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Fitness
702
Fitness
Fitness C B Krimbas Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.0460
Definition Fitness is a concept that is often considered to be central to population genetics, demography, and the synthetic theory of evolution. In population genetics, it is technically a relative or absolute measure of reproductive efficiency or reproductive success. The absolute or Darwinian fitness of a certain genetic constitution living in a defined homogeneous environment would be equated with the mean number (or the expected number) of zygotes sufficiently similar to that produced during its entire lifetime, whereas relative fitness would be the measure of the reproductive efficiency of a certain genotype, as defined above, compared with that of another from the same population. The term `sufficiently similar' needs explanation: it does not mean that the offspring of a certain genotype would necessarily share the same genotype with their parent (actually, in many instances, Mendelian segregation would prohibit this); rather, it indicates that genetic effects seriously affecting fitness with one generation delay should be taken into consideration and should affect the value of fitness of the parent genotype exclusively responsible for these delayed effects. Thus, the grandchildless mutants in Drosophila subobscura and D. melanogaster have such an effect: 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 are not formed. The mean number of offspring may not be sufficient to define the fitness of a genotype: the distribution of the number of its offspring may also be of importance. Thus, Gillespie has shown that genotypes having the same mean number of progeny, but differing in variances, have a different evolutionary fate. Everything else being equal, an increase in variance of the number of progeny (from generation to generation, or spatially, or developmentally) is, in the long run, disadvantageous. From the actual mean expected number of progeny we should subtract a quantity equal to 1/2s2 for the case of temporal variation (where s2 is the variance in offspring number) and 1/Ns2 for the case of developmental variation to arrive at an estimate of fitness. However, with the exception explained above, concerning the one-generation delayed effects of a certain genotype affecting reproduction,
we will restrict fitness definition to only one generation, (where N is the effective population size) thus avoiding the temporal variation. (The long-term evolutionary fate addressed by Thoday and Cooper will not be considered here.) Furthermore, we will restrict the definition of fitness to a certain homogeneous selective environment, thus avoiding complications such as those described by Brandon (1990), where a genotype having two different fitnesses in two environments, both lower than the respective two fitnesses of a different genotype, may end up having a higher mean fitness due to an unequal distribution of individuals of the two respective genotypes in these two environments]. The reason for these restrictions is that fitness values serve to put some flesh onto the models describing allelic frequency changes from generation to generation and thus allowing short-term genetic predictions. Fitness is a useful device in quantifying the kinetics of a genetic change; it is otherwise devoid of any other independent meaning and cannot serve as a substitute to the nebulous concept of adaptation. Of course in some models, one may consider complex fitness functions, e.g., the weighted mean fitness in two environments. Medawar (in Krimbas, 1984) expresses this view in the following statement: 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.
Historical Overview The first use of `fitness' with a loosely similar meaning is found in Darwin's On the Origin of Species. From the first to the sixth edition, Darwin employed the verb `fit' and the adjective `fitted' as synonyms for `adapt' and `adapted,' respectively. The noun first appears in 1859: 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. (Paul, 1992)
Of course, Darwin inherited the concept of a fitness between the organism and its environment from natural theology and from the concept of adaptation. In 1864, Herbert Spencer used the expression ``survival of the fittest'' as a synonym for natural selection, which was later used by Darwin. Thus, from the beginning, fit and fitness were seen to be semantically closely related to the process of natural selection and
Fitness 703 to `adaptation.' Even today, Brandon (1990) equates fitness with adaptedness. In 1798, Malthus compared the rates of increase of population size with the amount of food produced. According to Tort (1996), the ratio l of the number of individuals of one generation (Nt1) to that of its parental generation (Nt) is the Darwinian fitness or the Malthusian fitness. No differences among individuals are considered in this formulation, which describes a geometric or rather an exponential increase of population size, if l is constant. In 1838, Verhulst gave another formulation, taking into consideration the change in ratio as the population reaches its carrying capacity, K. Thus Verhulst distinguishes w, the biological fitness (the Verhulstian fitness is the number of offspring produced by an individual at its sexual maturity) and population fitness, which varies also according to K and to the present population size, Nt: Nt1 wNt
w
1 K
Nt 2
Thus, the relation between a nonconstant Malthusian fitness and a Verhulstian fitness is: t w
w
1 K
Nt
Let b be the percentage of the individuals in a population that during a small time interval Dt give birth to one individual (bDt) and d is the percentage of individuals dying at the same time interval (dDt), the net change in individuals at the same time interval will be: Nt b
dNt t
By substituting b d with m (where m is, according to Fisher, the Malthusian parameter) and integrating we get the form of increase of population size: Nt No emt Lotka, as well as Fisher, used mortality and fertility tables for the different biological ages to estimate fitness from m. The Darwinian fitness is related to the Malthusian parameter in the following: e
m
Furthermore, Fisher considered that Malthusian parameters, and thus fitnesses, are inherited, different genotypes having different fitnesses. The course of evolution is to maximize population fitness, that is
the (weighted) mean value of the individual fitnesses of a population. The rate of increase in fitness in any organism at any time is equal to its [additive] genetic variance in fitness at that time.
Since variances are always positive the change will always be in the direction of an increase of this quantity. Fisher considered this `fundamental theorem of natural selection' as a general law, equivalent to the second law of thermodynamics, which stipulates always an increase of a physical quantity, i.e., entropy. The generality of Fisher's law was questioned and, in some cases, it was shown not to hold true. Furthermore, as Crow and Kimura remarked, One interpretation of the theorem is to say that it measures the rate of increase in fitness that would occur if the gene frequency changes took place, but nothing else changed.
Thus an environmental deterioration that would affect fitness values, and thus decrease mean population fitness, is not considered by Fisher. Wright used the population fitness as varying according to the gene frequencies in the population. Excluding competition among individuals, Wright states that every genotype is characterized by a fitness value and each individual belonging to that genotype has an expected number of progeny, which is the fitÅ , is the ness of that genotype. The population fitness, W expected mean number of progeny of every individual Å is a composite function, of the parental generation. W the sum total of the products of all genotype frequencies by their specific fitnesses (or adaptive values). Contrary to Fisher, Wright, in his shifting balance theory, envisages most of the species to consist of many small and more or less isolated populations, each with its specific gene frequencies. Populations occupy the peaks of an adaptive surface, formed by Å (population fitnesses), for every point the values of W corresponding to certain gene frequencies. These peaks are positions of stable local equilibria. Due to drift, gene frequencies may change and, thus, 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.
Components of Fitness: Inclusive Fitness It is often stated that selection acts on survival and reproduction. This is not an exact phrasing: 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
704
Fitness
may be important only in those cases where it may affect the net reproductive effect. Selection is blind to longevity at a postreproductive age. This is the reason why the inherited pathological syndrome of Huntington disease, which appears after the reproductive years, seems not to be selected against. According to Hartl and Clark (1989), starting from the stage of the zygote, the components of fitness are as follows: viability; subsequently sexual selection operates favoring or prohibiting a genotype to find mates; 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 partners. For a simple one gene/ two alleles case, nine different fecundity values are defined. Before the formation of the zygote, gametic selection (one aspect of it being meiotic drive) may take place, and sometimes counteract the direction of selection exercised at the diploid phase. Fitness is estimated by counting zygotes produced by a zygote. A proposal to overcome the difficulty of counting zygotes in many animals was to start from another well-recognized stage of the biological cycle and complete this cycle to the same stage of the progeny. This proposal is, however, mistaken, since the progeny of a genotype do not necessarily have the same genotype as their parent. As a result this estimates fitness components corresponding to different genotypes. 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 unoccupied territory; r-selection). Lewontin (1965) examined the case of insects that follow a triangle schedule of oviposition (a triangular egg productivity function is characterized by three points: the age of first production, that of peak production, and that of the last production reported in a time coordinate and the number of eggs produced at the other). In his specific model, a shortening of developmental time may be equivalent to a doubling of total net fecundity. This shortening is equal to a 1.55 day decrease of the entire egg production program (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 at which the first egg is produced), leaving the other ages unchanged as well as the total number of eggs deposited. It is also equivalent to a 5.55-day decrease of the age of the highest egg production only (the peak of the triangle), other things remaining unchanged or, finally, to a 21-day decrease of the age at which the last egg is deposited, other variables remaining the same.
Hamilton's concept of `inclusive fitness' was formulated to provide a Darwinian explanation for altruistic actions that may 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-to-it genetic constitution. If the danger encountered is outweighed by the gain (all calculated in genes) then the performance of such acts may be fixed by natural selection. Estimations of inclusive fitness do not take into account only the individual's fitness but also that of its relatives (of similar genetic constitution): it is the sum total of two selective processes, individual selection and kin selection. In this case, in fact, 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 through its progeny.
Adaptation, Adaptedness and the Propensity Interpretation of Fitness 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 through the literature of all the important neo-Darwinists reveals that, in spite of the suggestion that adaptation has an autonomous meaning, it is used in fact as an alternative to selection. Van Valen seems to differ from all other authors because he equates adaptation with the maximization of energy appropriation, both for multiplying and for increasing biomass, thus solving the problem of lianas and other clone organisms. The concept of adaptation was shown to be completely dependent on that of selection (Krimbas, 1984). Brandon provided an argument proving the impossibility of establishing an independent of selection criterion or trait for adaptation. He argued that we may be able to select in the laboratory against any character except for one, fitness. There is no reason to exclude from natural selection the selection experiments performed in the laboratory, since the laboratory 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. Fitness is a variable substantiating and quantifying the selective process. While one would expect adaptation to disappear from the evolutionary vocabulary, it is still used for describing the selective process that changes or establishes a phenotypic trait as well as the trait itself. Sometimes the engineering approach is used:
Fitness 705 adaptation, it is argued, is in every case the optimal solution to an environmental problem. The difficulties with such an approach are twofold. First, we are often unable to define precisely the problem that the organism faces (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 to the nature of the problem the organism faces. Second, it is evident that several selection products are not necessarily the optimal solutions, the evolutionary change resembling more a process of tinkering rather than an application of an engineering design. Recently, several authors (Brandon, Mills and Beatty, Burian, and Sober; see Brandon, 1990) have supported the propensity interpretation of fitness (or adaptedness). In so doing they try first to disentangle `individual fitness' (something we are not considering here; as mentioned earlier we have taken into consideration only the fitnesses of a certain category or group of individuals) from the fitness that is expected from its genetic constitution. Indeed, all kinds of accidents may drastically modify the number of progeny one individual leaves behind. A sudden death may zero an individual's 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 to pass from the individual or actual fitness to the expected one, these authors are obliged to consider two different interpretations of `probability.' The first interpretation considers probability as the limit of a relative frequency of an event in an infinite series of trials, but since this series is never achieved, the observed frequency in a finite series of trials might be used instead. The second interpretation is that of propensity, where the very constitution, i.e., the physical properties, of the individual underlies the propensity for performing in a given way. This may be a dispositional property, i.e., it might be displayed in a certain way in some situations and in another way in others. The propensity interpretation of fitness attributes to physical causes, linked to the very structure of the individual, the tendency 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 adaptation. It is reminiscent of the Aristotelian potentia et actu, 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 the selection process depends most of the time on the properties of a genotype performing in a certain environment. But this may not be as general as one may think. There are situations in which the contribution to fitness from
the part of the organism is not clear or does not seem preponderent. Thus, 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 the mating disadvantage when they are frequent. It is a case of frequency-dependent selection. On the other hand, the definition of genotypic fitness might also suffer from some disadvantages. Let us consider the case of dextral and sinistral coiling in shells of certain species of snails. The direction of coiling is genetic, due to one gene with two alleles. The allele d (for dextral coiling) is dominant to the l allele (recessive). But the phenotype of the individual is exclusively determined by the genotype (not the phenotype) of its mother and not by its own genotype. Thus, there is a delay of one generation in phenotypic expression. Selection operates on phenotypes (the interactors of D. Hull). In the case of selection for dextral or sinistral direction of coiling, the phenotypic fitnesses may be clearly understood and simple but useless, while the genotypic fitnesses would be a complicated function depending on the frequency of the alleles in the population and the mating system. Thus, it seems better to consider genotypic fitness as a useful device in performing some kinetic studies regarding changes in gene frequencies or attraction to an equilibrium point. It is useless to attribute other qualities or properties to this device. Modern evolutionary theory is basically of a historical nature (although some processes may be repeated). A complete and satisfactory explanation of a specific case should comprise a historical narrative including information of the phenotypic trait being 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 change to selection of the genetic structure of the population, and the corresponding change in the phenotypes. In natural history, generality and the search for hidden and nonexisting entities and properties may only contribute to an increase in the metaphysical component of evolutionary theory inherited from natural theology.
On Population Fitness It is much more difficult to define population fitness: population geneticists use to calculate the mean adaptive value or the mean individual fitness in a population. But this exercise is quite futile when comparing 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 certain that a greater or denser population is better adapted, since it may suffer from
706
Fitness Landscape
parasites and epidemics; on the other hand, a population depleted of individuals may suffer collapse and extinction. I have argued (Krimbas, 1984) that according to the `Red Queen hypothesis' of Van Valen, all populations (at least of the same species) seem to have, a priori, the same probability of extinction, and thus possess, a priori, the same long-term population fitness. In addition, it is not clear enough how we should consider a group: a group is not an organism that 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 subject. Should we consider group extinction per unit of time to determine group fitness? What about group multiplication? In order to achieve a model in 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.
References
Brandon RN (1990) Adaptation and Environment. Princeton, NJ: Princeton University Press. Gillois M (1996) Fitness. In Tort P (ed.) Dictionnaire du Darwinisme et de l'Evolution, vol. 2, 1676±1688. Paris: Presses Universitaires de France. Hartl DL and Clark AG (1989) Principles of Population Genetics, 2nd edn. Sunderland, MA: Sinauer Associates. Krimbas CB (1984) On adaptation, neo-Darwinian tautology, and population fitness. Evolutionary Biology 17: 1± 57. Lewontin RC (1965) Selection for colonizing ability. In: Baker HG and Stebbins GL (eds) The Genetics of Colonizing Species, 77±94. New York: Columbia University Press. Paul D (1992) Fitness: historical perspectives. In: Fox Keller E and Lloyd EA (eds) Keywords in Evolutionary Biology, 112±114. Cambridge, MA: Harvard University Press.
are gene (or sometimes genotype) frequencies. It is usually pictured in three dimensions, but conceptually can involve a larger number. In some models it has an exact mathematical meaning, in others it is employed as a metaphor. The idea of an adaptive surface was introduced by Sewall Wright. He thought of a surface on which each point on the surface corresponded to a combination of allele frequencies on the abscissae. Figure 1 shows a simple two-locus example. Random mating proportions and linkage equilibrium are assumed. The two abscissae are the frequencies of the dominant A and B alleles. The relative genotype fitnesses of aa bb, A bb, aa B , and A B are 1, 1 s, 1 s, and 1 t, where s and t are both positive and A (or B ) indicates that the second allele can be either A or a (or B or b). The ordinate represents the average fitness of a population with particular allele frequencies. There are two peaks, one when the genotype AA BB is fixed, the other a lower peak for the genotype aa bb. Genotypes AA bb and aa BB are at the other two corners and are least fit. Ordinarily a population, located at a point on the surface, climbs the nearest peak, but not necessarily in a straight line. The complications of mutation, linkage, and epistasis may cause the path upward to be circuitous. And, as these complications are introduced, along with more loci, the mathematics becomes more difficult. This is the situation envisioned by Sewall Wright. A population cannot change from the lower peak to the higher one, because it has to pass through a less fit region. It was this dilemma that led Wright to propose his shifting-balance theory whereby a combination of random drift and differential migration make it possible to cross the valley and reach a higher peak. Wright regarded the fitness surface more as a 1+t
1
Fitness Landscape
fitness
See also: Adaptive Landscapes; Darwin, Charles; Fitness Landscape; Natural Selection
J F Crow AA bb
Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.0461
AA BB
1−s aa bb
A fitness landscape, or adaptive surface, is a geometrical construct in which the fitness or adaptive value of a genotype is the ordinate and the two abscissae
%A %B
Figure 1
aa BB
Example of a fitness landscape, with two loci.
Fitness
Fitness C B Krimbas Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.0460
Definition Fitness is a concept that is often considered to be central to population genetics, demography, and the synthetic theory of evolution. In population genetics, it is technically a relative or absolute measure of reproductive efficiency or reproductive success. The absolute or Darwinian fitness of a certain genetic constitution living in a defined homogeneous environment would be equated with the mean number (or the expected number) of zygotes sufficiently similar to that produced during its entire lifetime, whereas relative fitness would be the measure of the reproductive efficiency of a certain genotype, as defined above, compared with that of another from the same population. The term `sufficiently similar' needs explanation: it does not mean that the offspring of a certain genotype would necessarily share the same genotype with their parent (actually, in many instances, Mendelian segregation would prohibit this); rather, it indicates that genetic effects seriously affecting fitness with one generation delay should be taken into consideration and should affect the value of fitness of the parent genotype exclusively responsible for these delayed effects. Thus, the grandchildless mutants in Drosophila subobscura and D. melanogaster have such an effect: 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 are not formed. The mean number of offspring may not be sufficient to define the fitness of a genotype: the distribution of the number of its offspring may also be of importance. Thus, Gillespie has shown that genotypes having the same mean number of progeny, but differing in variances, have a different evolutionary fate. Everything else being equal, an increase in variance of the number of progeny (from generation to generation, or spatially, or developmentally) is, in the long run, disadvantageous. From the actual mean expected number of progeny we should subtract a quantity equal to 1/2s2 for the case of temporal variation (where s2 is the variance in offspring number) and 1/Ns2 for the case of developmental variation to arrive at an estimate of fitness. However, with the exception explained above, concerning the one-generation delayed effects of a certain genotype affecting reproduction,
we will restrict fitness definition to only one generation, (where N is the effective population size) thus avoiding the temporal variation. (The long-term evolutionary fate addressed by Thoday and Cooper will not be considered here.) Furthermore, we will restrict the definition of fitness to a certain homogeneous selective environment, thus avoiding complications such as those described by Brandon (1990), where a genotype having two different fitnesses in two environments, both lower than the respective two fitnesses of a different genotype, may end up having a higher mean fitness due to an unequal distribution of individuals of the two respective genotypes in these two environments]. The reason for these restrictions is that fitness values serve to put some flesh onto the models describing allelic frequency changes from generation to generation and thus allowing short-term genetic predictions. Fitness is a useful device in quantifying the kinetics of a genetic change; it is otherwise devoid of any other independent meaning and cannot serve as a substitute to the nebulous concept of adaptation. Of course in some models, one may consider complex fitness functions, e.g., the weighted mean fitness in two environments. Medawar (in Krimbas, 1984) expresses this view in the following statement: 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.
Historical Overview The first use of `fitness' with a loosely similar meaning is found in Darwin's On the Origin of Species. From the first to the sixth edition, Darwin employed the verb `fit' and the adjective `fitted' as synonyms for `adapt' and `adapted,' respectively. The noun first appears in 1859: 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. (Paul, 1992)
Of course, Darwin inherited the concept of a fitness between the organism and its environment from natural theology and from the concept of adaptation. In 1864, Herbert Spencer used the expression ``survival of the fittest'' as a synonym for natural selection, which was later used by Darwin. Thus, from the beginning, fit and fitness were seen to be semantically closely related to the process of natural selection and
Fitness 703 to `adaptation.' Even today, Brandon (1990) equates fitness with adaptedness. In 1798, Malthus compared the rates of increase of population size with the amount of food produced. According to Tort (1996), the ratio l of the number of individuals of one generation (Nt1) to that of its parental generation (Nt) is the Darwinian fitness or the Malthusian fitness. No differences among individuals are considered in this formulation, which describes a geometric or rather an exponential increase of population size, if l is constant. In 1838, Verhulst gave another formulation, taking into consideration the change in ratio as the population reaches its carrying capacity, K. Thus Verhulst distinguishes w, the biological fitness (the Verhulstian fitness is the number of offspring produced by an individual at its sexual maturity) and population fitness, which varies also according to K and to the present population size, Nt: Nt1 wNt
w
1 K
Nt 2
Thus, the relation between a nonconstant Malthusian fitness and a Verhulstian fitness is: t w
w
1 K
Nt
Let b be the percentage of the individuals in a population that during a small time interval Dt give birth to one individual (bDt) and d is the percentage of individuals dying at the same time interval (dDt), the net change in individuals at the same time interval will be: Nt b
dNt t
By substituting b d with m (where m is, according to Fisher, the Malthusian parameter) and integrating we get the form of increase of population size: Nt No emt Lotka, as well as Fisher, used mortality and fertility tables for the different biological ages to estimate fitness from m. The Darwinian fitness is related to the Malthusian parameter in the following: e
m
Furthermore, Fisher considered that Malthusian parameters, and thus fitnesses, are inherited, different genotypes having different fitnesses. The course of evolution is to maximize population fitness, that is
the (weighted) mean value of the individual fitnesses of a population. The rate of increase in fitness in any organism at any time is equal to its [additive] genetic variance in fitness at that time.
Since variances are always positive the change will always be in the direction of an increase of this quantity. Fisher considered this `fundamental theorem of natural selection' as a general law, equivalent to the second law of thermodynamics, which stipulates always an increase of a physical quantity, i.e., entropy. The generality of Fisher's law was questioned and, in some cases, it was shown not to hold true. Furthermore, as Crow and Kimura remarked, One interpretation of the theorem is to say that it measures the rate of increase in fitness that would occur if the gene frequency changes took place, but nothing else changed.
Thus an environmental deterioration that would affect fitness values, and thus decrease mean population fitness, is not considered by Fisher. Wright used the population fitness as varying according to the gene frequencies in the population. Excluding competition among individuals, Wright states that every genotype is characterized by a fitness value and each individual belonging to that genotype has an expected number of progeny, which is the fitÅ , is the ness of that genotype. The population fitness, W expected mean number of progeny of every individual Å is a composite function, of the parental generation. W the sum total of the products of all genotype frequencies by their specific fitnesses (or adaptive values). Contrary to Fisher, Wright, in his shifting balance theory, envisages most of the species to consist of many small and more or less isolated populations, each with its specific gene frequencies. Populations occupy the peaks of an adaptive surface, formed by Å (population fitnesses), for every point the values of W corresponding to certain gene frequencies. These peaks are positions of stable local equilibria. Due to drift, gene frequencies may change and, thus, 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.
Components of Fitness: Inclusive Fitness It is often stated that selection acts on survival and reproduction. This is not an exact phrasing: 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
704
Fitness
may be important only in those cases where it may affect the net reproductive effect. Selection is blind to longevity at a postreproductive age. This is the reason why the inherited pathological syndrome of Huntington disease, which appears after the reproductive years, seems not to be selected against. According to Hartl and Clark (1989), starting from the stage of the zygote, the components of fitness are as follows: viability; subsequently sexual selection operates favoring or prohibiting a genotype to find mates; 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 partners. For a simple one gene/ two alleles case, nine different fecundity values are defined. Before the formation of the zygote, gametic selection (one aspect of it being meiotic drive) may take place, and sometimes counteract the direction of selection exercised at the diploid phase. Fitness is estimated by counting zygotes produced by a zygote. A proposal to overcome the difficulty of counting zygotes in many animals was to start from another well-recognized stage of the biological cycle and complete this cycle to the same stage of the progeny. This proposal is, however, mistaken, since the progeny of a genotype do not necessarily have the same genotype as their parent. As a result this estimates fitness components corresponding to different genotypes. 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 unoccupied territory; r-selection). Lewontin (1965) examined the case of insects that follow a triangle schedule of oviposition (a triangular egg productivity function is characterized by three points: the age of first production, that of peak production, and that of the last production reported in a time coordinate and the number of eggs produced at the other). In his specific model, a shortening of developmental time may be equivalent to a doubling of total net fecundity. This shortening is equal to a 1.55 day decrease of the entire egg production program (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 at which the first egg is produced), leaving the other ages unchanged as well as the total number of eggs deposited. It is also equivalent to a 5.55-day decrease of the age of the highest egg production only (the peak of the triangle), other things remaining unchanged or, finally, to a 21-day decrease of the age at which the last egg is deposited, other variables remaining the same.
Hamilton's concept of `inclusive fitness' was formulated to provide a Darwinian explanation for altruistic actions that may 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-to-it genetic constitution. If the danger encountered is outweighed by the gain (all calculated in genes) then the performance of such acts may be fixed by natural selection. Estimations of inclusive fitness do not take into account only the individual's fitness but also that of its relatives (of similar genetic constitution): it is the sum total of two selective processes, individual selection and kin selection. In this case, in fact, 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 through its progeny.
Adaptation, Adaptedness and the Propensity Interpretation of Fitness 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 through the literature of all the important neo-Darwinists reveals that, in spite of the suggestion that adaptation has an autonomous meaning, it is used in fact as an alternative to selection. Van Valen seems to differ from all other authors because he equates adaptation with the maximization of energy appropriation, both for multiplying and for increasing biomass, thus solving the problem of lianas and other clone organisms. The concept of adaptation was shown to be completely dependent on that of selection (Krimbas, 1984). Brandon provided an argument proving the impossibility of establishing an independent of selection criterion or trait for adaptation. He argued that we may be able to select in the laboratory against any character except for one, fitness. There is no reason to exclude from natural selection the selection experiments performed in the laboratory, since the laboratory 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. Fitness is a variable substantiating and quantifying the selective process. While one would expect adaptation to disappear from the evolutionary vocabulary, it is still used for describing the selective process that changes or establishes a phenotypic trait as well as the trait itself. Sometimes the engineering approach is used:
Fitness 705 adaptation, it is argued, is in every case the optimal solution to an environmental problem. The difficulties with such an approach are twofold. First, we are often unable to define precisely the problem that the organism faces (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 to the nature of the problem the organism faces. Second, it is evident that several selection products are not necessarily the optimal solutions, the evolutionary change resembling more a process of tinkering rather than an application of an engineering design. Recently, several authors (Brandon, Mills and Beatty, Burian, and Sober; see Brandon, 1990) have supported the propensity interpretation of fitness (or adaptedness). In so doing they try first to disentangle `individual fitness' (something we are not considering here; as mentioned earlier we have taken into consideration only the fitnesses of a certain category or group of individuals) from the fitness that is expected from its genetic constitution. Indeed, all kinds of accidents may drastically modify the number of progeny one individual leaves behind. A sudden death may zero an individual's 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 to pass from the individual or actual fitness to the expected one, these authors are obliged to consider two different interpretations of `probability.' The first interpretation considers probability as the limit of a relative frequency of an event in an infinite series of trials, but since this series is never achieved, the observed frequency in a finite series of trials might be used instead. The second interpretation is that of propensity, where the very constitution, i.e., the physical properties, of the individual underlies the propensity for performing in a given way. This may be a dispositional property, i.e., it might be displayed in a certain way in some situations and in another way in others. The propensity interpretation of fitness attributes to physical causes, linked to the very structure of the individual, the tendency 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 adaptation. It is reminiscent of the Aristotelian potentia et actu, 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 the selection process depends most of the time on the properties of a genotype performing in a certain environment. But this may not be as general as one may think. There are situations in which the contribution to fitness from
the part of the organism is not clear or does not seem preponderent. Thus, 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 the mating disadvantage when they are frequent. It is a case of frequency-dependent selection. On the other hand, the definition of genotypic fitness might also suffer from some disadvantages. Let us consider the case of dextral and sinistral coiling in shells of certain species of snails. The direction of coiling is genetic, due to one gene with two alleles. The allele d (for dextral coiling) is dominant to the l allele (recessive). But the phenotype of the individual is exclusively determined by the genotype (not the phenotype) of its mother and not by its own genotype. Thus, there is a delay of one generation in phenotypic expression. Selection operates on phenotypes (the interactors of D. Hull). In the case of selection for dextral or sinistral direction of coiling, the phenotypic fitnesses may be clearly understood and simple but useless, while the genotypic fitnesses would be a complicated function depending on the frequency of the alleles in the population and the mating system. Thus, it seems better to consider genotypic fitness as a useful device in performing some kinetic studies regarding changes in gene frequencies or attraction to an equilibrium point. It is useless to attribute other qualities or properties to this device. Modern evolutionary theory is basically of a historical nature (although some processes may be repeated). A complete and satisfactory explanation of a specific case should comprise a historical narrative including information of the phenotypic trait being 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 change to selection of the genetic structure of the population, and the corresponding change in the phenotypes. In natural history, generality and the search for hidden and nonexisting entities and properties may only contribute to an increase in the metaphysical component of evolutionary theory inherited from natural theology.
On Population Fitness It is much more difficult to define population fitness: population geneticists use to calculate the mean adaptive value or the mean individual fitness in a population. But this exercise is quite futile when comparing 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 certain that a greater or denser population is better adapted, since it may suffer from
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parasites and epidemics; on the other hand, a population depleted of individuals may suffer collapse and extinction. I have argued (Krimbas, 1984) that according to the `Red Queen hypothesis' of Van Valen, all populations (at least of the same species) seem to have, a priori, the same probability of extinction, and thus possess, a priori, the same long-term population fitness. In addition, it is not clear enough how we should consider a group: a group is not an organism that 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 subject. Should we consider group extinction per unit of time to determine group fitness? What about group multiplication? In order to achieve a model in 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.
References
Brandon RN (1990) Adaptation and Environment. Princeton, NJ: Princeton University Press. Gillois M (1996) Fitness. In Tort P (ed.) Dictionnaire du Darwinisme et de l'Evolution, vol. 2, 1676±1688. Paris: Presses Universitaires de France. Hartl DL and Clark AG (1989) Principles of Population Genetics, 2nd edn. Sunderland, MA: Sinauer Associates. Krimbas CB (1984) On adaptation, neo-Darwinian tautology, and population fitness. Evolutionary Biology 17: 1± 57. Lewontin RC (1965) Selection for colonizing ability. In: Baker HG and Stebbins GL (eds) The Genetics of Colonizing Species, 77±94. New York: Columbia University Press. Paul D (1992) Fitness: historical perspectives. In: Fox Keller E and Lloyd EA (eds) Keywords in Evolutionary Biology, 112±114. Cambridge, MA: Harvard University Press.
are gene (or sometimes genotype) frequencies. It is usually pictured in three dimensions, but conceptually can involve a larger number. In some models it has an exact mathematical meaning, in others it is employed as a metaphor. The idea of an adaptive surface was introduced by Sewall Wright. He thought of a surface on which each point on the surface corresponded to a combination of allele frequencies on the abscissae. Figure 1 shows a simple two-locus example. Random mating proportions and linkage equilibrium are assumed. The two abscissae are the frequencies of the dominant A and B alleles. The relative genotype fitnesses of aa bb, A bb, aa B , and A B are 1, 1 s, 1 s, and 1 t, where s and t are both positive and A (or B ) indicates that the second allele can be either A or a (or B or b). The ordinate represents the average fitness of a population with particular allele frequencies. There are two peaks, one when the genotype AA BB is fixed, the other a lower peak for the genotype aa bb. Genotypes AA bb and aa BB are at the other two corners and are least fit. Ordinarily a population, located at a point on the surface, climbs the nearest peak, but not necessarily in a straight line. The complications of mutation, linkage, and epistasis may cause the path upward to be circuitous. And, as these complications are introduced, along with more loci, the mathematics becomes more difficult. This is the situation envisioned by Sewall Wright. A population cannot change from the lower peak to the higher one, because it has to pass through a less fit region. It was this dilemma that led Wright to propose his shifting-balance theory whereby a combination of random drift and differential migration make it possible to cross the valley and reach a higher peak. Wright regarded the fitness surface more as a 1+t
1
Fitness Landscape
fitness
See also: Adaptive Landscapes; Darwin, Charles; Fitness Landscape; Natural Selection
J F Crow AA bb
Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.0461
AA BB
1−s aa bb
A fitness landscape, or adaptive surface, is a geometrical construct in which the fitness or adaptive value of a genotype is the ordinate and the two abscissae
%A %B
Figure 1
aa BB
Example of a fitness landscape, with two loci.