Evolution of variance in offspring number: The effects of population size and migration

It was shown by Gillespie [1974. Am. Nat. 108, 145–151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is {ei65-1}, where w is the mean fitness, {ei65-2} is the variance in offspring number, and N is the total population size. The model also predicts that if a strategy has a higher arithmetic mean fitness and a higher variance than the competitor, the outcome of selection will depend on the population size (with larger population sizes favoring the highvariance, high-mean genotype). This suggests that for metapopulation sizes favoring the high-variance, high-mean genotype). This suggests that for metapopulations with large numbers of (relatively) small demes, a strategy with lower variance and lower mean may be favored if the migration rate is low while higher migration rates (consistent with a larger effective population size) favor the opposite strategy. Individual-based simulation confirms that this is indeed the case for an island model of migration, though the effect of migration differs greatly depending on whether migration precedes or follows selection. It is noted in the appendix that while Gillespie [1974. Am. Nat. 108, 145–151] does seem to be heuristically accurate, it is not clear that the definition of effective fitness follows from his derivation.     

Natural selection on fecundity variance in subdivided populations: kin selection meets bet hedging

In a series of seminal articles in 1974, 1975, and 1977, J. H. Gillespie challenged the notion that the "fittest" individuals are those that produce on average the highest number of offspring. He showed that in small populations, the variance in fecundity can determine fitness as much as mean fecundity. One likely reason why Gillespie's concept of within-generation bet hedging has been largely ignored is the general consensus that natural populations are of large size. As a consequence, essentially no work has investigated the role of the fecundity variance on the evolutionary stable state of life-history strategies. While typically large, natural populations also tend to be subdivided in local demes connected by migration. Here, we integrate Gillespie's measure of selection for within-generation bet hedging into the inclusive fitness and game theoretic measure of selection for structured populations. The resulting framework demonstrates that selection against high variance in offspring number is a potent force in large, but structured populations. More generally, the results highlight that variance in offspring number will directly affect various life-history strategies, especially those involving kin interaction. The selective pressures on three key traits are directly investigated here, namely within-generation bet hedging, helping behaviors, and the evolutionary stable dispersal rate. The evolutionary dynamics of all three traits are markedly affected by variance in offspring number, although to a different extent and under different demographic conditions.     

The Role of Life Cycle and Migration in Selection for Variance in Offspring Number

For two genotypes that have the same mean number of offspring but differ in the variance in offspring number, naturalselection will favor the genotype with lower variance. In such cases, the average growth rate is not sufficient as a measure of fitness or as a predictor of fixation probability. However, the effect of variance in offspring number on the fixationprobability of mutant strategies has been calculated under several scenarios with the general conclusion that variance in offspring number reduces fitness in proportion to the inverse of the population size [Gillespie, J., Genetics 76:601–606, 1974; Proulx, S.R., Theor. Popul. Biol. 58:33–47, 2000]. This relationship becomes more complicated under a metapopulation scenario where the “effective” population size depends on migration rate, population structure, and lifecycle. It is shown that in a life cycle where reproduction and migration (the birth-migration-regulation life cycle, or BMR)occur prior to density regulation within every deme, the fitness of a strategy depends on migration rate. When migration rates are near zero, the fitness of the strategy is determined by the size of individual demes, so that the strategy favoredin small populations tends to be fixed. As migration rate increases and approaches panmixis between demes, the fitness ofa reproductive strategy approaches what its value would be in a single, panmictic deme with a population size correspondingtothe census size of the metapopulation. Interestingly, when the life cycle is characterized by having density regulation in each deme prior to migration (the BRM life cycle) the fixation probability of a strategy is independent of migration rate. These results are found to be qualitatively consistent with the individual-based simulation results in Shpak [Theor. Biosci.124:65–85, 2005]. An erratum to this article can be found at     

Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

Reproductive diapause and life-history clines in North American populations of Drosophila melanogaster

Latitudinal clines are widespread in Drosophila melanogaster, and many have been interpreted as adaptive responses to climatic variation. However, the selective mechanisms generating many such patterns remain unresolved, and there is relatively little information regarding how basic life-history components such as fecundity, life span and mortality rates vary across environmental gradients. Here, it is shown that four life-history traits vary predictably with geographic origin of populations sampled along the latitudinal gradient in the eastern United States. Although such patterns are indicative of selection, they cannot distinguish between the direct action of selection on the traits in question or indirect selection by means of underlying genetic correlations. When independent suites of traits covary with geography, it is therefore critical to separate the widespread effects of population source from variation specifically for the traits under investigation. One trait that is associated with variation in life histories and also varies with latitude is the propensity to express reproductive diapause; diapause expression has been hypothesized as a mechanism by which D. melanogaster adults overwinter, and as such may be subject to strong selection in temperate habitats. In this study, recently derived isofemale lines were used to assess the relative contributions of population source and diapause genotype in generating the observed variance for life histories. It is shown that although life span, fecundity and mortality rates varied predictably with geography, diapause genotype explained the majority of the variance for these traits in the sampled populations. Both heat and cold shock resistance were also observed to vary predictably with latitude for the sampled populations. Cold shock tolerance varied between diapause genotypes and the magnitude of this difference varied with geography, whereas heat shock tolerance was affected solely by geographic origin of the populations. These data suggest that a subset of life-history parameters is significantly influenced by the genetic variance for diapause expression in natural populations, and that the observed variance for longevity and fecundity profiles may reflect indirect action of selection on diapause and other correlated traits.     

Parental effects in Plantago lanceolata L. III. Measuring parental temperature effects in the field

To determine the evolutionary importance of parental environmental effects in natural populations, we must begin to measure the magnitude of these effects in the field. For this reason, we conducted a combined growth chamber-field experiment to measure parental temperature effects in Plantago lanceolata. We grew in the field offspring of controlled crosses of chamber-grown parents subjected to six temperature treatments. Each treatment was characterized by a unique combination of maternal prezygotic (prior to fertilization), paternal prezygotic, and postzygotic (during fertilization and seed set) temperatures. Offspring were followed for three years to measure the effects of treatment on several life-history traits and population growth rate, our estimate of fitness. Parental treatment influenced germination, growth, and reproduction of newborns, but not survival or reproduction of offspring at least one year old. High postzygotic temperature significantly increased germination and leaf area at 17 weeks by approximately 35% and 2%, respectively. Probability of flowering and spike production in the newborn age class showed significant parental genotype x parental treatment interactions. High postzygotic temperature increased offspring fitness by approximately 50%. The strongest contributors to fitness were germination and probability of flowering and spike production of newborns. A comparison of our data with previously collected data for chambergrown offspring shows that the influence of parental environment on offspring phenotype is weaker but still biologically meaningful in the field. The results provide evidence that parental environment influences offspring fitness in natural populations of P. lanceolata and does so by affecting the life-history traits most strongly contributing to fitness. The data suggest that from the perspective of offspring fitness, natural selection favors parents that flower later in the flowering season in the North Carolina Piedmont when it is warmer. Genotypic-specific differences in response of offspring reproductive traits to parental environment suggest that parental environmental effects can influence the rate of evolutionary change in P. lanceolata.     

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 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.     

Natural Selection for within-Generation Variance in Offspring Number

In this paper it is shown that natural selection can act on the within-generation variance in offspring number. The fitness of a genotype will increase as its variance in offspring number decreases. The intensity of selection on the variance component is inversely proportional to population size, although the fixation probability of a gene which differs from its allele only in the variance in its offspring number is independent of population size. The concept of effective population size is shown to be of limited use when there is genetic variation in the variance in offspring number.     

Adaptive topography of fluctuating selection in a Mendelian population

An adaptive topography is derived for a large randomly mating diploid population under weak density-independent selection in a fluctuating environment. Assuming a stationary distribution of environmental states with no temporal autocorrelation, a diffusion approximation for population size and allele frequency, p, reveals that the expected change in p involves the gradient with respect to p of the stochastic intrinsic rate of increase (the density-independent long-run growth rate), r = r - sigma 2 e/2, where r is the mean Malthusian fitness in the average environment and is the environmental variance in population growth rate. The expected relative fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its fitness with population growth rate. The influence of fitness correlation between genotypes is illustrated by an analysis of the Haldane-Jayakar model of fluctuating selection on a single diallelic locus, and on two loci with additive effects on a quantitative character.     

A new demographic function maximized by life-history evolution

A goal of life-history theory has been to understand what combination of demographic traits is maximized by natural selection. In practice, researchers usually choose either density-independent population growth rate, lambda, or lifetime reproductive success, R0 (expected number of offspring produced in a lifetime). Others have shown that the maxima of density-independent lambda and R0 are evolutionarily stable strategies under specific density-dependent conditions: population regulation by equal density dependence among all age classes for lambda and by density dependence on a single age class for R0. Here I extend these connections between density-independent optimization models and density-dependent invasion function models in two ways. First, I derive a new demographic function for which a maximum corresponds to attainability of the equilibrium strategy or stability of the mean rather than stability of the variance of the strategy distribution. Second, I show explicitly a continuous range of cases with maxima between those for the lambda and R0. Graphical and biological interpretations are given for an example model. Finally, exceptions to a putative life-history generality (from lambda and R0 models), that high early-life mortality selects for high iteroparity, are shown.     

Demographic influences of translocated individuals on a resident population of house sparrows

Translocation of individuals from source populations to augment small populations facing risk of extinction is an important conservation tool. Here we examine sex‐specific differences between resident and translocated house sparrows Passer domesticus in reproductive success and survival, and the contribution of translocated individuals to the growth of a local population. We found evidence for assortative mating based on origin revealed by fewer parentages between translocated males and resident females than expected, and the total number of fledglings produced by such pairs was lower. The reproductive success of translocated males was positively related to the size of the throat badge (a sexual ornament), such that only translocated males with a large badge size were as successful as resident males. However, offspring with parents of different origin had higher survival than offspring with parents of the same origin, which suggests hybrid vigour. The contribution of resident and translocated individuals to the stochastic component of the long‐run growth rate of the population was similar; neither the mean individual contributions in fitness nor the demographic variance differed between the two groups. Thus, this experiment shows that translocated individuals may have a similar demographic influence on the growth of local populations as resident individuals. Still, the intermixing of translocated and resident individuals was low, and fitness differed according to origin in relation to individual differences in a sexually selected trait. In addition, hybrid vigour with respect to offspring recruitment seemed to partially decrease the negative fitness consequences of the assortative mating based on origin.     

Interactions between evolutionary processes at high mutation rates

Evolution at high mutation rates is minimally affected by six processes: mutation-selection balance, error catastrophes, Muller's Ratchet, robustness and compensatory evolution, and clonal interference. Including all of these processes in a tractable, analytical model is difficult, but they can be captured in simulations that utilize realistic genotype-phenotype-fitness maps, as done here by modeling RNA folding. Subjecting finite, asexual populations to a range of mutation rates revealed simple criteria that predict when particular evolutionary processes are important. Populations were initiated with a genotype encoding the most fit phenotype. When purifying selection was strong relative to mutation, the initial genotype was replaced by one more mutationally robust, and the maximally fit phenotype was maintained in a mutation-selection balance where the deleterious mutation rate determined mean fitness. With weaker purifying selection, the most fit genotypes were lost. Although loss of the best genotype was ongoing and might have led to a progressive fitness decline, continual compensatory evolution led to an approximate fitness equilibration. Per total genomic mutation rate, mean fitness was similar for strong and weak purifying selection. These results represent a first step at separating interactions between evolutionary processes at high mutation rate, but additional theory is needed to interpret some outcomes.     

RESPONSE TO NATURAL ENVIRONMENTAL HETEROGENEITY: MATERNAL EFFECTS AND SELECTION ON LIFE-HISTORY CHARACTERS AND PLASTICITIES IN MIMULUS GUTTATUS

Recent studies in plant populations have found that environmental heterogeneity and phenotypic selection vary at local spatial scales. In this study, I ask if there is evolutionary change in response to environmental heterogeneity and, if so, whether the response occurs for characters or character plasticities. I used vegetative clones of Mimulus guttatus to create replicate populations of 75 genotypes. These populations were planted into the natural habitat where they differed in mean growth, flowering phenology, and life span. This phenotypic variation was used to define selective environments. There was variation in fitness (flower production) among genotypes across all planting sites and in genotype response to the selective environment. Offspring from each site were grown in the greenhouse in two water treatments. Because each population initially had the same genetic composition, variation in the progeny between selective environments reveals either evolutionary change in response to environmental heterogeneity or environmental maternal effects. Plants from experimental sites that flowered earlier, had shorter life spans and were less productive, produced offspring that had more flowers, on average, and were less plastic in vegetative allocation than offspring of longer-lived plants from high-productivity areas. However, environmental maternal effects masked phenotypic differences in flower production. Therefore, although there was evidence of genetic differentiation in both life-history characters and their plasticities in response to small-scale environmental heterogeneity, environmental maternal effects may slow evolutionary change. Response to local-scale selective regimes suggests that environmental heterogeneity and local variation in phenotypic selection may act to maintain genetic variation.     

Sex‐specific selection under environmental stress in seed beetles

Sexual selection can increase rates of adaptation by imposing strong selection in males, thereby allowing efficient purging of the mutation load on population fitness at a low demographic cost. Indeed, sexual selection tends to be male‐biased throughout the animal kingdom, but little empirical work has explored the ecological sensitivity of this sex difference. In this study, we generated theoretical predictions of sex‐specific strengths of selection, environmental sensitivities and genotype‐by‐environment interactions and tested them in seed beetles by manipulating either larval host plant or rearing temperature. Using fourteen isofemale lines, we measured sex‐specific reductions in fitness components, genotype‐by‐environment interactions and the strength of selection (variance in fitness) in the juvenile and adult stage. As predicted, variance in fitness increased with stress, was consistently greater in males than females for adult reproductive success (implying strong sexual selection), but was similar in the sexes in terms of juvenile survival across all levels of stress. Although genetic variance in fitness increased in magnitude under severe stress, heritability decreased and particularly so in males. Moreover, genotype‐by‐environment interactions for fitness were common but specific to the type of stress, sex and life stage, suggesting that new environments may change the relative alignment and strength of selection in males and females. Our study thus exemplifies how environmental stress can influence the relative forces of natural and sexual selection, as well as concomitant changes in genetic variance in fitness, which are predicted to have consequences for rates of adaptation in sexual populations.     

The contributions of age and sex to variation in common tern population growth rate

1. The decomposition of population growth rate into contributions from different demographic rates has many applications, ranging from evolutionary biology to conservation and management. Demographic rates with low variance may be pivotal for population persistence, but variable rates can have a dramatic influence on population growth rate. 2. In this study, the mean and variance in population growth rate (lambda) is decomposed into contributions from different ages and demographic rates using prospective and retrospective matrix analyses for male and female components of an increasing common tern (Sterna hirundo) population. 3. Three main results emerged: (1) subadult return was highly influential in prospective and retrospective analyses; (2) different age-classes made different contributions to variation in lambda: older age classes consistently produced offspring whereas young adults performed well only in high quality years; and (3) demographic rate covariation explained a significant proportion of variation in both sexes. A large contribution to lambda did not imply a large contribution to its variation. 4. This decomposition strengthens the argument that the relationship between variation in demographic rates and variation in lambda is complex. Understanding this relationship and its consequences for population persistence and evolutionary change demands closer examination of the lives, and deaths, of the individuals within populations within species.     

SELECTION ON MOTHERS AND OFFSPRING: WHOSE PHENOTYPE IS IT AND DOES IT MATTER?

Reproductive and early life-history traits can be considered aspects of either offspring or maternal phenotype, and their evolution will therefore depend on selection operating through offspring and maternal components of fitness. Furthermore, selection at these levels may be antagonistic, with optimal offspring and maternal fitness occurring at different phenotypic values. We examined selection regimes on the correlated traits of birth weight, birth date, and litter size in Soay sheep (Ovis aries) using data from a long-term study of a free-living population on the archipelago of St. Kilda, Scotland. We tested the hypothesis that selective constraints on the evolution of the multivariate phenotype arise through antagonistic selection, either acting at offspring and maternal levels, or on correlated aspects of phenotype. All three traits were found to be under selection through variance in short-term and lifetime measures of fitness. Analysis of lifetime fitness revealed strong positive directional selection on birth weight and weaker selection for increased birth date at both levels. However, there was also evidence for stabilizing selection on these traits at the maternal level, with reduced fitness at high phenotypic values indicating lower phenotypic optima for mothers than for offspring. Additionally, antagonistic selection was found on litter size. From the offspring's point of view it is better to be born a singleton, whereas maternal fitness increases with average litter size. The decreased fitness of twins is caused by their reduced birth weight; therefore, this antagonistic selection likely results from trade-offs between litter size and birth weight that have different optimal resolutions with respect to offspring and maternal fitness. Our results highlight how selection regimes may vary depending on the assignment of reproductive and early life-history traits to either offspring or maternal phenotype.     

The evolution of alternative developmental pathways: footprints of selection on life-history traits in a butterfly

Developmental pathways may evolve to optimize alternative phenotypes across environments. However, the maintenance of such adaptive plasticity under relaxed selection has received little study. We compare the expression of life-history traits across two developmental pathways in two populations of the butterfly Pararge aegeria where both populations express a diapause pathway but one never expresses direct development in nature. In the population with ongoing selection on both pathways, the difference between pathways in development time and growth rate was larger, whereas the difference in body size was smaller compared with the population experiencing relaxed selection on one pathway. This indicates that relaxed selection on the direct pathway has allowed life-history traits to drift towards values associated with lower fitness when following this pathway. Relaxed selection on direct development was also associated with a higher degree of genetic variation for protandry expressed as within-family sexual dimorphism in growth rate. Genetic correlations for larval growth rate across sexes and pathways were generally positive, with the notable exception of correlation estimates that involved directly developing males of the population that experienced relaxed selection on this pathway. We conclude that relaxed selection on one developmental pathway appears to have partly disrupted the developmental regulation of life-history trait expression. This in turn suggests that ongoing selection may be responsible for maintaining adaptive developmental regulation along alternative developmental pathways in these populations.     

A DEMOGRAPHIC TRANSITION ALTERED THE STRENGTH OF SELECTION FOR FITNESS AND AGE‐SPECIFIC SURVIVAL AND FERTILITY IN A 19TH CENTURY AMERICAN POPULATION

Modernization has increased longevity and decreased fertility in many human populations, but it is not well understood how or to what extent these demographic transitions have altered patterns of natural selection. I integrate individual‐based multivariate phenotypic selection approaches with evolutionary demographic methods to demonstrate how a demographic transition in 19th century female populations of Utah altered relationships between fitness and age‐specific survival and fertility. Coincident with this demographic transition, natural selection for fitness, as measured by the opportunity for selection, increased by 13% to 20% over 65 years. Proportional contributions of age‐specific survival to total selection (the complement to age‐specific fertility) diminished from approximately one third to one seventh following a marked increase in infant survival. Despite dramatic reductions in age‐specific fertility variance at all ages, the absolute magnitude of selection for fitness explained by age‐specific fertility increased by approximately 45%. I show that increases in the adaptive potential of fertility traits followed directly from decreased population growth rates. These results suggest that this demographic transition has increased the adaptive potential of the Utah population, intensified selection for reproductive traits, and de‐emphasized selection for survival‐related traits.     

GENOTYPE‐BY‐TEMPERATURE INTERACTIONS MAY HELP TO MAINTAIN CLONAL DIVERSITY IN ASTERIONELLA FORMOSA (BACILLARIOPHYCEAE)

Marine and freshwater phytoplankton populations often show large clonal diversity, which is in disagreement with clonal selection of the most vigorous genotype(s). Temporal fluctuation in selection pressures in variable environments is a leading explanation for maintenance of such genetic diversity. To test the influence of temperature as a selection force in continually (seasonally) changing aquatic systems we carried out reaction norms experiments on co‐occurring clonal genotypes of a ubiquitous diatom species, Asterionella formosa Hassall, across an environmentally relevant range of temperatures. We report within population genetic diversity and extensive diversity in genotype‐specific reaction norms in growth rates and cell size traits. Our results showed genotype by environment interactions, indicating that no genotype could outgrow all others across all temperature environments. Subsequently, we constructed a model to simulate the relative proportion of each genotype in a hypothetical population based on genotype and temperature‐specific population growth rates. This model was run with different seasonal temperature patterns. Our modeling exercise showed a succession of two to several genotypes becoming numerically dominant depending on the underlying temperature pattern. The results suggest that (temperature) context dependent fitness may contribute to the maintenance of genetic diversity in isolated populations of clonally reproducing microorganisms in temporally variable environments.     

Mating frequency and inclusive fitness in Drosophila melanogaster

In many species, increased mating frequency reduces maternal survival and reproduction. In order to understand the evolution of mating frequency, we need to determine the consequences of increased mating frequency for offspring. We conducted an experiment in Drosophila melanogaster in which we manipulated the mating frequency of mothers and examined the survival and fecundity of the mothers and their daughters. We found that mothers with the highest mating frequency had accelerated mortality and more rapid reproductive senescence. On average, they had 50% shorter lives and 30% lower lifetime reproductive success (LRS) than did mothers with the lowest mating frequency. However, mothers with the highest mating frequency produced daughters with 28% greater LRS. This finding implies that frequent mating stimulates cross-generational fitness trade-offs such that maternal fitness is reduced while offspring fitness is enhanced. We evaluate these results using a demographic metric of inclusive fitness. We show that the costs and benefits of mating frequency depend on the growth rate of the population. In an inclusive fitness context, there was no evidence that increased mating frequency results in fitness costs for mothers. These results indicate that cross-generational fitness trade-offs have an important role in sexual selection and life-history evolution.