Brit. J. Phil. Sci. 55 (2004), 347–363, axh208

The Confusions of Fitness
André Ariew and R. C. Lewontin

ABSTRACT

The central point of this essay is to demonstrate the incommensurability of ‘Darwinian

fitness’ with the numeric values associated with reproductive rates used in population

genetics. While sometimes both are called ‘fitness’, they are distinct concepts coming

from distinct explanatory schemes. Further, we try to outline a possible answer to the

following question: from the natural properties of organisms and a knowledge of their

environment, can we construct an algorithm for a particular kind of organismic life-

history pattern that itself will allow us to predict whether a type in the population will

increase or decrease relative to other types?

1 Introduction

2 Darwinian fitness

3 Reproductive fitness and genetical models of evolution

4 The models of reproductive fitness

4.1 The Standard Viability Model

4.2 Frequency-dependent selection

4.3 Fertility models

4.4 Overlapping generations

5 Fitness as outcome

5.1 Fitness as actual increase in type

5.2 Fitness as expected increase in type

5.2.1 Expected increase within a generation

5.2.2 Expected increase between generations

5.2.3 Postponed reproductive fitness effects

6 The book-keeping problem

7 Conclusion

1 Introduction

No concept in evolutionary biology has been more confusing and has pro-

duced such a rich philosophical literature as that of fitness. The confusions

have arisen because a concept, originally introduced as an inexact metaphor

by Darwin, has come to play an analytic role in the formal quantitative

dynamics of evolutionary biology. The confusion has arisen from the mis-

taken belief that a single coherent definition of fitness is required by, and can

# British Society for the Philosophy of Science 2004



be applied over, all dynamics of evolutionary genetics. There is a conviction

among philosophers and biologists that somehow a property of fitness must be

included in dynamical explanations of evolution through natural selection.

Our purpose in this essay is to show that:

(1) The concept of ‘fit’ as introduced by Darwin in both the explanandum and

the explanans of his theory does not appear in quantitative dynamical theories

of genetic change in evolution.

(2) Any attempt to introduce a unitary analogous concept of ‘reproductive

fitness’ into dynamical models as a scalar ordinal, which will explain or predict

quantitative changes in the frequency of types, must fail.

(3) This failure is a consequence of the fact that, in different biological situa-

tions, different algorithms must be used to connect temporal changes in type

frequencies with quantitative information about reproduction, and that in an

important fraction of cases, even complete information on relative reproduc-

tive rates is insufficient to determine whether a type will increase or decrease

relative to others in the population.

(4) Finally, we discuss the central role played by the convention of counting

individuals in algorithms that allow prediction of evolutionary changes in

population composition.

2 Darwinian fitness

The concept of fitness for Darwin (he did not actually use the term ‘fitness’, but

did refer to individual organisms as being ‘fitter’, or more or less ‘fit’ than other

individuals) arose from his view of organism and environment. The essence of

Darwinism was the rupture between the causes of the properties of individual

living beings and the causes of the structure of the world they occupied. The

natural properties of individual organisms varied from individual to individual

within a species, and the sources of that variation were internal to the ontogeny

of the organism. At the same time, the organisms lived in an external world—

the environment—whose structure was causally independent of those organ-

isms. Different individual members of a species, then, ‘fit’ into the environment

to different degrees as a consequence of their variant natural properties, and

those that made the best ‘fit’ would survive and reproduce their kind better

than those whose ‘fit’ was poorer. The word ‘fit’ (‘fittest’, ‘fitness’) is a meta-

phorical extension of its everyday English meaning as the degree to which an

object (the organism) matches a pattern that is pre-existent and independently

determined (the environment). This metaphorical lock-and-key fitting of the

organism into the environment is reflected in the modern concept in ecology of

the environmental or ecological ‘niche’ that species are said to ‘occupy’.

348 André Ariew and R. C. Lewontin



In the original Darwinian structure, fitness is a derived property of the

natural properties of individuals living in a particular juxtaposition to the

structure of the environment. The characteristic Darwinian adaptive explana-

tion is a kind of engineering analysis in which particular natural properties of

individual organisms were shown to lead to greater expected reproduction by

those individuals in particular environments. This is the project of the

so-called ‘Ecological geneticists’. There is the implication that the qualitatively

diverse natural properties of organisms could be mapped, as a function of the

environment, onto a single ordinal variable, so that one organism can be said

to be more or less ‘fit’ than another even when the mediating natural proper-

ties are qualitatively different. In this explanatory scheme, the property of

fitness plays an ambiguous role, appearing both in the explanandum and in the

explanans. What is to be explained is the origin of the marvelous fit between

the natural properties of the individuals that make up a species and the

ecological niche that they occupy. The explanans is that:

(1) in a previously less fit species, an occasional variant individual arises whose

natural properties make it more fit to the environment;

(2) the variant natural properties are heritable;

(3) a consequence of the greater fit is a higher reproductive rate of the variant

individual, which, together with (2), results in:

(4) an increase in the representation of the more fit natural properties among

individuals of the species in future generations. This ‘Darwinian’ explanatory

structure can be schematized as:

(A) natural properties ! fitness to environment ! reproductive rates !
changes in representation in the population

The classic example of the use of this schema for an observed temporal

change is the attempt by Ford and Kettlewell to explain the increase in

the melanic form of the moth, Biston betularia, since the nineteenth century

(cf. Ford [1971]). A more recent and more detailed case is the study of changes

in body and bill shape over a 30-year period in two of Darwin’s Finches,

Geospiza fortis and G. scandens (cf. Grant and Grant [2002]).

What is consequential about this Darwinian explanation for the present

confusion about fitness is that the dynamic of the explanans does not, in fact,

depend on fitness, unless the explanandum also involves fitness. That is, if what

is to be explained is the greater (metaphorical) fitness of evolved species, then a

connection is required between (metaphorical) fitness of variant individuals

and their reproductive properties. But suppose what is to be explained is

simply the evolutionary change in the natural properties of species over time,

without reference to any claim about their ‘fit’ to the environment as in schema

The Confusions of Fitness 349



(A)? Then all that is needed in the explanans is that individuals with variant

natural properties appear, that these properties are heritable, and that they are

associated with higher reproductive rates, without any recourse to the notion

of ‘fit’ to the environment. This is the explanatory scheme for many genetical

models of evolution. To the extent that an engineering story is demanded, it is

that there be some mechanical connection between the variant natural proper-

ties whose evolution is being followed and the special set of natural properties

that constitute reproductive rate. That mechanical connection may be a nat-

ural historical one involving the ‘fit’ to environmental demands, as in schema

(A), but it may equally well involve purely internal physiological, morpho-

logical and molecular relationships or genetic correlations. Indeed, the ‘fit’ to

the external world of the favored variant may be significantly poorer. For

example, as we discuss below, in a species with overlapping generations, if the

population is decreasing in numbers, those types that reach reproductive age

late will increase in the population. Yet this retarded development may be a

consequence of poorer ability to gather the resources necessary for develop-

ment. Hence, a trait’s properties may be less ‘fit’ to the demands of the

environment but increase in the population nevertheless.

The present confusion over the concept of ‘fitness’ in evolutionary biology

has been the consequence of the attempt to find a general attribute, analogous

to Darwinian ecological fitness, that will appear in both explanandum and

explanans of evolutionary scenarios independently of any claim about ecology

and, indeed, without the requirement of an engineering story at any level. This

is the genesis of the concept of ‘reproductive fitness’ found in modern genetical

models of evolution. In the Darwinian theory of natural selection, the natural

properties of individuals are the causes of the fitness to the environment, and

the fitness to the environment is the cause of reproductive success. In the

genetical theory of evolution, the reproductive success of an individual

appears as a primary property, and a new kind of formal fitness, ‘reproductive

fitness’, is introduced. This is intended to be a scalar quantity that can be

calculated from information on reproduction and which then predicts changes

in the representation of types, without the necessity of connecting these

reproductive fitnesses to any other natural properties of the organisms.

The schema for this explanatory structure is:

(B) natural properties ! reproductive rates ! ‘reproductive fitness’ !
changes in representation in the population

3 Reproductive fitness and genetical models of evolution

With the rediscovery of the Mendelian principles of inheritance, including the

lack of a one-to-one correspondence between genotype and phenotype, and

the development of knowledge of the chromosomal basis for the statistical

350 André Ariew and R. C. Lewontin



properties of inheritance patterns during the first quarter of the 20
th

century, it

became apparent that the Darwinian outline of evolution was incomplete,

especially in its reliance on a simple resemblance of parent to offspring. The

result was the development of current, specifically genetical, theories of evolu-

tion under natural selection, theories that have essentially no natural historical

elements or even internal causal narratives (with the exception of genetic

mechanisms) and in which Darwinian ‘fit’ plays no role. These theoretical

structures, developed in R. A. Fisher’s ‘The Genetical Theory of Natural

Selection’ ([1930]), J. B. S. Haldane’s ‘The Causes of Evolution’ ([1932]),

and S. Wright’s ‘Evolution in Mendelian Populations’ ([1932]), provide the

model for modern evolutionary genetics. They have the following common

features:

(1) Population composition is characterized by the relative frequencies of

various genotypic or phenotypic classes; that is, by the numerosity of different

types. This particular form of book-keeping will turn out to be critical to the

general problem of fitness.

(2) Reproductive fitnesses (the exact term varies) are assigned to types, not

tokens. These fitnesses are the means (statistical expectations) of quantities

calculable from the details of reproductive performances of tokens, which vary

around the type mean as a consequence of accident, variation in environment,

and the segregation of other genes not included in the type definition. The way

in which reproductively relevant properties are used to calculate fitnesses also

turns out to be critical to the problem of fitness.

(3) ‘Evolution’ is described as a change in the relative frequency of the

classes over time. These changes are a consequence of reproductive fitness

differences, of mutations, of migrations. Account may or may not be taken of

the realized variation of these factors around their expectations from genera-

tion to generation and population to population.

(4) Alternatively, evolution may be described as a change in the population

mean reproductive fitness, averaged over all types (for recent discussions on

the difference between Darwinian fitness and statistical fitness, see Sober

[2001]; Matthen and Ariew [2002]; Walsh, Lewens and Ariew [2002]). The

explanation is then of the form:

(C) reproductive rates ! reproductive fitness ! change in representation of
types.

As we shall see, despite the attempt of these genetical theories of natural

selection to create a general abstract structure in which ecological and demo-

graphic details are irrelevant, no such structure is possible and no model-

independent measure of reproductive fitness can be derived (for a similar view

see Rosenberg [in preparation]). Indeed, in most cases the details of the

The Confusions of Fitness 351



reproductive performance of a type cannot be mapped onto any scalar

variable.

It is important to realize that the motivation for the genetical theory of

evolution is the failure of the Darwinian scheme to explain and predict the

direction of change of a population solely from the natural properties of

organisms and their environments. That failure is a result of the extra con-

siderations required to predict evolution which are the consequence of the

mechanisms of inheritance and the details of reproductive schedules. For

Darwin, without knowledge of the mechanical details of heredity, it seemed

clear that a type that left more offspring in the next generation would increase

in representation in the population. But there are two complications. First, the

segregation and recombination of genes in sexually-reproducing organisms

has the effect that the rate of reproduction by a genetic type is not the same as

the rate of reproduction of a genetic type. Second, for organisms with con-

tinuous reproduction and overlapping generations, the age at which a type

produces offspring is as consequential for changes in population composition

as is the total number of offspring produced by each type. Since these genetic

and demographic relationships vary from species to species, different algo-

rithms are required to connect information about reproduction of different

types with information about direction of change for populations, as discussed

in the next section.

The confusion about fitness is the result of ignoring the fact that a type’s

Darwinian ‘fitness’ to the environment implies a single ordinal scalar which

will predict the relative increase or decrease of the type, whereas for many

kinds of life histories no such predictive scalar quantity can be specified, even

though predictions of change can be made from all of the facts about the

reproductive schedules. But without such a scalar we cannot state that one

type is ‘more fit’ than another. Had we not ignored this problem, we would not

be trying to utilize ‘reproductive fitness’ (as in schema (C)) as if it were a

surrogate for ‘Darwinian fitness’ (schema (A)). Nor would we think that there

is a single unified concept of fitness that fits all dynamical explanations of

evolution where natural selection plays a role. Now, we turn to the models for

the proof of the failure to specify a scalar quantity that explains or predicts

quantitative changes in the frequency of types.

4 The models of reproductive fitness

4.1 The Standard Viability Model

Wright and Haldane, but not Fisher, base their formulations on a simple

model of simultaneous reproduction in a sexual population. A population

is represented as relative frequencies of alternative genotypes so that absolute

352 André Ariew and R. C. Lewontin



numbers of individuals do not enter the model. We need consider here only the

simplest case, where the alternative genotypes are the different diploid com-

binations of alternative alleles at some locus, say A1A1, A1A2 and A2A2. These

genotypes reproduce completely sexually, and successive generations are dis-

crete with no overlap of individuals. All reproduction can therefore be con-

sidered to be simultaneous. The model has the following formal structure

shown in Table 1.

A generation begins at the moment of the formation of zygotes from a union

of sperm and eggs produced by the previous generation, and the population is

characterized by the initial frequencies of the alternative alleles assumed to be

the same in the sperm and egg pool. The initial frequencies of the diploid

genotypes are a function of the allelic frequencies in the sperm and egg pools

and of the rules of mating. The zygotes then develop to sexual maturity when

they produce eggs and sperm according to Mendelian rules to form yet an-

other generation and so on. During the period of development from the

moment of fertilization to the time of sexual maturity, some individuals

survive to reproduce and others do not. The probability of survival of a

genotype from egg to adult is its viability, and this viability is the ‘reproductive

fitness’ of a genotype. It is assumed that there are no differences in fertility

among genotypes and that the viability differences among genotypes are

independent both of the relative frequencies of the genotypes and of the

absolute number of offspring. Finally, the mean (reproductive) fitness (via-

bility) of the population as a whole is calculated as the average viability of the

different genotypic classes weighted by their frequency. The evolution of the

population is then followed as the changes from generation to generation in

the frequencies of the alternative alleles at the locus in the sperm and

Table 1 Generation t

gametes A1 A2
frequencies pt 1 � pt

mating

zygotes at birth A1A1 A1A2 A2A2
frequencies R H D

survivorship

adults A1A1 A1A2 A2A2
frequencies R0 ¼ RV1/V H0 ¼ HV2/V D0 ¼ DV3/V

where Vi is the probability of survivorship of type i and V (mean population viability) ¼ RV1 þ HV2 þ DV3.

Table 2 Mendelian segregation

Generation t þ 1
gametes A1 A2
frequencies pt þ 1 ¼ R0 þ H0/2 1 � pt þ 1 ¼ D0 þ H0/2

The Confusions of Fitness 353



egg pools, or as the frequencies of genotypes at the same moment in the

reproductive cycle in successive generations, or as change in the mean popula-

tion fitness from generation to generation.

This Standard Viability Model predicts rates of change of the frequency of

allelic types across generations, and shows that if heterozygotes are more

viable than homozygotes an intermediate stable equilibrium of frequency will

be reached. Most powerful in its apparent implications is the analytic result

that the average fitness (viability) of the population as a whole increases

during the evolution (Fisher) and reaches a maximum when the selective

process comes to a final end (Wright), either because the population consists

of a single most-fit genotype, or because it is at the intermediate stable equilib-

rium of frequencies predicted from the viabilities in the case that heterozygotes

are more viable than homozygotes. This principle of the maximization of

mean reproductive fitness has done an immense amount of work in evolu-

tionary theory, especially because of its analogy with Darwinian notions of

ecological fitness.

4.2 Frequency-dependent selection

The assumption in the Standard Viability Model that fitnesses are indepen-

dent of the frequencies of the genotypes is generally incorrect. It is quite

common that rarer types are at an advantage, as in the famous cases of

butterfly mimicry where the advantage of having a pattern resembling

a species that is distasteful to predators decreases as the palatable mimic

increases in numbers. Fitness in frequency-dependent models is not a scalar

but a set of functions of genotypic frequency, so that it is not possible to order

the fitnesses of the genotypes except at a given frequency. It may be objected

that genotypic frequencies are simply an environmental variable and that it

has never been claimed that fitnesses are independent of environment, so no

added ambiguity is introduced by the frequency-dependent case. An addi-

tional problem is that in the frequency-dependent case, the induced change in

fitnesses consequent on changes in genotypic frequency may lead to a decrease

rather than an increase in mean population fitness, and no optimal fitness

principle applies (Lewontin [1958]).

4.3 Fertility models

When it is allowed that there are fertility as well as viability differences among

genotypes, the problem of assignment of fitnesses to genotypes becomes even

greater. In general, a mating pair determines fertility so that, in the simplest

case of a population with two allelic variants at a locus, there are nine mating

pair types and the net fertility of a given genotype is a function of the relative

354 André Ariew and R. C. Lewontin



frequencies with which these mating pair types form. Again it may be claimed

that the fitness of a genotype is simply contingent on its mate as it is on other

environmental circumstances, and that one can calculate the net (mean) fer-

tility of each genotype for the particular distribution of potential mates. The

problem, however, is that the genotypic identities of the offspring of an

individual of a given genotype also depend upon the genotype of its mate,

so these net (mean) fertilities are insufficient to generate the frequencies of

offspring in the next generation.

A second difficulty in the definition of fitnesses when there are fertility

differences arises when variations in absolute numbers of offspring are con-

sidered, even in the simplest case of asexual reproduction. An example is given

by Sober ([2001]). Suppose Type A always produces two offspring while Type

B produces one individual in some generations and three individuals in

others, with equal probability. Thus the expectation of the reproductive rate

of the two types is equal (two). Suppose we begin with two individuals of each

type. In the next generation there will be four Type As and either two or six

Type Bs with equal probability. Then the expected relative frequency of the

two types in the next generation is:

Type A ¼ ð:5Þð4=6 þ 4=10Þ ¼ :535

Type B ¼ ð:5Þð2=6 þ 6=10Þ ¼ :465

This discrepancy between the equality of expected reproductive rates and the

inequality of expected relative frequency in the next generation arises from the

difference between the expectation of a ratio and the ratio of expectations.

The type with the lower variation in reproductive rate has the greater long-

term expectation. Which, then, is the correct measure of fitness?

4.4 Overlapping generations

A major fraction of living species, like humans, do not have discrete, non-

overlapping generations. Each mating pair produces offspring over an

extended period and these in turn reproduce over many ages. As a consequence,

the time rate of change of a particular genotype in a population depends not

only on the total number of offspring of the genotype, but also on the ages at

which those offspring are produced, since it depends on the number of suc-

cessive offspring generations that are produced per unit time. Thus the

relevant reproductive information for a genotype is the complete age-specific

survivorship and fertility schedule of the type. What is the probability that an

individual will reach age x and, given that it reaches that age, what is the

expected number of births it will produce between age x and x þ dx? The
problem is to map the age-specific survivorship and fertility schedule onto

The Confusions of Fitness 355



a scalar, fitness. Fisher ([1930]) built his entire structure of evolutionary

genetics on the model of overlapping generations using an erroneous method

of converting age-specific survivorship and fertility into reproductive fitness.

He reasoned as follows: it is a basic result of demographic theory that a

population characterized by a particular age-schedule of survivorship and

fertility will eventually reach a stable distribution of ages, the stable age

pyramid. When it does so, the total population size will then grow at a steady

geometric rate m, given by the solution to the Euler equation:

Z
e�mxlxbx dx ¼ 1

where lx is the probability of surviving to age x, and bx is the expected number

of births to an individual aged x. He called m the Malthusian parameter. If a

population consists of a mixture of genotypes, each with a different lx and bx

schedule, then the Malthusian parameter for each should predict the rate of

increase of that genotype in the population relative to the other genotypes. The

error in this argument is that it leaves out sexual reproduction and Mendelism.

It confuses the rate of reproduction by a genotype with the rate of reproduc-

tion of a genotype. Mendelian segregation and reassortment has the effect that

heterozygotes produce both homozygotes and heterozygotes, while a homo-

zygote A1A1 will produce heterozygotes if it mates with a homozygote A2A2.

Thus, genotypes do not increase or decrease in a population as if they were

each separate species with characteristic age-specific reproductive rates. In

fact, there is no mapping possible of these age-specific rates onto scalar quan-

tities associated with genotypes that can be used to predict changes in genetic

composition of a sexual population. The minimum dynamic model for pre-

dicting genetic changes requires the complete specification of the age-specific

rates as calculating devices (Charlesworth and Giesel [1972]). Indeed, even the

complete relative age-specific rate schedules are not sufficient. It is also ne-

cessary to know whether the population as a whole is increasing or decreasing

in size, which requires both the absolute age-specific mortality and fertility

schedules and the age distribution of individuals in the population. Charles-

worth and Giesel ([Ibid.]) give an example of two genotypes with different

reproductive schedules that differ in the timing of reproduction, such that the

first produces its offspring at an early age, while the second delays reproduc-

tion to a later age. This is an example of the demonstration by Demetrius ([1992])

of the dependence of genotype dynamics on the demography and growth rate

of the population. If the population as a whole is increasing in size, the first,

precocious, genotype increases in frequency, while if the population size is

decreasing, it is the second genotype that increases relative to the first.

We are forced to conclude that for species with overlapping generations, i.e.

for a very large fraction of organisms, no scalar reproductive fitness measure

356 André Ariew and R. C. Lewontin



can be derived from reproductive schedules that allows statements of the form

‘Type A is more fit than type B.’

5 Fitness as outcome

The recognition of difficulties in deriving a general measure of reproductive

fitness from reproductive properties has led some evolutionary theorists and

philosophers to propose that reproductive fitness should be measured from the

trajectory of change in type abundances rather than as a scalar calculable from

reproductive information that would predict such change (see, for example

Price [1995]; Michod [1999]; Rosenberg [1983]). Our criticism of this move

follows the lines already laid down by others (see Krimbas [2002] for a detailed

analysis). First, it is unclear what work is done by a measurement of fitness as

effect. Since it identifies fitness differences with changes in frequency of types,

it has no power to explain those changes. Second, beyond a general extra-

polatory use, that changes in type frequency which have been observed will

continue in the future, it has only the weakest predictive power. It could not

predict, for example, prospective intermediate equilibrium of type frequencies.

Third, as we illustrate below, it may lead to incorrect conclusions, if fitness so

defined is taken to be an indicator of the causes of type frequency histories.

5.1 Fitness as actual increase in type

The problem with using observed frequency changes is that no distinction can

be made among different explanations of these changes, in particular between

different natural properties of individuals that are relevant to their expected

reproduction and factors that are orthogonal to those properties, so-called

‘random events’. Chief among these in a finite population of organisms, each

producing a small number of offspring, is the random sampling of the gamete

pool at each mating. If two types are in equal frequency in some initial

generation, they will become unequal in frequency and, if enough generations

elapse, one will disappear by this random drift process even in the absence of

expected differences in reproductive behavior. To associate the quality of

‘superior fitness’ to the one that survives while claiming that nothing causal

is implied is perverse, given the usual use of the notion of ‘fitness’. Either no

explanatory work is done, or an explanation is incorrectly implied.

5.2 Fitness as expected increase in type

5.2.1 Expected increase within a generation

Price ([1995]) defines the fitness of the i
th

type as

Wi ¼ f0i=f i

The Confusions of Fitness 357



where f 0 and f are the expected frequencies of the type before and after

selection within a generation. But such a definition is derived from the stan-

dard discrete generation viability model. Suppose, for example, that the gen-

otypes A1A1 and A2A2 are unable to reach adulthood, but that the

heterozygote is perfectly viable. The population reaches an equilibrium with

genotypic frequencies .25, .5 and .25 at conception, but at adulthood the

homozygotes are completely absent, so their fitnesses are estimated, reason-

ably, as 0. But suppose, in contrast, that the homozygotes are perfectly viable

but completely sterile while the heterozygote A1A2 is fertile. At equilibrium,

the three genotypes will be in frequencies .25, .5 and .25 throughout the

generation and offspring will be produced all during the generation in those

same proportions as a consequence of Mendelian segregation, so it must be

judged that there are no reproductive fitness differences, despite the large

differences in fertility.

Fisher ([1928]), on the other hand, defined the relative fitness as the

Malthusian parameter, m, but as we have seen, this erroneous use of the

Euler formula results in fitness values that have no determined relation to

changes in population composition.

5.2.2 Expected increase between generations

This definition confounds the absence of selective differences between types

with a stable equilibrium of types expected under some schemes of selection.

The cases of the sterile and inviable homozygotes given in the previous section

are examples. In no case where there is an equilibrium will fitness differences

appear when between-generation changes in type frequencies are used. It

might be claimed that if no changes in type frequencies are occurring then,

indeed, there are no net fitness differences at equilibrium, and that the equilib-

rium is a consequence of reproductive differences balancing out. But this

confounds differential reproduction with the effect of Mendelian segregation

and reassortment. There is no balance of reproductive differences at equilib-

rium. In the example of the inviable homozygotes, genotypes are being

removed from the population within a generation by differential death,

and they are being exactly replaced at the beginning of the next generation

by Mendelian segregation and reassortment from the heterozygotes. The

balance is not between fitnesses, but between survivorship differences on

the one hand and the Mendelian mechanism on the other. This can easily

be seen by imagining what would happen if sexual recombination were turned

off in this case and the genotypes reproduced entirely by vegetative means. In

a single generation all homozygotes would disappear permanently and the

population would consist of nothing but heterozygotes. The use of expected

changes between generations to define fitness confounds variation in the

358 André Ariew and R. C. Lewontin



natural properties of organisms that lead to differential reproduction with

the consequences of a mechanism of inheritance that is common to all the

organisms.

5.2.3 Postponed reproductive fitness effects

There are a number of cases in which the effect of a genotype is neither on the

viability nor the fertility of the immediate carrier of the genotype, but of its

offspring. For example, if a bird were deficient in the provisioning of its

nestlings, those malnourished offspring might have reduced fertility when

they, in turn, became reproductive adults. The classic example of a postponed

reproductive fitness effect is the recessive grandchildless (gs) mutation in

Drosophila subobscura. Females homozygous for the mutation (gs/gs) have

normal viability and fertility. However, the eggs they produce have an abnor-

mal internal structure which has the effect that the adults that develop from

these eggs cannot themselves produce sperm or eggs, irrespective of their own

genotype. Thus the gs/gs homozygous females have normal numbers of off-

spring which may be gs/gs or gs/ þ , but no ‘grandchildren’ of any genotype.
The attempt to characterize the reproductive fitness of gs/gs females by the

ratio of the frequency of this genotype at birth to the frequency among adults

within a generation will obviously miss the fertility effect. Using the ratio of

genotypes between equivalent stages of two successive generations will

certainly detect some change, but will appear as a deficiency in both gs/gs

and gs/ þ genotypes, even though it is only the former that is the source of the
reproductive fitness difference. Moreover the comparison of the apparent

reproductive fitness differences over a series of generations will show the

fitness difference to be frequency dependent, whereas it is, in fact, an uncondi-

tional defect of the gs/gs type.

6 The book-keeping problem

The purpose of assigning reproductive fitnesses to types is to make

possible some prediction or retrospective explanation of the change in repre-

sentation of those types over time. But to predict increases or decreases in

representation we need to begin with some decision about the variable in which

representation is to be measured. The traditional method has been to count

individuals of different types, but this apparently unproblematic individuation

does not always work. For example, violets reproduce in two ways. A flower

may set seed and these seeds, having dispersed, may each give rise to a new

plant. Alternatively, a violet stem may send out underground runners which,

at points along their lengths, put up flowering stalks. A plant produced from

seed is genet while one produced above ground asexually from a runner is a

The Confusions of Fitness 359



ramet. The problem that has plagued evolutionists who deal with organisms

that have both sexual and vegetative reproduction is how to count ramets and

genets in assigning reproductive fitness. Do all the ramets of a single original

stem count as belonging to a single individual, or is each to be counted as a

separate individual? It might be argued that since the ramets are all connected

as a single body, they are collectively one individual. But is the occurrence of a

break in the underground stem sufficient to produce a new individual for

accounting purposes? Moreover, the problem exists for trees. A tree consists

of a large number of flowering stems connected together by branches and

a trunk. Why should it matter that these flowering stems are connected above

ground rather than below? If a tree is a single individual then so is the

collection of all the ramets of a violet. How is fitness to be calculated in such

instances? Suppose an entire field is occupied by hundreds of ramets from

a single original plant, except that in one spot there is a single plant that is a

genet of a different type. Are the two types to be counted as equally frequent?

In a colonial organism, say a coral, is a type that produces a single colony that

spreads to occupy nearly the entire territory available to a species less

evolutionarily successful than a type that reproduces 100 scattered sexually-

reproduced organisms, each of small extent? It would appear that the problem

of fitness and relative evolutionary success demands a solution to the problem

of defining an individual.

The problem raised by individuation is a consequence of the Malthusian

origin of evolutionary theory. The book-keeping of evolutionary biology in

terms of numerosity is the transfer onto the evolutionary problematic

(and onto a great deal of ecological theory as well) of the central

problem of human demography, the growth in numbers that arises from

using as a model a sexual species that reproduces solely by giving birth

to clearly defined individual objects that all grow to approximately the

same size.

As an alternative it would be possible to build a dynamical theory that

used not numbers of denumerable objects, but a continuous measure of

occupancy of the external world, for example the total amount of living

protoplasm belonging to a given type. Indeed the Malthusian preoccupation

with numbers stemmed from a preoccupation with the supposed limit in the

resources available and the struggle to acquire those resources that were in

limited supply. But success in sequestering resources in short supply is

measured by the total amount sequestered. In the special case that there

are well-defined individuals of approximately the same size, numerosity is a

proxy for total resource, but it is only a proxy. (It should be noted that, in

present-day political analyses of human ecology, a great deal of attention is

paid to the fact that some people use a great deal more resources and

360 André Ariew and R. C. Lewontin



produce a great deal more pollutants than others.) The question, then, is

what continuous measure should be used for a dynamical theory. There

were some attempts to build a theoretical population ecology on the basis

of energy fluxes (see, for example, Margaleff [1968]), and population

geneticists have occasionally used biomass as a measure of population

fitness (Dobzhansky and Pavlovsky [1961]), but the relation between bio-

mass or energy flux and a dynamical genetical theory of natural selection is

not clear. A priori, the most direct connection between evolutionary change

and a continuous measure of fitness would be to use the proportion of

the limiting resources for species reproduction that is pre-empted by a

given type. Evolutionary change would then be measured as the change

in the total proportion of the limiting resource occupied by the various

types. Again, in the case of unproblematic individuation of objects of

roughly equal resource occupancy, simple numerosity would be an adequate

proxy.

The difficulty of replacing numerosity by limiting-resource occupancy

is that dynamic evolutionary models could no longer be usefully framed

in generalized abstract terms. Frequency-dependent selection is usually

ignored because predictions depend on the exact form of the frequency

dependence, and although there are classes of mathematical functions that

can be treated as essentially alike, it is necessary in each application to

determine to which of these function classes, if any, the problem belongs.

The use of a limiting-resource theory is even more difficult because

it demands detailed natural historical and physiological information in

each case.

7 Conclusion

It appears that the resolution of the confusions about fitness requires three

clarifications. First, we must not conflate the genetical notion of ‘reproductive

fitness’ with the Darwinian metaphor of organisms ‘fitting’ more or less into

an environmental niche. Second, we require the abandonment of the attempt

to make a general quantitative dynamical theory of evolutionary change in

which a unitary scalar, ‘reproductive fitness’, appears as a parameter, and the

acceptance of a diversity of specific dynamical models in which variation in

reproduction among heritable types appears in structurally quite specific

ways. Finally, if reproductive fitness differences are to predict or explain

changes in representation of types in evolution, it requires, in each case, a

decision about the nature of the scale on which the representation of different

types is to be measured.

The Confusions of Fitness 361



Acknowledgements

We would like to thank Alex Rosenberg, Elliott Sober, Denis Walsh, Mohan

Matthen, Peter Godfrey Smith, Tim Lewens, and an anonymous referee from

this journal for comments on previous drafts.

André Ariew

Department of Philosophy

University of Rhode Island

Kingston, RI 02881

U.S.A

ariew@uri.edu

R. C. Lewontin

Museum of Comparative Zoology

Harvard University

Cambridge, MA 02138

U.S.A

lewontin@oeb.harvard.edu

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