Biology and Philosophy 19: 185–203, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
On fitness
COSTAS B. KRIMBAS
Department of Philosophy and History of Science, University of Athens, Panepistimioupolis,
157 71 Ano Ilissia (Athens), Gr eece
Received 27 March 2001; accepted in revised form 9 September 2002
Key words: Fitness, Population genetics, Theory of evolution
Abstract. The concept of fitness, central to population genetics and to the synthetic theory
of evolution, is discussed. After a historical introduction on the origin of this concept, the
current meaning of it in population genetics is examined: a cause of the selective process and
its quantification. Several difficulties arise for its exact definition. Three adequacy criteria for
such a definition are formulated. It is shown that it is impossible to formulate an adequate
definition of fitness respecting these criteria. The propensity definition of fitness is presented
and rejected. Finally it is argued that fitness is a conceptual device, a useful tool, only for
descriptive purposes of selective processes, changing from case to case, and thus devoid of any
substantial physical counterpart. Any attempt to its reification is an apport to the metaphysical
load evolutionary theory has inherited from Natural Theology.
Introduction
Fitness is a concept considered of prime importance in population genetics
and demography and thus central to the synthetic theory of evolution. Despite
its apparently easy understanding, at least prima facie, this concept faces
several non trivial difficulties. After a brief discussion of the origin of the
concept I will offer some adequacy conditions for the definition of fitness
in population genetics. I will then formulate the best possible provisional
definition and subsequently show how it fails the meet the conditions of
adequacy. This is done by two means: a systematic analysis of the constraints
imposed by these criteria and also by offering counterexamples. Delayed
gene action, for the first time discussed in this respect, renders impossible a
correct definition of fitness. The impossibility of a correct definition is further
elaborated by considering the difficulties faced when overlapping generations
are considered or when the population size increases or decreases. Inclusive
fitness is not devoid of these difficulties. Furthermore I will challenge a
dispositional account of fitness by unraveling its metaphysical underpinnings.
Finally I will support the view that fitness is a useful device but devoid of any
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general physical counterpart, exactly as the concept of adaptation: it is only a
descriptive tool for the study of natural selection.
From origin of the concept of fitness in population genetics. From
Darwin through the demographers to Wright
Although Darwin barely ever used the word fitness in “The Origin of
Species”,
1
he clearly had the concept of it. He took it to capture a property
of an individual, viz., a physical property of the organism accommoda-
ting to its way of living, and thus a cause which explains the success
of individuals subjected to the process of natural selection. Fitness might
also carry robustness as a nuance, exactly as in ordinary language. Darwin
inherited this concept from Natural Theology, and employed fit and fitness
as synonymous to adapt and adapted, a fitting between the organism and its
environment. Even today, Brandon (1990) equates fitness with adaptedness.
Herbert Spencer made this term more popular using the unfortunate expres-
sion “survival of the fittest” as a synonym of natural selection and, following
him, Darwin repeated it.
2
Population demographers have used fitness to express in mathematical
formalism the kinematics of population growth. Malthusian fitness is the ratio
λ of the number of individuals of one generation (N
t+1
) to that of its parental
generation (N
t
). For a detailed exposition of the term in population demo-
graphers (Malthus, Verhulst, Lotka) see Gillois (1996) and Krimbas (2000).
In this approach all individuals of a population may be considered identical,
and thus fitness concept refers to a common individual property no less than
it characterizes the entire population.
Fisher was the first to introduce the concept of fitness in population
genetics. He used for this purpose mortality and fertility tables (inherited
from Lotka). He estimated the value of fitness from that of the Malthusian
parameter, m, the difference between the percentage b of the individuals that
give birth to one individual during a time interval t and the percentage d of
those dying at the same time period, that is b–d. The relation between m and
λ, the Malthusian fitness, that is according to him the ratio of the number of
individuals of one generation (N
t+1
) to that of its parental generation (N
t
), is
λ = e
m
.
Furthermore, Fisher considered that the Malthusian parameters, and
thus fitnesses, are inherited: different genotypes have different fitnesses.
According to him, the course of evolution is to maximize fitness: in an early
account he noted that “the fitness of any organism at any time” is maximized
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and the rate of increase in fitness is equal to its [additive] genetic variance in
fitness at that time. But in a later account he noted that “the average fitness of
a population” was to be maximized with a rate equal to the genetic variance
of fitness in that population.
3
Since variances are always positive, the change
will always be in the direction of an increase in fitness. R. Fisher considered
this fundamental theorem of natural selection to be a general law, equivalent
to the second law of thermodynamics, which stipulates always an increase of
a physical quantity, entropy. The generality of Fisher’s law was questioned
and, in some cases, the law was shown not to hold true.
4
The problems with Fisherian fitness is that the entire approach, although
suited for asexually reproducing organisms, fails if not precautions are
taken, to account to complication arising from the Mendelian segregation
in sexually reproducing organisms. If the ratio of a certain genotype in two
successive generation f
t+1
/f
t
is equated to its fitness, Mendelian segregation
is disregarded. As Maynard Smith (1991) remarked in the case of sickle-
cell anemia the homozygotes aa for the sickling allele have no offspring,
but the number of aa individuals in the next generation arise from the
matings between two heterozygotes Aa. Should these heterozygotes increase
in frequency (due to the prevalence of malaria, to which they are resistant), aa
should also increase in frequency: instead of having a zero fitness, it will be
allowed a positive value, greater than one. Otherwise in equilibrium condition
it should be equal to one. Thus “the genotype’s per capita rate of increase”
is not the way population geneticists employ to measure fitness. Another
qualm may be found in the way this procedure departs from the intention
of the original use of the term “fitness” by population geneticists, i.e., as a
mean to provide a cause for the selective process. Since the estimation of
fitness is performed a posteriori, that is after the occurrence of selection
and no the basis of the selective results, it might be taken that causes and
effects are confounded. It could be argued that this critique may also be
true regarding Wrightian fitnesses, to be considered below. However, the
practice of estimating Wrightian fitnesses by the enumeration of the number
of offspring produced together with the interposition of the segregation
mechanism renders this confounding effect undirect, if present at all.
5
S. Wright (1969, but the work goes back to the 30’s) used the popula-
tion fitness as varying according to the gene frequencies in the population.
Excluding competition among individuals, S. Wright states that every geno-
type is characterized by a fitness value, so that each individual belonging to
that genotype has an expected number of progeny which is the fitness of that
genotype. The population fitness
W is the expected mean number of progeny
of every individual of the parental population. W is a composite function: the
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sum total of the products of all genotype frequencies by their specific fitnesses
(or adaptive values).
6
Adequacy criteria for a definition of fitness
We will first offer three criteria for a satisfactory definition of fitness. Then we
will attempt to formulate a definition complying with these criteria, following
the tradition of population genetics and regarding the simple case of non over-
lapping generations. It will become obvious subsequently that satisfactory
definition is impossible.
A satisfactory definition of fitness should comply to the three following
criteria:
(a) It should be formulated in such a way that the results of chance events,
affecting the progeny output, should be avoided in fitness estimations.
Since the life history of an individual organism may be influenced by
chance events, his reproductive output could greatly differ from that
of another similar individual because of these chance events. Thus the
fitness definition should be restricted to a life history devoid of chance
events. Better it should be restricted to the mean of life histories of
individuals that may, or may not, face all possible chance events with
their natural frequency of occurrence. This drive us either to adopt as
a measure of fitness the expected number of children or their mean
number in an adequate sample of individuals of the same constitution.
According to this criterion Brandon’s (1990) suggestion to consider
fitness of individual organisms has to be excluded from consideration.
(b) Fitness should stem from an internal property of the organism belonging
to a certain class of individuals which have the same constitution (geno-
type, theirs mother genotype, or both). This constitution should lead to a
phenotypic trait, structural, functional or behavioural. Fitness should be
related to and result from this trait and therefore explain why individuals
belonging to this class leave such a number of offspring or why their
genes are represented in such a number in the next generation. Thus it
should provide an explanation for the outcome of the selective process.
(c) The number of offspring or genes these individuals leave should be
counted during their entire life history, ideally starting at the beginning
of it and ending at their death. However, in cases of maternal influence
a different starting and end point may be selected. Inspite of this, in the
case of a two gene genotype, we should not use different time periods for
each to estimate their fitness, but the same time period for their combined
effect. Ideally we should use the same time period for all possible kinds
189
of constitution. We will see that this criterion is difficult or impossible to
meet.
An attempt to define fitness according to the tradition of population
genetics. The case of non overlapping generations
Population geneticists regard “fitness” in its technical meaning as a relative
or absolute measure of reproductive efficiency or reproductive success. Peter
Medawar (1960: 160) expressed the following view regarding fitness, which
is apparently adopted by many population geneticists:
The genetical usage of “fitness” is an extreme attenuation of the ordinary
usage: it is, in effect, a system of pricing the endowments of organisms in
the currency of offspring; i.e., in terms of net reproductive performance.
It is a genetic valuation of goods, not a statement about their nature or
quality [my emphasis].
To comply with the first criterion we may at first consider as a measure
of fitness of a certain genotype the mean number of offspring it produces.
The only permissible way to perform this counting is to start counting the
zygotes produced by individuals of this genotype from the beginning of its
life as a zygote until its death. Counting from zygote to zygote may be a
difficult or problematic operation, since in different animals internal fertili-
zation may render these observations impossible. To bypass this difficulty,
it was suggested to transport the counting period starting the counting at a
convenient age after fertilization and ending it at the same age in the next
generation. This is a mistaken suggestion since it excludes a part of life
history of a genotype from consideration but instead it includes the corre-
sponding period of possible different genotypes, since Mendelian segregation
does not insure that offspring share the same genotype with their parent
(Actually, this is also the difficulty in using Fisher’s “fitnesses” or Malthusian
parameters in sexually reproducing species).
Even so, the mean number of offspring, when estimated, may not be suffi-
cient: the distribution of this number may be of importance. Thus Gillespie
(1973, 1977) has shown that genotypes which have the same number of
progeny but differ in variances have a different evolutionary fate. Everything
else being equal, an increase in variance (temporarily, that is from generation
to generation) is disadvantageous in the long run. From the actual mean of
expected number of progeny (that is among generations), a quantity should
be subtracted equal to 1/s
2
for the case of temporal variation (where s
2
is the
variance in offspring number). In the case of developmental variation (e.g.,
when one proportion of individuals of a genotype produces a different number
190
of offspring, while the arithmetic mean for all of them remains the same when
compared to another genotype which has the same mean number of offspring
but all individuals produce exactly the same number of offspring) Gillespie
(1974, 1975, 1977) has shown that the genotype with the increased variance is
disfavored. In this case again, a quantity equal to 1/Ns
2
should be subtracted
from the arithmetic mean in order to arrive at an estimate of fitness (where N
is the population size). The same is true for spatial variation.
The reason for all this, as Sober (2001) has insightfully explained, is that
the expected value of a quotient is not identical to the quotient of expected
values. This is the cause for the discrepancy observed in the next genera-
tion between those genotypes of which all individuals produce exactly the
same number of offspring and those of another genotype of which individuals
produce different numbers but overall display the same mean number.
In order to cover this complication we may restrict the definition of fitness
to one only generation (and thus avoid temporal variation). Furthermore, we
may restrict the fitness definition to a defined (homogeneous) environment
[and thus avoid complications as those described by Brandon (1990: 90),
where a genotype having two different fitnesses in two environments, both at
absolute value, which are lower than the respective two fitnesses of a different
genotype, may end up having a higher fitness due to an unequal distribution
of individuals in these two environments]. Taking these into consideration we
may try to formulate the following provisional definition of fitness:
In diploid organisms the absolute or Darwinian fitness of a certain
genetic constitution of individuals of the same species in a popula-
tion of non-overlapping generations living in a defined [homogeneous]
environment is equated to the mean number [or the expected number]
of zygotes produced by a zygote of this constitution during its entire
lifetime, whereas relative fitness will be the measure of the productive
efficiency of a certain genotype, as defined above, compared to that of
another from the same population.
As explained above, this definition does not cover the case of variance differ-
ence in the same generation at the same environment. This is not the only
difficulty encountered.
Let us now see what is needed for compliance to the second criterion of
adequacy.
Even if we make the correct counting from zygote to zygote, we face
another difficulty which emerges from the delayed effects of the parent geno-
types on the fitness of the offspring, effects independent of the offspring
genotype, but dependent on the genotype of the parent. The delay may involve
one or more generations to come. Although these effects seem to affect the
fitness of the offspring, or of grandchildren, or even of more remote descend-
191
ants, in fact finally these traits refer to and affect the fitness value of the
parent genotype, which is exclusively responsible for these delayed effects.
In this category are included maternal genes expressed (via messenger RNA)
in the early embryo [polar genes, genes determining dorsoventral axis, like
b-catenin in frogs (O. Pourquie 2001), anterioposterior and lateral (left to
right) axes, mac ho-1 gene determining myoplasm in ascidia, responsible for
the development of some muscles (Nishida and Sawada 2001)], as well as
the maternal genes in strains of Caenorhabditis elegans mutants of mortal
germline, that is deficient telomerase mutants.
Thus the grandchildless mutant of Drosophila subobscura (Spurway
1948; Suley 1953) as well as sililar polar mutants discovered later in Droso-
phila melanogaster (Niki and Okada 1981; Mariol 1981; Thierry-Mieg 1982)
have such effects: female homozygotes for the mutant allele produce sterile
offspring (regardless of the genotype of the male parent or that of the
offspring). The reason for this is that in their fertilized eggs the posterior
polar cells (from which gametes are derived) are not formed: there is no cell or
nuclear migration for the production of these cells, and the maternal genotype
(not that of the embryo) is exclusively responsible for it. Genes affecting the
direction of cell coiling, dextral or sinistral, in gasteropod mollusks (of the
genus Albinaria or of Limnaea, see Sturtevant and Beadle 1940: 330) belong
to the same category. The phenotype of the individual is not determined by
is own genotype but reflects the genotype of its mother (not necessarily from
its mother’s phenotype, which is determined by its grandmother genotype).
In these cases offspring counting for fitness estimation should be delayed by
one generation: grandchildren are to be counted. Actually, the entire cycle
of observation and counting is transposed by one generation: the fitness of
a homozygous for the grandchildless mother [the fitness of a female of the
genotype for this gene] is estimated by counting the number of grandchildren
produced by a fertilized egg of this mother.
Milk factor is another delayed character in horses. A foal may sometimes
die because its blood cells react with antibodies produced by its mother
and contained in its mother’s milk. Antibodies are produced after repeated
gestations when a foal inherits from the sire the ability to make a particular
antigen absent in the dam. Then, counting from zygote to zygote, or from
fertilized egg to fertilized egg to fertilized egg, does not provide an accurate
estimation of fitness (Srb and Owen 1952: 262–263). This case is similar to
that of Rhesus blood group types in men, the only difference being that in this
case the delayed response is manifested at the birth of the offspring.
An earlier appearance of the lethal effect in mice is observed when the
mother lacks a heat shock protein (Hsfl: heat protein factor 1). The Embryos
die after fertilization, at the stage of one or two cells (Christians et al. 2000).
192
There are several instances of delayed action one should take into account
in this respect, including the silencing of parental genes in the embryo
in mammals, either paternal or maternal, by methylation: the genomic
imprinting (Reik and Walter 2000). Another case of maternal effect combined
with the paternal phenotype is encountered in zebra finches: females deposit a
varying amount of testosterone in eggs according to the attractiveness of the
males they mate with, the greater the attractiveness the greater the amount
deposited. Testosterone plays an important role on the fitness of the offspring
(Birkhead et al. 2000). An egg to egg count misses this effect which is
independent of the offspring’s genotype, but depends on the parental male
phenotype (and eventually genotype). However, this case may be relegated
to the section discussing the fecundity component of fitness (see below) with
the addition of the presence of a delayed effect.
The problem is further complicated when the generation delay involves
not just one but many generations. Complete sterility may be produced by
mortal germline mutants in some strains of the round worm Caenorhabditis
elegans after four or even after sixteen generations, varying with the mutant
(Ahmed and Hodgkin 2000). These mutants exhibit progressive chromo-
some telomere shortening and accumulate end-to-end chromosome fusions in
later generations leading to complete sterility. Here the counting of progeny
should be delayed by several generations, varying according to the strain until
complete sterility is achieved.
These delayed effects present non trivial difficulties when the third
criterion of adequacy has to be met. The fitness of most of the genes may
be computed by counting from zygote to zygote, while those with delayed
effect may be computed in a different time schedule including, eventually,
one or more generations. Thus, for a composite genotype, two different fitness
evaluations should be considered in contradiction to the third criterion.
Using a quantitative genetic model Wolf and Wade (2001) have investi-
gated the effects of assigning fitness components of offspring to parent
fitnesses. A maternal behavioural character that contributes to children
survival could be assigned either to offspring fitness or to the fitness of the
mother. Provided that it is not assigned to both of them (thus being counted
twice, an obviously incorrect practice), it seems that the assignment to either
of them is not free of potential shortcomings. Assigning these components
of offspring fitness to the offspring avoids potential problems but may miss
a component of kin selection provided by the mother, not detected in selec-
tion analyses. Thus it goes against the second criterion. On the contrary, the
assignment to parent’s fitness (e.g., the effect on early survival due to maternal
care) of components of fitness of the offspring (when there is a genetic
correlation between the parental effect increasing offspring’s fitness and the
direct effect on offspring fitness) may lead to incorrect dynamic equations and
193
eventually to incorrect conclusions regarding the direction of evolution. But
this assignment is in accordance to the second criterion: it justifies the aim
of population geneticists to provide an explanatory version of the selective
process.
It is obvious that in defining fitness we do not want (following the third
criterion) to consider a longer or even an extremely long evolutionary fate, as
did J.M. Thoday (1953, 1958) and W.S. Cooper (1984), but a short one, of one
generation. The afore mentioned cases of delayed gene action affecting the
next or even more remote generations, mostly or rather completely neglected
in theor etical discussions until now, present a non trivial complication
rendering impossible a satisfactory definition of fitness.
Gametic selection and meiotic drive
Thus far we have only considered the fitness of diploid individuals. Selection
processes may apply as well to the haploid phase of the life cycle, the gametic
one. Although not differing in their mathematical treatment, two different
forms are distinguished: the meiotic drive, that is the production of gametes in
non-Mendelian proportions by a heterozygote, and simple gametic selection,
that is gametic differential viability or differential capacity to fertilize or be
fertilized (for a review see Birkhead and Moller 1998). Cases of meiotic drive
have been described in mice (the t alleles, Lewontin and Dunn 1960; Young
1967; Silver 1985) and in Drosophila species (SD system in D. melanogaster,
Hartl and Hiraizumi 1976; Hartl 1980; Brittnacher and Ganetsky 1984; Temin
and Marthas 1984; Sex-ratio system in D. affinis, D. subobscura, D. pseu-
doobscura, for a review see Krimbas and Powell 1992, and in D. simulans
Merçot et al. 1995). Several of these systems are complex, composed of a set
of genes, enhancers, inhibitors, etc.
To model these systems one may use coefficients similar to those used
when dealing with the diploid phase of organisms, that is coefficients similar
to fitness. When selection operates both at the haploid and the diploid phase,
a sequential combination of algorithms permits to deal with them. The same
could be applied in case on wishes to deal separately with selection operating
at different components of fitness (as we shall see below).
Components of fitness of non overlapping generations
It is often stated that selection acts on survival and reproduction (Brandon
1990: 15). This is not an exact formulation. Fitness is the mean number
of progeny left; therefore viability components (survival, longevity) are
important as far as they affect the net reproductive effect. Longevity may be
194
important in those cases where it may affect the net reproductive effect. Selec-
tion is blind to longevity at a post-reproductive age (including the component
of parental care to offspring). This is the reason why inherited pathological
syndrome of Huntington’s chorea appearing after the reproductive age seems
not to be selected against. On the other hand, there are cases of selection
against longevity, e.g., the adoption of a life strategy that promotes early
sexual maturation. As Reznick, Bryga and Endler (1990) have shown, when a
predator is present, some fishes are selected for this regime, contrary to what
happens in absence of predators (establishment of a life strategy for a later
sexual maturation).
According to D.L. Hartl (1989), starting from the stage of the zygote, the
components of fitness are the following: Viability; subsequently Sexual selec-
tion operates favoring or prohibiting a genotype to find mates (for a review
see Andersson 1994); in the general case every combination of genotypes
of the mating pair may correspond to a specific Fecundity. Thus, Fecundity
depends on the genetic constitution of both parents. For a simple one gene
two alleles case nine different Fecundity values are defined. It seems more
difficult to reconcile the factual data of this case with the presence of an indi-
vidual’s dispositional capacity or property postulated by the propensity theory
of fitness. It seems more plausible to consider interaction as a better explana-
tion, fecundity not being attached to the genotype but to the combination of
the genotypes of the two mating partners.
Before the formation of the zygote, gametic selection (one aspect of which
is meiotic drive) may take place, and sometimes counteract the direction of
selection exercised at the diploid phase. Gametic selection was discussed
above in a separate section.
There are cases of fecundity selection that may be improperly considered
as gametic selection, because selection operates at the gametic stage.
According to the “male function hypothesis” in hermaphrodite angiosperms,
once a certain number of female seeds is secured by hermaphrodite flowers,
it pays more to invest exclusively in male flowers. The production of male
flowers requires less energetic expenses than hermaphrodite, while it permits
the dissemination of the genetic constitution of the plant to a wider range
by fertilizing stigmata of receptive carpels of flowers of different individuals
(Burd and Callahan 2000). The capacity to produce male flowers is partly
genetical and characterizes the diploid individual.
Sperm displacement in Diptera is another relevant example. In a second
mating, the sperm of the last male displaces to a certain extent the sperm of
the previous mate. There are several devices to prevent this as well as counter
measures to these devices. The capacity of displacement is a phenotypic
character of the male, not of the sperm.
195
Components of fitness-overlapping generations
Developmental time is an important, but generally neglected or ignored,
component of fitness in populations of overlapping generations at the phase
of increase of their size (e.g., at the beginning of colonization of a new
umoccupied territory; r-selection, see Mac Arthur and Wilson 1967).
R.C. Lewontin (1965) examined the case of insects that follow a triangular
schedule of oviposition. A triangular egg productivity function is character-
ized by three points, apexes of the triangle, i.e., the age of first production, the
age of peak production, and the age of last production, all these being stated in
a time coordinate while the number of eggs produced per time unit is stated at
the other coordinate. In his specific model, a reduction of developmental time
may be equivalent to a doubling of total net production: The reduction is equal
to an 1.55-day decrease of the entire egg production schedule (what Lewontin
calls a transposition of the triangle to an earlier age), or to a 2.20-day decrease
only of the age of sexual maturity (the age of the first egg produced), leaving
the other ages as well as the total number of eggs deposited unchanged. It
is also equivalent to a 5.55-day decrease of only the age of the highest egg
production (the peak of the triangle) other things remaining unchanged or,
finally, to a 21.00-day decrease of the age at which the last egg is deposited,
other variables remaining the same.
However, when the population does not increase but remains stable (K-
selection) or shrinks, the genotype that produces earlier in its life-cycle the
same number of offspring is the one that is selected against, in comparison
to a genotype producing the same number of offspring later in its life-cycle.
The situation is inversed when the population increases. This is another case
of fitness not being a property of a genotype, but better understood as a result
of an interaction under the prevailing conditions. In this respect the work of
Brian Charlesworth and J.T. Giesel (1972) should be consulted.
Other capacities may play an important role when the population saturates
the environment. In K-selection it is not fecundity but a better exploitation
of environmental resources that is favoured by selection (Mac Arthur and
Wilson 1967).
Indirect selection schemes – inclusive fitness
W. Hamilton’s (1964) concept of inclusive fitness was formulated to provide
a Darwinian explanation for altruistic actions that endanger the life of the
individual performing such acts. An individual may multiply its genes in two
different ways, directly by its progeny, and indirectly by protecting the life of
other individuals of a similar genetic constitution. If the danger encountered is
196
overbalanced by the gain (as this is calculated in genes), then the performance
of such acts may be fixed by natural selection. Not only do inclusive fitness
estimations take into account the individual’s fitness, but also they take into
account the fitness of its relatives (of similar genetic constitution). Inclusive
fitness is the sum total of two selective processes, individual selection and kin
selection. In fact, in this case the counting tends to change from the number of
individuals in the progeny to the number of genes preserved by altruistic acts
in addition to those transmitted directly throughout the individual’s progeny.
Of course this way the traditional definition of fitness, already provided, is
rendered inadequate. To save it one should incorporate into the fitnesses of
genotypes all favorable results they are recipients, which originate from altru-
istic behavior of their relatives, and subtract all costs deriving from their own
altruistic behavior. In this way, one may reconvert inclusive fitness estima-
tions to usual fitness ones. It is an apparently feasible operation [and may be
recommended in the spirit of Wolf and Wade’s (2001) results, although they
do not address directly to this case]. However, acting this way, a significant
part of the natural history, regarding altruistic behavior, is obscured, lost or,
at least, rendered less obvious.
A digression on the disputed concept of adaptation
Natural selection acts on phenotypes: certain traits of these phenotypes are the
targets of selection. The individuals bearing some traits are said to be adapted.
However, no common and general property may characterize adaptation. A
search in the writings of all important neodarwinists reveals that, inspite of
the suggestion that “adaptation” has an independent meaning, it is in fact
used as an alternative to “selection”. L. Van Valen (1976) seems to differ
from all other authors, because he equates adaptation with the maximization
of energy appropriation, both for multiplying and for increasing the biomass,
solving thus the problem of lianas and other clone organisms. This is a recur-
ring problem, when organisms combine a mixture of vegetative and sexual
reproduction. Counting offspring may then be a difficult task. Are we to
consider as separate individuals those of a colony produced by vegetative
reproduction? And how can we distinguish between an enormous individual
and that of several independent, freshly separated by departing this enormous
individual? Should we count unseparated individuals as one and separated
as many? Isn’t this arbitrary? Although the solution Van Valen provided is
consistent, it has not been generally adopted. Anyway, it significantly departs
from the classical notion of fitness.
The concept of adaptation was shown to be completely dependent on the
concept of selection (Krimbas 1984). Brandon (1978) provided an argument
197
proving the impossibility to establish a criterion or trait for adaptation, which
is independent of selection. He argued that we may be able to select in
the laboratory against any character but one: fitness. There is no reason to
exclude from natural selection the selection experiments performed in the
laboratory, since the lab is also part of nature. Thus there is no character or
trait in the diploid organism that could be taken in advance as an indication of
adaptation independently of selection. Despite this demonstration, Brandon
was reluctant to abandon the concept of adaptation; however, Krimbas (1984)
has proposed to do so. According to him the “description of evolutionary
phenomena based entirely on terms of kinematics would be more adequate”,
where by “kinematics” he means the kinematics of reproductive agents during
selective processes. Fitness is a variable substantiating and quantifying the
selective process.
While one would expect that “adaptation” would disappear from the
evolutionary vocabulary, it is still used to describe the selective process
changing or establishing a phenotypic trait as well as the established by selec-
tion trait itself. Sometimes the engineering approach is used: adaptation, it is
argued, is in every case, the optimal solution to an environmental problem.
The difficulty with such an approach is twofold (Gould and Lewontin 1979).
First, we are often unable to define precisely the problem the organism faces
(e.g., it might be a composite problem) in order to determine in advance the
optimal solution and, as a result, we tend to adapt the “solution” encountered
in nature to the problem the organism faces. That is we “construct” the
problem the organism encounters. Second, it is evident that several selec-
tion outcomes are not necessarily the optimal solutions, the evolutionary
change resembling more a process of tinkering rather than an application of
an engineering design (sensu Jacob 1977).
Adaptedness and the propensity interpretation of fitness
Recently, several authors (Brandon 1978; Mills and Beatty 1979; Brandon
and Beatty 1983; Sober 1984; Brandon 1990) have supported the propensity
interpretation of fitness (which they equate to adaptedness). In doing so they
first try to disentangle individual fitness (something we are not considering
here; for as mentioned earlier, we take into consideration only the fitnesses of
a certain category or group of individuals), from the fitness that is expected
from the individual’s genetic constitution. Indeed, accidents of all sorts may
nullify its contribution to the next generation. But selection is a systematic
process in the sense that in similar situations similar outcomes are expected.
Thus, in order for these authors to pass from the individual or actual fitness to
the expected one, they are obliged to consider two different interpretations of
198
“probability”. The first, the limiting-frequency interpr etation, is to consider
probability as the limit of a relative frequency of an event in a finite series
of trials; but sine this series is never achieved, they might instead use the
observed frequency in a finite series of trials. The second interpretation is
the propensity interpretation. According to this, the very constitution, the
physical properties of the individual, underlie the propensity for performing
in a given way. This performance may rely on a dispositional property, a
property displayed in certain way in some situations, and differently in others.
The dispositional properties, according to a well known view, derive from
the physical structure of the reproducing individual, at that or even at a
lower (e.g., molecular) level, depending on more basic (categorical) but non
dispositional properties. Thus, according to the propensity interpretation of
fitness, the reproductive capacity of a genotype derives from its inherent
(categorical), non dispositional physical properties. This interpretation attrib-
utes fitness to physical causes, linked to the very structure of the individual,
and thus attribute to them the tendency for the individual to produce a specific
number of offspring in a particular selective environment. This is another way
of reifying fitness, and, via fitness, relative adaptedness, and finally adapta-
tion. It reminds us of the Aristotelian potentia et actu [dynamei kai energeia,
δυν ´αµει κα´ιενεργε´ια], where the propensity is “potentia” and the actual
mean number of offspring corresponds to the “actu”.
In some situations of viability selection this interpretation seems quite
satisfactory (e.g., in mice resistant to warfarin). No-one would deny that
selection depends most of the time on the properties of a genotype which
performs in a certain environment. But this may not be as general as one
may think. There is an array of cases from situations like the aforemen-
tioned resistance to warfarin, which agree with the propensity interpretation
of fitness, to those that gradually depart from it to the point of being alien to
it. In these situations the contribution to fitness from the part of the organism
is not clear or does not seem preponderant.
Consider, first, frequency dependent selection: a genotype being in
advantage when rare but in disadvantage when common. Should we attribute
its fitness to an inherent property? Is it not natural to describe the situation in
terms of interaction between the individuals of this genotype and individuals
of the remaining genotypes in the population (especially if a causal inter-
pretation is looked for)? In this interaction, since the two interacting parts
contribute equally to the outcome, they are of equal importance and status.
Consider a key and a lock. They may fit and from their interaction the lock
may be locked or unlocked. Describing the locking or unlocking as dependant
exclusively (or mainly) on the key, we are betraying reality. Using so-called
dispositional properties is an elegant way to neglect on half of the story,
199
focusing on one of the two partners. In a similar way it is more difficult and
much less satisfactory to attribute to a certain genetic constitution the mating
advantage of the males when they are rare and their mating disadvantage
when common.
A more extreme case regards the fecundity which characterizes the two
members of a mating pair. These fecundities depend generally on the male
partner as well as on the female one. In a simple case they characterize the
combination of the two mating genotypes. An extreme example is that of the
change of selective advantage of a genotype highly productive in offspring
when the population is expanding and when it is shrinking.
To ascribe dispositional properties to entities is to downgrade interactions
and to render natural history a preformed, preconditioned tale narrated in
advance. Its explanatory power is severily restricted. It reminds us of the
explanation provided in Le malade imaginaire of Molière for the dormitive
effect of a plant extract: it is attributed to the dormitive principle it contains!
The best solution is to consider genotypic fitness
7
as a usefull device to
perform some kinematic studies regarding changes in gene frequencies or
searching for an equilibrium point to which is the population attracted to. It
seems useless to attribute other qualities, properties, or a substantial role to
this device. It is useless to reify it. Its function is to permit the quantitative
description of changes or the establishment of an equilibrium point in any
one of the multifarious instances of selection. Modern evolutionary theory
is basically of historical nature (although some processes may be repeated).
A complete and satisfactory explanation of a specific case should comprise
a historical narrative including information on the phenotypic trait, which is
the target of selection, the (ecological, natural history or other) reason driving
the selective process (why this trait is being selected), the genetics of the trait,
the subsequent to selection change of the genetic structure of the population,
the corresponding to it change in the phenotypes. In natural history, genera-
lity and search for hidden and non-existing entities and properties may only
contribute to an increase of the metaphysical baggage of evolutionary theory,
an unwelcome baggage inherited from Natural Theology.
Conclusion
Fitness is a device to figure out the kinematics of gene frequency changes due
to selection in mendelian populations. Otherwise it is devoid of any meaning
or substance. A recent attempt to reify it, in the propensity interpretation of
fitness, is found in several cases inadequate (such as the cases of frequency
dependent selection and of fertility selection). This attempt of reification is
related also to the effort to provide for adaptation an independent meaning
200
from that of selection; I have argued already that adaptation is a concept
without independent meaning from that of the selective process.
Acknowledgements
Drs. Richard Lewontin, George Papagounos and Stathis Psilos have made
valuable comments on successive versions of this essay. I am acknowledging
their help but have not all times followed their advice.
Notes
1
“Fitness” first appears in “The Origin of Species” first edition 1859, on page 472: “Nor
ought we to marvel if all the contrivances in nature be not, as far as we can judge, absolutely
perfect; and if some of them be abhorrent to our idea of fitness”.
2
Herbert Spencer used this expression in (1864) page 311. There is an interesting exchange
of views on this subject among Darwin, A.R. Wallace and Spencer referred to in Spencer 1898
note in page 530.
3
See for this R. Michod 1999, page 59. Also regarding the fundamental theorem see the
discussion at Michod 1999 pages 57–62, which includes Price’s analysis.
4
Pollak (1978) has shown that if fitness is based only on fecundity (depending on the geno-
types of the two mating partners) then there is no equivalent to the fundamental theorem.
Fitness, e.g., mean fecundity, may decrease under selection.
J.F. Crow and M. Kimura (1970: 209) have also noted that “One interpretation of the
theorem is to say that it measure the rate of increase in fitness that would occur if the gene
frequency changes took place, but nothing else changed”. Thus environmental deterioration
that would affect fitness values, and thus decrease mean population fitness, is not considered
by Fisher.
5
Michod 1999 follows Fisher’s line regarding fitness. As he himself admits “he does object
to view fitness as a cause of anything, thus he cannot be charged of confusing causes and
effects. For him the kinematics of gene frequency change involves both causes and effects of
organism traits in the context of genetic system and environment”. Michod also (p. 50) defines
fitness as the expected number of gametes produced by individuals of given genotype. He
apparently means the number of gametes that contribute to the formation of zygotes.
6
Unlike Fisher, Sewall Wright, in his shifting balance theory, envisages most of the species
to consist of many small, more or less isolated populations, each having its specific gene
frequencies. Populations occupy the peaks of an Adaptive Surface, formed by the values of
W (population fitnesses), for every point corresponding to certain gene frequencies. These
peaks are positions of stable equilibria. Due to drift, gene frequencies may change and, hence,
populations may cross a valley of the adaptive surface and be attracted by another peak.
Equilibrium points are local highest points of population fitness values.
7
It is much more difficult to deal with population fitness. Population geneticists calculate the
mean individual fitness in a population. But this exercise is quite futile when we compare two
different populations. A group of adapted organisms is not necessarily an adapted group of
organisms. Demographers, earlier, equated size (or increase in size) with population fitness.
However, as Lewontin once remarked, it is not sure that a greater or denser population is better
201
adapted, since it may call for parasites and epidemics; on the other hand a population deplete of
individuals may suffer collapse and extinction. I have argued (Krimbas 1984) that according to
the Red Queen Hypothesis of L. Van Valen (1973), all populations (at least of the same species)
seem to have, a priori, the same probability of extinction, and thus posses, a priori, the same
long term population fitness. In addition it is not clear how we should consider a group: a
group is not an organism, which survives and reproduces. Although individuals of the group
interact in complex ways and thus provide some image of cohesion, the “individuality” of the
groups seems most of the time to be quite a loose matter. Should we consider group extinction
per unit of time to determine group fitness? What about group multiplication? In order to
achieve a modelization in various attempts to model group selection cases, one may resort
to different population selective coefficients, or population adaptive coefficients (something
related to the population fitness). In these cases the search for the nature of population fitness
becomes even more elusive. As a result population fitness is a parameter useful exclusively
for its expediency; no search for its hidden nature is justified.
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