A Game-Theoretic Analysis of the Baldwin Effect

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]

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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

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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

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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.


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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


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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.


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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.


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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


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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.


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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


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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


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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


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.


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.


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).


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.


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)


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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A Game-Theoretic Analysis of the Baldwin Effect

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