Selection in a Complex World: Deriving Causality from Stable Equilibrium

Abstract

It is an ongoing controversy whether natural selection is a cause of population change, or a mere statistical description of how individual births and deaths accumulate. In this paper I restate the problem in terms of the reference class problem, and propose how the structure of stable equilibrium can provide a solution in continuity with biological practice. Insofar natural selection can be understood as a tendency towards equilibrium, key statisticalist criticisms are avoided. Further, in a modification of the Newtonian-force analogy, it can be suggested that a better metaphor for natural selection is that of an emergent force, similar in nature to entropic forces: with magnitude and direction, but lacking a spatiotemporal origin or point of application.

Full text

ORIGINAL RESEARCH
Selection in a Complex World: Deriving Causality
from Stable Equilibrium
Hugh Desmond
1
Received: 19 April 2016 / Accepted: 21 February 2017
!Springer Science+Business Media Dordrecht 2017
Abstract It is an ongoing controversy whether natural selection is a cause of
population change, or a mere statistical description of how individual births and
deaths accumulate. In this paper I restate the problem in terms of the reference class
problem, and propose how the structure of stable equilibrium can provide a solution
in continuity with biological practice. Insofar natural selection can be understood as
a tendency towards equilibrium, key statisticalist criticisms are avoided. Further, in
a modification of the Newtonian-force analogy, it can be suggested that a better
metaphor for natural selection is that of an emergent force, similar in nature to
entropic forces: with magnitude and direction, but lacking a spatiotemporal origin or
point of application.
1 Introduction
Natural selection, both in biology textbooks and philosophical representations (e.g.
Sober 1984), is often represented as some kind of Newtonian force, with magnitude
and direction, originating in fitness differences and driving evolutionary change. By
contrast, this metaphor has been rejected by the ‘statisticalist’ view of natural
selection (e.g. Matthen and Ariew 2002,2009; Walsh et al. 2002), which claims
natural selection to be a mere book-keeping device, a way to keep count of the
genuinely causal interactions that take place between individual organisms. Not
even a cause, selection is an epiphenomenon, useful only for explanatory purposes.
While there are multiple ways of parsing this debate, the approach I will be
adopting is to examine how the statisticalist view arises from the complexity of the
organism-environment interaction and from ensuing reference class problems.
&Hugh Desmond
hugh.desmond@hiw.kuleuven.be
1
Higher Institute of Philosophy, KULeuven, Blijde Inkomststraat 108/11, 3000 Leuven, Belgium
123
Erkenn
DOI 10.1007/s10670-017-9889-z
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Complexity here refers to the very large number of independent processes that affect
how often an organism will have reproduced by the end of its life, and the reference
class problems that arise from this reflect the absence of any privileged way of
abstracting away from this complexity.
Such themes have been noted before (for example, Brandon 1990,2005; Kaplan
2013; Strevens 2016), but remain, on the whole, underemphasized. On the basis of a
few assumptions about organism-environment interaction, a principled argument for
the statisticalist view can be reconstructed, somewhat in the following vein (to be
laid out in detail later): most of the organism-environment interactions that affect
reproductive outcome are abstracted away from in an explanation by natural
selection, but it is the sum total of such difference-making interactions that in fact
causes populations to change. Hence natural selection is an epiphenomenon without
any causal impact, a statistical apportioning of the fundamental causal reality.
Some of the main causalist counterarguments, even when the force analogy is
abandoned, fail to make inroads on this (‘no-privileged-abstraction’) argument. One
such counterargument is that natural selection is a cause insofar as intervening on
natural selection at the population level ‘makes a difference’ in how populations
evolve (Reisman and Forber 2005; Millstein 2006; Shapiro and Sober 2007;
Glennan 2008; Gildenhuys 2014). Examples of interventions include modifying the
selection coefficients and fitness values (Reisman and Forber 2007; Shapiro and
Sober 2007), or introducing new phenotypes (Millstein 2006). This counterargu-
ment was rejected by Matthen and Ariew (2009) and Walsh (2007,2010), who
pointed out in various ways that the correlations between natural selection and
different population parameters are mathematical in nature, not causal.
Furthermore, attributing fitness values to a group of individual organisms already
presupposes a certain abstraction away from the complexity of organism-environ-
ment interaction, and thus such counterarguments beg the question. Hence, the
question to be focused on instead is: are the abstractions involved in explanations by
natural selection problematic for selection’s supposedly causal nature?
I will seek to undermine the no-privileged-abstraction (NPA) argument by
considering a class of counterexample: tendencies towards stable equilibrium. A
population tending towards stable equilibrium is strong evidence for natural
selection (Endler 1986); such tendencies also allow for certain abstractions to be
privileged over others. In particular, the individual-level processes which do not
make any causal difference at the longest time-scales (over multiple generations)—
and thus do not make a difference to the outcome state—may be abstracted away
from. In such cases natural selection may be understood as a force, with definite
direction and magnitude, driving populations towards equilibrium.
Many if not most instances of evolution by natural selection do not actually
approach stable equilibrium: environments may continually changing, and popu-
lations undergoing frequency-dependent selection may fail to settle down even in a
constant environment. I will argue how the equilibrium model may be extended to
such cases, so that the causal nature of selection in these cases may also understood
as the tendency towards stable equilibrium, even though equilibrium is never
realized.
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An intuitive draw to the account presented here is that it implies an alternative (or
modified
1
) metaphor to that of Newtonian force. Natural selection is closer in nature
to entropic forces, which are non-fundamental forces that originate in a system’s
statistical tendency to evolve towards a configuration with higher entropy.
2
How precisely the concept of entropy can be applied to evolutionary process is an
ongoing research programme (see e.g. Brooks and Wiley 1988; Barton and Coe
2009). What is important is that the analogy of entropic force captures two features
of natural selection that the analogy with Newtonian forces does not: the lack of a
localizable origin and the lack of a spatiotemporal point of application. Nonetheless,
entropic forces have real consequences (e.g. osmosis, the Casimir effect) and thus
are not simply epiphenomenal. In this way a key causalist intuition is supported.
The paper is structured as follows: in the first section I will make a principled
case for the statisticalist position, and in the second section will begin to undermine
it in light of how field biologists test the presence of natural selection. In the third
and fourth section I present a model of natural selection as a causal tendency
towards stable equilibrium, and deal with potential objections. The final section is a
discussion of force metaphors, and of an extension of the model to frequency-
dependent selection.
2 The No Privileged Abstraction Argument
The interaction between an organism and its environment is, generally speaking,
complex. More often than not, environments are chaotic, characterized by ever-
changing weather, geography and ecology. An organism itself is composed of many
interacting parts, across numerous hierarchical structures—organ systems, organs,
tissues, cells, nutrient gradients, etc. The resulting interaction between organism and
environment has such a vast number of degrees of freedom as to make any
parametrization practically impossible. Interactions can be biotic, such as compet-
itive, symbiotic and parasitic interactions, or abiotic, such as extracting resources
from the environment, or being affected by fundamental forces in the environment.
While ecological models focus on only a few of these interactions at a time, in
general we can assume that the number of degrees of freedom characterizing the
actual organism-environment interaction is very large.
3
However, not all processes will be causally relevant for the reproductive outcome
of an organism. For example, consider a population of camouflaged and non-
camouflaged moths. We can likely ignore how atmospheric pressure affects how
much energy a moth expends when flapping its wings; we can likely ignore how
slight variations in temperature have subtle effects on a moth’s metabolic rate.
1
There is no consensus as to what precisely are the defining conditions (e.g. additivity) of Newtonian
forces. A detailed discussion of this would bring us too far from the main argument of this paper, but see
Wilson (2007) or Stephens (2010).
2
Verlinde (2011) describes an entropic force as an ‘‘effective macroscopic force that originates in a
system with many degrees of freedom by the statistical tendency to increase its entropy.’’
3
To emphasize: complexity is here taken to refer to the number of degrees of freedom, not functional
complexity, or number of part-types (see Strevens 2003; McShea 2000).
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Instead, the vicinity of a moth to a forest fire or to a predator are variables we will
want to include when estimating a moth’s likely reproductive outcome.
Yet even among these difference-making interactions between organism and
environment, many will be abstracted away from in explanations by natural
selection. The vicinity of a moth to a forest fire is likely to be ignored—unless, of
course, the moth possesses some (perverse) heritable trait that makes it more likely
to seek out fires. Once-off interactions are ignored, and interactions linked to the
traits of an organism are included. On what basis are such traits selected, and what is
their relation to the fitness (understood as the expected reproductive outcome
4
) of
the organism?
The relation between trait and organism fitness is a difficult one—and, judging
from a recent exchange between Sober (2013) and Pence and Ramsey (2013a), the
two concepts seem intertwined. Pence and Ramsey have argued that definitions of
trait fitness depend on organismic fitness, roughly because relevance for organismic
reproductive success is the only measure by which to judge the relevance of a trait.
By contrast, Sober has argued that organismic fitness is an actuarial quantity,
estimated on the basis of how various traits affect organismic reproductive outcome.
Regardless of which fitness concept is the more fundamental one, statisticalists
have denied that either measure of fitness can be estimated in a non-arbitrary way.
Matthen (2009) has proposed that fitness measures are obtained by means of the
condition of metaconstancy: a process may be excluded from consideration only if it
is neutral with respect to (i.e. probabilistically uninfluenced by) all heritable
properties. There is no heritable trait of a moth that correlates with its proximity to
forest fires, and hence the evolutionary biologist may ignore it. Thus, in
explanations by natural selection the causal difference-making processes that do
not correlate with a heritable trait are to be ignored (see Fig. 1).
A fully detailed discussion of the implications of the reference class problem for
fitness is beyond the scope of this paper. However, the following brief discussion of
individual and trait fitness may convey the weight of the problem. First, the
consequence for individual fitness would be that there is no privileged way of
calculating the probability that an organism X will have noffspring (or have a
daughter population of some size at t¼1). This can be understood in the following
way. If we exclude all non-metaconstant processes, we may arrive at a probability p;
however, if we take some other non-metaconstant process (e.g. the strength of the
wind) into consideration, we might estimate a probability p06¼p. Even if we ignore
all non-metaconstant processes, there still be ambiguity as to the fitness value.
Could one not take all difference-making processes, both metaconstant and non-
metaconstant, into consideration in the definition of individual fitness? This would
be a strategy parallel to the well-known (but ultimately flawed) prescription of
taking all evidence into account in determining the reference class (Carnap 1947) or
taking the narrowest reference for which reliable statistics can still be compiled
(Reichenbach 1949). Such a strategy would inherit the general problems of Carnap’s
or Reichenbach’s strategies (see Ha
´jek 2007); one problem in particular can be
4
There are more accurate and sophisticated measures of fitness available (such as Pence and Ramsey
2013b): see the discussion of fitness models later on.
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pointed out. For example, consider individual A that is caught up in a forest fire and
dies without offspring; individual A0with identical traits but a different spatial
position avoids the forest fire and reproduces successfully. If one includes all
difference-making processes in the definition of an individual fitness propensity, A
and A0will be placed in different reference classes and will have different fitness
values. In this way the difference between selection and drift evaporates and fitness
ceases to be an explanatory notion.
Trait fitness faces similar issues. The probability of an individual having n
offspring given trait T may depend on an indefinite number of other unspecified
traits T1;T2;..., which may codify both metaconstant and non-metaconstant
organism-environment interactions. Depending on which of the other traits
T1;T2;... an organism possesses, a different probability will be obtained. If we
simply include all possible traits (including ephemeral, non-heritable properties,
such as the spatial position of a moth at a given moment in time), the distinction
between selection for a trait and drift will collapse (see ‘‘Appendix’’). Even
restricting attention to all possible heritable traits, the resulting fitness value may not
necessarily be explanatory of the dynamics in the actual population. For example, if
fireproof, camouflaged moths have much smaller fitness than fireproof, non-
camouflaged moths, this may lead to the trait of camouflage having a smaller fitness
than the trait of non-camouflage in the hypothetical population (in contrast to the
situation in the actual population, where fireproofness is absent).
Fundamentally, this argument is a restatement of the reference class problem in
biological context. Individual organisms can be classified into groups in many
different ways, due to the complexity of individual-environment interaction, and
hence there is the problem how the probabilities underlying the actual births and
deaths should be estimated. However, even if general resolutions to the reference
class problem may be lacking (Ha
´jek 2007), this does not entail that a more tailored
response to the NPA argument should not be possible.
In order to deepen the connection between statisticalism and the NPA argument, I
will finish the section by showing how three core statisticalist claims can be
reconstructed as corrollaries of the NPA argument:
(1) Fitness can only be estimated through regression. Since some difference-
making processes are excluded from the explanation by abstraction, there is no a
Fig. 1 Fitness abstracts away from most causal processes
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priori way of estimating their impact on the probabilities of surviving and
reproducing. Is the probability of having two offspring given the trait of camouflage
.9 or .5? The value of that probability will be affected by the various causal
processes impacting the individual, and these impacts will necessarily remain
unknown since they were deliberately abstracted away from (Matthen 2009). Fitness
values can be estimated only retrospectively, by a statistical regression on the
actually occurred births and deaths in a population. Only insofar it may be used to
extrapolate from past individual events can fitness have some predictive value. In
this way, fitness values are mere statistical descriptors, not causes of actual
frequencies of births and deaths.
5
(2) Fitness components are not additive. The probabilistic relevance of having
both traits T1and T2cannot be predicted from the relevance that T1and T2have by
themselves, because the traits may be causally dependent (Matthen and Ariew
2002,2009). For example (adapted from Stephens 2004), having resistance to
malaria may increase fitness by pand being able to run fast may increase fitness by
q, but in general we cannot know what fitness an organism will have when it has
both traits, due to the unknown interaction between the two traits. Selection is not a
causal force that can be simply divided into components.
(3) Natural selection refers to the mathematical relation between change in
frequencies and variance in rates, exemplified by Li’s theorem. Selection is
variation in fitness, and since fitness is only a statistical descriptor of actual
population, selection is not distinct from population change. To say a population is
changing and to say individuals are reproducing at differential rates is to say the
same thing. The upshot is that selection is not a cause mediating between fitness
differences and population change in the way that the gravitational force mediates
between mass distribution and acceleration of bodies (as represented in Sober
1984); rather it is more like the shadow of a flagpole (Walsh 2000; Matthen and
Ariew 2009).
This is also why, in this view, causalist appeals to interventionist causality fail
(Woodward 2003; Reisman and Forber 2005; Millstein 2006; Shapiro and Sober
2007; Glennan 2008): while it is conceivable to intervene on the gravitational force
alone while keeping mass distribution constant (for example by changing the value
of the gravitational constant), it is not conceivable to manipulate selection without
changing fitness differences. Neither does the argument imply that there are no
population-level causes (as claimed in Shapiro and Sober 2007): the epiphenom-
enality of selection is not a consequence of its population-level nature, but of its
mathematical nature.
In summary, the NPA argument can be represented in the following format:
5
Note that in this way I do not view what is sometimes termed the ‘metrological’ and ‘conceptual’ roles
of fitness (Pence and Ramsey 2013a) as wholly independent. Constructing quantitative fitness measures
and estimating fitness values is surely a separate endeavor from investigating whether fitness as a concept
allows for some causal interpretation. Nonetheless, the statisticalist argument against the possibility of a
privileged estimation of fitness as quantitative measure—i.e., the argument that any quantitative measure
of fitness is unavoidably dependent on explanatory interests—casts serious doubt on fitness as causal
concept.
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1. The space of life histories Xis characterized a high number of degrees of
freedom, where each independent variable makes a difference for the
reproductive outcome of a life history.
2. Fitness (expected reproductive outcome) is specified by ignoring all degrees of
freedom except a select few, dependent on explanatory interests.
3. Yet evolutionary change, being constituted by individual births and deaths, is
affected by all degrees of freedom of X, not a subset of them (from (1)).
4. )Natural selection, defined as variation in fitness, describes a particular pattern
in population change, but since it does not refer to the processes that define X, it
does not correspond to a cause of population change (from (2) and (3)).
3 Methodological Routes to Natural Selection
In light of the preceding argument, the interpretation of selection’s causal nature can
be reformulated in methodological terms: can selection (and drift) in principle be
estimated from complex, natural populations in a way that is not hopelessly
dependent on the explanatory interests a biologist might happen to have? In other
words, is there a privileged way of statistically apportioning the underlying causal
reality, or are there a plurality of ways, such that selection may assume any direction
or magnitude as explanatory interests change?
While a general solution to the reference class problem for unconditional
probabilities is likely impossible (Ha
´jek 2007), I will argue there is a way out in the
particular case of evolution by natural selection. In this section I will lay the ground
by showing how previous key causalist arguments presuppose a successful
resolution of the NPA argument and thus do not really address the NPA argument.
Instead, it is instructive to examine how field biologists test for selection in natural
populations. These field tests illustrate a class of case where the abstraction involved
can be argued to be unambiguous and unproblematic.
3.1 Null Models, Selection Coefficients, Taxonomies and Fitness Models
One way the causality for selection has been argued for is by taking deviations from
certain null models, such as Hardy–Weinberg equilibria, as sufficient evidence of
the causal impact and force-like character of selection (e.g. Sober 1984; Stephens
2004). Even if one does not hold to the force analogy, it has also been argued that
such deviation establishes that natural selection must be an objective cause of
evolutionary change, and not merely some arbitrary statistical redescription of
individual births and deaths (Gildenhuys 2014).
However, this line of argument does not help, because the question is whether
such null models are the result of arbitrary abstraction. Hence they cannot be used to
defend a causal interpretation of natural selection since the ambiguity in divvying
up the individual-level causal processes remains. For instance, if the frequency of
the recessive homozygous genotype aa is higher than the one expected by the
Hardy–Weinberg model, this only means that the genotype aa is correlated with a
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larger number of offspring in the population under consideration. It may turn out
that some other allele Bis not present at all in the population, and if it would be, that
different correlations between aa and offspring number would be obtained (see
discussion about trait fitness in previous section). Thus the test does not establish an
objective, privileged fitness differential between aa and the other genotypes.
A similar problem arises in the causalist strategy of drawing on direct estimates
of selection, through response to selection (by means of the breeder’s equation) or
selection coefficients. For instance, since manipulating selection coefficients
correlates with population change, this manipulation has been taken as a sign that
selection must be causal (e.g. Forber and Reisman 2007).
However, such a strategy merely shifts the problem from the interpretation of
selection to the interpretation of the selection coefficients, and the NPA argument
can be likewise applied to the selection coefficients. Coefficients are not
manipulated directly: what is manipulated in practise are traits, trait frequencies
and trait-environment interactions, and that such manipulations lead to population
change is perfectly compatible with a statisticalist interpretation of the selection
coefficients. Whether or not changes in selection coefficients can be estimated in a
privileged way given such manipulations is precisely the point of contention.
Another strategy is to propose a taxonomy of fitness measures, and to claim
differences in one type of fitness are causes of evolution (e.g. Sober 1984,2013;
Abrams 2012; Ramsey 2013). For instance, Abrams (2012) distinguishes between
various kinds of fitness measure, and argues that ‘parametric type fitness’ may be
given a causal interpretation, since this fitness parameter is what underlies the
empirical estimations of trait fitness values in actual populations.
However, such a taxonomy does not prevent the NPA argument from being
applied to the probabilities underlying parametric fitness (see discussion of trait
fitness in introduction). Abrams implicitly acknowledges this point when mention-
ing that the degree of certainty of our knowledge of parametric type fitness is
directly influenced by the method of estimation (Abrams 2012, 196: 4). However, a
thoroughgoing response to the NPA argument must involve delving deeper into the
details of these methodological inferences.
Fitness models, which integrate a relatively wide range of causal influences, face a
similar problem. For instance, the Pence–Ramsey model of fitness (Pence and Ramsey
2013b) integrates a variety of causal processes that had been wrongfully ignored by the
original propensity interpretation of fitness (Brandon 1978; Mills and Beatty 1979):
processes that affect the variance and skew (and higher moments) in reproductive
outcomes, processes that affect the expected reproductive outcome of offspring
generations (but not the parent generation), and processes that affect the timing when
reproduction happens within the life-history of a generation. These processes do not
directly affect the expected number of offspring of the parent generation, but do affect
the expected size of the daughter population many generations in the future.
However, while the Pence–Ramsey model is more inclusive of processes that
affect the ways in which probabilities are distributed over reproductive outcomes
and how this distribution changes over time, it does not address the origin of these
probabilities themselves. In assigning probabilities to possible daughter populations
(at infinite time), the skeptical NPA argument could once again be applied to show
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how explanatory interests influence the estimation of such probabilities (see
discussion of individual fitness in introduction).
3.2 Natural Populations
The approach that I suggest in this paper is that we should consider methods used by
field biologists to establish the presence of selection. Such methods strongly suggest
that, at least in certain cases, there is a non-arbitrary way out of the reference class
problem. How precisely natural selection may be considered a cause in such cases,
and how precisely this answers statisticalist objects are separate questions, and are
the subjects of the next two sections.
In field studies, estimating selection coefficients is often very difficult because of
the variability in the temporal dynamics of population change. Siepielski et al.
(2009), in a review of replicated field studies, indicate that, in general, natural
selection varies in strength, direction (positive and negative) and form (linear and
nonlinear selection) from one generation to the next.
This variability in selection dynamics is a reflection of the complexity of
individual-environment interaction. Environments are rarely static, and slight
changes in biotic or abiotic variables may have large effects on the patterns of births
and deaths exhibited. Ideally we should be able to exactly replicate population and
environmental structure as to establish whether population changes are simply noise
or follow an expected pattern; however, in the vast majority of cases this is not
possible. Even when adequate temporal replicates exist, the duration of the study is
very rarely longer than a couple of years (Siepielski et al. 2009).
In such cases, where variability is so ubiquitous, it becomes difficult to rebut
statisticalist challenges. Many of the assumptions in population genetics models
(infinite populations, static environments, absence of linkage, and so on) are made
in order to gain mathematical tractability. However, while variability and
complexity may be eliminated in abstract models, they are more or less permanent
features of real environments, and one may legitimately question whether such
abstract models can be used to judge on questions of causality when it is unclear
whether even the basic inputs of the models (such as selection coefficients) reflect
objective properties of organisms and populations.
Nonetheless, there is a powerful group of methods for cutting through short-term
and individual-level complexity: tests for stable equilibrium. Endler (1986)
describes two ways in which equilibria may be used to establish the presence of
natural selection. The first method (‘method V’) requires longitudinal studies on
trait frequency distributions, and tests either for long-term stability in frequencies,
or steady directional change. Of the two, an observed directionality is taken as
stronger evidence for natural selection. However, it is not fool-proof: Endler
describes how simulations of coin-toss runs surprisingly often give rise to
(temporary) directional trends. Even though a single unbiased coin-tossing
experiment leads to heads as often as it does to tails, the probability of a significant
run of either heads or tails is surprisingly high.
The second method (‘method VI’) has a manipulative character: a population at
stasis is perturbed, and a subsequent observation of directional change, either back
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to its previous state or towards a new state, is taken as strong evidence for natural
selection. One implementation of the perturbation entails manipulating the trait
frequencies of the population. Reversion to the previous distribution of frequencies
is taken as strong evidence for the presence of natural selection. Changes in the
environment constitute another type of perturbation. Such perturbations can be
human induced (e.g. pesticides) or natural (e.g. volcanic eruptions, epidemics), and
can occur abruptly or gradually. An example of where a gradual change in
environment is used to establish selection is the well-known study of moth evolution
in response to increasing air pollution in Britain (Kettlewell 1955).
Such methods are not always possible. Sometimes there are multiple equilibria in
the system, complicating the interpretation. Further, not all forms of natural
selection, such as certain types of frequency dependent selection, seem to tend
towards equilibrium. Nonetheless, when there is a tendency towards equilibrium, it
can be discerned in longitudinal studies as a long-term effective change in
population structure, despite short-term fluctuations.
4 The Equilibrium Model of Causality
While such methods undercut the generality of the no-privileged-abstraction
argument, in themselves they do not constitute a direct argument for the causality of
selection. In this section such a direct argument will be attempted. We will assume
that a natural population is undergoing directional change in its trait frequency
distribution, and is evolving towards a stable equilibrium. This assumption may be
thought of as the outcome of an empirical field investigation; in the next section the
assumption will be discussed more critically, especially with regards to the worry
that this introduces some arbitrary abstraction.
I will first argue that natural selection, as tendency towards equilibrium, is a
cause according to the (probabilistic) counterfactual understanding of causality (e.g.
Lewis 1973); subsequently I will argue it is a force with direction and magnitude.
4.1 Relation and Relata
Let us first briefly outline the landscape of accounts of the causality of selection
with regard to two reference points: the causal relation and causal relata. This will
allow for the view defended here to be situated with more precision.
Concerning relation, I subscribe to the statisticalist criticism that the relation is
not one of causal production (Matthen and Ariew 2002): evolution by natural
selection is not a spatiotemporally continuous process where some physical mark is
transmitted, or quantity conserved (Salmon 1984; Dowe 2000). However, most
causalist accounts have drawn on a difference-making relation. In light of problems
arising from the use of the interventionalist criterion of causality to adjudicate on
the epiphenomenality of population-level processes (Baumgartner 2010; Matthen
and Ariew 2009), and in light of the fact that such interventions often depend on
abstract models, I will avoid that specific conception of causality (as does e.g.
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Huneman 2012). Instead, I will consider whether natural selection represents a
probabilistic counterfactual relation between its relata (e.g. Lewis 1973).
Even within the counterfactual option there are a number of possible accounts
according to how the relata—the source and effect of natural selection—are to be
understood. One point of controversy concerns the level of analysis at which the
source and effect of natural selection are to be located. Bouchard and Rosenberg
(2004) propose that the source of natural selection consists in pair-wise individual-
level competitive differences and that the effect consists in pair-wise differences in
(expected) individual reproductive outcomes (Bouchard and Rosenberg 2004). I
follow Millstein’s (2006) criticism of this proposal, and consider natural selection at
the population level.
A further point of contention is whether the source of selection is (population-
level) fitness differences and whether the effect is changes in trait frequencies (e.g.
Millstein 2006; Sober 1984). One problem here is that natural selection and changes
in trait frequencies are mathematical, not causal, consequences of fitness differences
(Matthen and Ariew 2009). Another problem, as argued previously in this paper, is
that it is not clear whether fitness variables are objective in the same way mass or
acceleration are, and hence to claim selection is causal because fitness values can be
manipulated is to beg the question.
By contrast, the proposal of this paper can be summarized in following scheme:
population with trait distribution dand in environment E!natural selection
!directional change in trait frequencies
The vector d¼ðd1;d2;...;dnÞspecifies the relative frequency of each of the ntraits
that characterize organisms in the population. I will now argue that this proposal
ensures that each of the relations (between selection and source, and between
selection and effect) is causally counterfactual.
First, concerning the first relation, the combination of ntraits and environment
Egives rise to a great number of biotic and abiotic organism-environment
interactions. Some of those interactions will make no net difference to the effective
direction of population change, while others will. Natural selection is only
constituted by the latter interactions.
6
Understood in this way, natural selection is not a mathematical consequence of d
and Ebecause the causal interactions between organisms of the population and
between organisms and environment are not mathematical consequences of a
specification of dand E. (For example, if the laws of physics were changed, the
same dand Ewould give rise to different causal interactions.) Further, if dand
Ewere different, we would likely see different causal interactions, and thus a
different process of natural selection.
Second, the effect of natural selection is to be sought in the direction of change,
not the fact of change. This proposal contrasts with the accounts presented by
Huneman (2012), Millstein (2006) and Matthen and Ariew (2009), who all locate
6
This is continuous with Huneman’s (2012) definition of selection pressures as ecological ‘‘reliable
factors which differentially affect the trait types’’ (185). The only difference is that reliableness is
specifically defined here in reference to an effective directionality.
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the effect of natural selection in the fact of population change. The problem with the
latter proposal is that population change is just as likely to occur where natural
selection is absent—such as when drift is present, or when the population evolves
towards a Hardy–Weinberg equilibrium state. Hence the question to be asked is not
whether selection causes an accumulation of births and deaths, but whether
selection causes a stable trend in the accumulation of births and deaths.
One could compare the effect of natural selection on a population to the effect of
an electric field on the random walk of a charged particle in a gas. The gas has a
certain temperature, and the particles collide randomly; however, because of the
electric field there is a bias in a certain direction. The field does not cause the
movement of the particle itself, but does make a difference for the long-term
‘effective’ path the particle will take (Fig. 2). In this way natural selection’s causal
influence is to be sought in the effective direction of population change instead of
change itself, as the latter could also be the result of random fluctuation (drift).
A special case occurs when the effective path shrinks to a point, that is to say, if
the trait distribution dof the population is already in a stable equilibrium state. This
occurs with stabilizing selection, and in this case the causal effect of natural
selection is to hold the population in stable equilibrium. This effect becomes
observable when the trait distribution is perturbed to dþdd: given stablizing
selection, one would expect the population to evolve back towards equilibrium.
In general, the relation between natural selection and effect is causally
counterfactual: were natural selection not present, directional evolution would be
much less likely. Drift could in principle give rise to directional evolution, but the
probability of this occurring diminishes the longer the directional change lasts.
Further, natural selection is not sufficient for a directional change in frequencies
taking hold, as natural selection can be counteracted by drift.
At this point, one may rehearse an objection, going back to Sober (1983), namely
that equilibrium explanations are not causal (see also Huneman 2010 for a
generalization of this argument). Sober argued that explanations where the outcome
state is explained as a stable equilibrium state are not causal because such
explanations do not pick out the actual cause of the outcome state. For example, if a
marble is let go at the rim of a bowl, and proceeds to find its way to the lowest point
of the bowl, we explain its outcome state by the shape of the bowl, not by the
particular path the marble followed. In other words, we explain by referring to a
disjunction of possible causal scenarios (1983: 84): if a system had not followed this
Fig. 2 Actual versus effective
evolutionary change
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particular pathway to equilibrium, it would have attained equilibrium by another
path.
However, this does not present a problem, because Sober is drawing on a
different notion of causality. If we mean by cause the actual, specific path a
population takes on way to equilibrium, then indeed an explanation by natural
selection does not pick out any actual cause. However, a counterfactual difference-
making relation exists between the equilibrium state and the directionality of the
trend leading up to the equilibrium. Explanations by natural selection are causal
insofar they pick out directional trends as causes of the outcome state (equilibrium).
A second objection concerns how a population may undergo directional evolution
towards equilibrium even without natural selection or any causal force acting on it.
This is the case for the two main models of zero-force evolution: Hardy–Weinberg (H–
W) equilibria (Sober 1984) and drift (Brandon 2006, McShea and Brandon 2010). In
these models, the population either jumps to an equilibrium state (a H–W equilibrium),
or tends towards a state where a single allele has become fixated in the population. This
would seem to undermine the counterfactual relation between natural selection and
stable equilibrium, since a population may spontaneously tend towards equilibrium in
absence of natural selection or any causal force.
In response one can point out that neither zero-force model describes a
stable equilibrium. In the case of drift, the absorbing state of fixation is not a
stable equilibrium, but a neutral equilibrium state. Should the population be perturbed
from the state of fixation, it would not necessarily drift back to that same state, but may
drift to some other fixation state. Thus the process of drift is like a drunk man’s walk on
a sidewalk with a gutter on either side. Once the drunk man falls into the gutter he stays
there, but does not necessarily return to the gutter if pulled out by someone. There is no
tendency towards falling into one particular gutter.
Similarly, a H–W equilibrium state is not stable either. If (p,q,r) is a H–W
equilibrium state (pand rrepresent the relative frequencies of the homozygous traits
AA and BB; qrepresents the relative frequency of the heterozygous trait AB), and is
perturbed to ðpþdp;qþdq;rþdrÞ, then this perturbed state will only evolve back
towards (p,q,r) if dp¼drand dq¼%2dp(see ‘‘Appendix’’). H–W equilibrium
points are not stable equilibrium points, as they are stable only along one specific
line in state space.
In this way, if natural selection were not present, regardless of which zero-force
model one adheres to, there would not be a trend towards stable equilibrium. Drift
may lead to population change, but only selection leads to a robust, multigener-
ational trend in the change of population structure.
4.2 Direction and Magnitude
In instances where natural selection causes a population to trend towards a
stable equilibrium state, the stable equilibrium is a reference point that allows a
direction to be ascribed to the population change. Note that, stabilizing, disrupting
and directional selection all are ‘directional’ in this sense, since they tend either
towards the fixation of a particular trait, or towards stable polymorphism.
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The magnitude of selection can be estimated in the regular way, through the
response to selection. The only difference in the equilibrium framework is that what
matters is the effective response to selection. In the case only a single trait is
selected, the breeder’s equation is applicable.
7
Reff ¼H2seff
where H2is the heritability, Reff the effective response to selection, and seff the
(effective) strength of natural selection.
Thus, if a population never reaches the equilibrium state (N!1), the effective
response to selection is zero, even though the magnitude of selection may be
nonzero. In this case the tendency towards the equilibrium state does not translate
into any actual trend. This is a direct consequence of the breeder’s equation, and
some underlying reasons for this can be seen by separating heritability into genetic
and environmental variation: H2¼VG=ðVGþVEÞwhere VGis the portion of total
phenotypic variance that can be explained by genetic variance, and VEis the portion
explainable by variation in the environment. Thus, as drift increases, the
environment will have an increasingly variable effect on the population, and hence
the effective response to selection goes to zero. Likewise, if traits are transmitted
poorly between generations, the response to selection will be diminished.
5 Statisticalist Objections
In this section we consider two fundamental objections to the model. The first is that
the model simply reintroduces a different arbitrary abstraction away from the
complexity of organism-environment interaction. The second is that natural
selection still has an epiphenomenal character.
5.1 Directionality and Abstraction
Even limiting attention to cases where populations trend to stable equilibrium, one
objection could be that defining natural selection with respect to the effective
direction of population change is simply a different way of arbitrarily abstracting
away from the complexity of individual-level causal processes. Based on an
observed approach to stable equilibrium, the equilibrium model distinguishes
between processes that make a difference to an individual’s reproductive outcome
(D2) and those that make a difference to the stable equilibrium (D3—see Fig. 3).
However, or so the objection goes, in principle some explanatory interest in some
other feature of the population change could lead to some different distinction being
7
Determining the response to selection when traits are correlated through nonadditive genetic effects is
more complicated, but there are methods using multivariate regression, such as Lande’s equation:
R¼GP%1s, where Gand Pare the additive genetic and phenotypic variance-covariance matrices. In its
canonical formulation, this equation describes the response within a generation (see Lande and Arnold
1983), so it could be conceivably extended to describe the effective response over multiple generations by
means of an effective selection coefficient vector: Reff ¼GP%1seff :
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made among causal processes (D0
2and D0
3), and some other direction (if any at all) to
be ascribed to the population change.
In response, one must first emphasize that the issue is not whether abstraction can
be avoided in explanations by natural selection; it is whether the abstraction
involved precludes a causal interpretation of explanations by natural selection.
Hence the real problem that must be considered is whether some arbitrary
explanatory interests are smuggled into the equilibrium model.
To further specify the locus of the objection, note that not all dependence on
explanatory interests is automatically problematic. When observing the behavior of
natural populations, an evolutionary biologist will be interested in explaining
different types of outcome than, say, a biochemist, or an insurance agent.
Explanatory interests in such cases dictate the type of outcome that is considered the
explanandum. What is at stake is that, even when the outcome of interest is decided
on, whether explanatory interests may lead to the set of D3being defined differently,
so that there is no privileged way of (causally) explaining the evolutionary change.
The equilibrium model avoids this problem, since D3is not obtained from D2by
arbitrary selection, but by averaging out across many generations. Those causal
processes which do not average out to zero are part of D3, and these are the
processes which make no long-term difference to the structure of the population.
Explanatory interests cannot alter what makes a difference to the equilibrium state.
It is an objective matter of fact which processes do and which processes do not
make an overall difference. Furthermore, since equilibrium can be observed
independently of probability estimations, observations of equilibrium can serve as a
basis for a privileged estimation of the probabilities underlying fitness, allowing for
a way out of the NPA argument in these cases.
In this respect, the equilibrium model follows the causal interpretation of the
abstraction involved in explanations by natural selection (Strevens 2009; Woodward
2003): the individual-level interactions which average-out to zero are those which
are not relevant difference-makers, and hence may be abstracted away from. Even
though abstraction may lead to simplified or even distorted representations of causal
processes, this is justified because the abstraction cuts the causal difference-making
structure ‘at the joints’.
To what extent idealized models of population-level trends in general may be
considered causal is a question beyond the scope of the paper (but see Levins 1966;
Weisberg 2007). For instance various models in ecology do not represent
individual-level interactons veridically, such as Hubbell’s neutral theory (Hubbell
2001), which treats all individuals in a community as equivalent. Yet, the resulting
model is deemed surprisingly predictive of population-level biodiversity patterns
(Chave 2004). Likewise, models in population genetics take only a limited number
of loci into consideration, often (though not always) assume constant environments
(see Gillespie 2004), and yet have been used very succesfully to understand the
evolution of actual populations.
Given that idealized models typically cannot explain every aspect of a complex
phenomenon (so that some such as Levins 1966 have advocated the use of a cluster
of models), it is unsurprising that some explanatory-dependence cannot be avoided,
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since one type of idealization is chosen over alternative types. We mentioned the
choice of outcome state, and the other important dependence on explanatory
interests allowed for by the equilibrium model is that on time-scale. What makes a
difference on the long-term does not necessarily make a relevant difference on the
short-term, and vice versa (see next section).
8
However, once the target and scope of
the explanation is set, the equilibrium model does not possess any of the arbitrary
description-dependence assumed by the NPA argument.
5.2 Epiphenomenalism
One of key statisticalist challenges was to point to the epiphenomenal character of
natural selection: selection is a ‘tertium quid’ that could be eliminated from
consideration without affecting the causes actually driving evolution. The original
version of this challenge focused on the mathematical character of natural selection,
and while we already argued why natural selection is not a mathematical
consequence of the source of selection, one could still object that the causal
relations connecting organism-environment structure, natural selection and direc-
tional change could be eliminated without affecting directional change.
Figure 3schematically represents this objection: if natural selection were to be
eliminated from consideration, the causal relation between the processes determin-
ing individual births and deaths, D2, and directional change would still be intact.
8
See also Abrams (2009) for a discussion of how what Abrams calls the ‘reference environment’ is
dependent on the target explanandum.
Fig. 3 The solid lines represent causal relations; the dashed line represents a constitutive relation. D1
represents the set of all individual-level causal processes (defining a specific life-history), D2the set of all
individual-level processes affecting the reproductive outcome of a life-history, and D3the processes
which make a difference to the equilibrium distribution of trait frequencies
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Evolution by natural selection is still ‘just’ an accumulation of births and deaths in
the equilibrium model.
In response, one need only to point out that only the processes in D3, not D2,
cause directional change. Aspects of the causal processes impinging on organisms
in a population may be changed without changing the long-term outcome, but the
latter depends counterfactually on the long-term difference-making processes (D3).
To eliminate natural selection from the causal scheme is to eliminate the difference
between D2and D3—and this affects the causal scheme.
9
A related way of putting the same point is that natural selection contains more
information about the causal structure of population change than contained by the
mass of causal processes D2. Unlike D2, natural selection tells us something about
possible evolutionary changes, not only about actual changes. Specifically, it tells
that if the population would be perturbed, the population would tend to return to
equilibrium, in virtue of the processes in D3. Eliminating natural selection would
eliminate this information about the causal structure of population change.
6 Discussion: General Implications
6.1 What About Frequency-Dependence?
Throughout the paper we have alluded to cases such as frequency-dependent
selection, where evolution by natural selection most often does not tend towards
stable equilibrium (and even leads to ergodicity and chaotic dynamics: see for
example Doebeli and Ispolatov 2014). In fact, many real-life cases do not involve
any discernible approach towards stable equilibrium.
However, the equilibrium model may be extended to such cases by first
distinguishing between the realization of equilibrium and tendency towards
equilibrium. We already mentioned how the tendency towards equilibrium may
be counteracted by drift, so that equibrium is never attained, or so that a population
may not even exhibit a discernible tendency towards equilibrium. However, in cases
of frequency-dependence equilibrium may not be attained even if there is only
selection acting on a population.
Hence a further distinction must be made between a variable component
(variable direction) and an effective component (fixed direction) of natural
selection. The effective component would describe approaches to stable equilibria,
and in general, attractor states, while the variable component would describe the
rest. If there is no convergence to stable equilibrium, the effective component is
zero. This raises the question whether the equilibrium model allows for selection to
be considered causal in such cases.
To reduce cases where selection has no privileged direction (i.e., the direction of
selection averages out to zero over time) to the equilibrium model, one can analyze
9
In this respect, the account presented here is continuous with the suggestion that natural selection is a
structuring cause in the space of population life-histories (Ramsey 2015). See also Kaplan (2013) for the
suggestion that natural selection is some measure of robustness.
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a single process of frequency-dependent selection as a succession of different
selection processes, each tending towards (but not realizing) a stable equilibrium.
For example, consider frequency-dependent selection for color in populations of
Poecliid fish (cf. Huneman 2012): predators are tuned to prey on fish with majority
colors, so that any one color will undergo cycles of selection-for and selection-
against, depending on whether it is a majority or minority color. Is the same instance
of natural selection doing the selecting for and the selecting against? According to
this extension of the equilibrium model, the answer is no, as the interaction between
a fish with a given color and its environment changes in the two cases. Any cycle of
selection-for and selection-against is a succession of selection processes each
tending towards a different stable equilibrium.
To better understand this reduction, consider Brandon’s distinction between
‘homogeneous’ and ‘heterogeneous’ selective environments (Brandon 2005).
Fitness can only be ascribed to an organism or trait if the selective environment
is ‘homogeneous’ within the relevant region. If the selective environment is
heterogeneous, then the nature of the organism-environment interaction fluctuates
significantly, and Brandon terms the process of selection that arises from such an
environment ‘compound selection’. Similarly, frequency-dependent selection could
be understood as compound selection, where the selective environment is
temporally heterogeneous (due to changing biotic interactions).
It may not be easy to distinguish between heterogeneous environments and
fluctuating homogeneous environments. For example, a volcano eruption may be
interpreted as a fluctuation on a longer time-scale, or as a stable but short-lived part
of a heterogeneous succession of environments. In each case the population may be
driven to extinction, but in the first case the process will be classified as drift and in
the latter it may be classified as selection. A full discussion of this problem would
go beyond the scope of this paper (but see e.g. Abrams 2009); more important is to
emphasize that this ambiguity does not mean that the choice between the two
interpretations depends on arbitrary explanatory interests. As Brandon (2005:166)
notes, distinguishing between these cases will depend on the details of the
population, such as behavioral patterns. In this way, an equilibrium may be stable on
one scale and neutral on another: this means that the choice of appropriate scale
should depend on the precise nature of the organism-environment interaction.
To summarize, variable selection may be analyzed as a succession of different
instantaneous selection processes, each directed towards a different stable equilib-
rium that is never reached because the environment is continually changing. In this
way, even though determining the precise nature of the selective environment may
be difficult in practise, variable selection may be considered causal insofar it is a
type of compound selection, where each instance of selection is covered by the
equilibrium model.
6.2 What Kind of Force is Selection?
Finally, in order to both broaden the perspectives of the paper and to bring it to an
intuitive close, I would wish to consider natural selection at a more metaphorical
level. I have argued natural selection is a causal force on basis of certain formal
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characteristics (counterfactual dependence, direction, magnitude); however, it is fair
to wonder what kind of a force it is precisely. It is clearly not a classical Newtonian
force: neither its source, nor its effect is spatiotemporally localizable. There is also
no ‘field’ of force associated with natural selection. Is it possible to say something
more positive about what kind of force it is?
In their 2002 paper, Matthen and Ariew compare evolution by natural selection to
heat flow. During heat flow there is no transmission of a physical mark; it is instead
a statistical process where the concentration of fast-moving molecules in the warm
part of the gas spreads throughout the container. While the net result is that energy
smoothly diffuses, in reality this occurs one discontinuous collision at a time.
Similarly, evolution by natural selection is not the smooth diffusion of an
advantageous trait, but is mediated by individual births and deaths.
From this perspective, the concept of entropic force has some suggestive power.
Entropic forces are forces that originate in the statistical tendency of complex
systems with many degrees of freedom to increase their entropy. Natural
populations are not in thermodynamic equilibrium, and hence the concept of
thermodynamic entropy has little meaning in this context. However, the analogy
does hold insofar natural selection is an effective population-level force that
originates in a tendency of the population to reorganize its structure through
interaction with the environment.
Does this suggestion not undo the effort to argue against the epiphenomenalism
of selection? Not necessarily, because even though entropic forces emerge out of
lower-level interactions and thus are not fundamental, they can do work in
displacing objects. Osmosis is an example of a process driven by an entropic force.
Entropic forces have real effects, can be manipulated, and can be ascribed a
direction and magnitude. Thus they meet the criteria of many accounts of
difference-making, whether Woodward’s manipulationism or the probabilistic
counterfactual account.
Thus the fact that an entropic force is not fundamental but emerges out of lower-
level interactions does not in itself constitute an argument that such forces are
epiphenomenal and non-causal. Interestingly, it may be pointed out that a strict
distinction between a force being ‘fundamental’ and a ‘statistical byproduct’ is
increasingly under pressure in contemporary physics. Numerous proposals have
been made of how fundamental forces, including gravity, may actually be entropic
in nature (Verlinde 2011; Freund 2010).
7 Conclusion
The complexity of the organism-environment interaction means that the resulting
evolutionary change can, in principle, be statistically apportioned in many ways.
While statisticalists have argued that this multiplicity implies that any single
apportioning does not ‘cut nature at the joints’ and is instead dependent on arbitrary
explanatory interests, I have argued that, at least in some cases, a privileged
apportioning can be made. In cases where the population tends towards
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stable equilibrium, a clear distinction can be made between individual-level
interactions that do and do not make a difference to the outcome equilibrium state.
Cases where there is no discernible approach to equilibrium may be judged either
as cases where selection is counteracted, or (such as in cases of frequency-
dependent selection) as compound selection. The upshot is a vision of natural
selection as an entropic force: a non-fundamental force, arising out of statistical
tendencies at the level of individual interactions, with magnitude and direction.
Acknowledgments I would wish to thank Michael Strevens, Grant Ramsey, Andreas De Block, Charles
Pence, Philippe Huneman and an anonymous referee for helpful comments on previous versions of this
paper.
Appendix: Instability of H–W Equilibria
First, let us investigate when two distributions (p,q,r) and ðp0;q0;r0Þwill give rise
to the same H–W equilibrium. Then the following three identities must hold:
pþqþr¼p0þq0þr0¼1
pþq=2¼p0þq0=2
rþq=2¼r0þq0=2
These equations are dependent, and taking r0as a parameter, we get the following
set of solutions fðp%rþr0;1%pþr%2r0;r0Þjr02½0;1'g. This can be simplified
with the change of variable d¼r0%r, and thus we can say that the basin of the H–
W equilibrium ððpþq=2Þ2;2ðpþq=2Þðrþq=2Þ;ðrþq=2Þ2Þis
fðpþd;q%2d;rþdÞjd2½%r;1%r'g:
The basin of a single H–W equilibrium point is the line with direction ð1;%2;1Þin
distribution space. As one would expect, by letting d¼ðpþq=2Þ2%pone can see
that the H–W equilibrium itself is part of its own basin.
Hence we may conclude that there is no open neighbourhood Naround any H–
W point (p,q,r) such that Nis enclosed by the basin of (p,q,r). H–W equilibria are
stable only along one specific line, and hence are unstable equilibria.
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