The purpose of adaptation

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Research

Cite this article: Gardner A. 2017 The

purpose of adaptation. Interface Focus 7:

20170005.

http://dx.doi.org/10.1098/rsfs.2017 .0005

One contribution of 20 to a theme issue ‘New

trends in evolutionary biology: biological,

philosophical and social science perspectives’.

Subject Areas:

biomathematics

Keywords:

natural selection, fundamental theorem,

Darwinism, inclusive fitness, socia l evolution,

superorganism

Author for correspondence:

Andy Gardner

e-mail: andy.gardner@st-andrews.ac.uk

The purpose of adaptation

Andy Gardner

School of Biology, University of St Andrews, Dyers Brae, St Andrews KY16 9TH, UK

AG, 0000-0002-1304-3734

A central feature of Darwin’s theory of natural selection is that it explains the

purpose of biological adaptation. Here, I: emphasize the scientific impor-

tance of understanding what adaptations are for, in terms of facilitating

the derivation of empirically testable predictions; discuss the population

genetical basis for Darwin’s theory of the purpose of adaptation, with refer-

ence to Fisher’s ‘fundamental theorem of natural selection’; and show that a

deeper understanding of the purpose of adaptation is achieved in the context

of social evolution, with reference to inclusive fitness and superorganisms.

1. The purpose of adaptation

Darwinism is a theory of the process of adaptation, i.e. the appearance of design

in the biological world. The problem of how to explain adaptation is an ancient

one, and it famously provided the basis for William Paley’s [ 1] argument for

the existence of an intelligent, divine designer. This problem was decisively

solved by Charles Darwin [2], whose theory of evolution by natural selec-

tion—in which heritable variations associated with greater survival and

reproductive success are identified as being more likely to accumulate in natural

populations—explained the adaptation of organisms in purely naturalistic,

mechanical terms.

Darwinism is also a theory of the purpose of adaptation, i.e. the design

objective of biological organisms. Darwin argued that, as a consequence of

natural selection preferentially retaining those heritable variations associated

with greater survival and reproductive success, organisms will appear as if

they are designed to maximize their survival and reproductive success—that

is, their Darwinian fitness.

Indeed, Darwinism is the only scientific theory of the purpose of adaptation.

While some continue to maintain that mystical forces—such as external, divine

interv entions or internal, vitalis tic driv es—ar e responsible for adaptation, none

of these hypotheses yield clearly justified, testable predictions as to what the result-

ing adaptation is actually for (table 1). The question of purpose is often dodged, or

else a purpose is asserted without clear justification. Strangely, whereas one might

expect different drivers of adaptation to be associated with different design objec-

tives, those who dispute natur al selection’s role in biological adaptation often

nevertheless regard organisms as striving to maximize their Darwinian fitness.

For example, anti-Darwinis t James Shapiro [3, p. 137] views organisms as vitalistic

beings that inexplicab ly strive to maximize their ’survival, gro wth and repr oduc-

tion’ for reasons that hav e nothing to do with the action of natur al selection.

The idea of adaptive purpose does not imply that the design objective is

perfectly realized. Paley [1] emphasized that the hallmark of design is not per-

fection but rather that an organism’s or organ’s apparent purposiveness is

evident from its adaptive complexity, or ‘contrivance and relation of parts’.

Comparing organisms and their component parts to human artefacts like

pocket watches, he noted that even a broken watch manifests purposiveness

in its intricate design. However, Paley—and Darwin after him—marvelled at

how, in practice, nature abounds with exquisite adaptation that seems to

border upon perfection.

In recognition of the distinction between purposefulness and perfection,

it is useful to separate adaptationism into weak versus strong forms [4].

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Weak adaptationism is the idea that organisms manifest

apparent design and purpose, on account of the action of

natural selection. Weak adaptationism makes no commit-

ment to the idea of perfection, and recognizes that multiple

forces in addition to natural selection—such as spontaneous

mutation and random drift—contribute to the evolutionary

process in an often deleterious way. By contrast, strong adap-

tationism is a caricature of Darwinism in which organisms

are regarded as entirely optimal in their form and their be-

haviour. As a scientific hypothesis, strong adaptation is

trivially falsified by empirical observation.

Yet, strong adaptationism is the central conceit of a hugely

successful programme of scientific research, based upon optim-

ization theory [5]. Practitioners of the optimiza tion approach

consider wha t organisms would be like if they were optimally

fitted to the particular circums tances and challenges of their

environment, and thereby deriv e predictions that although

acknowledged to be only approximate are nevertheless, in

practice, often useful ones. Indeed, when there is a marked dis-

crepancy between prediction and empirical observation, this

usually means that a key aspect of the organism’s biology

has not been properly understood and remains to be incorpor-

ated into the optimiza tion model. Accordingly , by an itera tiv e

process of model adjustment, testable prediction and empirical

test, the optimiza tion approach pro vides an investiga tiv e tool

by which scientists learn how the biological world works.

The optimization approach is made possible only because

Darwinism yields such a clear prediction as to what biologi-

cal adaptation is actually for. Without knowing what

organisms are designed to do, it would be impossible to

decide which of a range of possible phenotypes represents

the optimum. This point clarifies why typical critiques of

the adaptationist research programme are misguided: the

perennial complaint that adaptationists fail to consider

‘other hypotheses’—for instance, that organisms may be to

some degree maladapted [6]—mistakes adaptationism for a

hypothesis when it is actually a research method. The mala-

daptation view is strictly correct but also completely useless

if it does not yield specific, testable predictions. And it is det-

rimental to scientific progress if it obstructs the application of

the successful adaptationist approach (cf. [7]).

2. The population genetics of purpose

The formal basis for evolutionary theory is the domain of

theoretical population genetics. Accordingly, it is proper

that Darwin’s theory of the purpose of adaptation be

framed in genetical terms. This was accomplished by

Ronald Fisher [8,9], with what he termed the ‘fundamental

theorem of natural selection’ (box 1). Fisher’s theorem pro-

vides a formal foundation for the view that natural

selection leads organisms to maximize their fitness—in the

sense that it will appear as if this is their purpose, rather

than in the sense that they will necessarily perfectly realize

this goal—and he rightly regarded it as taking centre stage

in his masterpiece The genetical theory of natural selection [8].

But it has had a turbulent history.

Fisher’s clearest verbal statement of the fundamental

theorem is: the increase of average fitness of the population ascrib-

able to natural selection is equal to the genetic variance of fitness

[9]. The salient point here is that, as variances are non-

negative, there is a fundamental directionality to the action

of natur al selection, alway s pointing in the direction of increased

fitness. That is, Fisher’s theorem describes the optimizing quality

of natural selection.

Despite Fisher’s clear focus on the immediate action of

natural selection, the fundamental theorem has long been

interpreted as a statement about the total change in the popu-

lation’s fitness from one generation to the next. The idea that

this would always increase was at first uncritically accepted

and then, decades later, suddenly rejected when simple

mathematical models revealed that population fitness is

capable of decreasing from generation to generation [13].

This led to a widely held view that the fundamental theorem

is not generally correct and—more damagingly—that any

notion of fitness maximization, or of there being a clear

purpose to Darwinian adaptation, is embarrassingly naive.

With regard to its correctness, George Price’s [14] careful

exposition of Fisher’s derivation established that the fundamen-

tal theor em is indeed mathematically sound (box 1). Price

clarified that the fundamental theorem concerns only the part

of change in av er age fitness across the individuals in the popu-

lation that is due to the action of natur al selection per se and not

to other, non-Darwinian changes that Fisher [8] referred to col-

lectively as deterioration of the environment. Figure 1 provides an

illustr ation of which parts of the evolutionary change in av er-

age fitness ar e ascribed by Fisher to the action of natur al

selection versus environmental deterioration.

Price admitted to being disappointed that this partial

result ‘does not say more’—presumably feeling that a descrip-

tion of the entirety of evolutionary change in population

fitness would be preferable. However, it is precisely because

the fundamental theorem is a partial result that it is so impor-

tant [15]. In isolating the part of the evolutionary process

responsible for adaptation—that is, natural selection—the fun-

damental theorem illuminates what is being adapted (the

individual) and for what purpose (maximizing her fitness).

Those individuals who achieve higher fitness are those

whose heritable constitutions will predominate in future gen-

erations, and accordingly it is these individuals who point out

the direction of the population’s evolutionary future.

For example, in the scenario depicted in figure 1, individ-

uals vary in their level of selfishness, with relatively selfish

individuals having relatively higher fitness and relatively

selfless individuals having relatively lower fitness, in com-

parison with their peers. Accordingly, the fitness-

maximizing quality of natural selection leads to an increase

in selfishness—as this is what directly increases the individ-

ual’s fitness. (A secondary consequence is that all

genotypes suffer reduced fitness on account of their carriers’

social partners now having a greater tendency to behave self-

ishly, and this deterioration in the social environment results

in a net decrease in average fitness.) That is, the idea that indi-

viduals strive to maximize their fitness correctly predicts the

direction of evolutionary change.

It is not clear why a mathematical account of the total

change in population fitness would be of much interest

Table 1. Darwinism is the only scientiﬁc (i.e. predictive) theory of the

purpose of adaptation.

Darwinism intelligent design, etc.

process natural selection divine intervention, etc.

purpose maximize ﬁtness ?

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anyway. The relationship between population composition

and population fitness does not point out the direction of

the future. For example, in the above scenario, a population

in which selflessness predominates enjoys greater fitness, but

evolutionary change proceeds in the exact opposite direction:

increased selfishness. This recovers the population geneticists’

discovery that population fitness is not maximized [13], and

makes clear that what they had rejected was not—as they

had supposed—the idea that fitness is maximized, but rather

the idea that adaptation works ‘for the good of the species’.

3. The purpose of social adaptation

The personal-fitness-maximization design principle emerging

from Fisher’s fundamental theorem is not a fully general

result. It may fail when social interactions occur between gen-

etic relatives. The application of the fundamental theorem to

social evolution serves to underline how Fisher intended the

theorem to be understood and yields deeper insights into the

purpose of adaptation.

In the absence of social interaction between genetic rela-

tives—including, for example, the model of selfishness

presented above—any correlation between an individual’s

genotype and her fitness may be taken to reflect a direct,

causal relationship

(figure 2a). That is, if an individual’s heri-

table constitution is associated with higher fitness, this is

because it actually increases her fitness. Accordingly, on

account of natural selection favouring those traits that are

associated with higher fitness, individuals will appear

designed to maximize their fitness.

Box 1. Fundamental theorem of natural selection.

Price’s equation—In very general terms, evolutionary change can be expressed as a sum of selection and transmission

components. This is captured by Price’s [10,11] equation, based upon a general mapping between two populations of

entities. Typically, one of these populations is descended from the other, and they are denoted ’parents’ and ’offspring’,

respectively.

To derive Price’s equation, assign every individual in the parent population a unique index i [ I and assign indices to

every individual in the offspring population according to which parent individual they are descended from. When a

given individual in the offspring population has more than one ancestor in the parent population (as in a sexual population),

each ancestor is awarded its genetic share of the offspring. Denote the relative abundance of the ith parent as q

, where

¼ 1. Typically, q

¼ 1/N, where N is the number of individuals in the parent population. Similarly, denote the relative

abundance of the ith parent’s descendants in the offspring population as q

. This allows a definition of the relative fitness of

any individual in the parent population as w

¼ q

. Finally, assign each individual in the parent population a value z

for

any character of interest, and denote the average character value of their offspring as z

¼ z

þ Dz

. The average character

value over the parent and offspring populations is E(z) ¼

and E(z

) ¼

, respectively. Hence, the change in

the population average value of the character of interest is DE(z) ¼ E(z

) 2 E(z), which may be re-written as:

DEðzÞ¼covðw, zÞþEðwDzÞ, ðB1:1Þ

where: cov denotes a covariance and E an expectation, each taken over the set of all individuals in the population. The covari-

ance term describes the change ascribed to the statistical association between an individual’s character and its relative fitness,

and defines selection. The expectation term describes the change ascribed to character differences between a parent and her

offspring, and defines changes associated with transmission.

Natural selection is a particular type of selection that involves genes, the fundamental units of heredity. Here, the char-

acter of interest is not an individual’s phenotype per se, but rather her (additive) genetic value for any phenotypic character of

interest, i.e. the heritable portion of her phenotype [10,12]. Moreover, change is defined across a single generation. Denoting

the genetic value by g

, the action of natural selection is given by

EðgÞ¼covðw, gÞ: ðB1:2Þ

That is, the change in the average value of the heritable character ascribed to the action of natural selection is equal to the

statistical covariance of that character and relative fitness, across all the individuals in the population. Importantly, equation

(B 1.2) describes the action of natural selection only, and not the entirety of evolutionary change.

Without loss of generality, this may be re-written as

EðgÞ¼

ðw, gÞ varðgÞ, ðB1:3Þ

where var(g) is the heritable variance in the character of interest and

(w, g) ¼ cov(w, g)/var(g) is the least-squares linear

regression of relative fitness against the heritable character. This form of Price’s equation highlights the basic Darwinian

logic that natural selection will act to drive change in the heritable constitution of the population (D

E(g) = 0) if and

only if there is heritable variation (var(g) . 0) in a character that is associated with individual fitness (

(w, g) = 0).

Fundamental theorem—If the character of interest is taken to be fitne ss itself, then this may be decomposed into its gen-

etical and e nvironmental components, w ¼ g þ e.Itfollowsthat

(w, g) ¼ 1,andsubstitutingthisintoequation(B1.3)

obtains:

EðgÞ¼varðgÞ: ðB1:4Þ

That is, the increase in average fitness ascribed to natural selection is equal to the genetic variance in fitness.

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By contrast, if genetic relatives interact, then any corre-

lation between an individual’s genotype and her fitn ess

may i nstead be due to her genotype being correlated with

that of her social p artner, and her social partner’s geno-

type mo dulating her own fitness (figure 2b). That is, an

individual’s heritable consti tution might be a ssociated

with higher fitness—and hence favoured by natural selec-

tion—even if it actually direct ly decreases her fitness.

Accordingly, natural selection need not lead the individ ual

to appear designed to maximize her person al fitness.

To be clear, social interaction between genetic relatives

does not invalidate the fundamental theorem (the increase

of average fitness of the population ascribable to natural

selection is equal to the genetic variance of fitness, irrespec-

tive of social interaction between relatives; box 1). It merely

prevents the fitness-maximization design interpretation

from being drawn. So it is revealing that Fisher felt it

necessary to assume the absence of social interaction between

genetic relatives

in his prelude to the fundamental theorem.

That Fisher made this assumption indicates that he, too,

drew the fitness-maximization design interpretation from

his theorem.

Does this correlation–causation difficulty mean that

natural selection is not responsible for organismal design

in the context of social interaction between genetic relatives?

Fortunately, this is not the case. The fund amental theorem

may be reformu lated using an alternative fitness

measure—inclusive fitness—which is defined by subtracting

from the ind ividual’s personal fitness all fitness effects due

to the actions of her social partners, and adding all the fitness

effects experienced by the focal individual’s social partners

as a c onsequence of her own actions, each increment or

decrement being weighted by the focal individual’s genetic

relatedness to the corresponding recipient (box 2; figure 2c;

individual level of selfishness

natural

selection

individual fitness

average

fitness

average

fitness

average

fitness

deterioration of

the environment

individual level of selfishness individual level of selfishness

Figure 1. Change in average fitness ascribed to natural selection versus deterioration of the environment. In this example, each individual achieves a higher fitness if

she behaves selfishly. Natural selection favours the fittest—i.e. most selfish—individuals, and the direct effect of this is to increase average fitness. However, the

consequent deterioration of the social environment—owing to an increased average level of selfishness—leads individuals of all genotypes to have reduced fitness.

The net effect is that average fitness decreases from one generation to the next.

–C

(b) personal fitness (social)(a) personal fitness (non-social) (c) inclusive fitness (social)

Figure 2. Personal fitness and inclusive fitness. (a) In the absence of social interaction between genetic relatives, the correlation between an individual’s genotype

and her personal fitness reflects the direct causal impact of her genotype on her personal fitness (2C ). (b) In the context of social interaction between genetic

relatives, the correlation between an individual’s genotype and her personal fitness reflects the direct causal impact of her genotype on her personal fitness (2C )

plus the correlation between her genotype and her social partner’s genotype (r) multiplied by the causal impact of her social partner’s genotype on her own

personal fitness (þ B). (c) In the context of social interaction between genetic relatives, the correlation between an individual’s genotype and her inclusive fitness

reflects the direct causal impact of her genotype on her personal fitness (2C) plus the causal impact of her genotype on her social partner’s personal fitness (þB)

multiplied by the relatedness valuation (r) she places upon her social partner’s fitness.

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[19]). That is, the fundamental theorem may be alternatively

expressed as: the change in average inclusive fitness ascribed to

the action of natural selection is equal to the genetic varianc e in

inclus ive fitness (box 2; cf. [20]).

By virtue of its definition, inclusive fitness is under the

individual’s full control, such that the correlation between

an individual’s genotype and her inclusive fitness reflects a

direct causal relationship. Accordingly, as a consequence of

the action of natural selection the individual appears

designed to maximize her inclusive fitness.

Though Darwinian ada ptation is conventionally viewed

as occurring at t he level of the individual organism, recent

years have s een growin g i nterest in the idea that whole

social groups may be viewed as ‘superorganisms’ in their

own right, wielding their own adaptations for their own

purposes. In some cases, this is simply a return to

the woolly thinking of the first half of the twentieth

century, w hen many biologists unreflectively regarded

natural selection as always working for the good of the

group or species. However, in other cases, there is a legiti-

mate recognition that—on rare, but i mportant, occasions—

groups of socially interacting individuals have undergone

a major transition in indivi duality, such as the transition

from unicellular to multicellular life, and from cooperative

breeding to eusociality [21,22].

The fundamental theorem approach may be brought to

bear on this question of group-level adaptation. Specifically,

the action of natural selection may be decomposed into the

component operating at the within-group level and the com-

ponent operating at the between-group level, and in taking

group fitness itself to be the character of focal interest a fun-

damental theorem of multi-level selection emerges that states:

the change in average group fitness owing to the action of natural

selection is equal to the genetic variance in group fitness if and

only if there is no selection within groups (box 3; [24]). This

result clarifies why certain animal groups—like the Portu-

guese man-of-war, a jellyfish-like colony of clonally related

zooids, within which there is essentially no genetic variation

and hence no scope for within-colony selection—can be con-

sidered adapted superorganisms in their own right, but most

animal groups—within which there is scope for conflict as

well as collaboration—cannot.

Box 2. Kin selection and inclusive fitness.

Kin selection—On the assumption that there is heritable variation in a focal character (var(g) . 0) then, from box 1 equation

(B 1.3), natural selection will act to increase the average value of this character (D

E(g) . 0) if and only if the character is

positively associated with individual fitness (

(w, g) . 0). There are two ways for a heritable character to be associated

with greater personal fitness: first, the character may directly improve the individual’s fitness (direct fitness benefit); and,

second, the character may be present among the individual’s social partners, such that its expression increases the individ-

ual’s fitness (indirect fitness benefit). Using the mathematics of multiple least-squares regression, this may be expressed as:

ðw, gÞ¼

ðw, g j g

Þþ

ðw, g

j gÞ

ðg

, gÞ, ðB2:1Þ

where

(w, g j g

) ¼ 2C is the effect of the individual’s own heritable character g upon her own fitness w, holding fixed the

heritable character of her social partner g

;

(w, g

j g) ¼ B is the effect of the individual’s social partner’s heritable character g

upon her own fitness w, holding fixed her own heritable character g; and

, g) ¼ r is the statistical association between

these social partners’ heritable characters (i.e. the kin-selection coefficient of genetic relatedness; [18]). For simplicity, equation

(B 2.1) assumes that the focal individual has only a single social partner, but the approach readily extends to scenarios in

which the focal individual has multiple social partners.

Accordingly, the condition for natural selection to favour an increase in the average value of the heritable character

(

(w, g) . 0) is 2C þ Br . 0, i.e. Hamilton’s [19] rule of kin selection, expressed here in its personal fitness (or ‘neigh-

bour-modulated fitness’) form.

Inclusive fitness—Noting that the statistical aggregate impact of social partners on the fitness of individuals within a

population is identical to the statistical aggregate impact of individuals upon their social partners in that population (i.e.

(w, g

j g) ¼

, g j g

), where w

denotes the relative fitness of an individual’s social partner), the kin selection partition

of natural selection into its direct and indirect components may alternatively be expressed in its inclusive fitness form:

ðw, gÞ¼

ðw, g j g

Þþ

ðw

, g j g

ðg

, gÞ: ðB2:2Þ

With some algebra, the action of natural selection can be expressed as:

EðgÞ¼covðh, gÞ¼

ðh, gÞvarðgÞ, ðB2:3Þ

where h ¼

(w, g j g

)g þ

, g j g

)

, g)g is the focal individual’s inclusive fitness, i.e. the sum of her heritable character’s

impact on her personal fitness and also on the personal fitness of her social partner, the latter being weighted by the degree of

genetic relatedness between the two parties [19].

Fundamental theorem—If the character of interest is taken to be inclusive fitness itself, then this may be decomposed into its

genetical and environmental components, h ¼ g þ e. It follows that

(h, g) ¼ 1, and substituting this into equation (B 2.3)

obtains

EðgÞ¼varðgÞ: ðB2:4Þ

That is, the increase in average inclusive fitness ascribed to natural selection is equal to the genetic variance in inclusive

fitness (cf. [20]).

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4. Conclusion

Explaining the purpose of adaptation is a central achievement

of Darwinism. Being able to predict what it is that organisms

are striving to achieve not only sets Darwinism apart from

intelligent design and other forms of mysticism, but also sets

the hugely successful adaptationist research programme

apart from scientifically sterile anti-adaptationist thinking

within evolutionary biology. Getting to grips with the purpose

of adaptation is especially important in the context of social

evolution, where different biological agents are expected to

have different, conflicting purposes, and where naive notions

of group-level adaptation are liable to be strongly misleading.

Happily, there is a maturing body of formal theory that equips

the evolutionary biologist with the tools required to navigate

these issues and to break new Darwinian ground.

Data accessibility.

This article has no additional data.

Competing interests. I declare I have no competing interests.

Funding. I am supported by an Independent Research Fellowship

awarded by the Natural Environment Research Council (NE/

K009524/1).

Acknowledgement. I thank Steven Frank and two anonymous reviewers

for helpful comments and discussion.

Endnotes

In full: ‘The increase of average fitness of the population ascribable

to a change in gene frequency dp will be 2

dp. Hence the rate of

increase in the average value of the Malthusian parameter ascribable

to natural selection acting on a single factor is 2pqa

, and the rate of

increase due to all factors will be 2

pqa

, equal to the genetic var-

iance of fitness due to all factors’ [9].

Spurious correlations between genotype and fitness may be classi-

fied as owing to chance (in which case, they may be removed by

defining fitness in terms of an expectation taken over uncertainty;

[16]) or to class (which is explicitly controlled for in Fisher’s [8] treat-

ment, but neglected here for simplicity; see also Price & Smith [17]).

‘There will also, no doubt, be indirect effects in cases in which an

animal favours or impedes the survival or reproduction of its rela-

tives; as a suckling mother assists the survival of her child, as in

mankind a mother past bearing may greatly promote the reproduc-

tion of her children, as a foetus and in less measure a sucking child

inhibits conception, and most strikingly of all as in the services of

neuter insects to their queen. Nevertheless such indirect effects will

in very many cases be unimportant compared to the effects of

personal reproduction’ [8, p. 27].

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Box 3. Fundamental theorem of multi-level selection.

Multi-level selection—In a group-structured population, the action of natural selection may alternatively be separated into its

between-group and within-group components:

ðg

Þ¼cov

ðw

, g

ÞþE

ðcov

ðw

, g

ÞÞ, ðB3:1Þ

where I have assigned every group a unique index j [ J; and, within a given group, I have assigned every individual a

unique index k [ K. The first term on the r.h.s. defines between-group selection and the second term on the r.h.s. defines

within-group selection [11,23].

Fundamental theorem—If the character of interest is taken to be group fitness itself, then this may be decomposed into its gen-

etical and environmental components, w

¼ g

þ e

. It follows that

, g

) ¼ 1, and hence cov

, g

) ¼

, g

)

var

) ¼ var

), and substituting this into equation (B 3.1) obtains

ðg

Þ¼var

ðg

Þ iff E

ðcov

ðw

, g

ÞÞ ¼ 0: ðB3:2Þ

That is, the increase in average group fitness ascribed to natural selection is equal to the genetic variance in group fitness

if and only if within-group selection is absent [24].

rsfs.royalsocietypublishing.org Interface Focus 7: 20170005

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20. Bijma P. 2010 Fisher’s fundamental theorem of

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ry E. 1995 The major

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Oxford, UK: Oxford University Press.

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anthropology (ed. R Fox), pp 133–155. New York, NY:

Wiley.

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jeb.12566)

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