Reinhard Bürger

Why intraspecific trait variation matters in community ecology

Natural populations consist of phenotypically diverse individuals that exhibit variation in their demographic parameters and intra- and inter-specific interactions. Recent experimental work indicates 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 and identify six general mechanisms by which trait variation changes the outcome of ecological interactions. These mechanisms include several direct effects of trait variation per se and indirect effects arising from the role of genetic variation in trait evolution.

Mutation Accumulation and the Extinction of Small Populations

Although extensive work has been done on the relationship between population size and the risk of extinction due to demographic and environmental stochasticity, the role of genetic deterioration in the extinction process is poorly understood. We develop a general theoretical approach for evaluating the risk of small populations to extinction via the accumulation of mildly deleterious mutations, and we support this with extensive computer simulations. Unlike previous attempts to model the genetic consequences of small population size, our approach is genetically explicit and fully accounts for the mutations inherited by a founder population as well as those introduced by subsequent mutation. Application of empirical estimates of the properties of spontaneous deleterious mutations leads to the conclusion that populations with effective sizes smaller than 100 (and actual sizes smaller than 1,000) are highly vulnerable to extinction via a mutational meltdown on timescales of approximately 100 generations. We point out a number of reasons why this is likely to be an overly optimistic view. Thus, from a purely genetic perspective, current management policies that provide formal protection to species only after they have dwindled to 100-1,000 individuals are inadequate. A doubling of the deleterious mutation rate, as can result from the release of mutagenic pollutants by human activity, is expected to reduce the longevity of a population by about 50%. As some investigators have previously suggested, the genetic load of a population can be readily purged by intentional inbreeding. However, this effect is at best transient, as intentional inbreeding can only enhance the probability of fixation of deleterious alleles, and those alleles that are purged are rapidly replaced with new mutations.

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT A QUANTITATIVE-GENETIC ANALYSIS

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 populations 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.

MUTATIONAL MELTDOWNS IN SEXUAL POPULATIONS

Although it is widely acknowledged that the gradual accumulation of mildly deleterious mutations is an important source of extinction for asexual populations, it is generally assumed that this process is of little relevance to sexual species. Here we present results, based on computer simulations and supported by analytical approximations, that indicate that mutation accumulation in small, random‐mating monoecious populations can lead to mean extinction times less than a few hundred to a few thousand generations. Unlike the situation in obligate asexuals in which the mean time to extinction (t̄e) increases more slowly than linearly with the population carrying capacity (K), t̄e increases approximately exponentially with K in outcrossing sexual populations. The mean time to extinction for obligately selfing populations is shown to be equivalent to that for asexual populations of the same size, but with half the mutation rate and twice the mutational effect; this suggests that obligate selfing, like obligate asexuality, is inviable as a long‐term reproductive strategy. Under all mating systems, the mean time to extinction increases relatively slowly with the logarithm of fecundity, and mutations with intermediate effects (similar to those observed empirically) cause the greatest risk of extinction. Because our analyses ignore sources of demographic and environmental stochasticity, which have synergistic effects that exacerbate the accumulation of deleterious mutations, our results should yield liberal upper bounds to the mean time to extinction caused by mutational degradation. Thus, deleterious mutation accumulation cannot be ruled out generally as a significant source of extinction vulnerability in small sexual populations or as a selective force influencing mating‐system evolution.

Muller's ratchet and mutational meltdowns

We extend our earlier work on the role of deleterious mutations in the extinction of obligately asexual populations. First, we develop analytical models for mutation accumulation that obviate the need for time‐consuming computer simulations in certain ranges of the parameter space. When the number of mutations entering the population each generation is fairly high, the number of mutations per individual and the mean time to extinction can be predicted using classical approaches in quantitative genetics. However, when the mutation rate is very low, a fixation‐probability approach is quite effective. Second, we show that an intermediate selection coefficient (s) minimizes the time to extinction. The critical value of s can be quite low, and we discuss the evolutionary implications of this, showing that increased sensitivity to mutation and loss of capacity for DNA repair can be selectively advantageous in asexual organisms. Finally, we consider the consequences of the mutational meltdown for the extinction of mitochondrial lineages in sexual species.

Understanding the Evolution and Stability of the G-Matrix

Abstract 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.

STABILITY OF THE G-MATRIX IN A POPULATION EXPERIENCING PLEIOTROPIC MUTATION, STABILIZING SELECTION, AND GENETIC DRIFT

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 variance‐covariance 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 G‐matrix 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.

Evolution and stability of the G-matrix on a landscape with a moving optimum.

Abstract In quantitative genetics, the genetic architecture of traits, described in terms of variances and covariances, plays a major role in determining the trajectory of evolutionary change. Hence, the genetic variance‐covariance matrix (G‐matrix) is a critical component of modern quantitative genetics theory. Considerable debate has surrounded the issue of G‐matrix constancy because unstable G‐matrices provide major difficulties for evolutionary inference. Empirical studies and analytical theory have not resolved the debate. Here we present the results of stochastic models of G‐matrix evolution in a population responding to an adaptive landscape with an optimum that moves at a constant rate. This study builds on the previous results of stochastic simulations of G‐matrix stability under stabilizing selection arising from a stationary optimum. The addition of a moving optimum leads to several important new insights. First, evolution along genetic lines of least resistance increases stability of the orientation of the G‐matrix relative to stabilizing selection alone. Evolution across genetic lines of least resistance decreases G‐matrix stability. Second, evolution in response to a continuously changing optimum can produce persistent maladaptation for a correlated trait, even if its optimum does not change. Third, the retrospective analysis of selection performs very well when the mean G‐matrix (Ḡ) is known with certainty, indicating that covariance between G and the directional selection gradient (3 is usually small enough in magnitude that it introduces only a small bias in estimates of the net selection gradient. Our results also show, however, that the contemporary Ḡ‐matrix only serves as a rough guide to Ḡ. The most promising approach for the estimation of G is probably through comparative phylogenetic analysis. Overall, our results show that directional selection actually can increase stability of the G‐matrix and that retrospective analysis of selection is inherently feasible. One ?riajor remaining challenge is to gain a sufficient understanding of the G‐matrix to allow the confident estimation of Ḡ.

THE MUTATION MATRIX AND THE EVOLUTION OF EVOLVABILITY

Abstract Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A populations immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, rμ, the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individuals value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individuals fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at –1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time.

HOW MUCH HERITABLE VARIATION CAN BE MAINTAINED IN FINITE POPULATIONS BY MUTATION-SELECTION BALANCE?

The joint effects of stabilizing selection, mutation, recombination, and random drift on the genetic variability of a polygenic character in a finite population are investigated. A simulation study is performed to test the validity of various analytical predictions on the equilibrium genetic variance. A new formula for the expected equilibrium variance is derived that approximates the observed equilibrium variance very closely for all parameter combinations we have tested. The computer model simulates the continuum‐of‐alleles model of Crow and Kimura. However, it is completely stochastic in the sense that it models evolution as a Markov process and does not use any deterministic evolution equations. The theoretical results are compared with heritability estimates from laboratory and natural populations. Heritabilities ranging from 20% to 50%, as observed even in lab populations under a constant environment, can only be explained by a mutation‐selection balance if the phenotypic character is neutral or the number of genes contributing to the trait is sufficiently high, typically several hundred, or if there are a few highly variable loci that influence quantitative traits.