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.

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.

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.

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.

Inbreeding depression maintained by recessive lethal mutations interacting with stabilizing selection on quantitative characters in a partially self-fertilizing population.

The bimodal distribution of fitness effects of new mutations and standing genetic variation, due to early-acting strongly deleterious recessive mutations and late-acting mildly deleterious mutations, is analyzed using the Kondrashov model for lethals (K), with either the infinitesimal model for selfing (IMS) or the Gaussian allele model (GAM) for quantitative genetic variance under stabilizing selection. In the combined models (KIMS and KGAM) high genomic mutation rates to lethals and weak stabilizing selection on many characters create strong interactions between early and late inbreeding depression, by changing the distribution of lineages selfed consecutively for different numbers of generations. Alternative stable equilibria can exist at intermediate selfing rates for a given set of parameters. Evolution of quantitative genetic variance under multivariate stabilizing selection can strongly influence the purging of nearly recessive lethals, and sometimes vice versa. If the selfing rate at the purging threshold for quantitative genetic variance in IMS or GAM alone exceeds that for nearly recessive lethals in K alone, then in KIMS and KGAM stabilizing selection causes selective interference with purging of lethals, increasing the mean number of lethals compared to K; otherwise, stabilizing selection causes selective facilitation in purging of lethals, decreasing the mean number of lethals.

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 environmental cues for phenotypic plasticity.

Phenotypically plastic characters may respond to multiple variables in their environment, but the evolutionary consequences of this phenomenon have rarely been addressed theoretically. We model the evolution of linear reaction norms in response to several correlated environmental variables, in a population undergoing stationary environmental fluctuations. At evolutionary equilibrium, the linear combination of environmental variables that acts as a developmental cue for the plastic trait is the multivariate best linear predictor of changes in the optimum. However, the reaction norm with respect to any single environmental variable may exhibit nonintuitive patterns. Apparently maladaptive, or hyperadaptive plasticity can evolve with respect to single environmental variables, and costs of plasticity may increase, rather than reduce, plasticity in response to some variables. We also find conditions for the evolution of an indirect environmental indicator that affects expression of a plastic phenotype, despite not influencing natural selection on it.

Maintenance of Quantitative Genetic Variance Under Partial Self-Fertilization, with Implications for Evolution of Selfing.

We analyze two models of the maintenance of quantitative genetic variance in a mixed-mating system of self-fertilization and outcrossing. In both models purely additive genetic variance is maintained by mutation and recombination under stabilizing selection on the phenotype of one or more quantitative characters. The Gaussian allele model (GAM) involves a finite number of unlinked loci in an infinitely large population, with a normal distribution of allelic effects at each locus within lineages selfed for τ consecutive generations since their last outcross. The infinitesimal model for partial selfing (IMS) involves an infinite number of loci in a large but finite population, with a normal distribution of breeding values in lineages of selfing age τ. In both models a stable equilibrium genetic variance exists, the outcrossed equilibrium, nearly equal to that under random mating, for all selfing rates, r, up to critical value, [Formula: see text], the purging threshold, which approximately equals the mean fitness under random mating relative to that under complete selfing. In the GAM a second stable equilibrium, the purged equilibrium, exists for any positive selfing rate, with genetic variance less than or equal to that under pure selfing; as r increases above [Formula: see text] the outcrossed equilibrium collapses sharply to the purged equilibrium genetic variance. In the IMS a single stable equilibrium genetic variance exists at each selfing rate; as r increases above [Formula: see text] the equilibrium genetic variance drops sharply and then declines gradually to that maintained under complete selfing. The implications for evolution of selfing rates, and for adaptive evolution and persistence of predominantly selfing species, provide a theoretical basis for the classical view of Stebbins that predominant selfing constitutes an "evolutionary dead end."

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.

Pollination ecology and inbreeding depression control individual flowering phenologies and mixed mating.

We analyze evolution of individual flowering phenologies by combining an ecological model of pollinator behavior with a genetic model of inbreeding depression for plant viability. The flowering phenology of a plant genotype determines its expected daily floral display which, together with pollinator behavior, governs the population rate of geitonogamous selfing (fertilization among flowers on the same plant). Pollinators select plant phenologies in two ways: they are more likely to visit plants displaying more flowers per day, and they influence geitonogamous selfing and consequent inbreeding depression via their abundance, foraging behavior, and pollen carry-over among flowers on a plant. Our model predicts two types of equilibria at stable intermediate selfing rates for a wide range of pollinator behaviors and pollen transfer parameters. Edge equilibria occur at maximal or minimal selfing rates and are constrained by pollinators. Internal equilibria occur between edge equilibria and are determined by a trade-off between pollinator attraction to large floral displays and avoidance of inbreeding depression due to selfing. We conclude that unavoidable geitonogamous selfing generated by pollinator behavior can contribute to the common occurrence of stable mixed mating in plants.

Raissa L. Berg's contributions to the study of phenotypic integration, with a professional biographical sketch.

Raissa L. Berg had a remarkable career in many respects and an impact on the study of phenotypic integration that continues to increase over 50 years after the publication of her seminal paper in that area. She was born and lived most of her life in Russia, with most of her research focused on measuring spontaneous mutation rates in Drosophila. She was forced to abandon this work during the height of Lysenko's power in Russia, so she turned temporarily to the study of correlation patterns in plants; ironically, this work has had a more enduring impact than her main body of research. She showed that floral and vegetative traits become decoupled into separate correlation 'pleiades' in plants with specialized pollinators, but floral and vegetative traits remain correlated in plants that have less specialized pollination. Unfortunately, her plant work is often mis-cited as providing evidence for increased correlations among floral traits due to selection by pollinators for functional integration, a point she never made and one that is not supported by her data. Still, many studies of correlation pleiades have been conducted in plants, with the results mostly supporting Berg's hypothesis, although more studies on species with generalized pollination are needed.

Evaluating a simple approximation to modeling the joint evolution of self-fertilization and inbreeding depression.

A comprehensive understanding of plant mating system evolution requires detailed genetic models for both the mating system and inbreeding depression, which are often intractable. A simple approximation assuming that the mating system evolves by small infrequent mutational steps has been proposed. We examine its accuracy by comparing the evolutionarily stable selfing rates it predicts to those obtained from an explicit genetic model of the selfing rate, when inbreeding depression is caused by partly recessive deleterious mutations at many loci. Both models also include pollen limitation and pollen discounting. The approximation produces reasonably accurate predictions with a low or moderate genomic mutation rate to deleterious alleles, on the order of U = 0.02-0.2. However, for high mutation rates, the predictions of the full genetic model differ substantially from those of the approximation, especially with nearly recessive lethal alleles. This occurs because when a modifier allele affecting the selfing rate is rare, homozygous modifiers are produced mainly by selfing, which enhances the opportunity for purging nearly recessive lethals and increases the marginal fitness of the allele modifying the selfing rate. Our results confirm that explicit genetic models of selfing rate and inbreeding depression are required to understand mating system evolution.

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.

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.

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.

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.

Evolution of a plastic quantitative trait in an age-structured population in a fluctuating environment.

We analyze weak fluctuating selection on a quantitative character in an age-structured population not subject to density regulation. We assume that early in the first year of life before selection, during a critical state of development, environments exert a plastic effect on the phenotype, which remains constant throughout the life of an individual. Age-specific selection on the character affects survival and fecundity, which have intermediate optima subject to temporal environmental fluctuations with directional selection in some age classes as special cases. Weighting individuals by their reproductive value, as suggested by Fisher, we show that the expected response per year in the weighted mean character has the same form as for models with no age structure. Environmental stochasticity generates stochastic fluctuations in the weighted mean character following a first-order autoregressive model with a temporally autocorrelated noise term and stationary variance depending on the amount of phenotypic plasticity. The parameters of the process are simple weighted averages of parameters used to describe age-specific survival and fecundity. The "age-specific selective weights" are related to the stable distribution of reproductive values among age classes. This allows partitioning of the change in the weighted mean character into age-specific components.