, J.; Mota, B.; Manger, P.R.; Herculano-Houzel, S. Cellular scaling rules for the brain of
Artiodactyla include a highly folded cortex with few neurons. Front. Neuroanat. 2014,8, 128.
Herculano-Houzel, S. The Human Advantage: A New Understanding of How Our Brain Became Remarkable;
MIT Press: Cambridge, MA, USA, 2016.
Venn-Watson, S.; Carlin, K.; Ridgway, S. Dolphins as animal models for type 2 diabetes: Sustained,
post-prandial hyperglycemia and hyperinsulinemia. Gen. Comp. Endocrinol. 2011,170, 193–199.
Mirceta, S.; Signore, A.V.; Burns, J.M.; Cossins, A.R.; Campbell, K.L.; Berenbrink, M. Evolution of Mammalian
Diving Capacity Traced by Myoglobin Net Surface Charge. Science 2013,340, 1234192.
Marino, L.; Connor, R.C.; Fordyce, E.R, Herman, L.M.; Hof, P.R.; Lefebvre, L.; Lusseau, D.; McCowan, B.;
Nimchinsky, E.A.; Pack, A.A.; et al. Cetaceans Have Complex Brains for Complex Cognition? PLoS Biol.
Herrmann, E.; Call, J.; Hernandez-LLoreda, M.V.; Hare, B.; Tomasello, M. Humans Have Evolved Specialized
Skills of Social Cognition: The Cultural Intelligence Hypothesis. Science 2007,317, 1360–1366.
van Schaik, C.P.; Burkart, J.M. Social Learning and evolution: The cultural intelligence hypothesis.
Philos. Trans. R. Soc. Lond. Biol. Sci. 2011,366, 1008–1026.
135. Zentall, T.R. Animal memory: The role of instructions. Learn. Motiv. 1997,28, 248–267.
2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).