Invasion fitness,inclusive fitness,and reproductive numbers in heterogeneous populations

How should fitness be measured to determine which phenotype or “strategy” is uninvadable when evolution occurs in a group‐structured population subject to local demographic and environmental heterogeneity? Several fitness measures, such as basic reproductive number, lifetime dispersal success of a local lineage, or inclusive fitness have been proposed to address this question, but the relationships between them and their generality remains unclear. Here, we ascertain uninvadability (all mutant strategies always go extinct) in terms of the asymptotic per capita number of mutant copies produced by a mutant lineage arising as a single copy in a resident population (“invasion fitness”). We show that from invasion fitness uninvadability is equivalently characterized by at least three conceptually distinct fitness measures: (i) lineage fitness, giving the average individual fitness of a randomly sampled mutant lineage member; (ii) inclusive fitness, giving a reproductive value weighted average of the direct fitness costs and relatedness weighted indirect fitness benefits accruing to a randomly sampled mutant lineage member; and (iii) basic reproductive number (and variations thereof) giving lifetime success of a lineage in a single group, and which is an invasion fitness proxy. Our analysis connects approaches that have been deemed different, generalizes the exact version of inclusive fitness to class‐structured populations, and provides a biological interpretation of natural selection on a mutant allele under arbitrary strength of selection.     

Heritability of individual fitness in female macaques

Heritability of fitness is an important parameter for evolutionary studies, but it is controversial and difficult to estimate this quantitative genetic statistic. I compare two single-generation proxies of individual fitness estimated from demographic information (lifetime reproductive success, LRS; and individual finite rate of increase, individual λ) and lifespan for the female members of a free-ranging population of rhesus macaques (Macaca mulatta). All three variables have moderate heritabilities (λ = 0.36, LRS = 0.38, lifespan = 0.43) that are consistently depressed when non-reproductive individuals are censored from the analysis. This reduction suggests a large portion of the genetic variation in the fitness proxies is due to survival to reproductive age and commencement of reproduction in this population. This may be related to relatively benign, homogeneous environmental conditions. Any time gaps in modeling an animal’s life cycle can introduce similar inaccuracies in heritability of fitness proxies, although the direction of error is likely to vary with environmental conditions. Genetic correlations between the three variables were all indistinguishable from +1 implying no independent genetic variation. The similarity of heritability estimates for λ and LRS and strong genetic correlations are attributed to the dominance of adult lifespan in determining fitness for female macaques which are slow-reproducing by mammalian standards. While the heritabilities of both proxies were similar in this study, they should both be estimated when possible because they may provide different information, particularly in taxa with larger broods.     

Evolution of polyembryony: Consequences to the fitness of mother and offspring

Polyembryony, referring here to situations where a nucellar embryo is formed along with the zygotic embryo, has different consequences for the fitness of the maternal parent and offspring. We have developed genetic and inclusive fitness models to derive the conditions that permit the evolution of polyembryony under maternal and offspring control. We have also derived expressions for the optimal allocation (evolutionarily stable strategy, ESS) of resources between zygotic and nucellar embryos. It is seen that (i) Polyembryony can evolve more easily under maternal control than under that of either the offspring or the ‘selfish’ endosperm. Under maternal regulation, evolution of polyembryony can occur for any clutch size. Under offspring control polyembryony is more likely to evolve for high clutch sizes, and is unlikely for low clutch sizes (<3). This conflict between mother and offspring decreases with increase in clutch size and favours the evolution of polyembryony at high clutch sizes, (ii) Polyembryony can evolve for values of “x” (the power of the function relating fitness to seed resource) greater than 0.5758; the possibility of its occurrence increases with “x”, indicating that a more efficient conversion of resource into fitness favours polyembryony. (iii) Under both maternal parent and offspring control, the evolution of polyembryony becomes increasingly unlikely as the level of inbreeding increases, (iv) The proportion of resources allocated to the nucellar embryo at ESS is always higher than that which maximizes the rate of spread of the allele against a non-polyembryonic allele.     

There is no fitness but fitness,and the lineage is its bearer

Inclusive fitness has been the cornerstone of social evolution theory for more than a half-century and has matured as a mathematical theory in the past 20 years. Yet surprisingly for a theory so central to an entire field, some of its connections to evolutionary theory more broadly remain contentious or underappreciated. In this paper, we aim to emphasize the connection between inclusive fitness and modern evolutionary theory through the following fact: inclusive fitness is simply classical Darwinian fitness, averaged over social, environmental and demographic states that members of a gene lineage experience. Therefore, inclusive fitness is neither a generalization of classical fitness, nor does it belong exclusively to the individual. Rather, the lineage perspective emphasizes that evolutionary success is determined by the effect of selection on all biological and environmental contexts that a lineage may experience. We argue that this understanding of inclusive fitness based on gene lineages provides the most illuminating and accurate picture and avoids pitfalls in interpretation and empirical applications of inclusive fitness theory.     

The Coevolution of Secrecy and Stigmatization

We propose a coevolutionary model of secrecy and stigmatization. According to this model, secrecy functions to conceal potential fitness costs detected in oneself or one’s genetic kin. In three studies, we found that the content of participants’ distressing secrets overlapped significantly with three domains of social information that were important for inclusive fitness and served as cues for discriminating between rewarding and unrewarding interaction partners: health, mating, and social-exchange behavior. These findings support the notion that secrecy functions primarily as a defense against stigmatization by suppressing information about oneself or one’s kin that evolutionarily has been devalued in mating and social exchange.     

From inclusive fitness to fixation probability in homogeneous structured populations

The methods of inclusive fitness provide a powerful analysis of the action of selection on social behaviour. The key component of this analysis is the concept of relatedness R. In infinite populations, a standard method of calculating relatedness coefficients is through coefficients of consanguinity using the notion of genetic identity by descent. In this paper, we show that this approach can also be made to work in finite populations and we assume here that the population has a homogeneous structure, such as an island model. We demonstrate that, under the assumption that genetic effects are small and additive, the resulting formulation of inclusive fitness is equivalent to other significant measures of selection in finite populations, including the change in average allele frequency and fixation probability. The results are illustrated for a model of the evolution of cooperation in a finite island population.     

Fitness and Propensity’s Annulment?

Recent debate on the nature of probabilities in evolutionary biology has focused largely on the propensity interpretation of fitness (PIF), which defines fitness in terms of a conception of probability known as “propensity”. However, proponents of this conception of fitness have misconceived the role of probability in the constitution of fitness. First, discussions of probability and fitness have almost always focused on organism effect probability, the probability that an organism and its environment cause effects. I argue that much of the probability relevant to fitness must be organism circumstance probability, the probability that an organism encounters particular, detailed circumstances within an environment, circumstances which are not the organism’s effects. Second, I argue in favor of the view that organism effect propensities either don’t exist or are not part of the basis of fitness, because they usually have values close to 0 or 1. More generally, I try to show that it is possible to develop a clearer conception of the role of probability in biological processes than earlier discussions have allowed.     

Dynamics of a small re-introduced population of wild dogs over 25 years: Allee effects and the implications of sociality for endangered species’ recovery

We analysed 25 years (1980–2004) of demographic data on a small re-introduced population of endangered African wild dogs (Lycaon pictus) in Hluhluwe-iMfolozi Park (HiP), South Africa, to describe population and pack dynamics. As small populations of cooperative breeders may be particularly prone to Allee effects, this extensive data set was used to test the prediction that, if Allee effects occur, aspects of reproductive success, individual survival and population growth should increase with pack and population size. The results suggest that behavioural aspects of wild dogs rather than ecological factors (i.e. competitors, prey and rainfall) primarily have been limiting the HiP wild dog population, particularly a low probability of finding suitable mates upon dispersal at low pack number (i.e. a mate-finding Allee effect). Wild dogs in HiP were not subject to component Allee effects at the pack level, most likely due to low interspecific competition and high prey availability. This suggests that aspects of the environment can mediate the strength of Allee effects. There was also no demographic Allee effect in the HiP wild dog population, as the population growth rate was significantly negatively related to population size, despite no apparent ecological resource limitation. Such negative density dependence at low numbers indicates that behavioural studies of the causal mechanisms potentially generating Allee effects in small populations can provide a key to understanding their dynamics. This study demonstrates how aspects of a species’ social behaviour can influence the vulnerability of small populations to extinction and illustrates the profound implications of sociality for endangered species’ recovery. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Hamilton's rule,inclusive fitness maximization,and the goal of individual behaviour in symmetric two‐player games

Hamilton's original work on inclusive fitness theory assumed additivity of costs and benefits. Recently, it has been argued that an exact version of Hamilton's rule for the spread of a pro‐social allele (rb > c) holds under nonadditive pay‐offs, so long as the cost and benefit terms are defined as partial regression coefficients rather than pay‐off parameters. This article examines whether one of the key components of Hamilton's original theory can be preserved when the rule is generalized to the nonadditive case in this way, namely that evolved organisms will behave as if trying to maximize their inclusive fitness in social encounters.     

Genetic structure of Brandt’s vole (<Emphasis Type="Italic">Lasiopodomys brandtii</Emphasis>) populations in Inner Mongolia,China, based on microsatellite analysis

Brandt’s vole (Lasiopodomys brandtii) distribution is discontinuous in Inner Mongolia with some populations isolated from others. Recently, some isolated populations have suffered extinction, and the factors responsible remain elusive. Genetic drift is one of the processes affecting population genetic differentiation, and can play a substantial role in the divergence of small, isolated populations. Using seven microsatellite markers, we genotyped four geographically isolated populations of Brandt’s vole, all of which exhibit episodic fluctuations in population density. The results showed a strong genetic differentiation among the geographically distinct populations (total F _ST = 0.124) and in particular, one population (Zhengxiangbaiqi) was isolated from all others (F _ST values were greatest between Zhengxiangbaiqi and other populations). Furthermore, high levels of inbreeding (F _IS values ranged from 0.205 to 0.290) within each distinct population suggest that inbreeding has and is likely occurring in Brandt’s vole populations. These processes can decrease average individual fitness and consequently increase the risk of extinction of the species.     

Overcoming Allee effects through evolutionary,genetic, and demographic rescue

Despite the amplified threats of extinction facing small founder populations, successful colonization sometimes occurs, bringing devastating ecological and economic consequences. One explanation may be rapid evolution, which can increase mean fitness in populations declining towards extinction, permitting persistence and subsequent expansion. Such evolutionary rescue may be particularly important, given Allee effects. When a population is introduced at low density, individuals often experience a reduction in one or more components of fitness due to novel selection pressures that arise from diminished intraspecific interactions and positive density dependence (i.e. component Allee effects). A population can avoid extinction if it can adapt and recover on its own (i.e. evolutionary rescue), or if additional immigration sustains the population (i.e. demographic rescue) or boosts its genetic variation that facilitates adaptation (i.e. genetic rescue). These various forms of rescue have often been invoked as possible mechanisms for specific invasions, but their relative importance to invasion is not generally understood. Within a spatially explicit modelling framework, we consider the relative impact of each type of rescue on the probability of successful colonization, when there is evolution of a multi-locus quantitative trait that influences the strength of component Allee effects. We demonstrate that when Allee effects are important, the effect of demographic rescue via recurrent immigration overall provides the greatest opportunity for success. While highlighting the role of evolution in the invasion process, we underscore the importance of the ecological context influencing the persistence of small founder populations.     

Reproductive skew and individual strategies: infanticide or cooperation?

Infanticide in species with shared reproduction may indicate attempts to control the degree of skew within groups. Alternatively, individuals that have done poorly in reproduction could use infanticide for hastening the next breeding attempt. Many factors influence the individual’s decision over whether it is best to cooperate or engage in destruction. We present a qualitative model incorporating kinship among adults and progeny, social status, group size and seasonality to predict behavioural options for individuals of diverse backgrounds. The social system used for the model was that of the guira cuckoo (Guira guira), a Neotropical bird that breeds communally. We suggest communal breeders utilise the best available predictors for enhancing seasonal reproductive success, with favourable consequences for lifetime inclusive fitness. Predictors rely upon parameters that change over time, including the individual’s assessment of present and future possibilities. The model produces predictions that may be tested through field observations and molecular analyses for species with similar social dynamics.     

The evolution of caste polymorphism in social insects:0 Genetic release followed by diversifying evolution

Caste polymorphism, defined as the presence within a colony of two or more morphologically differentiated individuals of the same sex, is an important character of highly eusocial insects both in the Hymenoptera (ants, bees and wasps) and in the Isoptera (termites), the only two groups in the animal kingdom where highly eusocial species occur. Frequently, caste polymorphism extends beyond mere variations in size (although the extent of variations in size can be in the extreme) and is accompanied by allometric variations in certain body parts. How such polymorphism has evolved and why, in its extreme form, it is essentially restricted to the social insects are questions of obvious interest but without satisfactory answers at the present time. I present a hypothesis entitled ‘genetic release followed by diversifying evolution’, that provides potential answers to these questions. I argue that genetic release followed by diversifying evolution is made possible under a number of circumstances. One of them I propose is when some individuals in a species begin to rely on the indirect component of inclusive fitness while others continue to rely largely on the direct component, as workers and queens in social insects are expected to do. Thus when queens begin to rely on workers for most of the foraging, nest building and brood care, and workers begin to rely increasingly on queens to lay eggs—when queen traits and worker traits do not have to be expressed in the same individual—I postulate the relaxation of stabilizing selection and new spurts of directional selection on both queen-trait genes and worker-trait genes (in contrasting directions) leading to caste polymorphism.     

Gene mobility and the concept of relatedness

Cooperation is rife in the microbial world, yet our best current theories of the evolution of cooperation were developed with multicellular animals in mind. Hamilton’s theory of inclusive fitness is an important case in point: applying the theory in a microbial setting is far from straightforward, as social evolution in microbes has a number of distinctive features that the theory was never intended to capture. In this article, I focus on the conceptual challenges posed by the project of extending Hamilton’s theory to accommodate the effects of gene mobility. I begin by outlining the basics of the theory of inclusive fitness, emphasizing the role that the concept of relatedness is intended to play. I then provide a brief history of this concept, showing how, over the past fifty years, it has departed from the intuitive notion of genealogical kinship to encompass a range of generalized measures of genetic similarity. I proceed to argue that gene mobility forces a further revision of the concept. The reason in short is that, when the genes implicated in producing social behaviour are mobile, we cannot talk of an organism’s genotype simpliciter; we can talk only of an organism’s genotype at a particular stage in its life cycle. We must therefore ask: with respect to which stage(s) in the life cycle should relatedness be evaluated? For instance: is it genetic similarity at the time of social interaction that matters to the evolution of social behaviour, or is it genetic similarity at the time of reproduction? I argue that, strictly speaking, it is neither of these: what really matters to the evolution of social behaviour is diachronic genetic similarity between the producers of fitness benefits at the time they produce them and the recipients of those benefits at the end of their life-cycle. I close by discussing the implications of this result. The main payoff is that it makes room for a possible new mechanism for the evolution of altruism in microbes that does not require correlated interaction among bearers of the genes for altruism. The importance of this mechanism in nature remains an open empirical question.     

Stability properties of underdominance in finite subdivided populations

IN ISOLATED populations underdominance leads to bistable evolutionary dynamics: below a certain mutant allele frequency the wildtype succeeds. Above this point, the potentially underdominant mutant allele fixes. In subdivided populations with gene flow there can be stable states with coexistence of wildtypes and mutants: polymorphism can be maintained because of a migration-selection equilibrium, i.e., selection against rare recent immigrant alleles that tend to be heterozygous. We focus on the stochastic evolutionary dynamics of systems where demographic fluctuations in the coupled populations are the main source of internal noise. We discuss the influence of fitness, migration rate, and the relative sizes of two interacting populations on the mean extinction times of a group of potentially underdominant mutant alleles. We classify realistic initial conditions according to their impact on the stochastic extinction process. Even in small populations, where demographic fluctuations are large, stability properties predicted from deterministic dynamics show remarkable robustness. Fixation of the mutant allele becomes unlikely but the time to its extinction can be long.     

Polymorphisms in a desaturase 2 ortholog associate with cuticular hydrocarbon and male mating success variation in a natural population of Drosophila serrata

Elucidating the nature of genetic variation underlying both sexually selected traits and the fitness components of sexual selection is essential to understanding the broader consequences of sexual selection as an evolutionary process. To date, there have been relatively few attempts to connect the genetic variance in sexually selected traits with segregating DNA sequence polymorphisms. We set out to address this in a well‐characterized sexual selection system – the cuticular hydrocarbons (CHCs) of Drosophila serrata – using an indirect association study design that allowed simultaneous estimation of the genetic variance in CHCs, sexual fitness and single nucleotide polymorphism (SNP) effects in an outbred population. We cloned and sequenced an ortholog of the D. melanogaster desaturase 2 gene, previously shown to affect CHC biosynthesis in D. melanogaster, and associated 36 SNPs with minor allele frequencies > 0.02 with variance in CHCs and sexual fitness. Three SNPs had significant multivariate associations with CHC phenotype (q‐value < 0.05). At these loci, minor alleles had multivariate effects on CHCs that were weakly associated with the multivariate direction of sexual selection operating on these traits. Two of these SNPs had pleiotropic associations with male mating success, suggesting these variants may underlie responses to sexual selection due to this locus. There were 15 significant male mating success associations (q‐value < 0.1), and interestingly, we detected a nonrandom pattern in the relationship between allele frequency and direction of effect on male mating success. The minor‐frequency allele usually reduced male mating success, suggesting a positive association between male mating success and total fitness at this locus.     

Darwinian adaptation,population genetics and the streetcar theory of evolution

 This paper investigates the problem of how to conceive a robust theory of phenotypic adaptation in non-trivial models of evolutionary biology. A particular effort is made to develop a foundation of this theory in the context of n-locus population genetics. Therefore, the evolution of phenotypic traits is considered that are coded for by more than one gene. The potential for epistatic gene interactions is not a priori excluded. Furthermore, emphasis is laid on the intricacies of frequency-dependent selection. It is first discussed how strongly the scope for phenotypic adaptation is restricted by the complex nature of ‘reproduction mechanics’ in sexually reproducing diploid populations. This discussion shows that one can easily lose the traces of Darwinism in n-locus models of population genetics. In order to retrieve these traces, the outline of a new theory is given that I call ‘streetcar theory of evolution’. This theory is based on the same models that geneticists have used in order to demonstrate substantial problems with the ‘adaptationist programme’. However, these models are now analyzed differently by including thoughts about the evolutionary removal of genetic constraints. This requires consideration of a sufficiently wide range of potential mutant alleles and careful examination of what to consider as a stable state of the evolutionary process. A particular notion of stability is introduced in order to describe population states that are phenotypically stable against the effects of all mutant alleles that are to be expected in the long-run. Surprisingly, a long-term stable state can be characterized at the phenotypic level as a fitness maximum, a Nash equilibrium or an ESS. The paper presents these mathematical results and discusses – at unusual length for a mathematical journal – their fundamental role in our current understanding of evolution. Received 22 April 1994; received in revised form 10 July 1995     

Attractive males do not sire superior daughters

Much of the recent work on the evolution of female choice has focused on the relative influence of direct and indirect benefits, and particularly whether direct costs can be offset by indirect benefits. Studies investigating whether attractive males benefit females by increasing the viability of their offspring often report mating advantages to sons consistent with the Fisher process, while detecting no or weak viability benefits. One potential reason for this is that sons may trade-off viability benefits with investment in costly traits that enhance mating success, leading to the suggestion that viability benefits may be better detected by examining daughters’ fitness. Here we investigate the relationship between male attractiveness and daughters’ fitness in Drosophila simulans. We measured daughter (and dam) lifetime reproductive success and longevity. We found no evidence that attractive males sire high fitness daughters. Additionally, neither daughters nor dams gained direct benefits from mating with attractive males. However, aspects of daughters’ fitness were related to dam characters.     

Deer herbivory and habitat type influence long-term population dynamics of a rare wetland plant

Pinpointing the factors that alter the population viability of long-lived organisms, such as perennial plants, is especially useful for informing conservation management policies for threatened and endangered species. In this study, I used 4 years of demographic data on rare plant Polemonium vanbruntiae (Eastern Jacob’s ladder, Polemoniaceae) to determine how white-tailed deer herbivory and habitat type (wet meadow and forest seep) affect long-term population viability. I incorporated these factors into matrix population models to estimate the deterministic and stochastic growth rates (λ and λs, respectively), stable stage distribution (SSD), the reproductive value for each stage class, the cumulative probability of extinction, and the elasticity values for all vital rates under each browsing and habitat scenario. Population growth rates of P. vanbruntiae in wet meadow sites are expected to increase at a slightly faster rate than at forest seep sites. Herbivory significantly decreased the predicted population growth rate under stochastic conditions. However, P. vanbruntiae ramets are expected to increase in the future as the population growth rate (λ) > 1 under both “browse” and “no browse” scenarios, but deer herbivory increased the extinction risk to a detectable level. Deer preferentially browsed vegetative and reproductive adult ramets over yearlings and seedlings, and browsing significantly reduced fertility of reproductive ramets and increased the probability of stasis for small and large vegetative ramets. Browsing shifted the elasticity values of vital rates and changed the potential for younger life histories stages, such as seedlings, to change future population growth. Under herbivore pressure, survival and stasis of large vegetative ramets have the largest potential impact on future population growth. This study provides empirical evidence that white-tailed deer are an important ecological factor affecting long-term population dynamics of rare plant populations and offers management suggestions for remaining populations of P. vanbruntiae.     

Crossing fitness valleys during the evolution of limpet homing behaviour

Evolution is often considered a gradual hill-climbing process, slowly increasing the fitness of organisms. Here I investigate evolution of homing behaviour in simulated intertidal limpets. While the simulation of homing is only a possible mechanism by which homing may have evolved, the process allows an investigation of how evolution may occur over different fitness landscapes. With some fitness landscapes, in order to evolve path integration as a homing mechanism, a temporary reduction in an organism’s fitness was required — since high developmental costs occurred before successful homing strategies evolved. Simple hill-climbing algorithms, therefore, only rarely resulted in the evolution of a functional homing behaviour. The inclusion of trail-following greatly increases the frequency of success of evolution of a path integration strategy. Initially an emergent homing behaviour is formed combining path integration with trail-following. This also demonstrates evolution through exaptation, since in the simulation, the original role of trail-following is likely to be unrelated to homing. Analysis of the fitness landscapes of homing in the presence of trail-following behaviour shows a high variability of fitness, which results in the formation of ‘stepping-stones’ of high fitness across fitness valleys. By using these stepping-stones, simple hill-climbing algorithms can reach the global maximum fitness value.