Natural populations consist of phenotypically diverse individuals that exhibit variation in their demographic parameters and intra-and interspecific interactions. Recent experimental work suggests that such variation can have significant ecological effects. However, ecological models typically disregard this variation and focus instead on trait means and total population density. Under what situations is this simplification appropriate? Why might intraspecific variation alter ecological dynamics? In this review, we synthesize recent theory, identifying six general mechanisms by which trait variation changes the outcome of ecological interactions. These include several direct effects of trait variation per se, and indirect effects arising from genetic variation's role in trait evolution.

No abstract

Abstract.-Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is de termined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.

The G-matrix summarizes the inheritance of multiple, phenotypic traits. The stability and evolution of this matrix are important issues because they affect our ability to predict how the phenotypic traits evolve by selection and drift. Despite the centrality of these issues, comparative, experimental, and analytical approaches to understanding the stability and evolution of the G-matrix have met with limited success. Nevertheless, empirical studies often find that certain structural features of the matrix are remarkably constant, suggesting that persistent selection regimes or other factors promote stability. On the theoretical side, no one has been able to derive equations that would relate stability of the G-matrix to selection regimes, population size, migration, or to the details of genetic architecture. Recent simulation studies of evolving G-matrices offer solutions to some of these problems, as well as a deeper, synthetic understanding of both the G-matrix and adaptive radiations.

Loss of fitness due to the accumulation of deleterious mutations appears to be inevitable in small, obligately asexual populations, as these are incapable of reconstituting highly fit genotypes by recombination or back mutation. The cumulative buildup of such mutations is expected to lead to an eventual reduction in population size, and this facilitates the chance accumulation of future mutations. This synergistic interaction between population size reduction and mutation accumulation leads to an extinction process known as the mutational meltdown, and provides a powerful explanation for the rarity of obligate asexuality. We give an overview of the theory of the mutational meltdown, showing how the process depends on the demographic properties of a population, the properties of mutations, and the relationship between fitness and number of mutations incurred.

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.

Abstract. Quantitative genetics theory provides a framework that predicts the effects of selection on a phenotype consisting of a suite of complex traits. However, the ability of existing theory to reconstruct the history of selection or to predict the future trajectory of evolution depends upon the evolutionary dynamics of the genetic variancecovariance matrix (G-matrix). Thus, the central focus of the emerging field of comparative quantitative genetics is the evolution of the G-matrix. Existing analytical theory reveals little about the dynamics of G, because the problem is too complex to be mathematically tractable. As a first step toward a predictive theory of G-matrix evolution, our goal was to use stochastic computer models to investigate factors that might contribute to the stability of G over evolutionary time. We were concerned with the relatively simple case of two quantitative traits in a population experiencing stabilizing selection, pleiotropic mutation, and random genetic drift. Our results show that G-matrix stability is enhanced by strong correlational selection and large effective population size. In addition, the nature of mutations at pleiotropic loci can dramatically influence stability of G. In particular, when a mutation at a single locus simultaneously changes the value of the two traits (due to pleiotropy) and these effects are correlated, mutation can generate extreme stability of G. Thus, the central message of our study is that the empirical question regarding Gmatrix stability is not necessarily a general question of whether G is stable across various taxonomic levels. Rather, we should expect the G-matrix to be extremely stable for some suites of characters and unstable for others over similar spans of evolutionary time. Modern quantitative genetics theory provides points of connection between microevolution and macroevolution (Arnold et al. 2001). For a phenotype comprising multiple traits, the single-generation response to selection is given by the multivariate version of the breeder's equation (Lande 1979), ⌬z ϭ G␤, where z is a vector of population trait means, ␤ is a vector of directional selection gradients, and G is the genetic variance-covariance matrix (the G-matrix). Hence, the response to selection depends upon the intensity and direction of selection, as well as upon the amount of genetic variation and the nature of genetic correlations among traits. This equation for the change in the mean phenotype can be extrapolated over multiple generations to reconstruct the history of selection or to predict the future trajectory of the phenotype as a consequence of selection. This potential for extrapolation provides a connection between microevolutionary processes and macroevolutionary patterns (Lande 1979; but see Zeng 1988). However, such an extrapolation is possible only if the G-matrix remains relatively constant over long spans of evolutionary time. An extremely unstable G-matrix would render the goal of understanding selection over evolutionary time unachievable within the ...

How much gene flow is needed to inhibit speciation by the accumulation of Dobzhansky-Muller incompatibilities (DMIs) in a structured population? Here, we derive these limits in a classical migration-selection model with two haploid or diploid loci and unidirectional gene flow from a continent to an island. We discuss the dependence of the maximum gene-flow rate on ecological factors (exogeneous selection), genetic factors (epistasis, recombination), and the evolutionary history. Extensive analytical and numerical results show the following: (1) The maximum rate of gene flow is limited by exogeneous selection. In particular, maintenance of neutral DMIs is impossible with gene flow. (2) There are two distinct mechanisms that drive DMI evolution in parapatry, selection against immigrants in a heterogeneous environment and selection against hybrids due to the incompatibility. (3) Depending on the mechanism, opposite predictions result concerning the genetic architecture that maximizes the rate of gene flow a DMI can sustain. Selection against immigrants favors evolution of tightly linked DMIs of arbitrary strength, whereas selection against hybrids promotes the evolution of strong unlinked DMIs. In diploids, the fitness of the double heterozygotes is the decisive factor to predict the pattern of DMI stability.T HE (Bateson-) Dobzhansky-Muller model (DMM) (Bateson 1909; Dobzhansky 1936; Muller 1942) is the standard model to explain the evolution of intrinsic postzygotic isolation. A variety of theoretical studies show the plausibility of this model (reviewed in Coyne and Orr 2004; Gavrilets 2004), and numerous empirical studies report DobzhanskyMuller incompatibilities (DMIs) across several species of animals and plants (see reviews by Lowry et al. 2008 and Presgraves 2010).The appeal of the DMM is its generality: Speciation happens as a by-product of divergence without the need of special selection scenarios or complex adaptations to cross fitness valleys (cf. Orr 1995). The sole, but crucial, assumption is sufficient evolutionary time to let the process unfold and the spatial separation of the incipient species during this phase. The plausibility of the DMM as a mechanism for speciation and the widespread belief in the prevalence of allopatric speciation (Mayr 1942; Coyne and Orr 2004) go hand in hand. However, given that even tiny amounts of gene flow (of the order of a single migrant per generation) can have substantial effects on divergence (Slatkin 1987), it is clear that the assumption of strict allopatry is an idealization. This poses the question of the relevance of the DMM in parapatry and thus whether DMIs can originate or be maintained in the presence of gene flow. It has been suggested that the accumulation of DMIs in parapatry is possible (e.g., Gavrilets 1997Gavrilets , 2004 Porter and Johnson 2002; Kondrashov 2003; Agrawal et al. 2011; Nosil and Flaxman 2011). However, usually only the limit of weak migration has been studied. In contrast, we focus on the maximum rates of gene flow th...