Evolutionary theory is the general framework for modern biology, in the sense that all living phenomena have an evolutionary history which somehow accounts for them being the way they are. Ernst Mayr usefully distinguished, in biology, two sets of inquiries: the “functional biology”, looking for “proximate causes” of a trait in an organism, i.e. causes pertaining to the life time of the individual, and the “evolutionary biology”, looking for “ultimate causes”, namely causes at the level of the history of the species to which belongs the individual. The former includes physiology, molecular biology, developmental biology, etc., whereas the latter includes paleontology, population genetics, behavioral ecology, systematics, etc. Evolutionary explanation is the set of explanatory styles to be met in this field.
Explananda and explanantia.
Evolutionary theory, as it was formulated by Darwin, holds two key ideas: all living forms share a common history and (as the naturalists hypothesized) a common origin; natural selection is a process responsible for many of the features of this Tree, and of the species and organisms it includes. In the usual theory, called the “Modern Synthesis“, namely a synthesis of Darwinism and Mendelism on the basis of population genetics in the 30s, evolution is related to the dynamics of gene frequencies.
Let’s first specify what evolutionary explanations are intended to explain. First, they explain evolution; then, they should explain: the diversity of living beings; the adaptedness of organisms to their environments - on the basis of the fact that they display features which suit them to their environment, for example the webbed feet of ducks are suited to swimming. So they explain the traits themselves, which are adaptations. Given that Modern Synthesis has defined evolution as the “change in allelic frequencies”, a first explanandum is the change in thew relative frequency of genes. The existence of a trait in this context is explained when the fixation of a gene underlying it is explained.
The set of explanantia mostly used to explain those explananda are: natural selection; genetic drift; and “constraints”. The last of these is loosely defined. It includes “phylogenetics inertia”, i.e. the fact that a same trait in a population is indeed a character state of an ancestor and did not happen through natural selection even if it is adaptive. It also means “developmental constraints” (see developmental explanation). Natural selection is the process of differential reproduction of individuals carrying traits which give them different chances of having their traits represented in the next generation. As soon as a population of individuals has traits which are varying and heritable, and if those traits causally influence their chances of reproduction, then we have natural selection. This third property means that those traits have, or contribute to, fitness. Finally, drift is the statistical effect due to the fact that generation after generation a stochastic sampling of the population takes place. The smaller the population, the higher the expected amount of drift; whereas in an infinite population, selection would be the sole causal factor, hence the fittest traits or alleles would in general go to fixation.
Thus, evolutionary explanation is always a population level explanation. All factors are differential, so the whole process needs a population of varying individual; it contrasts with an explanation which would consider an individual and explain its traits by investigating how they developed. To this extent, population level and individual level explanations are rather complementary than competing: “why does individual A have trait X?” can be answered by considering its history, whereas population level explanations answer questions such as: “why does each individual in the population have trait X?”, or “why do many of them (or: a minority) have trait X?” (For example, why are some people left handed ?)
Two evolutionary questions.
Evolutionary explanations often build models, analytic or simulated, which on plausible assumptions describe the evolutionary dynamics at stake or the way it may have produced the explanandum; model-building and comparing with data are the two stages of the explanation. Fitness and population size influence evolutionary dynamics (as well as migration and mutation rates). Yet fitness is a probabilistic term, and has causes: all the interactions within which an organism can enter, and into which the trait of interest is involved, determine in the end the fitness value of the trait or of the organism. This entails a difference between two kinds of questions:
How does selection proceed? With fitness as a variable, one can build a model describing the dynamics of a population of alleles with specific genetic structure (epistasis, pleiotropy, dominance, etc.) and fitness values. This is what population genetics does.
Why is / was there selection? One can investigate the causes of the fitness values, which implies considering the physiology of individuals and the ecology of the population. Behavioral ecology, asking about the function of various traits - i.e. the effect which led them to spread into the population and allows for its maintenance - exemplifies such research program, as well as paleontology.
In (a), population genetics explicates the process of natural selection and shows which combinations of fitness values, size and mutation rates will plausibly lead a trait to fixation. In this context an evolutionary explanation of the frequency of traits in a population would start from equilibrium considerations: the Hardy-Weinberg formula for two alleles with initial frequencies p and q in a sexual panmictic population defines the equilibrium frequencies that each allele would have with no selection in a panmictic infinite isolated population. This is a null hypothesis for the system, like the inertia principle in mechanics (Sober, 1984). Then, one compares the actual population to the model; if there is deviation from this equilibrium, one will hypothesize drift and selection as causes. Factoring in the fitness values as they are measured in nature in the equations, will give predictions about the frequencies; differences with such frequencies in the actual population are therefore caused by drift (Gillespie 2004). In several cases an explanation can prove that a trait is here because of selection, while not being able to show what selection was for – because the causes of fitness or selection are unknown, ecological context being insufficiently understood.
With question (b) one is interested in knowing why a trait is there, whether it is by selection and for which selective pressures. The pervasiveness of altruism (i.e. behaviors increasing other’s fitness at the cost of one’s fitness), whereas selfishness by definition seems privileged by natural selection, compelled biologists to consider selection at the level of genes, where altruism towards kin appear evolutionarily favored since the relatedness of the beneficiary of the act mitigates the cost of altruism. Thus “kin selection” (West et al. 2007), together with sexual selection, is another form of natural selection to which evolutionary explanations must appeal.
Several kinds of explanation are therefore possible, which need not take the genetic makeup into account, and which involve basically the idea that selection, being the over-reproduction of the fittest, optimized the traits. Comparisons between species are also used in addition, or independently.
Optimality modeling. If one shows how a trait makes the highest contribution to fitness amongst all the actual or possible variants, then it is highly plausible that it results from natural selection. Often, one picks up a proxy for fitness, such as energy intake, chances of survival at some age, etc., not necessarily correlated to fitness in a linear way. An evolutionary explanation would therefore model one of these values as a function of the trait, given some parameters representing the selective pressures in the environment (Fig.1): for example the scarcity of resources, the chances of meeting a predator, and so on. If the extant trait values in various environments are the maxima of the function, this is evidence for the trait being selected for meeting those environmental demands. The optimal value for one selective pressure may not be the same as the optimum for another; hence the result of natural selection should be a trade-off between those demands, for example foraging and looking for mates. As a methodology, this adaptationism is extensively used in behavioral ecology. If reality does not match an optimality model, one can say either that the selective pressures have not been correctly identified, or that genetic structure, amount of genetic variation, drift or other factors affect the evolutionary process, so that the models only show what the trait would be if selection were acting alone.
Fig. 1. Optimality model for time t spent in patches when foraging (E is calorific intake, s is the mean time spent to move between patches); t* is optimal because of the law of diminishing returns which makes increasing t less and less beneficial. (After Charnov 1976)
Game-theoretic modeling. Often, the fitness of traits depends on the frequency of traits-carriers in a population: for example, a camouflage is all the more efficient when it is not so frequent. Frequency dependence is pervasive when it comes to social interactions, where the payoffs of the possible traits depend upon what the others will do, so that the evolutionary dynamics at one moment in turn depends upon the chances of meeting an interactor of a given type (e.g. altruist, selfish, aggressive, etc.). Evolutionary explanation of social behavior therefore relies on Evolutionary Stable Strategies models (Maynard-Smith, 1982), an ESS being a strategy such that if all the population adopts it, it is not vulnerable to invasions. Often ESS is a mixed strategy (for example: cooperate at a chance 0.7, defect at a chance 0.3). The distribution of traits in a population matching what an ESS model would predict is clear evidence that the maintenance of those traits results from natural selection. Often, ESS models are devised in the frameworks of replicator dynamics. Recently, “adaptive dynamics” (Metz 2008) has provided a specific way of modeling evolutionary dynamics on the basis of “invasion fitness”, i.e. the probability of each mutant (individual or species) to invade a population, therefore synthesizing population genetics, behavioral and community ecology.
Those explanations concern the maintenance of traits, rather than their origin; ESS models are built on the assumption of a strategy set but the evolutionary origins of strategies do not matter. Explaining origins of traits is another evolutionary question, which one undertakes for example in paleontology, where the environment of the organisms is not known. In such context, an available method is reverse engineering: given the traits and their mechanisms, reconstruct the environmental demands to which they may have responded.
Comparisons. Comparing a trait in an environment with one in a sister or ancestor species, and whose origin is already known, allows one to check whether it is simply inherited, or whether it is an adaptation for analogous selective pressures (Endler 1986). Those comparisons may justify a claim that some trait results from selection, but also supplement other evolutionary models, e.g. in order to exclude rival non-selective hypotheses. Comparative methods are therefore pervasive.
Experimental tests may be used, for instance changing the trait value enables one to check whether selective pressures exist which will reestablish the original value of the trait – a strong argument for its being maintained by selection (Williams 1966). A complete explanation of a trait therefore relies on: ecological knowledge (of the environment), phylogenetic knowledge (for comparisons) and genetics (the underlying genetic make-up, and the heritability of traits) (Brandon, 1990).
Evolutionary biology is a historical science –hence acknowledging an important role for contingency -but heavily relies on mathematical modeling (e.g. Hamilton’s rule for the evolution of altruism). Adaptive dynamics provide for those models a “canonical equation” of change of fitnesses, yet it’s often hardly solvable (Metz 2008). Many equations of the population genetics models can be derived from Price equation. Other models of natural selection are stated in terms of replicator’s dynamics (especially with ESS). Many models are indeed simulated rather than analytic.
Optimization as an assumption is supposedly derived from Fisher’s fundamental theorem of natural selection, which states that the mean fitness of a population increases equally to the genetic additive variance (by nature always positive). Fisher’s result has been discussed and is indeed very restricted, concerning only the evolutionary change in fitness due to the direct action of natural selection (Frank and Slatkin, 1992). It can be derived from the Price equation, when the value z considered is the fitness itself. Optimality assumptions of behavioral ecologists seem at odds with results of population genetics emphasizing the large restrictions on optimization (especially, in cases of frequency-dependence selection, e.g. social interactions). However there is now (Grafen 2007) a formal proof of an isomorphism between population genetics models of natural selection dynamics and optimization, which provides a mathematical basis to the implicit pervasive intuition that natural selection is an optimizing process. The maximand of such process is inclusive fitness. Therefore optimality modeling and ESS receive a formal justification from the mathematics of allele frequencies.
References Brandon R. (1990) Adaptation and environment. Cambridge: MIT Press.
Frank S., Slatkin M. (1992) “Fisher's Fundamental Theorem of Natural Selection.” TREE, 7, 3: 92-95.
Gillespie J. (2004) Population Genetics – A Concise Guide. Baltimore :The John Hopkins University Press .
Grafen, A. (2007) “The formal Darwinism project: a mid-term report.” Journal of Evolutionary Biology, 20: 1243–1254.
Maynard-Smith J (1982) Evolution and the theory of games. Cambridge: Cambridge University Press
Metz J.A.J. (2008) “Fitness.” In Jørgensen S., Fath B. (Eds.) Evolutionary Ecology. Encyclopedia of Ecology II, pp. [1599-1612] Oxford: Elsevier.
Ridley M. (2001) Evolution. Oxford: Oxford University Press
Sober E. (1984) The nature of selection. Cambridge: MIT Press.
West S., Griffin A., Gardner A. (2007) „Social semantics: altruism, cooperation, mutualism, strong reciprocity and group selection.” Journal of Evolutionary Biology 20: 415-432.
Williams G.C. (1966) Adaptation and natural selection. Princeton: Princeton University Press.
Adaptation; fitness; function; Price equation; relatedness; replicator’s dynamics; sexual selection.
Adaptation. “Adaptation” may name a process or a state, can be used in physiological or evolutionary contexts, and concerns organisms or traits. An individual organism has abilities to physiologically adapt to its environment, for example by changing the values of some parameters of its metabolism (pulse, body temperature, etc.). Its being adapted is the result of such physiological process. In evolutionary biology it may be useful to talk of adaptedness of organisms, namely their being adjusted to their environments, and of traits themselves as adaptations. Adaptedness is always relative to an environment. Traits as adaptations, fitness and adaptedness of organisms are basically related by natural selection, namely the process by which the more adapted organisms, having higher chances of survival and reproduction (i.e. higher fitness), on the average leave more offspring, and hence increase the frequency of their heritable traits in the next generations, and finally lead to the fixation of those traits, namely the adaptations.
In neo-Darwinian biology, a trait is an adaptation when it results from natural selection (Burian, 2005). To this extent, adaptation is, defined by natural selection; calling a trait an adaptation is therefore a historical statement. The longstanding amazement of naturalists in front of the adaptation of species to their milieu has been explained by Darwin’s hypothesis of natural selection as the main process accounting for organismal traits. Natural selection explains the presence of a trait, but this explanation is not complete if one does not know an “adaptation for what” the trait is, i.e. to which selective pressures it owes its existence (Brandon, 1990). Notably, a trait can be shown to be an adaptation, i.e. shaped by natural selection, whereas we do not know an adaptation for what (for example, Kreitmann tests on genome sequences may show they result from selection, but give no idea of the reasons for which they have been selected).
Yet in the context of the explanation of maintenance of traits some behavioral ecologists defined an adaptation as the fittest phenotypic variant, notwithstanding its evolutionary origin (Reeve and Sherman, 1993), especially because many evolutionary explanations do not take the historical context into account.
Concerning the link between adaptations and adaptedness, one could argue that, the more adaptations an organisms has, the more adapted it is; in this sense evolutionary biologist Julian Huxley called organisms “bundles of adaptations” (though this not exactly being his own view), yet this position can be criticized as too much adaptationist. The set of adaptations characterizing organisms constitute what is often called its “design”. Given that natural selection somehow increases inclusive fitness, it is plausible to say that organisms are designed to maximize their inclusive fitness.
However, two adaptations for distinct environmental demands can be conflicting, and therefore they do not increase the fitness of organisms in an additive manner. For example, risky behavior is some species are shown to have the function of attract female mates (e.g. through the “handicap principle”, see Sexual selection), yet it conflicts with many adaptations which increase the survival chances of the organisms (fear reactions, etc.)
With a given genotype, some individuals may display a range of various phenotypes adapted to their environment – this is called “phenotypic plasticity”. For instance, some species of fish will turn into either males or females depending on the temperature of water. It is useful to distinguish this plasticity from the evolutionary notion of adaptation, which refers to the genotypic underpinning of traits.
Brandon R. (1990) Adaptation and environment. Cambridge: MIT Press.
Burian, R. (2005 ) “Adaptation.” In Burian, R. The Epistemology of Development, Evolution, and Genetics. Cambridge: Cambridge University Press, pp. 54-80.
Reeve H.K., Sherman P. (1993) “Adaptation and the goals of evolutionary research.” Quarterly Review of Biology 68: 1–32
Adaptationism. Assuming that each trait of an organism is the result of an optimization process, driven by natural selection, and then is somehow optimal. Steven Jay Gould and Richard Lewontin (1978) famously forged the term and criticized it, because it overlooks the fact that organisms display a cohesive unity, and because adaptationist explanations are often not falsifiable. However Godfrey-Smith (2001) usefully distinguished three brands of adaptationism: adaptationism can be either methodological (Maynard Smith 1984), and then unlikely to be right or wrong; or an empirical claim, whose testing is not yet uncontroversial, or finally explanatory, namely, express the belief that the most “interesting traits” (e.g. complex adaptations) are due to selection (yet the notion of “interesting” is irreducibly subjective). Methodological adaptationism emphasizes that optimality models allows one to discover constraints – e.g. developmental or historical constraints – which prevent real organisms to reach the optima predicted by the models; therefore it does not underlie an empirical claim that organic nature is perfectly adapted, or that natural selection always leads to optimization.
Gould S.J., Lewontin R. (1978) “The spandrels of san Marco and the panglossian paradigm: A critique of the adaptationist programme.” Proc R Soc Lond B 205: 581–598
Godfrey-Smith (2001) “Three kinds of adaptationism.” In: Orzack SH, Sober E (eds.) Adaptationism and optimality. Cambridge: Cambridge University Press,, pp 335–357
Maynard‐Smith J. (1984) “Optimization theory in evolution.” Annual Review of Ecology and Systematics, 9: 31–56
Fitness. The word comes from the phrase “survival of the fittest” which Darwin borrowed from Spencer in the last edition of the Origin of species due to his own hand. Fitness has two components, survival and reproduction. If an organism is very well adjusted to its milieu, but does not reproduce, it has no evolutionary impact; hence reproduction is often taken as crucial, and survival considered as a proxy for reproduction (the longer X survives, the higher the chances it has offspring). However, even if often correct, those approximations prove to be controversial, e.g. when some organisms grow rather than reproduce. In some contexts one has to model the two components of fitness separately, for instance when the issue is to understand how individual resources are partitioned between reproduction and survival.
More formally, fitness can be defined as the probability distribution of the representation of a gene, a trait or an individual at the next generation; yet often equations can consider only the expectancy (fitness meaning expected offspring number of an individual). Because it concerns expected rather than actual offspring, fitness is often metaphysically considered as a propensity (sometimes called “expected fitness”) rather than as a categorical property (then called “realized fitness”).
Sometimes several generations have to be taken into account to understand the evolutionary dynamics (for example when explaining the constancy of sex-ratio, which involves considering the effect on grand-children) (Sober, 2002). The case of altruism compels biologists to consider selection at the level of genes. According to Hamilton’s rule, the relatedness between actor and beneficiary may account for the selection of the altruistic act because the degree of relatedness mitigates the cost: if the act increases the number of altruistic alleles at the next generation (as compared to the selfish alleles), be they directly alleles of the offspring of the actor, or alleles of the offspring of the beneficiaries of its altruistic acts, then altruism evolves. One can therefore reason by including within fitness all those alleles due to the altruist activities of the focal individual. Inclusive fitness is therefore the number of genes directly passed on to the next generation by a focal individual, plus the ones that are passed on by its kin . What is therefore increased by selection is rather inclusive than individual fitness, even though calculating inclusive fitness may be difficult in practice (Grafen 2009).
Even if mathematically speaking the construal of fitness is clear and how to construe it in a given problem is often straightforward, the issue of the bearer of fitness is difficult. Originally organisms had fitness, which was often computed as the number of offspring; with Modern Synthesis and the formulation of evolution in terms of gene frequencies in the context of population genetics, fitness is also ascribed to genes and genotypes. These values are interdependent because the fitness of a gene can be seen as the contribution it makes to the fitness of the organism, but only in the case of asexual organisms the number of offspring equals the number of copies of a given gene. Moreover, fitness is often seen as lifetime fitness, i.e. computed along the whole life of the organism; yet in behavioral ecology, one mainly considers individually each act and ascribes fitness to it (for example, costs and benefits of various strategies are measured in terms of fitness).
Often the absolute fitness cannot be measured, but only the relative fitness is evolutionarily important (individuals with identical fitnesses don’t undergo natural selection). Sometimes, one measures a posteriori the fitness of types of organisms by counting the number of offspring. Otherwise one can consider fitness as strictly correlated to the way individual face environmental demands, and then it can be computed a priori by estimating the performances of various trait types (race speed, rate of metabolism, visual acuity, etc.), provided that one has an idea about the relative importance of all factors for survival and reproduction.
Bouchard F., Rosenberg A. (2008) “Fitness” Stanford on-line encyclopedia of philosophy
Sober, E. (2002) “The Two Faces of Fitness,” in Thinking about Evolution: Historical,Philosophical, and Political Perspectives. (Krimbas R., ed.) Cambridge: Cambridge University Press.
Grafen A. (2009) “Formalizing Darwinism and inclusive fitness theory.” Phil. Trans. R. Soc. B. 364, 1: 3135-3141.
Hamilton’s rule. Due to Hamilton (1964), it is a rule concerning the fixation by natural selection of an altruistic behavior: an act with cost c for its actor and benefit b for its beneficiary will evolve if and only if c < br, where r is the relatedness of the beneficiary to the focal individual. C and b are measured in terms of fitness. Originally supposed to underpin the process of kin selection, it proved to be the general rule for the evolution of cooperation, given that many cases where cooperation emerges amongst non-kin behave according to such rule; the main reason is that relatedness as such measures a statistical association between individuals rather than a degree of kinship, even if the latter yields ipso facto an association.
Frank, S. A. (1998) The foundations of social evolution. Princeton: Princeton University Press.
Van Veelen M. (2007) “Hamilton’s missing link.” Journal of Theoretical Biology, 246, 3 : 551-554
Hardy-Weinberg law. In a panmictic infinite population of diploid sexual individuals with no selection, the frequencies p and (1-p) of two alleles A and a (recessive) at one locus would reach an equilibrium given by the Hardy-Weinberg formula: p² AA, 2p (1-p) Aa, (1-p)² aa. The infinity of the population is requested in order to avoid the effects of genetic drift.
Gillespie J. (2004) Population Genetics – A Concise Guide. Baltimore :The John Hopkins University Press .
Price equation. Mathematically derived formula of evolutionary change due to population geneticist George Price in 1970, this equation expresses the between-generation change in a trait mean value in the following way :
z= Cov (wi , zi) / w + E (wi zi) / w
where z (resp. w) is the mean trait value (resp. fitness), wi is the fitness of individuals i and zi their value of the trait, and zi the change of this value between individual and offspring. The equation decomposes evolutionary change between the action of natural selection (as covariance between fitnesses and traits) and the transmission biases.
Price equation is derived mathematically, hence it is an apriori statement and does not rely on specificities of biology. It can be formulated in several ways, one of it being crucial because involved in the evolutionary biology of cooperation. The two terms can indeed be written in such a way that, given a population divided in subgroups, the first term will be the effect of selection in each group, whereas the second term will provide the effect of selection between groups. Therefore, it formulates what several theorists call “multi-level selection”, understood as the addition of the selection within group and the selection between groups.
Frank, S.A. (1995). "George Price's contributions to Evolutionary Genetics". Journal of Theoretical Biology 175 (3): 373–388.
Gardner, A. (2008). "The Price equation". Curr. Biol. 18 (5): R198–R202
Price G. (1970). "Selection and covariance". Nature 227: 520–521.
Relatedness. The relatedness between two individuals in a population, when considering a given locus, is the probability that they are identical at this locus, measured against the mean probability that two randomly taken individuals in the population are identical by descent at this locus. As such, relatedness measures a statistical association, notwithstanding its biological causes, but the degree of kinship provides often a good proxy for relatedness.
In the context of the evolution of altruism and cooperation, the relatedness measures the excess-on-average probability that an individual will have the altruistic allele, therefore will be more likely than the average to be altruistic in return. Therefore relatedness is a key causal factor in the evolution of altruism and cooperation.
Frank, S.A. 2006. “Social selection.” In: Evolutionary Genetics: Concepts and Case Studies (Fox C.W., Wolf J.B., eds). Oxford: Oxford University Press, pp. 350-363.
Queller, D.C., Strassman, J.E. (2002) “Quick Guide: Kin Selection.” Current Biology, 12: R832.
Taylor, P. D., Frank, S. A.( 1996) “How to make a kin selection model.” Journal of Theoretical Biology, 180: 27–37.
Replicator dynamics. Generalizing evolution by natural selection in biology, it models the dynamics of replicating abstract entities according to a replicator equation
where x is a vector defined by the proportions of each type i, and fi (x) is the fitness of type i, and the average fitness. Lotka-Volterra equations in population ecology (capturing the dynamics of a prey-predator relationship) and Price equation can be derived from such equation under some conditions.
Nowak M. (2006) Evolutionary dynamics: exploring the equations of life. New-York: Harvard University Press.
Selectivepressure. In a given environment, environmental parameters which impinge differently on different organisms’ chances of reproduction and survival, according to the values of their heritable traits (for example, rates of predators, scarcity of resources, heat, etc.). The selective pressures are not always known, especially in small populations.
Lewens T. (2009) “The natures of selection.” British Journal for Philosophy of Science, 1–21.
Sexual selection. Selection for traits which impinge on chances of reproduction by giving an advantage either in the competition for mates, or regarding the female choice; one distinguishes sexual selection from natural selection, even if they may not be two really distinct processes, because the sexually selected traits as such may prima facie go against selection (e.g. the feathers of the peacock which increase its chances to get parasites and prevent him to run fast, etc.). This divergence has been accounted for by two main theories, the runaway selection, defended by Fisher (1915), which states that a slight preference of females for an arbitrary trait will push its values to a limit which can often differ from its optimal adaptive value; and the handicap principle, elaborated by Zahavi since the 1980s, which states that sexual characters are a costly signal of the genetic capacity of their bearer to face environmental demands. Their being costly makes them honest, since costly to fake, so females “have interest” to pick those males because they reliably signal that they have “good” genes. According to the handicap principle, peacocks develop long tails precisely because they display their high ability to run even though they carry such handicap, and also that they have few parasites because those are extremely visible on the symmetrical motives decorating their tails. Both runaway selection and handicap principle have been mathematically modeled.
Fisher, R.A. 1915 “The evolution of sexual preference.” Eugenics Review, 7: 184-192
Grafen, A. (1990) “Biological signals as handicaps.” Journal of Theoretical Biology , 144:517-546.
Zahavi A., Zahavi, A. (1997) The handicap principle: a missing piece of Darwin's puzzle. Oxford : Oxford University Press.