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Cultural transmission and biological markets (accepted 2018 version)

Authors:

Abstract

Active cultural transmission of fitness-enhancing behavior (sometimes called "teaching") can be seen as a costly strategy: one for which its evolutionary stability poses a Darwinian puzzle. In this article, we offer a biological market model of cultural transmission that substitutes or complements existing kin selection-based proposals for the evolution of cultural capacities. We explicitly demonstrate how a biological market can account for the evolution of teaching when individual learners are the exclusive focus of social learning (such as in a fast-changing environment). We also show how this biological market can affect the dynamics of cumulative culture. The model works best when it is difficult to have access to the observation of the behavior without the help of the actor. However, in contrast to previous non-mathematical hypotheses for the evolution of teaching, we show how teaching evolves even when innovations are insufficiently opaque and therefore vulnerable to acquisition by emulators via inadvertent transmission. Furthermore, teaching in a biological market is an important precondition for enhancing individual learning abilities. Abstract Active cultural transmission of fitness-enhancing behavior (some-times called "teaching") can be seen as a costly strategy: one for which its evolutionary stability poses a Darwinian puzzle. In this article, we o↵er a biological market model of cultural transmission that substitutes or complements existing kin selection-based proposals for the evolution of cultural capacities. We demonstrate how a biological market can account for the evolution of teaching when individual learners are the exclusive focus of social learning (such as in a fast-changing environment). We also show how this biological market can a↵ect the dynamics of cumulative culture. The model works best when it is difficult to have access to the observation of the behavior without the help of the actor. However, in contrast to previous non-mathematical hypotheses for the evolution of teaching, we show how teaching evolves, even when innovations are insuciently opaque and therefore vulnerable to acquisition by emulators via inadvertent transmission. Furthermore, teaching in a biological market is an important precondition for enhancing individual learning abilities.
Name of the Authors: Claude Loverdo & Hugo Viciana
Title: Cultural transmission and biological markets
Affiliations:
Claude Loverdo,
Laboratoire Jean Perrin
UMR 8237 - CNRS Sorbonne Université
4, place Jussieu, Tour 32-33
75252 Paris Cedex 05, France
Hugo Viciana,
Juan de la Cierva Research Fellow
Instituto de Estudios Sociales Avanzados-CSIC
Plaza Campo Santo de los Mártires, 7
14004, Córdoba, Spain
Shared first authorship.
Corresponding author:
Hugo Viciana,
email address: Hviciana@iesa.csic.es
telephone number: +34-957760625
ORCID:
Claude Loverdo: 0000-0002-0888-1717
Hugo Viciana: 0000-0002-4569-3635
Abstract: Active cultural transmission of fitness-enhancing behavior (sometimes called
“teaching”) can be seen as a costly strategy: one for which its evolutionary stability poses a
Darwinian puzzle. In this article, we offer a biological market model of cultural transmission
that substitutes or complements existing kin selection-based proposals for the evolution of
cultural capacities. We explicitly demonstrate how a biological market can account for the
evolution of teaching when individual learners are the exclusive focus of social learning (such
as in a fast-changing environment). We also show how this biological market can affect the
dynamics of cumulative culture. The model works best when it is difficult to have access to the
observation of the behavior without the help of the actor. However, in contrast to previous
non-mathematical hypotheses for the evolution of teaching, we show how teaching evolves
even when innovations are insufficiently opaque and therefore vulnerable to acquisition by
emulators via inadvertent transmission. Furthermore, teaching in a biological market is an
important precondition for enhancing individual learning abilities.
Keywords: Social learning · comparative advantage · teaching · cumulative culture · partner choice
Acknowledgments: HV received support from a La Caixa Foundation Scholarship at the initial stage of the
preparation of this work. This article has benefited from feedback of audiences at the University of
Cambridge, the University of Granada, the University of Louvain-la-neuve, and the University of Paris 1.
Special thanks should be given to Camilo Cela-Conde, Jean Gayon, Gabi Lipede, Pierre Livet, Hugo
Mercier, Susana Monsó, Dan Sperber, Neftalí Villanueva, and several anonymous reviewers for comments
Title Page
Accepted but unedited final draft: Please refer to the online/printed version in journal Biology & Philosophy
Biology & Philosohy manuscript No.
(will be inserted by the editor)
Cultural transmission and biological markets
Claude Loverdo ·Hugo Viciana
Received: date / Accepted: date
Abstract Active cultural transmission of fitness-enhancing behavior (some-
times called “teaching”) can be seen as a costly strategy: one for which its
evolutionary stability poses a Darwinian puzzle. In this article, we oer a bio-
logical market model of cultural transmission that substitutes or complements
existing kin selection-based proposals for the evolution of cultural capacities.
We demonstrate how a biological market can account for the evolution of teach-
ing when individual learners are the exclusive focus of social learning (such as
in a fast-changing environment). We also show how this biological market can
aect the dynamics of cumulative culture. The model works best when it is dif-
ficult to have access to the observation of the behavior without the help of the
actor. However, in contrast to previous non-mathematical hypotheses for the
evolution of teaching, we show how teaching evolves, even when innovations
are insuciently opaque and therefore vulnerable to acquisition by emulators
via inadvertent transmission. Furthermore, teaching in a biological market is
an important precondition for enhancing individual learning abilities.
Keywords Social Learning ·Comparative Advantage ·Teaching ·Cumulative
Culture ·Partner Choice
C. Loverdo
Laboratoire Jean Perrin, UMR 8237 - CNRS – Sorbonne Universite
Tel.: +33-144272823
E-mail: claude.loverdo@upmc.fr
H. Viciana
Juan de la Cierva Research Fellow
Institute for Advanced Social Studies (IESA-CSIC)
Tel.:+34-957760261
E-mail: Hugo.Viciana@normalesup.org
Blinded Manuscript Click here to view linked References
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Accepted but unedited final draft: Please refer to the online/printed version in journal Biology & Philosophy
2 Claude Loverdo, Hugo Viciana
1 Introduction
Cultural transmission is sometimes considered to confer a straightforward ad-
vantage unto the group or the individual’s kin. However, if the active trans-
mission of culture is such a successful strategy, then where has it occurred in
the animal kingdom? Despite the fact that social learning and certain forms
of animal traditions are common among many non-human species, active cul-
tural transmission or teaching is a far rarer phenomenon (Boyd and Richerson
1996; Thornton and Raihani 2008).
Strictly speaking, cultural transmission is broadly defined (Viciana 2018).
By cultural transmission, one might refer to any process of social learning or
the social transmission of artifacts. The set of all types of cultural transmission
is huge and variate indeed. It is something that researchers of animal behavior
and the evolution of culture are generally well aware of (Hoppitt and Laland
(2013), chapter 4). Without being exhaustive, cultural transmission might en-
compass the process of inadvertent social learning (Danchin et al 2004) (where
one individual reproduces the behavior of another individual when triggered
by the observation of some unintended eect of that behavior), processes of
cultural communication (Origgi and Sperber 2000), epidemiological processes
of cultural attraction (Miton et al 2015), active cultural transmission or teach-
ing (of which there are dierent kinds)(Kline 2015), and even cultural niche
construction (Odling-Smee et al 2003).
On the production side of active cultural transmission, “natural pedagogy”
(i.e., the dispositions and eorts of adults to make themselves easily under-
stood by children in order to facilitate the transmission of cultural knowledge)
is certainly part of the human pattern of cultural transmission (Hewlett et al
2011). This form of teaching is a good candidate for a universal trait of our
species, and perhaps even a biological adaptation (Csibra and Gergely 2009).
Such considerations suggest a vertical-transmission view of the evolution of
human culture i.e., the direct transmission from a parental generation to its
ospring. Nonetheless, another view that is widely accepted among ethnogra-
phers claims that adult-infant instruction is rare in hunter-gatherers groups
(Atran and Sperber 1991). Moreover, as several case studies in cultural trans-
mission have indicated, non-vertical transmission (the transmission to children
from other children or slightly older individuals, as opposed to much older
adults) is far more important for cultural transmission than what is often as-
sumed (Aunger 2000; Morin 2015). It has even been argued that non-vertical
transmission might constitute a key component of children’s and young adults’
adoption of much of the cultural repertoire (Harris 1998).
From a population genetics perspective, other considerations also call into
question the primacy of vertical transmission in the evolution of culture. Cul-
tural capabilities were plausibly “built for speed” and adaptability (Richerson
and Boyd 2000). However, pure vertical cultural transmission is more similar to
genetic adaptation than horizontal transmission. Thus, vertical transmission
may exhibit properties that make culture adaptive to a lesser extent: verti-
cal transmission is more often subject to maladaptive lag and inertia than
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Cultural transmission and biological markets 3
other forms of cultural transmission (McElreath and Boyd 2008). In changing
environments, mother does not always know best. The facilitation of cultural
transmission via genetic relatedness, namely as a form of evolved nepotism,
conceivably plays a role. However, this role could be easily exaggerated. There
are conflicts of interest between parents and siblings (Trivers 1974). In prin-
ciple, parental manipulation could be selected for, which, in return, could
prompt the evolution of devices that counteract the eects of vertical cultural
transmission among siblings (Trivers 2011).
Active cultural transmission is fundamentally problematic in light of its
cost-benefit structure. If what is learned by an individual is so demonstrably
useful in terms of fitness that acquiring it makes sense for other individuals,
then why bother actively transmitting it? From the standard inclusive fitness
perspective of evolution, it follows that traits that do not benefit kin need to
benefit their carriers in order to evolve by way of natural selection (Dessalles
2001, 2006). However, in humans a great deal of cultural transmission is di-
rected at non-kin and costly enough to pose a Darwinian puzzle. The question
thus remains: why transmit culturally?
The seemingly altruist cultural transmission of fitness-enhancing informa-
tion yields a free-rider problem that is structured similarly to the standard pris-
oner’s dilemma. Briefly, since active cultural transmission of fitness-enhancing
information (“teaching”) is a form of cooperation, every individual would be
better oif other individuals cooperate, while he or she does not cooperate.
Therefore, all else being equal, a population of individuals capable of teaching
could be expected to evolve toward a sub-optimal equilibrium: one in which
teaching is simply not practiced.
Early on, teaching was characterized by ethologists as a form of biologi-
cal altruism (Caro and Hauser 1992). In principle, ecological conditions linked
to kin selection and alloparentality might have facilitated the evolution of
certain cultural capacities (Hrdy 2009; Flinn and Ward 2005). Consequently,
the immense majority of formal models that have been used to investigate
the evolution of teaching have relied on genetic relatedness in order to ex-
plain its stability (Castro and Toro 2014; Fogarty et al 2011). More recently,
Castro et al (2010) have argued that “humans have developed psychological
mechanisms that enable cultural transmission by being receptive to parental
advice.” Nevertheless, the abovementioned theoretical and empirical consid-
erations largely justify the exploration of complementary, if not alternative,
evolutionary pathways through which cultural capacities related to teaching
can reach an adaptive equilibrium in a given population (see Sytsma (2012)
for a similar argument).
1.1 Biological trade and the ecology of social learning
In this article, we analyze conditions for the evolution of oblique or hori-
zontal active cultural transmission as a behavioral phenotype in a biological
market model. Originally proposed by behavioral ecologists Ronald No¨e and
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4 Claude Loverdo, Hugo Viciana
Peter Hammerstein, biological markets arise when associations between bio-
logical individuals are suciently uncoerced such that competition occurs not
so much by force or its threat, but as a need to oer more of what the choosing
party “demands.” The idea of biological markets thus sheds light on certain
selective mechanisms: namely, market eects in which “members of one class
can “force” members of another class to evolve traits that would have a neg-
ative eect on fitness in the absence of the cooperative interaction(No¨e and
Hammerstein, 1994, p. 2).
Along with other ecological forces, part of the evolutionary rationale be-
hind active cultural transmission might be the result of biological markets.
Models and hypotheses akin to biological markets have already found appli-
cations in other arenas of evolutionary psychology, including the psychology
of cooperation and mutualism (Frank 1988; Baumard 2010; Andr´e and Bau-
mard 2011). To our knowledge, Henrich and Gil-White (2001) first proposed
that cultural abilities and knowledge could enter into a market-like exchange
of “information goods” and “prestige”. Based on previous anthropological ob-
servations (Barkow et al 1975), they formulated a theory in which dominance
and prestige hierarchies dier and mix in the context of human hierarchical
strategies. In humans, hierarchical status is attainable not only through use of
force (i.e., the “dominance” strategy) or power, but also through demonstra-
tions of expertise in certain cultural domains: an ability that, when socially
acknowledged, is usually referred to as “prestige” (Cheng et al 2013). Since
status tends to be associated with reproductive success, and since the use of
force by way of sheer dominance has probably been selected against during the
evolution of our species (Boehm 1999), pursuing competence might have been
an advantageous reproductive strategy of primary importance in the history
of our species. In what follows, we explicitly incorporate that ecological force
into the study of the evolution of cultural transmission.
It is customary to examine the eects of changing environments in the
study of cultural evolution. In a very stable environment, a social learner, who
has learned a technique from an individual learner, can be copied by another
social learner, who can then be copied by another social learner, and so on. In
this case, the proportion of individual learners tends to be very low or non-
existent (Rogers 1988). When the environment changes very quickly, acquiring
older innovations becomes less and less adaptive. Thus, individual learners will
be favored, and their population will increase proportionately.
Here, we choose to study another eect: realistically, there is a limit in
the number of individuals who can learn from one individual (be it through
emulation or active teaching). Additionally, it might be dicult to reproduce
the innovative behavior by observation without the help of the actor. Thus,
access to expert individuals to learn from can be subject to market forces. We
examined two limits. Models 1 and 2 can be understood as ecologies of inno-
vation in which the environment is changing very quickly such that learning
innovations from social learners (who have learned from individual learners)
introduces too long of an adaptive lag compared to the pace of change in the
environment. The other limit is in model 3, which can be understood as a
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Cultural transmission and biological markets 5
non-changing environment. With no further assumptions, this would lead to
a population with a fraction of individual learners tending to 0. However, we
present a scenario that allows for a cumulative culture, including a limited
period in an individual’s life history where innovation is possible. That can
lead to interesting results, which we will discuss.
2 Model 1: Absence of teaching
To underscore the necessity of introducing a perspective focused on biological
markets, we begin by considering a simple producer/scrounger scenario with
frequency dependence that is based on previous attempts to capture basic
processes in the evolution of social learning (Boyd and Richerson 2004; for a
review, see Aoki and Feldman 2014). This model and the subsequent models
that we introduce in this article focus on the transmission of adaptive behav-
ioral innovations. As highlighted in the introduction, there are multiple forms
of cultural transmission. In terms of interpretation, one can think of models
1–3 as representing the acquisition of recent behavioral innovations (as op-
posed to, for instance, the acquisition of “already cultural” traits or traits
that derive their adaptive value from the fact that they are shared by others,
such as the traits of a specific language or local cultural norms).
IIndividual learning strategy (with or without teach-
ing)
SSocial learning strategy (either by inadvertent social
transmission or apprenticeship)
freqXFrequency of strategy Xin the population
WXFitness of strategy X
Tabl e 1 Abbreviations
We first suppose a minimal case in which there is no active teaching. Agents
in the population can follow one of several strategies, each of which has the
same baseline fitness, W0, in addition to the frequency-dependent fitness based
on characteristics of the strategy.
The strategies reproduce in the next generation with probability propor-
tional to the fitness: if at time Tthere are nIindividuals with strategy Iof
fitness WI, then the number of individuals with strategy Iat time T+1will
be nIWI
PjnjWj. Such an idealization represents either the result of genetic evo-
lution in an haploid panmictic asexual population or the dynamics resulting
from social learning focused on the relative success of other strategies in the
population.
In the simplest preliminary form of this scenario, a part of the population
follows the strategy of individual learning. Those agents bear a cost, c, of
learning individually. (This is a common assumption in this type of model.
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6 Claude Loverdo, Hugo Viciana
Such a cost could represent either the cost of committing costly errors while
learning by oneself, or the opportunity cost of investing time in individual
learning instead of something else.) At the same time, the strategy of individual
learning also yields a benefit, b. To simplify, we suppose here that agents who
learn individually always discover an innovation of fitness value, b. In section
1 of the online appendix, we show that if hiding the innovation is costly,
then actively hiding individually acquired innovations is not an evolutionarily
stable strategy. Since this finding or discovery is partially observable, it is
possible that other agents in the group will attempt to copy the solution by
following a social learning strategy. We call agents using this latter strategy
“emulators,” and the process of social learning without active transmission of
fitness enhancing behavior is referred to as “inadvertent social transmission.”
(One can think of emulators as the “scroungers” in the producer/scrounger
dynamics of this first model.) In our modelling of the dynamics of individual
learners and emulators (models 1 and 2), we will consider the background
environment to be changing fast enough such that the value of the previous
innovation cancels after each generation. Thus, emulators do not copy other
emulators. In model 3, we will study a stationary environment in which social
learners can become teachers.
To begin, we assume two conditions: First, only rarely does inadvertent
social transmission produce perfect copies of behavior. Emulators who adopt
the solution discovered by other agents thus benefit to the degree of lbin
which l1 is a transformation or “loss factor” associated with social learning
(see Enquist et al., 2007 on the maladaptiveness of social learning). Second,
we suppose that the relative ease of social learning is directly proportional
to the number of individual learners (Pagel 2012). In our model, we codify
that constraint by imposing a limited number of social learners Newho can
learn socially from a given individual learner. That condition is ecologically
plausible, at least for a wide range of learning processes used to acquire certain
techniques. Furthermore, it is easy to imagine that only a finite number of
agents can have access to a given individual learner for the behavior to be
adopted1.
The average fitness of an agent who learns socially is then dependent on
the frequency of those who learn individually according to the following rule:
WS=W0+lbmin(1,N
efreqI/freqS) (1)
where freqXis the proportion of strategy Xin the population (Ifor in-
dividual learning, Sfor social learning), and min denotes a selection of the
minimal value between 1 and the eective proportion of emulators that can
1Mathematically, this condition helps to prevent singularities: without it, a single learning
agent suces in order for all social learners in a large population to be able to acquire the
innovation (N1). However, the number of social learners would abruptly collapse (and
become 0) when the proportion of individual learners decreases from 1/N to 0. It is not
incoherent to state that social learning is facilitated when the proportion of individual
learners in the population is greater.
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Cultural transmission and biological markets 7
acquire the behavior given the number of individual learners in the population
NefreqI/freqS.
If NefreqI>freq
S, then all emulators can find a model to copy and their
fitness will therefore equal WS=W0+lb. In the opposite case, certain but
not all emulators can find a model to learn from. The probability of learning
socially is then NefreqI/f reqS.Iflb<bc, then the individual learning
strategy is always more advantageous than the social learning one. At the same
time, if lb>bc, then the number of social learners will tend to increase
until lbNefreqI/freqS=bc, that is, to the point at which both
strategies have the same fitness. At that equilibrium, it is the case that:
freqI=bc
lbNe+bc.(2)
3 Model 2: Teaching in a biological market
3.1 Analytical model
A crucial feature of model 1 is that there is a maximum number Neof emula-
tors that can learn at a given time from one individual learner. At equilibrium,
not all emulators have the same kind of access to an individual learner. Indeed,
this is the precondition on which the very existence of the market is premised:
the individual learners “sell” privileged access to their skills in exchange for
biological services, which amounts to “deference” and can take many forms
in an informal apprenticeship. To introduce the possibility of teaching, we as-
sume that agents who learn individually —with a frequency in the population
freqI— can also follow a strategy by which they actively teach the acquisi-
tion of their technique. In addition to the cost of individual learning c,such
a strategy will have a cost tlinked to teaching. As with the previous model,
we assume that there is a maximum Naof individuals who can learn from a
single teacher as “apprentices2” contemporaneously.
Another assumption of our model is that social learners who acquire the
technique directly from the teacher will reproduce a perfectly ecacious copy
of the teacher’s innovation. Although admittedly an idealization (Morin 2016),
the point is simply that, for this modality of technological learning, social
learning without a teacher sometimes tends to produce a less fit solution than
does social learning within the context of a teacher-apprentice relationship.
Thus, if there is a teacher, the fitness value of the socially learned technique
becomes binstead of lb. However, individuals who learn socially from a
teacher will recompense the teacher via deference mechanisms that have a
cost mand that return mgto the teacher. It seems reasonable to assume
that most of the time g>1; however, our model does not strictly depend on
that assumption.
2We make no assumption concerning the specific social configuration of the teacher-
apprentice relationship, except that there is some nonzerosumness or collaboration in the
basic terms described in the model.
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8 Claude Loverdo, Hugo Viciana
For deference to evolve in social learning, its cost mmust be less than the
cost of individual learning c. Consequently, at its greatest value mis equal
to c. For the evolution of teaching, the cost tof teaching must therefore be
inferior to Nagc.
Calculating the equilibrium state of the system is not straightforward, as
both freqSrelative to freqIand the value of mmay evolve. Additionally, it
could be that not all the individuals have the same preference m.
One method is to examine the evolution of the frequencies and of minde-
pendently. We can start assuming that all the individuals in a population have
a fixed preference m. We can write the fitness values for the teachers and ap-
prentices and obtain their equilibrium frequencies for which their fitnesses are
equal (see section 2.1 of appendix). Then, we assume that the frequencies are
fixed, the whole population has preference m, except that there are mutants.
If NafreqI<freq
S, not all apprentices are matched with a teacher, and thus
a mutant apprentice with a slightly higher mwill be favored, and thus the
preference mof the apprentices will evolve towards higher values, allowing the
preference of the teachers mto also evolve towards higher values. Conversely,
if NafreqI>freq
S, not all teachers are paired with Naapprentices, thus m
is driven to decrease for the teachers, which then leads to a decrease in mfor
the apprentices. The next step is to study the eect of the change in mon
the frequencies. For the initial m, the frequencies were such that apprentices
and teachers had the same fitness. If mdecreases (respectively increases), then
teachers are less (respectively more) fit than apprentices, then the teacher’s
frequency decreases (resp. increases). Thus the equilibrium point is:
NafreqI=freqS,(3)
which is equivalent to:
freqI=1
1+Na
(4)
and:
m=meq =c+t
Nag+1 (5)
in which meqis the value of mat equilibrium (see more detailed discussion in
section 2.2 of the online appendix).
By extension, another condition for the evolution of teaching is that b>
meq : an apprentice has to gain more through the acquired technique than
the cost of deference. That condition is really constraining for teaching only
at very high values of cor t. It is most reasonable that gis at least equal to
1, and Naat least equal to 1. Therefore, as an example: if cand tremain less
costly than b, then that condition is fulfilled.
An interesting property of meq is that it is the mvalue maximizing the
fitness of the population (see section 2.3 of appendix). The evolutionary stable
equilibrium is also the state of the system with the highest fitness. In our
model, the so-called Rogers’ paradox (Aoki and Feldman 2014) does not occur.
We considered here that all social learners have the same preference m,
with m>0, i.e. the social learners reward their teachers. But, there could be
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W0Baseline fitness
bBenefit of the behavioral innovation
cCost of individual learning
lLoss factor : emulators acquire a technique of value
lb
NeMaximum number of emulators that can learn the
technique from one single individual learner
NaMaximum number of apprentices that can be taught
a technique by one single individual learner
NPopulation size
tCost of teaching
mPreference for deference (cost for the apprentice)
(that can also be seen as the “market value” of com-
petency)
meq Equilibrium value of m
g m gis the deference benefit gained by the teacher
Tabl e 2 Parameters and variables of models 1 and 2
a distribution of preferences min the population, and as in model 1, there
could also be social learners (the “emulators”) who only try to copy without
being taught, provided that lbbm(when m=meq (5), this condi-
tion is equivalent to l>1c+t
(Nag+1)b). Interestingly, the presence of these
emulators modifies neither the equilibrium between the frequencies of the in-
dividual learning and apprentice strategies, nor the evolution of m.Evenwhen
lb>bm, apprentices are not driven to extinction by emulators. In other
words, teaching may evolve even if social learning without teaching (“inad-
vertent social transmission”) is still an available and profitable strategy in
the population. We can calculate the expected frequency of emulators: their
frequency increases until there are not enough individual learners, so that
lbNefreqI/freqemul =bm. This ultimately leads to3:
freqI=1
1+Na+lbNe
bmeq
(6)
Even if deference is relatively costly, the apprentice strategy can be on
par with the emulator strategy, because it enables better access to individual
learners who are a source of innovation. In fact, both strategies could still
coexist with l= 1 — although the greater the value of l, the smaller the
frequency of the apprentice strategy. As a result, the assumption that l<1is
not necessary.
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10 Claude Loverdo, Hugo Viciana
Teaching and emulating
l>1meq
b(5) m=meq =c+t
Nag+1
t< (6) freqI=1
1+Na+lbNe
bmeq
NagcTeaching
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Nag+1
(4) freqI=1
1+Na
Emulating
l>1c
bno m
t> (2) freqI=bc
b(1+lNe)c
NagcIndividual learning only
l<1c
bNo m
freqI=1
Tabl e 3 Summary analytical regimes
Fig. 1 Simulation example. Frequency of individual learners (dark blue) and mean m val-
ues of interactions (light purple) for 10 dierent simulations, as a function of time (in
generations). The horizontal thicker lines represent the predicted values of the frequency of
individual learners (dark blue dashed line) and m(light purple solid line). For a population
of 200 individuals, with Na=2,Ne=5, W0=0.01, b=1, c=0.8, l=1, g=1, t=0.5, and the
typical change in mwhen transmitting a strategy m=0.02. At the beginning of the sim-
ulations: 90% of the population are individual learners, a random mval ue i s at tr ib ut ed t o
each individual, taken from a uniform distribution between 0 and 1.
3.2 Simulation
The analytical calculations assumed mostly homogeneous mpreferences, and
the evolution of the frequencies and mwere considered separately. But both
will actually evolve simultaneously, and if mmutates when the strategy is
reproduced, the preferences of teachers and apprentices cannot be exactly
equal because a mutation towards a slightly higher mfor a teacher or a slightly
3See more details in section 3 of the appendix
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lower mfor an apprentice would lead to the inability to enter into a teaching
relationship in the first place, thus decreasing the second-generation fitness.
To check that the system converges towards our analytical results, we coded
an agent-based simulation. Each individual jis either an individual learner or
a social learner, and attributes the reservation value mjto teaching. Random
pairs are formed between social learners who have not yet acquired the skill,
and individual learners who have not yet taught to Nasocial learners. If for
a given pair, the reservation value mis smaller for the social learner, nothing
occurs. But in the opposite case, the individual learner teaches the skill to the
social learner at a price mthat is taken as the average between the mvalues
of the two individuals. (Any intermediate value between the two values would
yield similar results, see supplementary figure 14 in appendix.) This method of
estimating the actual exchange value of mbuilds on the idea that there will be
some form of bargaining between the two individuals. Pairs are formed until
there is no possible additional interaction. Then the population is renewed,
with new strategies taken at random proportionally to their fitness in the
previous round, and the values miattributed to teaching in these strategies
are copied with small random errors (to allow for the evolution of m). The
frequencies of the dierent strategies and the average value of mtend to the
state defined in equations (6) and (5), albeit with fluctuations around these
values (see figure 2, supplementary figures 4 to 15 in appendix, and sections 4
and 5 of appendix). Having validated the results, we can now discuss them.
3.3 Results
As confirmed by the numerical simulations, there are four dierent regimes,
which are summarized in table 3. Teaching is a stable strategy if the cost of
teaching tis smaller than Nagc. Teaching is clearly facilitated when one
individual can teach to more apprentices (Na) (Table 3 and supplementary
figure 4), when receiving deference provides a higher gain (g) (Table 3 and
supplementary figures 7 and 11), and if learning the technique individually
is costly (c) (Table 3 and supplementary figures 5 and 9). Interestingly, this
condition does not depend on the characteristics of inadvertent social trans-
mission (Neand l) (Table 3 and panels B and C of figure 2). Profiting from
“inadvertent social transmission” as emulators do is a stable strategy if the
loss in the technique value (1 l)bis smaller than the cost of retributing a
teacher (meq) if there is teaching (Table 3 and figure 2C), or smaller than the
cost of learning the technique individually (c) if there is no teaching involved
(Table 3 and supplementary figure 9).
In the case of teaching, the value of the deference mat equilibrium increases
with c,t, and decreases with Naand g: deference has to be higher to oset
a higher cost of individual learning and teaching, and the higher the number
of apprentices per teacher and the higher the factor g, the less the deference
cost per apprentice (table 3 and figures). The frequency of the teachers is such
that there are Naapprentices per teacher. If there are no emulators, then the
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Fig. 2 Dependence of the frequency of individual learners (dark blue) and average value
of min exchanges (light purple) with the dierent parameters. Results obtained from sim-
ulations (symbols) carried out and averaged over 10 simulations, for generations 100 to 200
(see supplementary figure 3), and errors-bars represent the standard deviation. Theoreti-
cal curves : m(5) (solid purple lines), freqIwith teachers, apprentices, and emulators (6)
(dashed blue) or with teachers and apprentices only (4) (dot-dashed blue). For all the sim-
ulations, the population is taken as 200 individuals, with the base fitness W0=0.01, the
technique benefit b= 1, the typical mutational change on mm=0.02, and when the inter-
action happens, mis taken as the average between the preferences of the two individuals.
Initially 50% of the population are individual learners, with for all individuals, mtaken at
random between 0 and 1. Except if stated otherwise, the other parameters are Na=2,
Ne=3,c=0.8, t=0.5, l=1,g= 1. Panel A: dependence on Na. Panel B: dependence on
Ne(t=0.1, l=0.9). Panel C: dependence on l(t=0.1). For panels A, B and C, freqIin
simulations is represented by triangles, and mby disks. Panel D: We vary c(supplementary
figure 5), t(supplementary figure 6) and g(supplementary figure 7). In the regime with both
apprentices and emulators, the dependence of freqIon t,gand cis predicted to occur only
through the value of m. Then, instead of representing mand freqIas a function of each
of these three parameters separately, we represent them in this panel as a function of the
predicted m(5). Supplementary figures 5, 6 and 7 show the dependence for each parameter
individually.
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Cultural transmission and biological markets 13
teachers’ frequency depends only on Na. The teachers’ frequency is lower when
there are emulators and depends on c,t,gonly through its dependence on m
(table 3 and figure 2D). It decreases with land Ne: the greater the number of
emulators, the fewer the teachers and apprentices (table 3 and panels B and
C of figure 2). It is maximum for some intermediate value of Na(table 3 and
figure 2A).
Another result is that, under a biological market of the type described here,
for individual learning to be beneficial, it is sucient that the cost of individual
learning cis smaller than b(Nag+ 1) t, which, except when tis large and
Nais small, is likely to be much larger than b. Hence, there are investments
in skills for which benefits would not be sucient in themselves, which thus
become attractive because of the extra incentive linked to the sociability of
teaching.
Our model assumed that apprentices do not become teachers. There are two
main reasons for which this hypothesis can be valid for certain technological
skills. One is if teaching a technique requires a deeper level of understanding
that can be acquired by individual learning only. For instance, most university
teaching is done by people who are also researchers, partly because it is thought
that complex notions are more eciently taught by individuals having an
understanding of them deeper than the base level needed to merely use them.
The other reason is in the case of the environment changing fast enough such
that the techniques become obsolete, thus leaving an inadequate amount of
time for second-hand teaching. If it was possible for apprentices to become
teachers later on, the model would need to take into account a more complex
time dimension and study the interaction of the time scales of changes in
the environment versus the amount of time needed for individual learning,
emulation, apprenticeship, and the integration of the fitness over the lifetime
of an individual. In our next model, we allow for the possibility that apprentices
become teachers.
4 Model 3: Cumulative culture
Previous research has shown that social learning per se does not automati-
cally lead to cumulative culture, that is, sustained evolution of ever increas-
ingly adaptive cultural techniques (Enquist and Ghirlanda 2007). In model
2, we have shown that the market for deference supports the increased costs
of innovations. Accordingly, we believe that taking those sorts of biological
markets seriously can shed light on ecological forces active in the evolution of
cumulative culture.
Until now, we have considered the skill to be fixed. Here, however, we
consider a dierent model, in which the skill of value bcan be improved by an
increment bwith probability when eort Cis invested into innovation. We
consider that at each time step, a new individual enters the population of size
N, whereas the “oldest” individual dies. The entrance can represent either a
birth — more realistically a child’s coming of age and being prepared for the
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14 Claude Loverdo, Hugo Viciana
bImprovement in the behavioral skill
CEort to be invested in improving upon the skill
Probability that the eort at innovating will lead to
an improvement
Tabl e 4 Additional parameters for the cumulative culture model (model 3)
apprenticeship — or a migration. If there is no active teaching, then the new
individual copies the best skill in the population, of value b(T); however this
is achieved imperfectly. The individual will thus have a skill of value lb(T),
in which Trepresents the moment in time when the technique is copied by
the newly arrived agent. We assume that individuals can recognize the best
skill, and access the value of parameters C,band . We also assume that
innovation can occur only during the period when the new individual enters
the group and acquires its skill. This latter assumption represents the idea that
some periods are more prone to innovation than others. The new individual
can decide whether to invest in innovation depending on whether b>C.If
b<C, then no innovation is ever made, and, provided that l<1, the skill
will be completely lost in the population over time. If b>C, the skill will
be improved upon by bper each 1/new individuals on average. Population
size matters (Kline and Boyd 2010): if 1/N, then the innovations will
not occur often enough to preserve the skill in the population. If 1/N,
then the value of the skill over time will tend toward the point at which the
imperfect copy and the innovation compensate: b=b/(1l). A more detailed
discussion can be found in section 6 of the appendix.
For active teaching, when the new individual enters the population, many
potential teachers are available, meaning that there will be active teaching as
long as mg>t. Due to competition among teachers, mwill tend to t/g.
If t/g < (1 l)b, then the new individual will prefer to learn the technique
via active teaching instead of emulation, and thus end up learning the best
skill bof the population. At that point, when choosing whether to invest in
innovation, the individual will compare the investment cost Cnot only with
the direct benefit (b), but also the direct benefit plus the benefit expected
from teaching the innovation to the rest of the population. Since the new
individual has a monopoly on the skill (assuming that time constraints make
that all the individuals in the population want to acquire the technique as soon
as possible, rather than waiting for second-hand teaching from apprentices),
other individuals in the population will tend to reward his or her teaching by
a maximum of at least m=(1l)(b+b). As a result, the expected benefit
from teaching is min(N,Na)g(1 l)(b+b)t(see section 7 of appendix).
In summary, populations with active teaching dier from those with only
inadvertent social learning in two ways. First, because the skill can be learned
more accurately, cumulative innovations are facilitated and the value of the
skill can continue to increase. Second, innovation is favored because its ben-
efits might also derive from deference and prestige. Accordingly, in biological
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markets, evolved teaching has the double eect of both promoting cumulative
culture and, most importantly, enhancing individual learning.
5 Discussion and conclusions
Modeling evolutionary social dynamics oers proof of the internal consistency
of hypothesized evolutionary selective pressures (McElreath and Boyd 2008).
Thus, the models presented here corroborate the logical soundness of some
intuitions previously formulated in purely verbal arguments (Henrich and Gil-
White (2001), see section 1). They also provide a well-articulated mathematical
framework that addresses the current dearth of models for the evolutionary
milestone that is the evolution of teaching (Kline 2015).
Reciprocity-based models are not usually well-equipped to accommodate
the kinds of hierarchies and asymmetries that we describe in model 2. Further-
more, reciprocity-based cooperation models usually focus more on turn-taking
and the partner control aspect of repeated interactions than on partner choice,
outside options, and active discrimination. We have shown that market eects
can account for relevant dimensions of the sociability of teaching, such as the
propensity to transmit fitness-enhancing information, as well as the evolution
of deference. We believe that these important aspects of human social learning
are better studied by focusing on the supply and demand demographic dynam-
ics of a biological trade, rather than on the standard reciprocity mechanism.
We have provided a partner-choice model for the evolution of teaching,
which focuses on the functional aspects of teacher-apprentice cooperation.
This account does not oer an exhaustive evolutionary characterization of the
emergence of teaching. Teaching is, after all, a complex ethological category
that subsumes dierent — and presumably related — types of phenomena
(Kline 2015). Moreover, the models presented are not intended to be so much
of a realistic depiction of the actual evolutionary process as an exploration
of general ecological conditions for the evolution of teaching. However, our
work nevertheless points to possible evolutionary pathways, which, one can
only surmise, have received little attention because they have not been math-
ematically modeled. One such possible paleoanthropological pathway is that
the structure of communication and nonzerosumness inherent in the form of
the basic apprenticeship system described here might have preceded (instead
of followed) the evolutionary emergence of modern (i.e., Middle Paleolithic)
human inventiveness (McBrearty and Brooks 2000).
We have additionally shown that teaching can evolve under certain condi-
tions. First, individual learning or learning without relying on others’ experi-
ence is costly. Second, certain techniques are constrained in terms of the num-
ber of individuals who can socially learn the technique from a single expert.
Under those conditions, demographic dynamics could force social learners,
who want to acquire the adaptive behavior discovered by individual learners,
to pay a price in the form of deference. Furthermore, although it is unnec-
essary, the evolution of teaching is facilitated for learning certain techniques
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16 Claude Loverdo, Hugo Viciana
if social learning without explicit teaching —“eavesdropping” (Danchin et al
2004)— yields imperfect copying in which adaptive value can be lost. Crucially,
genetic relatedness and parent-ospring nepotism (Castro and Toro 2004) are
not strictly necessary either.
An important observation that emerges from our work is that evolved
teaching might be the mother of invention. In other terms, natural pedagogy
and communication skills may precede, but not necessarily follow, the appear-
ance of complex forms of culture. This dynamic runs counter to the perspec-
tive sometimes advanced, which holds that teaching evolved for novices as
a response to increasingly complex “opaque” cultural forms (Caldwell 2015;
Gergely and Csibra 2006). In keeping with this evolutionary hypothesis, com-
plex cumulative culture necessarily preceded evolved teaching. However, as we
show here, teaching might constitute an evolutionarily stable strategy, even if
the existing cultural forms are not opaque enough for novices. Thus, teaching
could evolve when inadvertent social transmission (i.e., social learning without
teaching) remains a thriving strategy in the population.
Undoubtedly, access to various forms of social learning cannot be con-
trolled in such a way as to give rise to biological exchange markets: “eaves-
dropping” or inadvertent social facilitation could be the most frequent form of
social learning in nature (and perhaps even in humans). Nevertheless, in hu-
mans, important forms of technique acquisition can be reasonably controlled
and even monopolized to some extent. For instance, ethnographic studies of
stone-tool production (Stout et al 2002) confirm that the adult acquisition of
certain sophisticated skills can be perceived as a form of transferable intel-
lectual property. Such a capacity for transmission is endowed with a form of
authority that is often safeguarded and administered in a teacher-apprentice
system via manifestations of personal commitment. In more modern settings,
partner choice has widely been observed to be crucial in acquiring competence
within organizations (Blau 1964).
In contrast to non-human social learning, certain forms of human social
learning are characterized by both the sophistication of cognitive mechanisms
at work and the important constitutive role played by collaboration and nonze-
rosumness. These characteristics eventually give rise to apprenticeship struc-
ture (Waal 2001; Sterelny 2012). In this article, we have shown how those
behavioral strategies can attain evolutionary equilibrium and persist in a pop-
ulation.
Naturally, not all forms of cultural diusion rely on competence-based part-
ner choice, a point that can hardly be overemphasized. However, some forms
of human social learning depend far more on competence-based partner choice
than others — a fact that helps explain the existence of several interesting
regularities in the human psychology of competence assessment, admiration,
and deference (Fessler 2006).
At the proximate level, hierarchical tendencies of this sort are not entirely
specific to humans. In fact, other animals have been observed to behave in
ways consistent with the predictions of biological markets. In particular, non-
human primates, such as chimpanzees (Pan troglodytes), have demonstrated
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Cultural transmission and biological markets 17
an ability to discriminate possible partners based on their abilities (Melis et al
2006). Moreover, experimental studies have shown how dierent species of
primates can temporarily adjust their hierarchical behavior after individuals in
their group have acquired some valuable cultural competence (see Stammbach
(1988) for interesting work on Rhesus macaques). Grooming behavior has been
shown to adapt to the supply and demand characteristics of a biological market
in which at least one individual in a group has learned to use a tool in order to
obtain a valuable, shareable food (Fruteau et al 2009). Indeed, it has even been
suggested that, for some species, grooming could be a form of proto-currency
in primate exchange markets (Barrett and Henzi 2006).
In humans, considerable evidence points to the existence of both com-
petence assessment and prestige-signaling behavior, the latter being a form
of communicating that one excels in a given domain (Tracy and Matsumoto
2008). Although the human ability to detect competence in a given domain
is certainly far from perfect (Mauboussin 2012), it nevertheless functions as
a satisfying heuristic in many settings. Competence is assessed through both
fast and slow processes of cognition. At its most rapid rate, the adult judgment
of competence can be made in as little as 100 milliseconds, and those judg-
ments are sometimes highly persistent and dicult to override (Fiske et al
2007). Early on, children also begin to pay special attention to individuals
judged as competent in a given domain (Keil et al 2008). The current consen-
sus maintains that children commonly use two dierent pathways to judge the
reliability of an informant: one related to trust and benevolence and the other
related to competence and ability (Mascaro and Sperber 2009; Harris 2012).
In models 2 and 3, we have included relevant characteristics associated with
the sociability of certain forms of active cultural transmission. However, we
have only scratched the surface of what biological trade models could oer in
terms of modeling social learning dynamics. It would be interesting to further
explore the evolutionary dynamics linked to maladaptive biases related to the
human psychology of competence and prestige detection. For instance, we
did not explore here the complex dynamics that could follow if social learners
were to adopt the techniques and behaviors of other social learners, who are no
longer tracking the environment through individual learning and innovation,
but who might receive some form of social reward due to further transmitting
a highly prized form of “knowledge,” regardless of whether that knowledge
proves to be ineectual or of little direct use. Moreover, the amount of eort
that cultural mentors invest in teaching their apprentices even when they are
not genetically related to them, the diminishing fitness values of the technology
if shared, or the reliability of the deference provided by the apprentices are
all interesting features for which genetic conflict and partner choice could be
fruitfully modeled. We hope to encourage further work in this area.
Regarding important aspects of the evolution of cultural transmission,
we have suggested that the partner-choice framework (Nesse 2009) is bet-
ter equipped than other theoretical frameworks that rely exclusively on either
partner control or nepotistic genetic relatedness (No¨e and Voelkl 2013). The
free-rider problems linked to fitness-enhancing cultural transmission, along
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with cultural parental manipulation, are largely by-passed by evolutionary
systems, such as those described in this article. Nearly a century ago, Lev
Vigotsky characterized human social learning as an eminently cooperative ac-
tivity. Biological market models can incorporate the nonzerosumness of human
social learning, account for findings related to the anthropology of deference
and prestige, and reveal surprising evolutionary processes that lead to cumu-
lative culture.
Data availability
An online appendix including further analytic details, supplementary figures,
and simulation code is provided.
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Acknowledgements HV received support from a La Caixa Foundation Scholarship at
the initial stage of the preparation of this work. This article has benefited from feedback
of audiences at the University of Cambridge, the University of Granada, the University of
Louvain-la-neuve, and the University of Paris 1. Special thanks should be given to Camilo
Cela-Conde, Jean Gayon, Gabi Lipede, Pierre Livet, Hugo Mercier, Susana Monso, Dan
Sperber, Neftali Villanueva, and several anonymous reviewers for comments on earlier ver-
sions of this work. In remembrance of Jean Gayon (1949-2018).
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Online appendix
Click here to access/download
Electronic Supplementary Material
appendix_evoteaching.pdf
Code for the simulation
Click here to access/download
Electronic Supplementary Material
Simulation_v6_evo_teaching.R
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