ORI GIN AL ARTICLE
A Game-Theoretic Analysis of the Baldwin Effect
Graciela Kuechle • Diego Rios
Received: 4 May 2010 / Accepted: 26 May 2011 / Published online: 23 July 2011
� Springer Science+Business Media B.V. 2011
Abstract The Baldwin effect is a process by which learnt traits become gradually
incorporated into the genome through a Darwinian mechanism. From its inception,
the Baldwin effect has been regarded with skepticism. The objective of this paper is
to relativize this assessment. Our contribution is two-fold. To begin with, we pro-
vide a taxonomy of the different arguments that have been advocated in its defense,
and distinguish between three justificatory dimensions—feasibility, explanatory
relevance and likelihood—that have been unduly conflated. Second, we sharpen the
debate by providing an evolutionary game theoretic perspective that is able to
generalize previous results. The upshot of this paper is that the mechanism envis-
aged by Baldwin is less puzzling than commonly thought.
1 Introduction
The Baldwin effect is a process by which learnt traits are integrated into the genome
over many generations through a Darwinian mechanism that mimics Lamarckian
evolution (Baldwin 1896). The Baldwin effect has been the object of much debate.
The criticisms addressed to Baldwin target three distinctive issues. First, the
feasibility of the Baldwin effect: it is claimed that the Baldwin effect is impossible
within the context of non-Lamarckian evolution (Watkins 1999). Second, the
explanatory relevance of the Baldwin effect: some critics argued that there are no
significant biological phenomena justifying its introduction as an explanatory
hypothesis (Griffiths 2003; Watkins 1999). Third, the likelihood of the Baldwin
G. Kuechle � D. Rios (&)
Witten Herdecke University, Witten, Germany
e-mail: [email protected]
G. Kuechle
e-mail: [email protected]
123
Erkenn (2012) 77:31–49
DOI 10.1007/s10670-011-9298-7
effect: the objection here is that the paucity of conditions that could foster
Baldwinian evolution makes the mechanism evolutionary negligible.
The strategy we follow in this paper is one of moderate vindication. First, we
evaluate the arguments that have been purported to avert the mentioned criticisms,
assessing the extent to which they provide solid justifications in terms of the
feasibility, explanatory relevance and likelihood of the Baldwin effect. We argue
that the debate on these matters has unduly conflated these criteria, creating the
impression that we have a single problem requiring explanatory hypotheses of the
same level. Second, we present a game-theoretic perspective, capable of providing a
more general framework, to evaluate the Baldwin effect. We believe this
perspective captures essential aspects of the Baldwin effect that are presup-
posed—although not explicitly—in mainstream accounts of this mechanism. To this
effect, we argue that asymptotic stability may play a crucial, distinctive role in
Baldwinization.
We proceed as follows. In Sect. 2, we introduce the main idea underlying the
Baldwin effect. In Sect. 3, we present and rebut Watkins’ impossibility claim
according to which the Baldwin effect is committed to Lamarckianism. In Sect. 4,
we discuss Papineau’s explanatory relevance argument for the Baldwin effect. In
Sect. 5, we scrutinize a prominent likelihood argument that exploits the notion of
positive frequency dependence. In Sect. 6, we specify the game-theoretic necessary
conditions underlying Baldwinization. In Sect. 7 we further specify our treatment of
the positive frequency dependence account. Last but not least, close our
investigation with some conclusions.
2 The Baldwin Effect
The main thrust of the Baldwin Effect is that what was originally acquired through
costly learning is genetically incorporated as selection acting on behaviors gradually
changes the distributions of genes in a population. The Baldwin effect would then
be able to account, in principle, for any forms of instinctual or innate behavior in
terms of ancestral learning plus natural selection for genes facilitating that learning.
An example may illustrate the mechanics of the process. Imagine that in a
population of tits a new skill emerges—for instance, a trick to opening milk-bottles
by pecking. How this new trait emerged is of no major significance. It could have
been by sheer luck or by the clever discovery of an individual of the population. The
crucial element is that the new skill is fitness-enhancing. From that moment on, any
genetic mutation facilitating the adoption of the trait will be selected.1 The upshot of
the process is the genetic fixation at the population level of originally learnt skills.2
1 Strictly speaking, mutations are not necessary for the Baldwin effect, because even in the absence of
new mutations, Baldwinian selection could operate on already existing genetic variation as long as this
variation affects the likelihood of acquiring a phenotype. Consequently, the scarcity of mutations is not an
argument against the Baldwin effect.2 There are different aspects of the Baldwin effect that must be mentioned (Ancel 1999, 2000; Zollman and
Smead 2009). First, in the Baldwin-Simpson Effect the focus is on the role of plasticity—first selected for
and then selected against—in the assimilation of acquired traits. Second, in the Baldwin Expediting Effect
32 G. Kuechle, D. Rios
123
According to the usual account, the spread of the novel trait across the population
is performed through social learning. In the example mentioned in the previous
paragraph, the new skill spreads as tits learn the behavior from other conspecifics.
Yet, although social learning is of paramount importance for understanding the
Baldwin effect, it is not the only avenue leading to Baldwinization. Asocial learning
alone could also contribute to genetic assimilation through a similar path. Consider
the case of filial imprinting (Lorenz 1965). It has been argued that mother-following
behavior was, at the beginning, acquired through trial and error; ancestral chicks
wandered around to find their own mothers (Ewer 1956; Avital and Jablonka 2000).
Those organisms having discovered, through individual trial and error, that
movement is a statistically reliable cue of parental presence, would enjoy a
comparative advantage. Thereafter, any genetic mutation facilitating the adoption of
this behavior would be selected for. Much of the attention in the literature has been
given to the social learning version of the Baldwin effect (Papineau 2005; Godfrey-
Smith 2003). One of the main contentions of this paper is that—without denying the
crucial importance of the social learning—a complete account of Baldwinization
needs to accommodate both versions. We will argue that the game-theoretic account
that we develop in Sect. 6 is able to capture both types of Baldwinization.
There are three major aspects of the Baldwin effect that must be mentioned. First,
it allows the organism to economize on the costs of learning. By saving
advantageous learnt traits into the hardware, the organism liberates working
capacity that was otherwise employed in costly trial and error exploration of the
environment. Second, the Baldwin effect helps to increase the reliability of adaptive
performance, requiring fewer interactions with the environment to fix the adaptive
behavior. This feature is particularly important in the case of behaviors whose
misperformance entails disastrous consequences for the organism (Godfrey-Smith
1996). Third, fixed behavior may free the organism from the requirement of a
complex cognitive structure to grasp the environment in order to condition behavior.
In this way, adaptive behavior will be achieved with a low resolution represen-
tational map (Godfrey-Smith 1996).
It must be acknowledged that the advantages just mentioned must be weighed
against their costs (Godfrey-Smith 1996). For instance, a fixed behavior may
become maladaptive when the environmental conditions affecting its fitness change.
In general, frequent and regular changes in the environment will most likely reduce
the fitness of fixed behaviors and favor the maintenance or re-adoption of
phenotypic flexibility as long as the organism is capable of tracking its environment
(Godfrey-Smith 1996). Yet, changing environments may act not only against
genetic fixation, but also against any attempt to acquire knowledge with the aim of
exploiting regularities present in recurring events (Avital and Jablonka 2000;
Godfrey-Smith 1996; Mayley 1996).
Footnote 2 continued
the crucial issue is the role of plasticity in speeding up the process of identifying optimal behavior. Last
but not least, in the Baldwin Optimizing Effect the existence of plastic individuals directs the population
away from sub-optimal equilibria and toward global optimum. The main focus of our paper is on the
Baldwin-Simpson Effect.
A Game-Theoretic Analysis of the Baldwin Effect 33
123
It is clear that the stability of the environment crucially bears on the possibility
and desirability of learning and therefore on the chances of Baldwinization. By
environment we mean the set of exogenous elements affecting the fitness of an
organism, including not only the physical habitat but also the behavior of unrelated
species. In particular, from the point of view of every individual of a species, the
environment also includes the behavior of other individuals.
In this paper we consider cases in which the fitness of an organism is frequency
dependent, namely, cases in which its environment endogenously changes with the
behavior of the whole population. Since we focus on this type of environmental
change, we assume other environmental elements to be fixed. In like manner, we
assume that the mentioned advantages outweigh their costs, since this is a
precondition for the Baldwin effect.
Beyond the dynamic aspects of the arithmetic of fitness, time plays a crucial role
in the process leading to fixation. The Baldwin effect does not require that the
assimilated trait remains adaptive forever. On this ground, the Baldwin effect
responds to the same constraints as natural selection simpliciter. It just requires that
the adopted behavior remains adaptive until genetic assimilation takes place. Once
the trait has been saved into the hardware, the Baldwin effect has been completed;
from that point on, the trait may or may not continue being adaptive.
3 Watkins’ Unfeasibility Argument
In this section we deal with the unfeasibility argument raised by John Watkins
(1999). To better understand Watkins’ criticism we adopt Godfrey-Smith’s
characterization of the three stages in which the Baldwin effect takes place
(Godfrey-Smith 2003):
Stage 0: A new trait emerges in the population (a new technique for opening
coconuts, for instance).3
Stage 1: The new trait spreads through the population by learning.
Stage 2: New genetic mutations that facilitate the acquisition of the new trait are
selected, contributing to the fixation of the originally adopted trait.
Watkins’ objection is that the transitional stage 1 is either superfluous or
committed to Lamarckianism. According to Watkins’ own words, the Baldwin
effect assumes that ‘‘hitting on B (e.g. some adaptive behavior), as a successful
solution to a recurrent problem, increases the probability that a gene b for B will get
established. But why, and how? ‘With genetic mutations the wind bloweth where it
listeth’. It would be Lamarckian to impute to the acquired characteristic B a
propensity to engender b’’ (Watkins 1999, p. 421).
We claim that this is not the right way to uncover the structure of the mechanism
governing Baldwinization. As Dupre briefly argued, the crucial idea is that if gene bmakes behavior B adaptive, then in the population of adopters of behavior B, ‘‘those
with the partial genetic base to their behavior, will by hypothesis, be favoured over
3 It is of no relevance whether the original new trait emerges out of a genetic or a cultural mutation.
34 G. Kuechle, D. Rios
123
those without it’’ (Dupre 2000, p. 478). In other words, the issue is not that the
adoption of behavior B increases the probability of assimilating gene b, but rather
that b facilitates the appearance of adaptive behavior B both in the present and
future generations. Take the example of imprinting mentioned in the previous
section. Assume that the mutation contributing to the identification of the mother
using movement as a cue occurs with probability p. Suppose furthermore that those
individuals without the propitiating mutation incur in higher costs to acquire the cue
and are less good at calibrating it. Although any organism having used the cue will
be selected for, it is clear—pace Watkins—that those having the facilitating
mutation will flourish in the population. In this way, organisms with the right
genetic make-up will increase their share in the population.
Figure 1 shows a simplified description of such an evolutionary path. For
simplicity and without loss of generality, we assume that at time t, a percentage pt of
the population adopts the imprinting behavior B. To facilitate the exposition and
cover the case of individual learning, we assume that each generation lives one
period and that they do not overlap. At the beginning of t ? 1 the old generation
disappears, leaving descendants in proportion to the fitness of their behaviors (to
simplify the analysis, we consider the case of asexual reproduction). Moreover, we
assume that at time t ? 1, the offspring of adopters and non-adopters have the same
probability of having the facilitating mutation, bt?1(Pr(bt?1/Bt) = Pr(bt?1/
* Bt) : k). In this way, we avert any trace of Lamarckianism. Finally note that
because the behavior B is adaptive, those who perform B increase their share and
are thereby more likely to transmit their genes to the next generation.
Watkins acknowledges that mutations have better chances of being transmitted if
they occur in adopters of B, and that it may in this sense be that the adoption of B
1+tβ
λ−1
λ−1
θ
θ−1
σ−1
σ
θ
θ−1
σ−1
σ
λ
λ
1~ +tβ
1+tβ
1~ +tβ
Fig. 1 Fixation of mutations
A Game-Theoretic Analysis of the Baldwin Effect 35
123
fosters mutation b. Of course, this is uncontroversial. However, the crucial idea
absent in Watkins’s analysis is that b facilitates the emergence of B, and not that B
raises the propensity of obtaining b. For the Baldwin effect to have a significant
evolutionary relevance, it is sufficient that those individuals having mutation b have
higher chances of displaying the adaptive behavior B at t ? 1 than those individuals
lacking the mutation b. The crucial conditional probability is the probability of
displaying behavior B, given that mutation b is present—to wit, Pr(Bt?1/bt?1).
Figure 1 shows this mechanism in more detail.
If at any point in time Pr(B/b) : r[ Pr(B/*b) : h then, by Bayes’ rule, it can
be shown that the probability of the mutation, given that the behavior B has been
adopted, is higher than the probability of this mutation arising through blunt
variation (k).4 To see this, first calculate the probability of the mutation given that
the behavior B has been adopted:
Prðb=BÞ ¼ PrðB=bÞ PrðbÞPrðB=bÞ PrðbÞ þ PrðB=� bÞ Prð� bÞ :
Using the parameters in the tree, we obtain that Prðb=BÞ ¼ rkrkþhð1�kÞ [ k, if and
only if r[ h. If mutated individuals are more likely to adopt the imprinting
behavior, the proportion of individuals with mutation b amongst those who
displayed behavior B at any period is greater than the proportion of mutated
individuals in the whole population. In other words, the conditional probability of
the mutation, given the imprinted behavior, is larger than the unconditional
probability of the mutation. Note that the fostering of betas by behavior B only
mimics a Lamarckian process without being itself Lamarckian.
Before continuing, and in order to avoid misunderstandings, it is important to call
the attention of the reader on how to interpret Fig. 1. As we have pointed out before,
the Baldwin effect is a populational mechanism, not a developmental one. If the
genetic assimilation of originally learnt traits were not cast in inter-generational
terms, then Watkins would be right in pointing out its inevitable commitment to
Lamarckianism. Yet this is not what is at stake in Fig. 1. We carefully depicted the
passage from generation 1 to generation 2 using a dotted line. All that is on the right
of the dotted line takes place in the second generation. Note that mutations play an
important role in this process. The sequential paths in Fig. 1 do not follow the
potential fate of a single individual, but rather the progressive fixation of favorable
genetic material in the whole population. Thanks to having learnt a new trait, the
organism unintentionally contributes in directing the genetic material toward
convergence, facilitating, in its turn, the acquisition—by future generations—of the
aforementioned advantageous traits.
Consider the case in which there is a deleterious mutation, and let us denote it by
*b. Watkins argues that adopters will carry all their mutations—both the
facilitating and the deleterious ones—into the next generation. Our results show
that not all the genetic material of adopters will be transmitted with equal
likelihood. The reason is that while adopters are themselves increasing their share in
the population, facilitating mutations will grow amongst B adopters in detriment of
4 We exclude the time subscripts to simplify notation since they all refer to the same period.
36 G. Kuechle, D. Rios
123
deleterious ones. This can be seen by calculating the updated probability of the
deleterious mutation amongst the B adopters, Pr(*b/B). Since Pr(*b/B) = 1 -
Pr(b/B), from the previous paragraph we deduce that Prð� b=BÞ ¼ hð1�kÞrkþhð1�kÞ\1�
k if and only if r[ h. As long as individuals with the deleterious mutation are less
likely to acquire the adaptive trick, the proportion of individuals with mutation *bgiven the behavior B is smaller than the unconditional probability of the deleterious
mutation.
According to our previous analysis, the adoption at some point in time of the
adaptive behavior B is enough to generate a path along which facilitating genes (b)
outcompete deleterious ones (*b). We should reckon that our argument relies upon
two crucial assumptions. First, we assume that B is adaptive and second, we suppose
that individuals with facilitating genes are more likely to perform B in any given
generation (Pr(B/b) [ Pr(B/*b)). By assuming that B is adaptive, we have ruled
out any kind of environmental instability that may render B maladaptive before
genetic fixation occurs. This seems a reasonable assumption at this point since we
want to concentrate upon the process by which B fosters the assimilation of betas.
But, what does the second supposition depend on?
The claim that a facilitating genetic base yields B more reliably seems justified
on the grounds that those individuals without the genetic base, namely those who
have to engage in a process of trial and error to perform B, may err more frequently
and fail to perform it. Nevertheless, some limitations to this claim should be
acknowledged. First, if B were a very simple behavior, individuals might be able to
perform B regardless of whether they have b. Second, if B were a considerably
complex behavior, partial assimilation of betas could be insufficient to render the
adoption of B more likely. In these two cases, the second assumption would not hold
(Pr(B/b) = Pr(B/*b)) and correspondingly, the process described in Fig. 1, by
which betas become progressively accumulated, would not obtain.
Note that Watkins’ argument and our contention do not explicitly take into
account the complexity of the behavior in question and the type of learning that
leads to adoption. As we are going to see later on, these two ingredients are
powerful factors for Baldwinization. We do not assume them in this section, just to
show that, even in the most favorable scenario for Watkins—to wit, when there is no
social learning and the traits are not complex—his argument fails. As we are going
to see later on, allowing for the existence of social learning and complex traits will
make the results of this section more compelling.
To sum up: Watkins fails to show that the Baldwin effect is inevitably
Lamarckian, and consequently not a serious option to take into account. We have
demonstrated that under the assumptions just specified, the Baldwin effect is a
possible, non-Lamarckian evolutionary mechanism. This result, nevertheless, is
agnostic as to the likelihood or the explanatory relevance of the Baldwin effect. In
next section we will briefly introduce the explanatory relevance account advocated
by David Papineau, to later turn—in Sect. 5—into a systematic assessment of the
likelihood account, defended by Peter Godfrey-Smith and Terrence Deacon.
A Game-Theoretic Analysis of the Baldwin Effect 37
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4 Papineau on the Explanatory Relevance of the Baldwin Effect
David Papineau has argued that the Baldwin effect would be particularly suited to
account for the evolution of complex behavioral traits in environments characterized
by social learning (Papineau 2005). This mechanism is known in the literature as the
‘Papineau effect’ (Griffiths 2006). The argument relies on the existence of sub-traits
that are not adaptive in isolation but rather when simultaneously combined. Imagine
a complex trait—the opening of coconuts by smashing them against a stone—
involving several sub-traits (grasping the coconut, being able to climb down the
coconut tree with the coconut and hitting the coconut against a sharp stone). Assume
that each one of these sub-traits is not advantageous in itself. Nevertheless, when all
these sub-traits co-occur, there is an evolutionary advantage for the individuals
having them. Papineau argues that the Baldwin effect provides a more plausible
explanation to account for these complex traits than natural selection simpliciter on
the grounds that the existence of complexity places higher barriers for selection to
operate. Natural selection is well suited to deal with piecemeal improvements.
Whenever a new advantageous trait emerges, it is selected for. Given that the
advantageous trait involves the co-occurrence of several mutually independent sub-
traits that are not individually advantageous, for natural selection to operate we need
to assume the unlikely coincidence that these sub-traits co-occur in a single
individual. Obviously, Papineau does not deny that this is a theoretical possibility.
He argues, nevertheless, that an alternative, more plausible account could be given
using the Baldwinian framework.
According to Papineau, the Baldwin effect exploits two mutually reinforcing
mechanisms. The first mechanism concerns the transmission of the advantageous
behavior through social learning, assuming that social learning characterizes those
situations where ‘‘the display of some behavior by one member of a species
increases the probability that other members will perform that behavior’’ (Papineau
2005). Clearly, social learning facilitates the dissemination of newly adopted
behaviors and increases the chances that they persist in the population. In this
manner, social learning contributes to speed up the process of convergence of
mutually independent mutations whose simultaneous occurrence would be
otherwise highly unlikely.
The second mechanism has been illustrated in the previous section. According to
it, there is a leverage effect connecting past with future mutations. In the same way
that having adopted an advantageous behavior raises the probability of fixating
facilitating sub-traits, having fixated one sub-trait increases the probability of
fixating further ones. Once the new complex behavior emerges, the very fixation of
the underlying sub-traits increases behavioral performance, this way generating
more pressures for genetic assimilation of the remaining sub-traits. Although the
emergence of new mutations is statistically independent of the mutations already
present in the organisms, their selective retention is not. Thanks to this scaffolding
mechanism of mutually reinforcing mutations, the Baldwin effect is able to fulfill
the requirement of having a highly improbable combination of otherwise
individually not adaptive sub-traits. Combining the social learning mechanism
38 G. Kuechle, D. Rios
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with the scaffolding effect, Papineau is able to provide a particularly plausible
account of the Baldwin effect.
At this stage it is important to note a tension within the structure of Papineau’s
framework. On one hand, the argument appeals to the notion of complexity to
support the claim that Baldwinization might be crucial to achieve genetic fixation.
Note, however, that there are plenty of complex traits that have evolved by natural
selection without Baldwinization (Dawkins 1986, 1996). The evolution of the
human eye is a good example, yet non-Baldwinian natural selection can easily
account for it. Making gestures toward complexity then falls short of justifying the
Baldwin effect. Nevertheless, this is certainly not Papineau’s claim. Papineau
makes the much more moderate claim that Baldwinization might be a plausible
factor relaxing the involvement of concomitant genetic mutations. This will
ultimately not only speed up the process but will also increase the chances of its
accomplishment.
On the other hand, the argument relies on the crucial contribution of social
learning as an alternative supplier of new resources to achieve—despite the lack of
underlying favourable mutations—adaptive behavior. A paradox concerning the
role of social learning may arise at this point. Why should an individual fix behavior
genetically if it is abundantly present in the population and it could be easily
acquired through social learning? In such scenarios, social learning could reduce the
advantage of fixating behavior through genetic assimilation. Paradoxically, very
high (and also very low) rates of social learning would have the effect of preventing,rather than increasing, the relative frequency of facilitating genes over deleterious
ones in the population.
According to Papineau, it is the conjunction of complexity and social learning
that makes the Baldwin effect explanatorily powerful. First note that the
effectiveness of social learning does not only depend on the frequency of the
behavior, but also on the difficulty with which it can be adopted. For social learning
to contribute to genetic fixation, the behavior must be relatively easy to learn; but
not too easy, since this would beg the question regarding the need of genetic
fixation. If it is so easy to copy it, why would it be advantageous to genetically fixate
it? Take the population of tits that learn to open milk bottles: if the behavior is easily
acquired through social learning, then we should expect pure cultural evolution
rather than Baldwinization (Richerson and Boyd 2005). In a nutshell, both too easy
and too difficult behaviors would not be sensible targets for Baldwinization: it is in
the middle range cases that Papineau’s argument offers the most promising support
for Baldwin.
Note that Papineau’s framework does not account for all possible cases of
Baldwinization. We earlier mentioned the evolution of imprinting as a putative case
of Baldwinian evolution (Ewer 1956). It is controversial whether this example
involves complex or simple traits; but it does not seem to involve social learning at
all. Assuming that this is truly a case of Baldwinization, Papineau’s complexity-
cum-social learning framework will be of no use to account for it. We are going to
show that our own game-theoretic account is able to provide a perspective capable
of accommodating Baldwinization, even in the absence of complexity and social
learning.
A Game-Theoretic Analysis of the Baldwin Effect 39
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Papineau’s argument can be characterized as an inference to the best explanation.
His main concern is not to provide an argument for the possibility of Baldwin.
Papineau assumes that Baldwin effects are at least theoretically possible, and he
focuses on its explanatory potential. There is much to praise in Papineau’s analysis.
His framework provides a good case for the explanatory relevance of the Baldwin
effect, given the existence of complex traits. Furthermore, it has the great merit of
being able to generate empirical consequences—such as the hypothesis that complex
traits would be more frequent among species that are social learners than among
species that are not social learners. Nevertheless, a caution note must be added here.
From a Bayesian perspective, the evaluation of a hypothesis should take into account
not only the likelihood of the hypothesis, namely the conditional probability of the
evidence given the hypothesis, but also the hypothesis’ antecedent plausibility (Sober
1994). In this respect, the natural selection hypothesis enjoys a priori higher records
of plausibility than the Baldwin effect. Nevertheless, confirmatory instances like the
ones provided by complex traits in environments characterized by social learning,
should increase the posterior probabilities of the Baldwinian Hypothesis.
5 Positive Frequency Dependence as a Likelihood Argument for Baldwin
In the previous section, we interpreted Papineau’s reasoning as contending that the
evolution of complex traits rendered Baldwin’s hypothesis explanatory relevant. In
this section we explore a set of arguments identifying conditions that may foster the
Baldwin effect. While Papineau focuses on the support that the existence of
complex traits lends to the explanatory power of Baldwin effects, the account we
discuss in this section focuses on the conditions that provide fertile grounds for the
Baldwin effect. Among the circumstances that propitiate Baldwininan processes, the
existence of positive frequency dependence phenomena occupies a prominent place.
Positive frequency dependence occurs whenever the advantage of having a trait
increases with the proportion of individuals in the population who have a convergent
trait (Deacon 1997; Godfrey-Smith 2003; Suzuki and Arita 2008; Suzuki et al. 2008).
Consider for instance the case of language. There are two mechanisms through which
the advantage of acquiring a language depends on the relative frequency of its
speakers; and both promote Baldwinization, albeit through different channels.
According to the first mechanism, a rise in the relative size of the linguistic community
increases the chances of interacting with someone who has adopted the language.
Since interactions resulting in successful communication confer higher fitness, the
larger the proportion of speakers, the higher the expected payoff of becoming one of
them. According to the second mechanism, a growth in the population of speakers
makes the acquisition of language more accessible for imitation. Whereas the first
mechanism affects the extent to which the behavior is adaptive, the latter provides ripe
material for social learning through imitation. Once the practice flourishes in the
population, genetic mutations favoring the adoption of the new trait will be selected,
thereby contributing to the fixation of the originally learnt skill.
The idea of positive frequency dependence has much intuitive appeal.
Nevertheless, we believe that it fails to pinpoint crucial ingredients underlying
40 G. Kuechle, D. Rios
123
Baldwinization. Note that positive frequency dependence is a form of increasing
returns because the payoff to adoption increases with the proportion of adopters.
Although several phenomena display this feature, there are many interactions
characterized by constant and even decreasing returns to adoption that may,
nevertheless, qualify for genetic assimilation. In the case of constant returns, the
advantage of adopting a phenotype does not depend on the proportion of adopters
and, in the case of decreasing returns, the advantage decreases with the frequency of
adopters. The trick to opening coconuts provides an example of this last situation:
the higher the proportion of individuals who have adopted the trick, the more
difficult it will be to find coconuts to open. However, adopting the trick is adaptive
even if it improves the fitness of the adopters at a decreasing rate. This example
shows that the relevant criterion for adoption is not determined by the type of
frequency dependence, but by the best-response nature of this behavior, given what
other individuals are doing.
In strategic environments, the payoffs to each individual depend on their own
behavior and on the behaviors of the others. The relative frequency of phenotypes
affects the likelihood that phenotypes interact with each other and therefore, the
payoffs expected from these interactions. The resulting frequency of behaviors is
thus crucial to determine the fitness of a phenotype. However, the relevant question
is whether adopting a certain phenotype is fitter than not adopting it. In a nutshell,
from a game-theoretic perspective, what matters is not how the fitness of a
phenotype varies with its frequency, but whether adopting a phenotype is an above-
average response at the population level, given the current proportion of phenotypes
in the population. It is of no direct significance whether these interactions involve
increasing, decreasing or constant returns to adoption.
For this reason, the positive frequency account fails to accommodate canonical
examples of the Baldwin effect involving decreasing returns to adoption. Compare
the example of the adoption of a language with the trick to opening coconuts.
Adopting a language as a means of communication is essentially a matter of
coordination (Lewis 1969; Deacon 1997); the larger the frequency of adopters, the
higher the payoff to conforming to the convention. The positive frequency
framework regards this example as a favorable case for the Baldwin effect, albeit for
essentially inadequate reasons. Acquiring a new trick to open coconuts is an
advantageous behaviour regardless of the behaviors of other individuals, and
despite the fact that its relative fitness decreases with the frequency of adopters. The
positive frequency-dependence argument cannot at all capture the significance of
this latter example as a potential case of Baldwinization. Nevertheless, if we think in
terms of best-response, as we are suggesting here, we might plausibly argue that the
coconuts example is a strong candidate for evolution through Baldwinization, an
argument that we develop in depth in the next section.
6 The Baldwin Effect From an Evolutionary Game-Theoretic Perspective
In the previous section we discussed the positive frequency dependence thesis. We
claimed that a game-theoretic perspective is more adequate in providing a general
A Game-Theoretic Analysis of the Baldwin Effect 41
123
and accurate account of the evolutionary grounds potentially enabling Baldwinian
effects. In this section we go a step further in this direction, unpacking the details of
our account.
The Baldwinization of a phenotype assures the fixation of a behavior and saves
the organism the trouble of acquiring it through trial and error (Mayley 1996).
However, this occurs at a cost; once a behavior is placed under genetic control, the
corresponding phenotypic flexibility of the carrying organism is lost (Godfrey-
Smith 1996). For this reason, we argue that Baldwinization is only possible when
the corresponding behavior remains adaptive at least until genetic assimilation is
completed. In other words, it is not enough that a certain behavior be adaptive in the
present period. It also needs to be able to resist the incurrence of mutant behaviors
that may threaten its persistence. If this argument is correct, then Baldwinization
requires some kind of dynamic stability.
Evolutionary processes of natural selection involve a mutation mechanism,
which produces variation, and a selection mechanism, which favors some variants
over others. The long run behavior of these processes can be studied through either
evolutionary stability, through which the role of mutations is emphasized, or
dynamic stability, which focuses on the role of selection (Weibull 1995). Although
under the working assumptions of this paper there is a straightforward correspon-
dence between these two approaches, this is by no means the case at a general level.
For this reason we want to emphasize that the notion of dynamic stability is the one
that provides a sound criterion to address issues related to the fixation of behaviors,
as it deals with the long-run growth of populations of different phenotypes.
Multiple factors affect the dynamics of phenotypes at the population level. A
prominent one is the structure of the interactions among individuals –namely, the
payoffs of the different profiles of phenotypes, the sequence of play and the nature
of the strategy set. Other factors include the process governing the selection and
reproduction of phenotypes, the size of the population, the type of mutations by
which new phenotypes arise, the pairing rules and the spatial nature of the
interactions. These factors crucially affect the dynamics of behaviors. The payoff
matrix, for instance, and the sequence of play in games in which players do not play
simultaneously, determines the set of Nash equilibria. The rule governing the
replication of phenotypes constrains the growth of behaviors. The size of the
population determines the role of drift, whereas the size and frequency of mutations,
as well as the process by which they arise, affects the chances that a population may
drastically change the frequency of behaviors. Finally, the rules governing the
pairing process (including spatial constrains) affect the scope of the interactions and
therefore the fixation of phenotypes (Alexander and Skyrms 1999; Zollman 2005).
In this paper, we restrict ourselves to symmetric 2 9 2 games in which
individuals play simultaneously and focus on how the payoffs of the game affect the
long-run dynamics of the system. Furthermore, we consider a particular type of
dynamics—namely, the continuous-time version of the replicator dynamics- as its
properties extend to several classes of more general processes that are compatible
with different kinds of learning and imitative behavior.
The replicator dynamics consists of a system of differential equations describing
the change over time in the relative frequency of a set of phenotypes under the
42 G. Kuechle, D. Rios
123
condition that they produce error-free copies of themselves and that behaviors with
above-average fitness increase their frequency in the population. It concentrates
mainly on the role of selection and although mutations are not explicitly modeled, it
is implicitly assumed that they perturb the system albeit in an isolated manner. It
should be kept in mind that different assumptions concerning the process by which
mutations arise may require other selection dynamics. In particular, the replicator
dynamics provides an insufficient account for long-run stability when the effects of
each perturbation accumulate instead of dying out in between.5 Two basic notions
of dynamic stability are of interest in our case, namely, Lyapunov and asymptotic
stability. An equilibrium is Lyapunov stable if starting from all nearby states the
system remains close to it, whereas it is asymptotically stable, if in addition, it has
the property that all nearby states converge to it.
In contrast to dynamic stability, evolutionary stability analysis focuses on how
mutations affect the share of strategies in the population. In this approach the notion
of evolutionary stable strategy is the main stability concept as evolutionary stable
strategies (ESS) satisfy two conditions: they perform better or equal against
themselves than any other strategy, and if there is a strategy that performs as well
against them as they do against themselves, then the ESS performs strictly better
against this strategy than this strategy does against itself (Maynard Smith and Price
1973). The first condition is the requirement that a profile of ESS be a Nash
equilibrium. The second condition accounts for the possibility that a share of the
population plays a mutant strategy and gurantees that, if this share is below a
positive invasion barrier, mutants do worse in the post entry scenario than the
incumbent strategy and therefore are not able to spread.
As for the relationship between dynamic and evolutionary stability, while ESS
are asymptotically stable for a large class of dynamics which include the replicator
dynamics, not every asymptotically stable steady state needs to be an ESS.
Nevertheless, if mixed strategies in finite games are also allowed to replicate, then
the concepts of ESS and asymptotic stability are equivalent under the replicator
dynamics (Weibull 1995). Since the assessment of evolutionary stability only
requires knowledge of the payoffs of the game and due to the fact that in the games
considered in this paper the relationship between dynamic and evolutionary stability
is straightforward, we will frame our arguments in terms of evolutionary stable
strategies (ESS) instead of working with explicit evolutionary dynamics and the
concept of asymptotic stability. However it should be kept in mind that asymptotic
stability is a more general and therefore suitable necessary condition for the
Baldwin effect.
To illustrate our argument about the connection between positive frequency
dependence and the Baldwin effect, consider the example of the adoption of a new
trick to opening coconuts from a game theoretic perspective. To simplify the
analysis and without loss of generality, as far as this example is concerned, we deal
with pairwise interactions instead of the more realistic set-up in which phenotypes
5 In this case, stochastic stability is the appropriate tool (Foster and Young 1990). We should note that
there are several models of selection dynamics as well as concepts of evolutionary stability. We do not
engage in the discussion about dynamic models since it falls beyond our purposes. Which model better
fits a certain living system is, after all, an empirical matter.
A Game-Theoretic Analysis of the Baldwin Effect 43
123
play the field. Table 1 depicts the relative fitness of each individual for each profile
of behaviors. We gave numerical values for the sake of concreteness, but the
important relationships between the payoffs are as follows: The biological fitness of
adopting the trick is higher when the other individual does not adopt it, and the
fitness of not adopting it does not depend on the behavior of the other individuals. In
this game, the payoff to adopting the trick is negative frequency dependent since the
higher the number of adopters, the lower the relative fitness of the adopters.6
Nevertheless, adopting the trick dominates the other phenotype, and thus fares
better, irrespectively of its frequency in the population.
The Nash equilibrium of this game has each individual adopting the trick as this
strategy strictly dominates the other- no player can do better by changing his or her
behavior if the other conforms to it. Furthermore, this Nash equilibrium is Pareto
optimal. No feasible rearrangement of payoffs can make an individual better off
without making the other worse off. It is straightforward to check that in these
circumstances ‘‘adopt the trick’’ is an ESS and a global attractor of the replicator
dynamics.7 This means that, regardless of the initial conditions, we expect the whole
population to adopt the trick in the long run (Weibull 1995).8
As stated before, evolutionary stability is concerned with scenarios in which
mutations are isolated phenomena so that they cannot easily kick the system out of
the original equilibrium. The focus is on why a population remains in a certain
equilibrium and not whether this equilibrium will be reached and how. This issue is
better understood with the use of dynamic stability. However, in the particular case
of the game in Table 1, ‘‘adopt the trick’’ is globally stable so that it will attract the
dynamics regardless of the initial distribution of behaviors and the nature of the
mutations. Yet, this need not be the case in other games.
We have argued that the adoption of the trick satisfies an important condition for
Baldwinization. Note that we have not argued that evolutionary stability or, for that
matter, asymptotic stability is sufficient for Baldwinization. To see why, simply take
into account that evolutionary stable phenotypes or asymptotic equilibria need not
be unique. If a game has more than one evolutionary stable equilibrium and the
Baldwin effect occurs, it will at most concern one of these equilibria. Therefore,
Table 1 Interaction with a
dominant strategyAdopt the
trick
Do not adopt
the trick
Adopt the trick (2, 2) (3, 1)
Do not adopt the trick (1, 3) (1, 1)
6 This effect could for instance be caused by a fixed supply of coconuts. The payoffs to adoption and non
adoption assume that the new technology to open coconuts allows adopters to eat more than non-adopters
per unit of time and that this larger intake enhances their reproductive survival.7 When the basin of attraction of an asymptotic equilibrium (i.e., the set of initial conditions which
converge to an equilibrium) is equal to the entire state space, then it is globally stable. Since ‘‘do not
adopt the trick’’ is strictly dominated, the replicator dynamics will eventually eliminate it (Weibull 1995).8 Negative frequency dependent phenotypes need not be dominating. Depending on the payoff structure
of alternative behaviors, selection may lead to the coexistence of different phenotypes or mixed
populations.
44 G. Kuechle, D. Rios
123
there will always be some ESS (or asymptotic equilibrium) that has not been subject
to genetic fixation. Our claim is rather that evolutionary or, more generally,
asymptotic stability is a necessary condition for Baldwinization. Now we turn to the
question of whether this requirement is too strong.
But before doing that, it is important to mention a few facts about evolutionary
stable strategies. Evolutionary stable strategies as well as asymptotically stable
states, constitute a subset of Nash equilibria; yet, they may fail to exist. If the
evolutionary dynamics has no asymptotically stable state, no behavior will be able
to repel invasions and re-attract the population after small perturbations. In such
scenario, we should not expect Baldwinization to take place. Another element that
should be taken into account is that the basin of attraction of an ESS may be
arbitrarily small. In this case the prospects for Baldwinization would be reduced.
However, this need not compromise the argument concerning the necessity of
stability.
Another issue that calls for consideration is that in some games the replicator
dynamics leads to states that are only Lyapunov stable and not asymptotically
stable. As we said before, a state is Lyapunov stable if small perturbations do not
induce a movement away from it (Weibull 1995). The so called neutrally stablestrategies (NSS) are Lyapunov stable.9 In an evolutionary stable state no mutant
strategy persists (in the sense of earning an equal or higher payoff than the
incumbent strategy) whereas in a neutrally stable state no mutant strategy grows (in
the sense of earning a higher payoff than the incumbent strategy). This raises the
question of whether the less stringent criterion of Lyapunov stability is enough for
Baldwinization.
Even when Lyapunov stability may be enough in some contexts, it can be argued
that asymptotic stability is a more reliable property than Lyapunov stability when it
comes to asserting the long run behavior of a dynamic system. The main reason is
that Lyapunov stability does not protect against unmodelled evolutionary drift
(Weibull 1995). Since small perturbations of the population state may pass
undetected by the dynamics, a sequence of such shocks may carry the population
into a state from where the replicator dynamics leads it far away. Asymptotic
stability, on the other hand, guarantees a return to status quo after any small
perturbation of the populations state. Hence robust evolutionary predictions call for
asymptotic stability.
Both ESS and NSS and more generally any form of stationarity require Nash
equilibrium. Stationary states that are not Nash equilibrium are neither evolutionary
nor Lyapunov stable. They are dynamically unstable because, by definition, there is
always some unused pure strategy that earns a higher payoff against the pure
strategies in the non-Nash state. Therefore, if some arbitrarily small but positive
fraction of the population switches to this unused profitable strategy, then these
mutated individuals will earn a higher payoff, increase their population share and
9 A neutrally stable strategy satisfies the first condition for ESS given above and the second condition
with a weak inequality (Maynard Smith 1982). The concepts of ESS, NSS and Nash equilibrium (NE)
relate as follows: ESS ? NSS ? NE. Evolutionary stability implies asymptotic stability in the replicator
dynamics and neutral stability implies Lyapunov stability (Weibull 1995).
A Game-Theoretic Analysis of the Baldwin Effect 45
123
eventually lead the dynamics away from the original stationary state. In this sense,
being a Nash equilibrium is the default necessary condition for Baldwinization.
As we said at the beginning of this section, there are different approaches to
evolutionary dynamics, as well as different concepts of stability and models of
selection dynamics. We have only considered the replicator dynamics and its
relationship with different equilibrium concepts such as ESS, NEE, Nash
equilibrium and applied it to very simple 2 9 2 games. Settings involving non-
simultaneous play, more than two strategies and non-symmetric payoff structure
may lead to less straightforward conclusions.10 In this light, and taking into account
the plethora of factors shaping evolutionary dynamics left out in our analysis, our
argument amounts to stress the importance of the notions of asymptotic stability in
Baldwinian processes.
7 The Positive Frequency Dependence Argument Revisited
The positive frequency dependence argument asserts that traits whose fitnesses
increase with their frequency in the population reinforce the case for the Baldwin
effect. In Sect. 6 we argued that this account overlooks a decisive factor in
evolutionary dynamics, namely, the fitness of alternative behaviors, which is
captured by the notion of evolutionary stability. If one acknowledges that natural
selection acts upon relative fitness, it should come as no surprise that positive
frequency dependence is incapable of providing a necessary condition for
evolutionary stability. The example of the trick to opening coconuts (Table 1)
meets necessary conditions for Baldwinization although it does not involve positive
frequency dependent strategies.11 In this section, we further explore the relationship
between positive frequency dependence and evolutionary stability to fully assess its
impact upon Baldwinization. We are going to show that positive frequency is not
sufficient for evolutionary stability.
To show that behaviors characterized by positive frequency dependence need not
be evolutionary stable, we provide a counterexample. Consider the payoff matrix in
Table 2. Only the first strategy displays increasing returns to adoption (3 [ 2).
However, since both strategies are strategic substitutes, namely, S1 is the best
response to S2 and vice versa, they will coexist in any evolutionary stable
equilibrium. The dynamics will not converge to a state in which every individual
chooses the behavior exhibiting positive frequency dependence. The positive
frequency account would argue that S1 is a candidate for Baldwinization, when in
fact S1 is not an evolutionary stable strategy. Our account based on the notions of
equilibrium and stability, would be agnostic concerning the implementation of the
resulting evolutionary state. Given that this state could be reached by either a
10 See Huttegger (2010) for an analysis of the impact of nonselective processes upon evolutionary
trajectories for games in extensive form.11 In the two-player games analyzed in this paper, a strategy that exhibits positive frequency dependence
yields higher payoffs if both players choose it than when only one player does.
46 G. Kuechle, D. Rios
123
homogeneous population with pluralistic behavior or a biomorphism commited to
each strategy, we believe that this agnosticism is advisable.
It is interesting to compare our model with that of Zollman and Smead (2009)
who adopt a game-theoretic framework to analyze the interaction between fixed and
flexible behavior (modeled respectively as commitment to a pure strategy and
reinforcement learning) to determine the conditions under which plasticity is
asymptotically eliminated. They focus on interactions characterized by more than
one evolutionary end point. In those scenarios, they investigate whether individuals
who adopt flexible strategies or those who adopt fixed strategies will come to
predominate in the long rum. The authors analyze different kinds of interactions
such as the prisoner’s dilemma and signaling games, which in the latter case
captures the conventional aspect of communication. As for evolution of language,
Zollman and Smead consider the relative fitness of flexible types (learners) and
types which are commited to a fixed signal. They show that once a population
acquires a language—an outcome that is achieved thanks to the presence of both
types—fixed types start to predominate. Although learners enjoy a temporary
existence they help to avoid the evolution towards suboptimal signalling systems.
The model of Zollman and Smead shares with ours an evolutionary game-
theoretic focus; however both pursue different objectives. Zollman and Smead are
trying to isolate local roads leading to genetic assimilation. We are rather interested
in specifying the general conditions underlying any form of Baldwinization. These
two projects are certainly not rival. While our project is taxonomical in nature,
Zollman and Smead’s focuses on isolating specific instantiations of the Balwin
effect. In a way these two frameworks reinforce each other. We provide indirect
support to Zollman and Smead because the examples that they explore qualify—
according to our own standards—for Baldwinian status. On the other hand, Zollman
and Smead lend support to our hypothesis by showing that their cases of
Baldwinization also satisfy the conditions of asymptotic stability present in our
analysis. If there is a role for evolutionary game-theoretic analysis of the Baldwin
effect, this kind of complementarity and theoretical integration must be much
welcomed.
To sum up: the findings of Sects. 6 and 7 show that the positive frequency
dependency is neither a necessary nor a sufficient condition for evolutionary
stability. Consequently, it is a poor guide for possible sources of Baldwinization.
8 Conclusion
It is time to close this paper summarizing the main conclusions. The Baldwin effect
has been regarded with some skepticism. We have attempted to remove at least
Table 2 Positive frequency
dependent behavior that is not
evolutionary stable
S1 S2
S1 (3, 3) (2, 4)
S2 (4, 2) (1, 1)
A Game-Theoretic Analysis of the Baldwin Effect 47
123
some of the reasons underlying this assessment. To this intent, we clarified the
different hypotheses concerning the Baldwin effect, and we provided a game-
theoretic perspective specifying the enabling conditions for Baldwinization. We
argued that the game-theoretic framework captures prototypic examples of
Baldwinization that would be otherwise difficult to taxonomize.
To begin with, we considered Watkins’ challenge to the feasibility of the
Baldwin effect. We argued that Watkins’ analysis is flawed due to an incorrect
assessment of the conditional probabilities involved in the Baldwin effect. We
contended that the crucial condition required by the Baldwin effect is that the
corresponding genetic mutations facilitate the adoption of adaptive behavior, and
not—as suggested by Watkins—that the learnt behavior increases the propensity of
the facilitating mutations. Furthermore, we explored the explanatory relevance
argument advocated by Papineau, and we distinguished it from likelihood
arguments. We finally undertook a systematic analysis of the positive frequency
account, which is a paradigmatic example of likelihood argument (Deacon 1997;
Godfrey-Smith 2003).
We have made the case for the use of an evolutionary game theoretic framework.
We claimed that this account is capable of providing bold insights as to the
plausibility of certain dynamics. This has allowed us to clarify the factors enabling
Baldwinization and to show that the focus on positive frequency dependence as an
explanatory framework fails to capture prototypic cases of Baldwinization. We
contended that interactions, whose asymptotic stable states involve a dominant
phenotype, provide paradigmatic grounds for Baldwinization, especially when the
equilibrium is Pareto optimal. Furthermore, we showed that these factors apply even
in the presence of negative frequency dependence. Asymptotic stability turns out to
be a pre-condition for the completion of Baldwinian processes and therefore, we do
not expect this effect to occur in the case of phenotypes that may be adaptive but
which are not asymptotically stable.
Acknowledgments We had the opportunity to discuss some of the issues explored in this paper with
different scholars in congresses and seminars. We would like to thank Pablo Abitbol, Nicolas Claidiere
Till Grune-Yanoff, Tommi Kokkonen, Jaakko Kuorikoski, Jason Alexander Mackenzie, David Papineau,
Dan Sperber, and Petri Ylikoski as well as two reviewers of Erkenntnis for their stimulating objections
and comments. None of them should be held responsible for the ideas advocated here.
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