Developmental integration and evolution of labile plasticity in a complex quantitative character in a multiperiodic environment.

Labile plasticity in a complex quantitative character is modeled, with multiple components contributing to net plasticity in the character. Each component has a specific development rate, norm of reaction, and cost of plasticity. For example, thermal adaptation in mammals includes seasonal fat deposition and fur growth, short-term shivering and sweating or panting, and movement between warm and cold sites. Norms of reaction do not reveal patterns of developmental integration, which must be investigated by studies of developmental dynamics in a changing environment. In a periodic environment, a labile character with a single component of plasticity is constrained by filtering environmental frequencies above the development rate and by the cost of plasticity. With multiple components of plasticity, some patterns of integration can alleviate these constraints to greatly improve fidelity of the mean phenotype tracking multiperiodic cycles in the optimum phenotype. This occurs by environmental signal amplification or inhibition through developmental integration among components and by an augmented development rate of net plasticity in the character that reduces environmental frequency filtering. When development of a component with high cost of plasticity is regulated partly by the norm of reaction of another component, evolution can diminish the reaction norm slope of the costly component without curtailing its development, thereby reducing the loss of fitness from its cost of plasticity. Apparent maladaptation in a component of plasticity may be an integral part of an adaptive pattern of developmental integration by mutual inhibition between components and compensatory evolution of a negative component reaction norm slope.

Evolution of sexual cooperation from sexual conflict.

In many species that form pair bonds, males display to their mate after pair formation. These displays elevate the female's investment into the brood. This is a form of cooperation because without the display, female investment is reduced to levels that are suboptimal for both sexes. The presence of such displays is paradoxical as in their absence the male should be able to invest extra resources directly into offspring, to the benefit of both sexes. We consider that the origin of these displays lies in the exploitation of preexisting perceptual biases which increase female investment beyond that which is optimal for her, initially resulting in a sexual conflict. We use a combined population genetic and quantitative genetic model to show how this conflict becomes resolved into sexual cooperation. A cooperative outcome is most likely when perceptual biases are under selection pressures in other contexts (e.g., detection of predators, prey, or conspecifics), but this is not required. Cooperation between pair members can regularly evolve even when this provides no net advantage to the pair and when the display itself reduces a male's contributions to raising the brood. The findings account for many interactions between the sexes that have been difficult to explain in the context of sexual selection.

Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations.

We analyze the stochastic demography and evolution of a density-dependent age- (or stage-) structured population in a fluctuating environment. A positive linear combination of age classes (e.g., weighted by body mass) is assumed to act as the single variable of population size, [Formula: see text], exerting density dependence on age-specific vital rates through an increasing function of population size. The environment fluctuates in a stationary distribution with no autocorrelation. We show by analysis and simulation of age structure, under assumptions often met by vertebrate populations, that the stochastic dynamics of population size can be accurately approximated by a univariate model governed by three key demographic parameters: the intrinsic rate of increase and carrying capacity in the average environment, [Formula: see text] and [Formula: see text], and the environmental variance in population growth rate, [Formula: see text] Allowing these parameters to be genetically variable and to evolve, but assuming that a fourth parameter, [Formula: see text], measuring the nonlinearity of density dependence, remains constant, the expected evolution maximizes [Formula: see text] This shows that the magnitude of environmental stochasticity governs the classical trade-off between selection for higher [Formula: see text] versus higher [Formula: see text] However, selection also acts to decrease [Formula: see text], so the simple life-history trade-off between [Formula: see text]- and [Formula: see text]-selection may be obscured by additional trade-offs between them and [Formula: see text] Under the classical logistic model of population growth with linear density dependence ([Formula: see text]), life-history evolution in a fluctuating environment tends to maximize the average population size.

Mating systems and avoidance of inbreeding depression as evolutionary drivers of pollen limitation in animal-pollinated self-compatible plants.

Background and Aims: Most theory addressing the evolution of pollen limitation in flowering plants focuses on stochasticity in the relative abundance of plant and pollinator populations affecting trade-offs in resource allocation to ovule production or pollinator attraction vs. seed maturation. Mating system evolution is an underappreciated but potentially widespread additional mechanism for the evolutionary emergence of pollen limitation in animal-pollinated self-compatible plants. Methods: We model individual plant flowering phenologies influencing both pollinator attraction and geitonogamous self-fertilization caused by pollinator movements among flowers within plants, incorporating demographic but not environmental stochasticity. Plant phenology and the resulting pollen limitation are analysed at evolutionarily stable equilibria (ESS). Pollen limitation is measured by two quantities: the proportion of unpollinated flowers and the reduction in maternal fitness caused by inbreeding depression in selfed seeds. Key Results: When pollinators visit multiple flowers per plant, pollen limitation is never minimized at an ESS and results from the evolution of flowering phenologies balancing the amount and genetic composition (outbred vs. inbred) of pollen receipt. Conclusions: Results are consistent with previous theory demonstrating that pollen limitation can be an evolved property, not just a constraint; they complement existing models by showing that plant avoidance of inbreeding depression constitutes a genetic mechanism contributing to evolution of pollen limitation, in addition to ecological mechanisms previously studied.

Inbreeding depression under mixed outcrossing, self-fertilization and sib-mating.

BACKGROUND: Biparental inbreeding, mating between two relatives, occurs at a low frequency in many natural plant populations, which also often have substantial rates of self-fertilization. Although biparental inbreeding is likely to influence the dynamics of inbreeding depression and the evolution of selfing rates, it has received limited theoretical attention in comparison to selfing. The only previous model suggested that biparental inbreeding can favour the maintenance of stable intermediate selfing rates, but made unrealistic assumptions about the genetic basis of inbreeding depression. Here we extend a genetic model of inbreeding depression, describing nearly recessive lethal mutations at a very large number of loci, to incorporate sib-mating. We also include a constant component of inbreeding depression modelling the effects of mildly deleterious, nearly additive alleles. We analyze how observed rates of sib-mating influence the mean number of heterozygous lethals alleles and inbreeding depression in a population reproducing by a mixture of self-fertilization, sib-mating and outcrossing. We finally use the ensuing relationship between equilibrium inbreeding depression and population selfing rate to infer the evolutionarily stable selfing rates expected under such a mixed mating system. RESULTS: We show that for a given rate of inbreeding, sib-mating is more efficient at purging inbreeding depression than selfing, because homozygosity of lethals increases more gradually through sib-mating than through selfing. Because sib-mating promotes the purging of inbreeding depression and the evolution of selfing, our genetic model of inbreeding depression also predicts that sib-mating is unlikely to maintain stable intermediate selfing rates. CONCLUSIONS: Our results imply that even low rates of sib-mating affect plant mating system evolution, by facilitating the evolution of selfing via more efficient purging of inbreeding depression. Alternative mechanisms, such as pollination ecology, are necessary to explain stable mixed selfing and outcrossing.

Evolution of phenotypic plasticity in colonizing species.

I elaborate an hypothesis to explain inconsistent empirical findings comparing phenotypic plasticity in colonizing populations or species with plasticity from their native or ancestral range. Quantitative genetic theory on the evolution of plasticity reveals that colonization of a novel environment can cause a transient increase in plasticity: a rapid initial increase in plasticity accelerates evolution of a new optimal phenotype, followed by slow genetic assimilation of the new phenotype and reduction of plasticity. An association of colonization with increased plasticity depends on the difference in the optimal phenotype between ancestral and colonized environments, the difference in mean, variance and predictability of the environment, the cost of plasticity, and the time elapsed since colonization. The relative importance of these parameters depends on whether a phenotypic character develops by one-shot plasticity to a constant adult phenotype or by labile plasticity involving continuous and reversible development throughout adult life.

Evolutionary consequences of nonselective harvesting in density-dependent populations.

There is now considerable empirical evidence that evolutionary changes in many phenotypic characters, such as body mass, age at maturation, and timing of breeding, often occur in populations subject to intense harvesting over longer periods. Here, we analyze the evolutionary component of the selection due to nonselective harvesting, which will operate even under selective harvesting and may generate a large evolutionary response. If phenotype affects susceptibility to density dependence-for example, through resource limitation-then nonselective harvesting can induce evolutionary change through its effect on population density. We provide a model for evolution of a quantitative character in such a fluctuating density-dependent population, using the diffusion approximation to describe jointly the temporal changes in mean phenotype and log population size. We show how nonselective harvesting in particular generates r-selection governed by genetic variation in the strength of density regulation and the magnitude of population fluctuations. We show that r-selection caused by nonselective harvesting is proportional to the mean fraction of the population harvested. We then compare the short-term as well as the long-term evolutionary impact of nonselective harvesting for different harvesting strategies by using the mean harvest fraction for different strategies. This comparison is performed for three different harvesting strategies: constant, proportional, and threshold harvesting. The more ecologically sustainable strategies also produce smaller evolutionary changes.

Evolution of discrete phenotypes from continuous norms of reaction.

Discrete phenotypic variation often involves threshold expression of a trait with polygenic inheritance. How such discrete polyphenisms evolve starting from continuously varying phenotypes has received little theoretical attention. We model the evolution of sigmoid norms of reaction in response to variation in an underlying trait or in a continuous environment to identify conditions for the evolution of discontinuity. For traits with expression depending on a randomly varying underlying factor, such as developmental noise, polyphenism is unstable under constant phenotypic selection for two selective peaks, and reaction norm evolution results in a phenotypic distribution concentrated at only one peak. But with frequency-dependent selection between two adaptive peaks, a steep threshold maintaining polyphenism can evolve. For inducible plastic traits with expression conditioned on an environmental variable that also affects phenotypic selection, the steepness of the evolved reaction norm depends both on the differentiation of the environment in time or space and on its predictability between development and selection. Together with recent measurements of genetic variance of threshold steepness, these predictions suggest that quasi-discrete phenotypic variation may often evolve from continuous norms of reactions rather than being an intrinsic property of development.

A quantitative genetic model of r- and K-selection in a fluctuating population.

We analyze a stochastic quantitative genetic model for the joint dynamics of population size N and evolution of a multidimensional mean phenotype (z) under density-dependent selection. This generalizes our previous theories of evolution in fluctuating environments to include density-dependent (but frequency-independent) selection on quantitative characters. We assume that appropriate constraints or trade-offs between fitness components exist to prevent unlimited increase of fitness. We also assume weak selection such that the expected rate of return to equilibrium is much slower for (z) than N. The mean phenotype evolves to a stationary distribution around an equilibrium point z(opt) that maximizes a simple function determined by ecological parameters governing the dynamics of population size. For any (z), the expected direction of phenotypic evolution is determined by the additive genetic covariance matrix G and the gradient of this function with respect to the mean phenotype. For the theta-logistic model of density dependence, evolution tends to maximize the expected value of N(θ).

Evolution of displays within the pair bond.

Although sexual selection is an important cause of display evolution, in socially monogamous species (e.g. many birds), displays continue after formation of the pair bond. Here, we consider that these displays evolve because they stimulate the partner to increase investment in offspring. Our study is motivated by elaborate mutual displays in species that are largely monomorphic and have long-term pair bonds (e.g. the great crested grebe, Podiceps cristatus) and by many empirical results evidencing that display manipulation affects parental investment. Using population genetic models, we show that a necessary condition for the permanent establishment of mutual displays in the pair bond is that the benefit of investment by the pair is more than twice that resulting from investment by a single individual. Pre-existing biases to respond to displays by increased investment are a necessary component of display evolution. We also consider examples where one sex (e.g. males) stimulates increased investment in offspring by the other sex. Here, display and additional investment cannot evolve permanently, but can increase and linger at high frequency for a long time before loss. We discuss how such transient effects may lead to the evolution of permanent displays as a result of evolution at additional loci.

Adaptation, plasticity, and extinction in a changing environment: towards a predictive theory.

Many species are experiencing sustained environmental change mainly due to human activities. The unusual rate and extent of anthropogenic alterations of the environment may exceed the capacity of developmental, genetic, and demographic mechanisms that populations have evolved to deal with environmental change. To begin to understand the limits to population persistence, we present a simple evolutionary model for the critical rate of environmental change beyond which a population must decline and go extinct. We use this model to highlight the major determinants of extinction risk in a changing environment, and identify research needs for improved predictions based on projected changes in environmental variables. Two key parameters relating the environment to population biology have not yet received sufficient attention. Phenotypic plasticity, the direct influence of environment on the development of individual phenotypes, is increasingly considered an important component of phenotypic change in the wild and should be incorporated in models of population persistence. Environmental sensitivity of selection, the change in the optimum phenotype with the environment, still crucially needs empirical assessment. We use environmental tolerance curves and other examples of ecological and evolutionary responses to climate change to illustrate how these mechanistic approaches can be developed for predictive purposes.

Population regulation and character displacement in a seasonal environment.

Competition has negative effects on population size and also drives ecological character displacement, that is, evolutionary divergence to utilize different portions of the resource spectrum. Many species undergo an annual cycle composed of a lean season of intense competition for resources and a breeding season. We use a quantitative genetic model to study the effects of differential reproductive output in the summer or breeding season on character displacement in the winter or nonbreeding season. The model is developed with reference to the avian family of Old World leaf warblers (Phylloscopidae), which breed in the temperate regions of Eurasia and winter in tropical and subtropical regions. Empirical evidence implicates strong winter density-dependent regulation driven by food shortage, but paradoxically, the relative abundance of each species appears to be determined by conditions in the summer. We show how population regulation in the two seasons becomes linked, with higher reproductive output by one species in the summer resulting in its evolution to occupy a larger portion of niche space in the winter. We find short-term ecological processes and longer-term evolutionary processes to have comparable effects on a species population size. This modeling approach can also be applied to other differential effects of productivity across seasons.

Seasonal cycles of species diversity and similarity in a tropical butterfly community.

1. Studies of seasonality in ecological diversity rarely extend over more than a few years, and few studies of seasonal diversity have explicitly investigated the influence of environmental factors on seasonal community composition, especially in tropical communities. 2. Our 10 years of monthly sampling in Amazonian Ecuador yielded 20 996 individuals of 137 fruit-feeding butterfly species. Seasonal cycles of rainfall drive annual cycles in species diversity and community similarity. Undetermined processes operating most strongly during the dry season maintain species diversity and high community similarity across years. 3. Seasonal cycles in community diversity and similarity are superimposed on a gradual decline in similarity between community samples on a decadal time-scale because of long-term changes in species abundances. 4. Monitoring and analysis of changes in community composition over a range of time-scales can be used to refine models of community dynamics by incorporating environmental factors necessary to predict the ecological impact of future climate change.

Estimating Brownian motion dispersal rate, longevity and population density from spatially explicit mark-recapture data on tropical butterflies.

1. We develop a Bayesian method for analysing mark-recapture data in continuous habitat using a model in which individuals movement paths are Brownian motions, life spans are exponentially distributed and capture events occur at given instants in time if individuals are within a certain attractive distance of the traps. 2. The joint posterior distribution of the dispersal rate, longevity, trap attraction distances and a number of latent variables representing the unobserved movement paths and time of death of all individuals is computed using Gibbs sampling. 3. An estimate of absolute local population density is obtained simply by dividing the Poisson counts of individuals captured at given points in time by the estimated total attraction area of all traps. Our approach for estimating population density in continuous habitat avoids the need to define an arbitrary effective trapping area that characterized previous mark-recapture methods in continuous habitat. 4. We applied our method to estimate spatial demography parameters in nine species of neotropical butterflies. Path analysis of interspecific variation in demographic parameters and mean wing length revealed a simple network of strong causation. Larger wing length increases dispersal rate, which in turn increases trap attraction distance. However, higher dispersal rate also decreases longevity, thus explaining the surprising observation of a negative correlation between wing length and longevity.

Generation time and temporal scaling of bird population dynamics.

Theoretical studies have shown that variation in density regulation strongly influences population dynamics, yet our understanding of factors influencing the strength of density dependence in natural populations still is limited. Consequently, few general hypotheses have been advanced to explain the large differences between species in the magnitude of population fluctuations. One reason for this is that the detection of density regulation in population time series is complicated by time lags induced by the life history of species that make it difficult to separate the relative contributions of intrinsic and extrinsic factors to the population dynamics. Here we use population time series for 23 bird species to estimate parameters of a stochastic density-dependent age-structured model. We show that both the strength of total density dependence in the life history and the magnitude of environmental stochasticity, including transient fluctuations in age structure, increase with generation time. These results indicate that the relationships between demographic and life-history traits in birds translate into distinct population dynamical patterns that are apparent only on a scale of generations.

Reproductive value and the stochastic demography of age-structured populations.

The dynamics of an age-structured population in a fluctuating environment is determined by the stochastic individual contributions from annual survival and fecundity to the total reproductive value of the population the next year. All parameters required to describe the population dynamics are simple properties of the distribution of these individual demographic contributions, which we call individual reproductive value. The asymptotic population growth rate in the average environment and the demographic and environmental variances are respectively the mean individual reproductive value over individuals through time and the variance within and between years. Our approach leads to an intuitive understanding of demographic and environmental variances in age-structured populations and their decomposition into additive age-specific components due to survival and reproduction. We show how to apply this approach to estimate the demographic and environmental variances and their components. The estimates are based on yearly random samples of individual vital rates and require no information about the total population size.

Adaptation to an extraordinary environment by evolution of phenotypic plasticity and genetic assimilation.

Adaptation to a sudden extreme change in environment, beyond the usual range of background environmental fluctuations, is analysed using a quantitative genetic model of phenotypic plasticity. Generations are discrete, with time lag tau between a critical period for environmental influence on individual development and natural selection on adult phenotypes. The optimum phenotype, and genotypic norms of reaction, are linear functions of the environment. Reaction norm elevation and slope (plasticity) vary among genotypes. Initially, in the average background environment, the character is canalized with minimum genetic and phenotypic variance, and no correlation between reaction norm elevation and slope. The optimal plasticity is proportional to the predictability of environmental fluctuations over time lag tau. During the first generation in the new environment the mean fitness suddenly drops and the mean phenotype jumps towards the new optimum phenotype by plasticity. Subsequent adaptation occurs in two phases. Rapid evolution of increased plasticity allows the mean phenotype to closely approach the new optimum. The new phenotype then undergoes slow genetic assimilation, with reduction in plasticity compensated by genetic evolution of reaction norm elevation in the original environment.

Fixation probability of beneficial mutations in a fluctuating population.

We compute an accurate approximation to the probability of fixation for a beneficial mutation in a population fluctuating with a stationary distribution of population size. The population dynamics are described by the theta-logistic model with environmental variance, assuming that the population size is large enough to ignore demographic variance. We show that stochastic fluctuations of population size reduce the probability of fixation. However, it is not the magnitude of the population fluctuations per se that creates this reduction. Only the environmental variance has a substantial effect on the probability of fixation. The strength of density dependence (or expected return time to equilibrium) and the functional form of density-regulation, given by the parameter theta in the theta-logistic model, have little effect on the fixation probability. Effective population size based on harmonic mean population size will therefore underestimate the expected fixation rate of beneficial mutations in fluctuating populations.

Incipient allochronic speciation due to non-selective assortative mating by flowering time, mutation and genetic drift.

We model the evolution of flowering time using a multilocus quantitative genetic model with non-selective assortative mating and mutation to investigate incipient allochronic speciation in a finite population. For quantitative characters with evolutionary parameters satisfying empirical observations and two approximate inequalities that we derived, disjunct clusters in the population flowering phenology originated within a few thousand generations in the absence of disruptive natural or sexual selection. Our simulations and the conditions we derived showed that cluster formation was promoted by limited population size, high mutational variance of flowering time, short individual flowering phenology and a long flowering season. By contrast, cluster formation was hindered by inbreeding depression, stabilizing selection and pollinator limitation. Our results suggest that incipient allochronic speciation in populations of limited size (satisfying two inequalities) could be a common phenomenon.

A general model for analyzing Taylor's spatial scaling laws.

Taylor's spatial scaling law concerns the relation between the variance and the mean population counts within areas of a given size. For a range of area sizes, the log of the variance often is an approximately linear function of the mean with a slope between 1 and 2, depending on the range of areas considered. In this paper, we investigate this relationship theoretically for random quadrat samples within a large area. The model makes a distinction between the local point process determining the position of each individual and the population density described by a spatial covariance function. The local point process and the spatial covariance of population density both contribute to the general relationship between the mean and the variance in which the slope may begin at 1, increase to 2, and decrease to 1 again. It is demonstrated by an example that the slope theoretically may exceed 2 by a small amount for very regular patterns that generate spatial covariance functions that increase in certain intervals. We also show how properties of population dynamics in space and time determine this relationship.