On a genetic model of intraspecific competition and stabilizing selection

A genetic model is investigated in which two recombining loci determine the genotypic value of a quantitative trait additively. Two opposing evolutionary forces are assumed to act: stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the underlying genetics, in particular recombination rate and relative magnitude of allelic effects, interact with the conflicting selective forces and derive the resulting, surprisingly complex equilibrium patterns. We also investigate the conditions under which disruptive selection on the phenotypes can be observed and examine how much genetic variation can be maintained in such a model. We discovered a number of unexpected phenomena. For instance, we found that with little recombination the degree of stably maintained polymorphism and the equilibrium genetic variance can decrease as the strength of competition increases relative to the strength of stabilizing selection. In addition, we found that mean fitness at the stable equilibria is usually much lower than the maximum possible mean fitness and often even lower than the fitness at other, unstable equilibria. Thus, the evolutionary dynamics in this system are almost always nonadaptive.     

Genetic and phenotypic models of natural selection

The following theorem is proposed: when two phenotypes differ in attributes affecting their relative fitness, selection will cease to cause further evolutionary change when the two phenotypes have the same fitness, provided that certain modes of inheritance apply; in particular, all genotypes specifying the same phenotype must have the same average fitness. If these conditions of “uniform fitness” patterns of inheritance are not met, particular genetic models of natural selection should replace an analysis of phenotypes. If the conditions are met, an analysis of the stationary conditions when the phenotypes have equal fitnesses permits quantitative statements about the outcome of selection without recourse to genetic models. Phenotypic analyses of natural selection are illustrated by models of sex ratios in plants, sexual versus asexual reproduction in plants, and parental investment by animals.     

Evolutionary stasis of a heritable morphological trait in a wild fish population despite apparent directional selection

Comparing observed versus theoretically expected evolutionary responses is important for our understanding of the evolutionary process, and for assessing how species may cope with anthropogenic change. Here, we document directional selection for larger female size in Atlantic salmon, using pedigree‐derived estimates of lifetime reproductive success as a fitness measure. We show the trait is heritable and, thus, capable of responding to selection. The Breeder's Equation, which predicts microevolution as the product of phenotypic selection and heritability, predicted evolution of larger size. This was at odds, however, with the observed lack of either phenotypic or genetic temporal trends in body size, a so‐called “paradox of stasis.” To investigate this paradox, we estimated the additive genetic covariance between trait and fitness, which provides a prediction of evolutionary change according to Robertson's secondary theorem of selection (STS) that is unbiased by missing variables. The STS prediction was consistent with the observed stasis. Decomposition of phenotypic selection gradients into genetic and environmental components revealed a potential upward bias, implying unmeasured factors that covary with trait and fitness. These results showcase the power of pedigreed, wild population studies—which have largely been limited to birds and mammals—to study evolutionary processes on contemporary timescales.     

Remarks on the Evolutionary Effect of Natural Selection

The so-called "Fundamental Theorem of Natural Selection", that the mean fitness of a population increases with time under natural selection, is known not to be true, as a mathematical theorem, when fitnesses depend on more than one locus. Although this observation may not have particular biological relevance, (so that mean fitness may well increase in the great majority of interesting situations), it does suggest that it is of interest to find an evolutionary result which is correct as a mathematical theorem, no matter how many loci are involved. The aim of the present note is to prove an evolutionary theorem relating to the variance in fitness, rather than the mean: this theorem is true for an arbitrary number of loci, as well as for arbitrary (fixed) fitness parameters and arbitrary linkage between loci. Connections are briefly discussed between this theorem and the principle of quasi-linkage equilibrium.     

Theories of social selection in human populations.

Using Huntington disease, mental retardation, and schizophrenia, it has been shown that two individuals with identical genotypes or phenotypes have different fitnesses because of affected nuclear family members. Such fitness interaction seems to occur because of cultural and social reactions due to the presence of affected individuals, and the interaction has been termed "social selection." Without assuming any specific genetic control for the social behavior, we can study the effect of social behavior on the incidence of a genetic disease.     

The effects of intraspecific competition and stabilizing selection on a polygenic trait

The equilibrium properties of an additive multilocus model of a quantitative trait under frequency- and density-dependent selection are investigated. Two opposing evolutionary forces are assumed to act: (i) stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and (ii) intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the equilibrium structure, in particular, number, degree of polymorphism, and genetic variance of stable equilibria, is affected by the strength of frequency dependence, and what role the number of loci, the amount of recombination, and the demographic parameters play. To this end, we employ a statistical and numerical approach, complemented by analytical results, and explore how the equilibrium properties averaged over a large number of genetic systems with a given number of loci and average amount of recombination depend on the ecological and demographic parameters. We identify two parameter regions with a transitory region in between, in which the equilibrium properties of genetic systems are distinctively different. These regions depend on the strength of frequency dependence relative to pure stabilizing selection and on the demographic parameters, but not on the number of loci or the amount of recombination. We further study the shape of the fitness function observed at equilibrium and the extent to which the dynamics in this model are adaptive, and we present examples of equilibrium distributions of genotypic values under strong frequency dependence. Consequences for the maintenance of genetic variation, the detection of disruptive selection, and models of sympatric speciation are discussed.     

Convergence to constant equilibrium for a density-dependent selection model with diffusion

We consider the classical single locus two alleles selection model with diffusion where the fitnesses of the genotypes are density dependent. Using a theorem of Peter Brown, we show that in a bounded domain with homogeneous Neumann boundary conditions, the allele frequency and population density converge to a constant equilibrium lying on the zero population mean fitness curve. The results agree with the case without diffusion obtained by Selgrade and Namkoong. Frequency and density dependent selection is also considered.Research partially supported by NSF grant DMS-8601585     

Community heritability measures the evolutionary consequences of indirect genetic effects on community structure

The evolutionary analysis of community organization is considered a major frontier in biology. Nevertheless, current explanations for community structure exclude the effects of genes and selection at levels above the individual. Here, we demonstrate a genetic basis for community structure, arising from the fitness consequences of genetic interactions among species (i.e., interspecific indirect genetic effects or IIGEs). Using simulated and natural communities of arthropods inhabiting North American cottonwoods (Populus), we show that when species comprising ecological communities are summarized using a multivariate statistical method, nonmetric multidimensional scaling (NMDS), the resulting univariate scores can be analyzed using standard techniques for estimating the heritability of quantitative traits. Our estimates of the broad-sense heritability of arthropod communities on known genotypes of cottonwood trees in common gardens explained 56-63% of the total variation in community phenotype. To justify and help interpret our empirical approach, we modeled synthetic communities in which the number, intensity, and fitness consequences of the genetic interactions among species comprising the community were explicitly known. Results from the model suggest that our empirical estimates of broad-sense community heritability arise from heritable variation in a host tree trait and the fitness consequences of IGEs that extend from tree trait to arthropods. When arthropod traits are heritable, interspecific IGEs cause species interactions to change, and community evolution occurs. Our results have implications for establishing the genetic foundations of communities and ecosystems.     

Whose trait is it anyways? Coevolution of joint phenotypes and genetic architecture in mutualisms

Evolutionary biologists typically envision a trait’s genetic basis and fitness effects occurring within a single species. However, traits can be determined by and have fitness consequences for interacting species, thus evolving in multiple genomes. This is especially likely in mutualisms, where species exchange fitness benefits and can associate over long periods of time. Partners may experience evolutionary conflict over the value of a multi-genomic trait, but such conflicts may be ameliorated by mutualism’s positive fitness feedbacks. Here, we develop a simulation model of a host–microbe mutualism to explore the evolution of a multi-genomic trait. Coevolutionary outcomes depend on whether hosts and microbes have similar or different optimal trait values, strengths of selection and fitness feedbacks. We show that genome-wide association studies can map joint traits to loci in multiple genomes and describe how fitness conflict and fitness feedback generate different multi-genomic architectures with distinct signals around segregating loci. Partner fitnesses can be positively correlated even when partners are in conflict over the value of a multi-genomic trait, and conflict can generate strong mutualistic dependency. While fitness alignment facilitates rapid adaptation to a new optimum, conflict maintains genetic variation and evolvability, with implications for applied microbiome science.     

Selection and genetic (co)variance in bighorn sheep

Genetic theory predicts that directional selection should deplete additive genetic variance for traits closely related to fitness, and may favor the maintenance of alleles with antagonistically pleiotropic effects on fitness-related traits. Trait heritability is therefore expected to decline with the degree of association with fitness, and some genetic correlations between selected traits are expected to be negative. Here we demonstrate a negative relationship between trait heritability and association with lifetime reproductive success in a wild population of bighorn sheep (Ovis canadensis) at Ram Mountain, Alberta, Canada. Lower heritability for fitness-related traits, however, was not wholly a consequence of declining genetic variance, because those traits showed high levels of residual variance. Genetic correlations estimated between pairs of traits with significant heritability were positive. Principal component analyses suggest that positive relationships between morphometric traits constitute the main axis of genetic variation. Trade-offs in the form of negative genetic or phenotypic correlations among the traits we have measured do not appear to constrain the potential for evolution in this population.     

The heritability of fitness: Bad news for 'good genes'?

Some models of sexual selection depend on a female preference for 'good genes': females choose conspicuous males as these are advertising their possession of genes for fitness characters which can be inherited by their offspring. In contrast, Fisher's fundamental theorem of natural selection - which underlies much of population genetics theory - predicts that in a population at equilibrium there can be no additive genetic variation in fitness. Recent work on collared flycatchers in the wild shows that characters influencing fitness do indeed have a relatively low heritability. However, other studies of the inheritance of fitness in the laboratory suggest that under some circumstances a population may retain considerable genetic diversity for fitness characters. Genetically based female choice might hence have the potential to control the evolution of male sexual ornaments. More work on natural populations is needed; and birds may be a good place to start looking.     

Accuracy of marker-assisted selection with auxiliary traits

Genetic information on molecular markers is increasingly being used in plant and animal improvement programmes particularly as indirect means to improve a metric trait by selection either on an individual basis or on the basis of an index incorporating such information. This paper examines the utility of an index of selection that not only combines phenotypic and molecular information on the trait under improvement but also combines similar information on one or more auxiliary traits. The accuracy of such a selection procedure has been theoretically studied for sufficiently large populations so that the effects of detected quantitative trait loci can be perfectly estimated. The theory is illustrated numerically by considering one auxiliary trait. It is shown that the use of an auxiliary trait improves the selection accuracy; and, hence, the relative efficiency of index selection compared to individual selection which is based on the same intensity of selection. This is particularly so for higher magnitudes of residual genetic correlation and environmental correlation having opposite signs, lower values of the proportion of genetic variation in the main trait associated with the markers, negligible proportion of genetic variation in the auxiliary trait associated with the markers, and lower values of the heritability of the main trait but higher values of the heritability of the auxiliary trait.     

An experimental assessment of artificial within-family selection for fitness in conservation programs

Equalizing familiar contributions is the simplest recommended strategy to maintain genetic diversity in conservation programs. However, this method implies a relaxation of natural selection and the possibility of accumulation of deleterious mutations. Computer simulations have shown that performing selection within families for fitness traits in a conservation program can be useful to alleviate such problems. We thus carried out an experiment with the model species Drosophila melanogaster in order to assess whether or not selection for fitness traits can be useful. We considered a fitness trait (pupa productivity) that was first checked to perform as a typical fitness component. The trait showed an inbreeding depression of 1.2 per 1 % increase in inbreeding and an asymmetrical response to selection with average realized heritabilities of about 0.04 in the upward direction and an order of magnitude larger (0.36) in the downward direction. The management experiment indicated that artificial within-family selection for fitness had only a marginal success for two reasons. First, there was not an appreciable decline in fitness across the experiment despite the low population sizes assumed (N = 10 or 20), even in the population not subjected to selection. This result is compatible with fitness models which imply the segregation of few deleterious mutations of large effect. Second, artificial selection within families had a limited impact on the trait, as one expects for a typical fitness component with very low heritability.     

Maximization principles for frequency-dependent selection II: the one-locus multiallele case

In this article we study a single-locus multiallele version of the pairwise-interaction model (PIM) in discrete and continuous time and a density-dependent version of this model (D-PIM) in continuous time. The PIM assumes that the fitnesses of genotypes are proportional to the average amount of competition resulting from pairwise interactions. Hence, fitness is frequency dependent. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles analogous to Fisher’s Fundamental Theorem for constant selection. We provide a systematic analysis and illustrate our results by concrete examples. We show that in discrete time the mean fitness is nondecreasing along every trajectory provided the interaction coefficients are nonnegative and symmetric. For asymmetric interactions this is in general not true. However, for what we call pseudo-symmetric interactions a function similar to, but in general not identical to, the mean fitness: the adjusted-mean fitness, is nondecreasing along trajectories. For asymmetric interactions, we also provide sufficient conditions for the mean fitness, and more generally for the adjusted-mean fitness, to be nondecreasing and sufficient conditions when it is not. In continuous time, we provide similar but stronger results. If the interaction coefficients are pseudo-symmetric, the adjusted-mean fitness is nondecreasing in the D-PIM.     

The evolution of alternative mating strategies in variable environments

Summary We assessed the influence of phenotypic plasticity in age at maturity on the maintenance of alternative mating strategies in male Atlantic salmon,Salmo salar. We calculated the fitness,r, associated with the parr and the anadromous strategies, using age-specific survival data from the field and strategy-specific fertilization data from the laboratory. The fitness of each strategy depended largely on mate competition (numbers of parr per female, i.e. parr frequency) and on age at maturity. Fitness declined with increasing numbers of parr per female with equilibrium frequencies (at which the fitnesses of each strategy are equal) being within the range observed in the wild. Equilibrium parr frequencies declined with decreasing growth rate and increasing age at maturity. Within populations, the existence of multiple age-specific sets of fitness functions suggests that the fitnesses of alternative strategies are best represented as multidimensional surfaces. The points of intersection of these surfaces, whose boundaries encompass natural variation in age at maturity and mate competition, define an evolutionarily stable continuum (ESC) of strategy frequencies along which the fitnesses associated with each strategy are equal. We propose a simple model that incorporates polygenic thresholds of a largely environmentally-controlled trait (age at maturity) to provide a mechanism by which an ESC can be maintained within a population. An indirect test provides support for the prediction that growth-rate thresholds for parr maturation exist and are maintained by stabilizing selection. Evolutionarily stable continua, maintained by negative frequency-dependent selection on threshold traits, provide a theoretical basis for understanding how alternative life histories can evolve in variable environments.     

THE EVOLUTION OF FITNESS

In every generation, the mean fitness of populations increases because of natural selection and decreases because of mutations and changes in the environment. The magnitudes of these effects can be measured in two ways: either directly, by comparing the fitnesses of selected and unselected populations, or indirectly, by measuring the additive variance of fitness and making use of the fundamental theorem of natural selection. The available data suggest that the amount by which natural selection increases mean fitness each generation (or degradation decreases mean fitness) will usually be between 0.1% and 30%; more tentatively, it is suggested that values will typically fall between 1% and 10%. These values can be used to set an upper limit of 5%–10% on the genetic advantage of mate choice.     

Comparing Evolvability and Variability of Quantitative Traits

There are two distinct reasons for making comparisons of genetic variation for quantitative characters. The first is to compare evolvabilities, or ability to respond to selection, and the second is to make inferences about the forces that maintain genetic variability. Measures of variation that are standardized by the trait mean, such as the additive genetic coefficient of variation, are appropriate for both purposes. Variation has usually been compared as narrow sense heritabilities, but this is almost always an inappropriate comparative measure of evolvability and variability. Coefficients of variation were calculated from 842 estimates of trait means, variances and heritabilities in the literature. Traits closely related to fitness have higher additive genetic and nongenetic variability by the coefficient of variation criterion than characters under weak selection. This is the reverse of the accepted conclusion based on comparisons of heritability. The low heritability of fitness components is best explained by their high residual variation. The high additive genetic and residual variability of fitness traits might be explained by the great number of genetic and environmental events they are affected by, or by a lack of stabilizing selection to reduce their phenotypic variance. Over one-third of the quantitative genetics papers reviewed did not report trait means or variances. Researchers should always report these statistics, so that measures of variation appropriate to a variety of situations may be calculated.     

Heritability of interpack aggression in a wild pedigreed population of North American grey wolves

Aggression is a quantitative trait deeply entwined with individual fitness. Mapping the genomic architecture underlying such traits is complicated by complex inheritance patterns, social structure, pedigree information and gene pleiotropy. Here, we leveraged the pedigree of a reintroduced population of grey wolves (Canis lupus) in Yellowstone National Park, Wyoming, USA, to examine the heritability of and the genetic variation associated with aggression. Since their reintroduction, many ecological and behavioural aspects have been documented, providing unmatched records of aggressive behaviour across multiple generations of a wild population of wolves. Using a linear mixed model, a robust genetic relationship matrix, 12,288 single nucleotide polymorphisms (SNPs) and 111 wolves, we estimated the SNP‐based heritability of aggression to be 37% and an additional 14% of the phenotypic variation explained by shared environmental exposures. We identified 598 SNP genotypes from 425 grey wolves to resolve a consensus pedigree that was included in a heritability analysis of 141 individuals with SNP genotype, metadata and aggression data. The pedigree‐based heritability estimate for aggression is 14%, and an additional 16% of the phenotypic variation was explained by shared environmental exposures. We find strong effects of breeding status and relative pack size on aggression. Through an integrative approach, these results provide a framework for understanding the genetic architecture of a complex trait that influences individual fitness, with linkages to reproduction, in a social carnivore. Along with a few other studies, we show here the incredible utility of a pedigreed natural population for dissecting a complex, fitness‐related behavioural trait.     

Experimental life-history evolution: selection on the allocation to sexual reproduction and its plasticity in a clonal plant

Abstract.— Allocation to sexual reproduction is an important life-history trait in clonal plants. Different selection pressures between competitive and competition-free environments are likely to result in the evolution of specialized genotypes and to maintain genetic variation in reproductive allocation. Moreover, selection may also result in the evolution of plastic allocation strategies. The necessary prerequisite for evolution, heritable genetic variation, can best be studied with selection experiments. Starting from a base population of 102 replicated genotypes of the clonal herb Ranunculus reptans , we imposed selection on the proportion of flowering rosettes in the absence of competition (base population: mean = 0.391, broad-sense heritability = 0.307). We also selected on the plasticity in this trait in response to competition with a naturally coexisting grass in a parallel experiment (base population: 14% lower mean in the presence of competition, broad-sense heritability = 0.072). After two generations of bidirectional selection, the proportion of flowering rosettes was 26% higher in the high line than in the low line (realized heritability ± SE = 0.205 ± 0.017). Moreover, genotypes of the high line had 11% fewer carpels per flower, a 22% lower proportion of rooted rosettes, and a 39% smaller average distance between rosettes within a clone. In the second experiment, we found no significant responses to selection for high and low plasticity in the proportion of flowering rosettes (realized heritability ± SE =–0.002 ± 0.013). Our study indicates a high heritability and potential for further evolution of the proportion of flowering rosettes in R. reptans , but not for its plasticity, which may have been fixed by past evolution at its current level. Moreover, our results demonstrate strong genetic correlations between allocation to sexual reproduction and other clonal life-history characteristics.     

DEVELOPMENTAL INSTABILITY IS GENETICALLY CORRELATED WITH PHENOTYPIC PLASTICITY,CONSTRAINING HERITABILITY,AND FITNESS

Although adaptive plasticity would seem always to be favored by selection, it occurs less often than expected. This lack of ubiquity suggests that there must be trade‐offs, costs, or limitations associated with plasticity. Yet, few costs have been found. We explore one type of limitation, a correlation between plasticity and developmental instability, and use quantitative genetic theory to show why one should expect a genetic correlation. We test that hypothesis using the Landsberg erecta × Cape Verde Islands recombinant inbred lines (RILs) of Arabidopsis thaliana. RILs were grown at four different nitrogen (N) supply levels that span the range of N availabilities previously documented in North American field populations. We found a significant multivariate relationship between the cross‐environment trait plasticity and the within‐environment, within‐RIL developmental instability across 13 traits. This genetic covariation between plasticity and developmental instability has two costs. First, theory predicts diminished fitness for highly plastic lines under stabilizing selection, because their developmental instability and variance around the optimum phenotype will be greater compared to nonplastic genotypes. Second, empirically the most plastic traits exhibited heritabilities reduced by 57% on average compared to nonplastic traits. This demonstration of potential costs in inclusive fitness and heritability provoke a rethinking of the evolutionary role of plasticity.