2006 Sewall Wright Award. Brian Charlesworth.
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Awards and Prizes↗
Biomedical subjects
Russell Lande
Publications and source records attributed to Russell Lande.
Using reproductive value to estimate key parameters in density-independent age-structured populations.
The dynamics of reproductive value are used to provide a simple derivation of Tuljapurkar's approximation for the long-run growth rate and environmental variance of lnN, in a density-independent age-structured population in a random environment. With no environmental autocorrelation, the dynamics of total population size, N, generally shows time lags and autocorrelation caused by life history, which may strongly bias estimates of environmental variance obtained by ignoring age structure. In contrast, the total reproductive value, V, is Markovian and obeys a first-order autoregressive process. This suggests a simple method for estimating the environmental variance, and avoiding potentially large bias due to age-structure fluctuations, by converting a multivariate time series of age structure to a univariate time series of lnV. We illustrate the method by estimating the long-run growth rate and the environmental variance in an exponentially growing population of Bighorn Sheep.
Age Distribution↗
Estimating density dependence from time series of population age structure.
Population fluctuations are caused by demographic and environmental stochasticity, time lags due to life history, and density dependence. We model a general life history allowing density dependence within and among age or stage classes in a population undergoing small or moderate fluctuations around a stable equilibrium. We develop a method for estimating the overall strength of density dependence measured by the rate of return toward equilibrium, and we also consider a simplified population description and forecasting using the density-dependent reproductive value. This generality comes at the cost of requiring a time series of the population age or stage structure instead of a univariate time series of adult or total population size. The method is illustrated by analyzing the dynamics of a fully censused population of red deer (Cervus elaphus) based on annual fluctuations of age structure through 21 years.
Age Distribution↗
Population genetic models of male and mutual mate choice.
Examples of male mate choice are becoming increasingly common, even in polygynous species. We create a series of population genetic models to examine the evolutionary equilibria and dynamics resulting from male mate choice during polygyny, alone and in the context of mutual mate choice by both sexes. We find that unless males with a preference are able to increase their overall courtship output, male preference will be lost. This loss can be counteracted if males choose females not based on arbitrary traits, but based on a trait that indicates high fertility or viability. We also conclude that if male and female preferences and traits are all controlled by different loci, the male and female mate choice systems are decoupled; the presence of a male preference then has no influence on the equilibria or dynamics of female mate choice. If male and female traits are coupled by pleiotropy, it becomes possible for a male preference to be maintained, regardless of whether preferences between the sexes are pleiotropic or controlled by separate loci.
Animals↗
Ecological and reproductive character displacement on an environmental gradient.
Character displacement, in which coevolution of similar species alters their phenotypes, can be difficult to identify on the basis of observational data alone. In two-species systems, the most commonly identified (i.e., classic) resulting pattern is greater phenotypic difference between species in sympatry than allopatry. We show that restricting studies to this pattern may exclude many instances of character displacement, particularly in the presence of spatial environmental gradients. We present four spatial models of character displacement in quantitative traits affecting competition and hybridization between the species. Our models highlight the connections between range limits and character displacement in continuous space. We conclude that the classic pattern is less likely to occur for a trait affecting resource acquisition than for a trait affecting mate choice. We also show that interspecific hybridization (when hybrids are inviable), even in very small amounts, has marked effects on the shape and stability of borders between species and the nature of character displacement. A survey of the empirical literature shows that character displacement studies often lack analysis of spatial phenotype and abundance data. We recommend more careful spatial sampling in character displacement studies, and we illustrate how comparison of clines in mean phenotype in sympatry and allopatry can be used to suggest the action of character displacement.
Animals↗
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.
Aging↗
Effective size of a fluctuating age-structured population.
Previous theories on the effective size of age-structured populations assumed a constant environment and, usually, a constant population size and age structure. We derive formulas for the variance effective size of populations subject to fluctuations in age structure and total population size produced by a combination of demographic and environmental stochasticity. Haploid and monoecious or dioecious diploid populations are analyzed. Recent results from stochastic demography are employed to derive a two-dimensional diffusion approximation for the joint dynamics of the total population size, N, and the frequency of a selectively neutral allele, p. The infinitesimal variance for p, multiplied by the generation time, yields an expression for the effective population size per generation. This depends on the current value of N, the generation time, demographic stochasticity, and genetic stochasticity due to Mendelian segregation, but is independent of environmental stochasticity. A formula for the effective population size over longer time intervals incorporates deterministic growth and environmental stochasticity to account for changes in N.
Age Factors↗
Diversity, endemism, and age distributions in macroevolutionary sources and sinks.
Quantitative tests of historical hypotheses are necessary to advance our understanding of biogeographic patterns of species distributions, but direct tests are often hampered by incomplete fossil or historical records. Here we present an alternative approach in which we develop a dynamic model that allows us to test hypotheses about regional rates of taxon origination, extinction, and dispersal using information on ages and current distributions of taxa. With this model, we test two assumptions traditionally made in the context of identifying regions as "centers of origin"--that regions with high origination rates will have high diversity and high endemism. We find that these assumptions are not necessarily valid. We also develop expressions for the regional age distributions of extant taxa and show that these may yield better insight into regional evolutionary rates. We then apply our model to data on the biogeography and ages of extant genera of marine bivalves and conclude that diversity in polar regions predominantly reflects dispersal of taxa that evolved elsewhere rather than in situ origination-extinction dynamics.
Animals↗
Extinction in relation to demographic and environmental stochasticity in age-structured models.
The demographic variance of an age-structured population is defined. This parameter is further split into components generated by demographic stochasticity in each vital rate. The applicability of these parameters are investigated by checking how an age-structured population process can be approximated by a diffusion with only three parameters. These are the deterministic growth rate computed from the expected projection matrix and the environmental and demographic variances. We also consider age-structured populations where the fecundity at any stage is either zero or one, and there is neither environmental stochasticity nor dependence between individual fecundity and survival. In this case the demographic variance is uniquely determined by the vital rates defining the projection matrix. The demographic variance for a long-lived bird species, the wandering albatross in the southwestern part of the Indian Ocean, is estimated. We also compute estimates of the age-specific contributions to the total demographic variance from survival, fecundity and the covariance between survival and fecundity.
Age Factors↗
Reproductive compensation in the evolution of plant mating systems.
Reproductive compensation, the replacement of dead embryos by potentially viable ones, is known to play a major role in the maintenance of deleterious mutations in mammalian populations. However, it has received little attention in plant evolution. Here we model the joint evolution of mating system and inbreeding depression with reproductive compensation. We used a dynamic model of inbreeding depression, allowing for partial purging of recessive lethal mutations by selfing. We showed that reproductive compensation tended to increase the mean number of lethals in a population, but favored self-fertilization by effectively decreasing early inbreeding depression. When compensation depended on the selfing rate, stable mixed mating systems can occur, with low to intermediate selfing rates. Experimental evidence of reproductive compensation is required to confirm its potential importance in the evolution of plant mating systems. We suggest experimental methods to detect reproductive compensation.
Biological Evolution↗
Loss of gametophytic self-incompatibility with evolution of inbreeding depression.
Gametophytic self-incompatibility (SI) in plants is a widespread mechanism preventing self-fertilization and the ensuing inbreeding depression, but it often evolves to self-compatibility. We analyze genetic mechanisms for the breakdown of gametophytic SI, incorporating a dynamic model for the evolution of inbreeding depression allowing for partial purging of nearly recessive lethal mutations by selfing, and accounting for pollen limitation and sheltered load linked to the S-locus. We consider two mechanisms for the breakdown of gametophytic SI: a nonfunctional S-allele and an unlinked modifier locus that inactivates the S-locus. We show that, under a wide range of conditions, self-compatible alleles can invade a self-incompatible population. Conditions for invasion are always less stringent for a nonfunctional S-allele than for a modifier locus. The spread of self-compatible genotypes is favored by extremely high or low selfing rates, a small number of S-alleles, and pollen limitation. Observed parameter values suggest that the maintenance of gametophytic SI is caused by a combination of high inbreeding depression in self-incompatible populations coupled with intermediate selfing rates of the self-compatible genotypes and sheltered load linked to the S-locus.
Alleles↗
Ecology. Hatcheries and endangered salmon.
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Adaptation, Physiological↗
Estimation of genetically effective breeding numbers using a rejection algorithm approach.
Polygynous mating results in nonrandom sampling of the adult male gamete pool in each generation, thereby increasing the rate of genetic drift. In principle, genetic paternity analysis can be used to infer the effective number of breeding males (Nebm). However, this requires genetic data from an exhaustive sample of candidate males. Here we describe a new approach to estimate Nebm using a rejection algorithm in association with three statistics: Euclidean distance between the frequency distributions of maternally and paternally inherited alleles, average number of paternally inherited alleles and average gene diversity of paternally inherited alleles. We quantify the relationship between these statistics and Nebm using an individual-based simulation model in which the male mating system varied continuously between random mating and extreme polygyny. We evaluate this method using genetic data from a natural population of highly polygynous fruit bats (Cynopterous sphinx). Using data in the form of mother-offspring genotypes, we demonstrate that estimates of Nebm are very similar to independent estimates based on a direct paternity analysis that included data on candidate males. Our method also permits an evaluation of uncertainty in estimates of Nebm and thus facilitates inferences about the mating system from genetic data. Finally, we investigate the sensitivity of our method to sample size, model assumptions, adult population size and the mating system. These analyses demonstrate that the rejection algorithm provides accurate estimates of Nebm across a broad range of demographic scenarios, except when the true Nebm is high.
Algorithms↗
Coevolution of an avian host and its parasitic cuckoo.
We use a quantitative genetic model to examine the coevolution of host and cuckoo egg characters (termed "size" as a proxy for general appearance), host discrimination, and host and cuckoo population dynamics. A host decides whether to discard an egg using a comparison of the sizes of the eggs in her nest, which changes as host and cuckoo eggs evolve. Specifically, we assume that the probability that she discards the largest egg in her nest depends on how much larger it is than the second largest egg. This decision rule (i.e., the acceptable difference in egg sizes) also evolves, changing both the chance of successful rejection of a cuckoo egg in parasitized nests and the chance of mistaken rejection of a host egg in both parasitized and unparasitized nests. We find a stable equilibrium for coexistence of the host and cuckoo where there is cuckoo egg mimicry, evolutionary displacement of the host egg away from the cuckoo egg phenotype, and host discrimination against unusual eggs. Both host discrimination and host egg displacement are fairly weak at the equilibrium. Cuckoo egg mimicry, although imperfect, usually evolves more extensively and quickly than the responses of the host. Our model provides evidence for both the evolutionary equilibrium and evolutionary lag hypotheses of host acceptance of parasitic eggs.
Animals↗
Spatial Scale of Population Synchrony: Environmental Correlation versus Dispersal and Density Regulation.
A stochastic model is developed to analyze the equilibrium spatial pattern of population synchrony, the correlation of temporal fluctuations in population density between localities. The expected population dynamics and the distribution of individual dispersal distance are homogeneous in space. Environmental stochasticity is caused by temporal fluctuations in the intrinsic rate of increase and/or carrying capacity of local populations that are correlated in space (but not time), the environmental correlation decreasing with distance. We analyze a linearized model for small fluctuations. Employing the standard deviation of a function in a given direction as a measure of scale, the spatial scale of population synchrony, lρ, is related to the spatial scales of environmental correlation, le, and individual dispersal, l, by the simple general formula [Formula: see text], where m is the individual dispersal rate and γ is the strength of population density regulation (or rate of return to equilibrium, [Formula: see text] in the logistic model). Relative to environmental correlation (the Moran effect), the contribution of individual dispersal to the spatial scale of synchrony is magnified by the ratio of the individual dispersal rate to the strength of density regulation. Thus, even if the scale of individual dispersal is smaller than that of environmental correlation, dispersal can substantially increase the scale of population synchrony for weakly regulated populations.
Moran effect↗