Evolution of dispersal in density regulated populations: A haploid model

The evolution of dispersal is explored in a density-dependent framework. Attention is restricted to haploid populations in which the genotypic fitnesses at a single diallelic locus are decreasing functions of the changing number of individuals in the population. It is shown that migration between two populations in which the genotypic response to density is reversed can maintain both alleles when the intermigration rates are constant or nondecreasing functions of the population densities. There is always a unique symmetric interior equilibrium with equal numbers but opposite gene frequencies in the two populations, provided the system is not degenerate. Numerical examples with exponential and hyperbolic fitnesses suggest that this is the only stable equilibrium state under constant positive migration rates (m) less than . Practically speaking, however, there is only convergence after a reasonable number of generations for relatively small migration rates ( ). A migration-modifying mutant at a second, neutral locus, can successfully enter two populations at a stable migration-selection balance if and only if it reduces the intermigration rates of its carriers at the original equilibrium population size. Moreover, migration modification will always result in a higher equilibrium population size, provided the system approaches another symmetric interior equilibrium. The new equilibrium migration rate will be lower than that at the original equilibrium, even when the modified migration rate is a nondecreasing function of the population sizes. Therefore, as in constant viability models, evolution will lead to reduced dispersal.     

The genetic effects of roads: A review of empirical evidence

Roads exert various effects of conservation concern. They cause road mortality of wildlife, change the behaviour of animals and lead to habitat fragmentation. Roads also have genetic effects, as they restrict animal movement and increase the functional isolation of populations. We first formulate theoretical expectations on the genetic effects of roads with respect to a decrease in genetic diversity and an increase in genetic differentiation or distance of populations or individuals. We then review the empirical evidence on the genetic effects of roads based on the available literature. We found that roads often, but not always, decrease the genetic diversity of affected populations due to reduced population size and genetic drift. Whether the reduction in genetic diversity influences the long-term fitness of affected populations is, however, not yet clear. Roads, especially fenced highways, also act as barriers to movement, migration and gene flow. Roads therefore often decrease functional connectivity and increase the genetic differentiation of populations or the genetic distance among individuals. Nevertheless, roads and highways rarely act as complete barriers as shown by genetic studies assessing contemporary migration across roads (by using assignment tests). Some studies also showed that road verges act as dispersal corridors for native and exotic plants and animals. Genetic methods are well suited to retrospectively trace such migration pathways. Most roads and highways have only recently been built. Although only few generations might thus have passed since road construction, our literature survey showed that many studies found negative effects of roads on genetic diversity and genetic differentiation in animal species, especially for larger mammals and amphibians. Roads may thus rapidly cause genetic effects. This result stresses the importance of defragmentation measures such as over- and underpasses or wildlife bridges across roads.     

THE EFFECT OF DELAYED POPULATION GROWTH ON THE GENETIC DIFFERENTIATION OF LOCAL POPULATIONS SUBJECT TO FREQUENT EXTINCTIONS AND RECOLONIZATIONS

I investigated the effects of delayed population growth on the genetic differentiation among populations subjected to local extinction and recolonization, for two different migration functions; (1) a constant migration rate, and (2) a constant number of migrants. A delayed period of population growth reduces the size of the newly founded populations for one or several generations. Whether this increases differentiation among local populations depends on the actual pattern of migration. With a constant migration rate, fewer migrants move into small populations than into large, thus providing ample opportunity for drift to act within a population. A prolonged period of population growth thus makes the conditions for enhanced differentiation between local populations less restrictive and also inflates the actual levels of differentiation. The effect depends on the relative magnitudes of k_e, the effective number of colonizers and k, the actual number of colonizers. When there is a constant number of migrants into a population per generation, migration into small populations is increased. This increase of migration in small populations counteracts the effects of genetic drift due to small population size. It increases the rate by which populations approach equilibrium, as small populations are swamped by migrants from larger populations closer to genetic equilibrium, and overall levels of differentiation are thus reduced. I also discuss situations for which the results of this paper are relevant.     

Joint estimation of migration rate and effective population size using the island model

Using the island model of population demography, I report that the demographic parameters migration rate and effective population size can be jointly estimated with equilibrium probabilities of identity in state calculated using a sample of genotypes collected at a single point in time from a single generation. The method, which uses moment-type estimators, applies to dioecious populations in which females and males have identical demography and monoecious populations with no selfing and requires that offspring genotypes are sampled following reproduction and prior to migration. I illustrate the estimation procedure using the infinite-island model with no mutation and the finite-island model with three kinds of mutation models. In the infinite-island model with no mutation, the estimators can be expressed as simple functions of estimates of the F-statistic parameters F(IT) and F(ST). In the finite-island model with mutation among k alleles, mutation rate, migration rate, and effective population size can be simultaneously estimated. The estimates of migration rate and effective population size are somewhat robust to violations in assumptions that may arise in empirical applications such as different kinds of mutation models and deviations from temporal equilibrium.     

Population dynamics in migratory networks

Migratory animals are comprised of a complex series of interconnected breeding and nonbreeding populations. Because individuals in any given population can arrive from a variety of sites the previous season, predicting how different populations will respond to environmental change can be challenging. In this study, we develop a population model composed of a network of breeding and wintering sites to show how habitat loss affects patterns of connectivity and species abundance. When the costs of migration are evenly distributed, habitat loss at a single site can increase the degree of connectivity (mixing) within the entire network, which then acts to buffer global populations from declines. However, the degree to which populations are buffered depends on where habitat loss occurs within the network: a site that has the potential to receive individuals from multiple populations in the opposite season will lead to smaller declines than a site that is more isolated. In other cases when there are equal costs of migration to two or more sites in the opposite season, habitat loss can result in some populations becoming segregated (disconnected) from the rest of the network. The geographic structure of the network can have a significant influence on relative population sizes of sites in the same season and can also affect the overall degree of mixing in the network, even when sites are of equal intrinsic quality. When a migratory network is widely spaced and migration costs are high, an equivalent habitat loss will lead to a larger decline in global population size than will occur in a network where the overall costs of migration are low. Our model provides an important foundation to test predictions related to habitat loss in real-world migratory networks and demonstrates that migratory networks will likely produce different dynamics from traditional metapopulations. Our results provide strong evidence that estimating population connectivity is a prerequisite for successfully predicting changes in migratory populations.     

Will small population sizes warn us of impending extinctions?

Several models are used to show that population sizes are often relatively insensitive to deteriorating environmental conditions over most of the range of environments that allow population persistence. As conditions continue to worsen in these cases, equilibrium population sizes ultimately decline rapidly toward extinction from sizes similar to or larger than those before environmental decline began. Consumer-resource models predict that equilibrium or average population size can increase with deteriorating environmental conditions over a large part of the range of the environmental parameter that allows persistence. The initial insensitivity or increase in the population of the focal species occurs because changes in the populations of other components of the food web compensate for the decline in one or more fitness components of the focal population. However, the compensatory processes are generally nonlinear and often approach their limits abruptly rather than gradually. When there is steady directional change in the environment, populations lag behind the equilibrium population size specified by current environmental conditions. The environmental variable can then decline below the level required for population persistence while the population size is still close to or greater than its original value. Efficient consumers and self-reproducing resources are especially likely to produce this outcome. More complex models with adaptive behavior, additional consumers, or additional resources often exhibit similar trajectories of population size under environmental deterioration.     

Local extinction and recolonization, species effective population size, and modern human origins

A primary objection from a population genetics perspective to a multiregional model of modern human origins is that the model posits a large census size, whereas genetic data suggest a small effective population size. The relationship between census size and effective size is complex, but arguments based on an island model of migration show that if the effective population size reflects the number of breeding individuals and the effects of population subdivision, then an effective population size of 10,000 is inconsistent with the census size of 500,000 to 1,000,000 that has been suggested by archeological evidence. However, these models have ignored the effects of population extinction and recolonization, which increase the expected variance among demes and reduce the inbreeding effective population size. Using models developed for population extinction and recolonization, we show that a large census size consistent with the multiregional model can be reconciled with an effective population size of 10,000, but genetic variation among demes must be high, reflecting low interdeme migration rates and a colonization process that involves a small number of colonists or kin-structured colonization. Ethnographic and archeological evidence is insufficient to determine whether such demographic conditions existed among Pleistocene human populations, and further work needs to be done. More realistic models that incorporate isolation by distance and heterogeneity in extinction rates and effective deme sizes also need to be developed. However, if true, a process of population extinction and recolonization has interesting implications for human demographic history.     

Does habitat fragmentation reduce genetic diversity and subpopulation connectivity?

The estimation of levels of genetic variation has received considerable attention because it is generally thought to be indicative of overall species vitality and the potential for evolutionary responses to environmental changes. Here, we use allozymes markers and two distinct collections of Cakile maritima, an annual species from sandy coastal habitats (2000 generation and 2005 generation collected from 9 populations in their natural habitats), to assess the magnitude of expected genetic change. We compared genetic diversity between generations (all populations combined), and then between populations at each generation. Based on 13 loci scored from the eight enzymes examined, a high genetic diversity was detected at both the population and generation level as compared to other herbaceous species. However, allelic richness reduction in the 2005 generation suggested restricted gene flow and a high risk of future genetic bottlenecks, if larger tracts of coastal areas disappear. Most loci showed deviation from Hardy‐Weinberg equilibrium due to excess of heterozygotes in all populations suggesting that this species has an allogamic mode of reproduction. It appears most likely that this species has experienced a recent decrease in population size, and that genetic drift in small populations has resulted in a loss of alleles occurring at low frequency. Despite the deterioration process, maintenance of high genetic diversity suggests that there are some ecological factors determining population structure.     

Kin groups and trait groups: population structure and epidemic disease selection

A Monte Carlo simulation based on the population structure of a small-scale human population, the Semai Senoi of Malaysia, has been developed to study the combined effects of group, kin, and individual selection. The population structure resembles D.S. Wilson's structured deme model in that local breeding populations (Semai settlements) are subdivided into trait groups (hamlets) that may be kin-structured and are not themselves demes. Additionally, settlement breeding populations are connected by two-dimensional stepping-stone migration approaching 30% per generation. Group and kin-structured group selection occur among hamlets the survivors of which then disperse to breed within the settlement population. Genetic drift is modeled by the process of hamlet formation; individual selection as a deterministic process, and stepping-stone migration as either random or kin-structured migrant groups. The mechanism for group selection is epidemics of infectious disease that can wipe out small hamlets particularly if most adults become sick and social life collapses. Genetic resistance to a disease is an individual attribute; however, hamlet groups with several resistant adults are less likely to disintegrate and experience high social mortality. A specific human gene, hemoglobin E, which confers resistance to malaria, is studied as an example of the process. The results of the simulations show that high genetic variance among hamlet groups may be generated by moderate degrees of kin-structuring. This strong microdifferentiation provides the potential for group selection. The effect of group selection in this case is rapid increase in gene frequencies among the total set of populations. In fact, group selection in concert with individual selection produced a faster rate of gene frequency increase among a set of 25 populations than the rate within a single unstructured population subject to deterministic individual selection. Such rapid evolution with plausible rates of extinction, individual selection, and migration and a population structure realistic in its general form, has implications for specific human polymorphisms such as hemoglobin variants and for the more general problem of the tempo of evolution as well.     

The dynamics of transposable elements in structured populations

We analyzed the dynamics of transposable elements (TEs) according to Wright's island and continent-island models, assuming that selection tends to counter the deleterious effects of TEs. We showed that migration between host populations has no impact on either the existence or the stability of the TE copy number equilibrium points obtained in the absence of migration. However, if the migration rate is slower than the transposition rate or if selection is weak, then the TE copy numbers in all the populations can be expected to slowly become homogeneous, whereas a heterogeneous TE copy number distribution between populations is maintained if TEs are mobilized in some populations. The mean TE copy number is highly sensitive to the population size, but as a result of migration between populations, it decreases as the sum of the population sizes increases and tends to reach the same value in these populations. We have demonstrated the existence of repulsion between TE insertion sites, which is established by selection and amplified by drift. This repulsion is reduced as much as the migration rate is higher than the recombination rate between the TE insertion sites. Migration and demographic history are therefore strong forces in determining the dynamics of TEs within the genomes and the populations of a species.     

Selection in autotetraploids

Summary Theoretical studies indicated that response to selection would always be greater in diploid than in autotetraploid populations when gene frequency was the same in both, and that situations in which little or no response to selection could be expected would be more frequent in autotetraploids. Interpretation of the coefficient of selection in terms of escape from infection in a program of selection for disease or insect resistance indicated that moderate levels of escape from infection can drastically reduce response to selection in some cases.The zygotic constitution of an autotetraploid population will change as it approaches a new random mating equilibrium once selection pressure is relaxed. The changes will result in no change in the population mean if the trait under selection exhibits no dominance, but the mean will decrease slightly if there is dominance.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Variation in dental occlusion and arches among Melanesians of Bougainville Island, Papua New Guinea. II. Clinical variation, geographic microdifferentiation and synthesis

Patterns of geographic microdifferentiation for dental occlusion and the size and shape of the dental arches are described for 14 villages on Bougainville Island, Papua New Guinea. Occlusal variables, such as overjet, overbite, molar relationships, crowding or spacing, and malalignment vary less among villages than do arch length and width. Arch length and width decrease in size from north to south. The pattern of biological distance among villages for occlusal variables and arch size correspond poorly to anthropometric, linguistic, geographic and migrational distances. The value of occlusal variables and arch size for discriminating among populations, the biological interpretation of multivariate data and the objectives of research on geographic microdifferentiation are discussed.     

The anomalous effects of biased mutation

A model is presented in which alleles at a number of loci combine to influence the value of a quantitative trait that is subject to stabilizing selection. Mutations can occur to alleles at the loci under consideration. Some of these mutations will tend to increase the value of the trait, while others will tend to decrease it. In contrast to most previous models, we allow the mean effect of mutations to be nonzero. This means that, on average, mutations can have a bias, such that they tend to either increase or decrease the value of the trait. We find, unsurprisingly, that biased mutation moves the equilibrium mean value of the quantitative trait in the direction of the bias. What is more surprising is the behavior of the deviation of the equilibrium mean value of the trait from its optimal value. This has a nonmonotonic dependence on the degree of bias, so that increasing the degree of bias can actually bring the mean phenotype closer to the optimal phenotype. Furthermore, there is a definite maximum to the extent to which biased mutation can cause a difference between the mean phenotype and the optimum. For plausible parameter values, this maximum-possible difference is small. Typically, quantitative-genetics models assume an unconstrained model of mutation, where the expected difference in effect between a parental allele and a mutant allele is independent of the current state of the parental allele. Our results show that models of this sort can easily lead to biologically implausible consequences when mutations are biased. In particular, unconstrained mutation typically leads to a continual increase or decrease in the mean allelic effects at all trait-controlling loci. Thus at each of these loci, the mean allelic effect eventually becomes extreme. This suggests that some of the models of mutation most commonly used in quantitative genetics should be modified so as to introduce genetic constraints.     

Density-dependent migration and human population structure in historical Massachusetts

Studies of population structure often focus on the effects of population size and migration rates on genetic variation. Few studies, however, have investigated the relationship between these two factors. The purpose of this paper is to determine the extent to which migration (and gene flow) is density-dependent (that is, affected by population size) for populations in historical Massachusetts. Data from 4,859 marriage records were analyzed from four populations in north-central Massachusetts during the time period 1741 to 1849. These data were placed into 29 samples defined in terms of population and time cohort. Within each cohort the overall exogamy rate was computed along with three estimates of gene flow based on marital migration: local migration (k), long-distance migration (m), and effective migration rate (me). Three samples show unusually low rates that reflect the history of settlement. Regression analyses were used with the remaining samples, and they show nonlinear density-dependent migration that is unrelated to temporal trends. Migration is highest in samples with small population sizes (less than 800) and large population sizes (greater than 1,600). Migration is lowest in medium-sized populations. Two processes are suggested to explain this curvilinear relationship of migration and population size. In small populations, the lack of suitable potential mates and/or availability of settled land leads to an increase in migration into the population. As population size increases, this migration decreases. After populations reach a certain size, migration increases again, most likely reflecting the economic pull of larger populations. These patterns could act to enhance, or counter, genetic drift, depending on the direction of density dependence.     

The average lifetime of a population in a varying environment

I derive an approximate formula relating the average time to extinction of a population in a varying environment to its initial size, its equilibrium size (if it is self-regulated), its innate capacity for natural increase, and the impact upon it of environmental variation. The greater the impact of environmental variation, the more slowly a population's prospective lifetime increases with increase in its equilibrium size. The lifetimes of populations greatly influenced by environmental variation are more sensitive to the relative amplitude of fluctuation in their numbers than to their equilibrium size. Since species tend to avoid competitive displacement by specializing, rendering themselves more sensitive to environmental change, and since populations are no more likely to risk extinction in one environment than in another, the degree to which a community's populations fluctuate will be unrelated to environmental stability.     

Resource partitioning among competing species—A coevolutionary approach

A reasonably general theory for predicting the outcome of coevolution among interacting species is developed. It is applied to a model for resource partitioning among competing species.Current theory for resource partitioning is based on derivations of a “limiting similarity”—i.e., a limit to how similar competitors can be to one another consistent with coexistence. This theory presumes there is a mechanism, perhaps invasion and extinction, which causes competitors to attain the limiting similarity. The view taken in this paper is that partitioning is an evolutionary compromise between pressures for character displacement and disadvantages inherent in the shift to different resource types.A set of principles is offered for the evolution of the parameters in ecological models. (1) For single population models natural selection causes the parameters ultimately to assume those values which produce the highest equilibrium population size. (2) For models of interacting populations, but without interspecific frequency-dependence, natural selection causes the parameters to assume values which produce either the highest or lowest equilibrium population size for any species depending on the sign of the “feedback” in the community obtained by deleting that species. (3) For models of interacting populations with interspecific frequency dependence natural selection leads to parameter values which produce intermediate equilibrium population sizes. A function called the conditional equilibrium population size is introduced. Provided (a) the mean fitness is a maximum in each species at a stable coevolutionary equilibrium and (b) there is negative density-dependence in each species then natural selection causes the parameters to assume values which produce the highest conditional equilibrium population size for each species.These coevolutionary principles, applied to a model for resource partitioning, entail that the niche separation between species relative to given niche widths, increases with the variety of available resources and decreases with the number of competing populations. Also, the evolution of character displacement between two species does not proceed far enough to maximize the equilibrium population sizes of the species involved. These results imply that the relationship between the niche overlap (of nearest neighbors) and species diversity is qualitatively different depending on whether the variety of resources at any place covaries with the species diversity there. Without covariation niche overlap increases with species diversity; with covariation overlap may decrease with species diversity. This study provides the beginning of a theory for the convergent evolution of community structure.     

TEMPORAL FLUCTUATIONS IN DEMOGRAPHIC PARAMETERS AND THE GENETIC VARIANCE AMONG POPULATIONS

Contrary to assumptions commonly made in the study of population genetics, the demographic properties of many populations are not always constant. Important characteristics of populations such as migration rate and population size may vary in time and space. Moreover, local populations often come and go; the rate of extinction and the properties of colonization may also vary. In this paper, the approach to equilibrium following a disturbance in the genetic variance among populations is described. The rate of migration is shown to be critical in determining the extent to which extinction and recolonization affects genetic differentiation. Perturbations and variations through time and space in demographic parameters such as population size and migration rate are shown to be important in determining the partitioning of genetic variance. Equations are given to predict the average through time of genetic differentiation among populations in the event of a single disturbance or in constant fluctuations in the pertinent demographic parameters. In general, these fluctuations increase the F_ST of a species. Spatial demographic variation affects F_STmuch more than temporal variation. These demographic properties make some species unsuitable for the empirical analysis of migration with indirect genetic measures. Demographic instability may play a large role in the evolution of genetic variation.     

Effects of population size and isolation on heterosis, mean fitness, and inbreeding depression in a perennial plant

? In small isolated populations, genetic drift is expected to increase chance fixation of partly recessive, mildly deleterious mutations, reducing mean fitness and inbreeding depression within populations and increasing heterosis in outcrosses between populations. ? We estimated relative effective sizes and migration among populations and compared mean fitness, heterosis, and inbreeding depression for eight large and eight small populations of a perennial plant on the basis of fitness of progeny produced by hand pollinations within and between populations. ? Migration was limited, and, consistent with expectations for drift, mean fitness was 68% lower in small populations; heterosis was significantly greater for small (mean?=?70%, SE?=?14) than for large populations (mean?=?7%, SE?=?27); and inbreeding depression was lower, although not significantly so, in small (mean?=?-0.29%, SE?=?28) than in large (mean?=?0.28%, SE?=?23) populations. ? Genetic drift promotes fixation of deleterious mutations in small populations, which could threaten their persistence. Limited migration will exacerbate drift, but data on migration and effective population sizes in natural populations are scarce. Theory incorporating realistic variation in population size and patterns of migration could better predict genetic threats to small population persistence.