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.     

THE INFLUENCE OF MATING SYSTEM AND OVERLAPPING GENERATIONS ON EFFECTIVE POPULATION SIZE

The effective population size (N_e) depends strongly on mating system and generation time. These two factors interact such that, under many circumstances, N_e is close to N/2, where N is the number of adults. This is shown to be the case for both simple and highly polygynous mating systems. The random union of gametes (RUG) and monogamy are two simple systems previously used in estimating N_e, and here a third, lottery polygyny, is added. Lottery polygyny, in which all males compete equally for females, results in a lower N_e than either RUG or monogamy! Given nonoverlapping generations the reduction is 33% for autosomal loci and 25% for sex-linked loci. The highly polygynous mating systems, harem polygyny and dominance polygyny, can give very low values of N_e/N when the generation time (T) is short. However, as T is lengthened, N_e approaches N/2. The influence of a biased sex ratio depends on the mating system and, in general, is not symmetrical. Biases can occur because of sex differences in either survival or recruitment of adults, and the potential for a sex-ratio bias to change N_e is much reduced given a survival bias. The number of juveniles present also has some influence: as the maturation time is lengthened, N_e increases.     

INCREASED PROBABILITY OF EXTINCTION DUE TO DECREASED GENETIC EFFECTIVE POPULATION SIZE: EXPERIMENTAL POPULATIONS OF CLARKIA PULCHELLA

We established replicated experimental populations of the annual plant Clarkia pulchella to evaluate the existence of a causal relationship between loss of genetic variation and population survival probability. Two treatments differing in the relatedness of the founders, and thus in the genetic effective population size (N_e), were maintained as isolated populations in a natural environment. After three generations, the low N_e treatment had significantly lower germination and survival rates than did the high N_e treatment. These lower germination and survival rates led to decreased mean fitness in the low N_e populations: estimated mean fitness in the low N_e populations was only 21% of the estimated mean fitness in the high N_e populations. This inbreeding depression led to a reduction in population survival: at the conclusion of the experiment, 75% of the high N_e populations were still extant, whereas only 31% of the low N_e populations had survived. Decreased genetic effective population size, which leads to both inbreeding and the loss of alleles by genetic drift, increased the probability of population extinction over that expected from demographic and environmental stochasticity alone. This demonstrates that the genetic effective population size can strongly affect the probability of population persistence.     

THE SELECTION BARRIER BETWEEN POPULATIONS SUBJECT TO STABILIZING SELECTION

The introgression of genes carried by a small group of immigrants is studied. The recipient and the donor populations differ at several autosomal loci subject to weak selection, and two allelic forms of each gene are considered. Fitness variation is determined by additive allelic effects, by dominance effects, and by two-locus additive-by-additive epistatic interaction of the effects of the alleles. The fate of the group of immigrants is quantified by the selection barrier that describes the cumulative mean fitness of the hybrids and hybrid descendants relative to the fitness of the resident population. The monomorphic and the polymorphic loci of the recipient population contribute differently to the selection barrier. If the genetic difference between recipient and donor population is small, then the contribution of the monomorphic loci is dominated by a positive term dependent on the difference in gene frequencies. The contribution of the polymorphic loci depends only on the difference of the leading order in the pairwise linkage disequilibria between the two populations. This contribution may be positive or negative; and, thus, polymorphic loci may either contribute to the barrier or inflate the introgression.     

THE EFFECTS OF POPULATION BOTTLENECKS ON CLONAL INTERFERENCE, AND THE ADAPTATION EFFECTIVE POPULATION SIZE

Clonal interference refers to the competition that arises in asexual populations when multiple beneficial mutations segregate simultaneously. A large body of theoretical and experimental work now addresses this issue. Although much of the experimental work is performed in populations that grow exponentially between periodic population bottlenecks, the theoretical work to date has addressed only populations of a constant size. We derive an analytical approximation for the rate of adaptation in the presence of both clonal interference and bottlenecks, and compare this prediction to the results of an individual-based simulation, showing excellent agreement in the parameter regime in which clonal interference prevails. We also derive an appropriate definition for the effective population size for adaptive evolution experiments in the presence of population bottlenecks. This "adaptation effective population size" allows for a good approximation of the expected rate of adaptation, either in the strong-selection weak-mutation regime, or when clonal interference comes into play. In the multiple mutation regime, when the product of the population size and mutation rate is extremely large, these results no longer hold.     

THE MAINTENANCE OF OBLIGATE SEX IN FINITE,STRUCTURED POPULATIONS SUBJECT TO RECURRENT BENEFICIAL AND DELETERIOUS MUTATION

Although there is no known general explanation as to why sexual populations resist asexual invasion, previous work has shown that sexuals can outcompete asexuals in structured populations. However, it is currently unknown whether costly sex can be maintained with the weak structure that is commonly observed in nature. We investigate the conditions under which obligate sexuals resist asexual invasion in structured populations subject to recurrent mutation. We determine the level of population structure needed to disfavor asexuals, as calculated using the average F_st between all pairs of demes. We show that the critical F_st needed to maintain sex decreases as the population size increases, and approaches modest levels as observed in many natural populations. Sex is maintained with lower F_st if there are both advantageous and deleterious mutation, if mutation rates are sufficiently high, and if deleterious mutants have intermediate selective strengths, which maximizes the effect of Muller’s ratchet. Additionally, the critical F_st needed to maintain sex is lower when there are a large number of subpopulations. Lower F_st values are needed to maintain sex when demes vary substantially in their pairwise distances (e.g., when arrayed along one dimension), although this effect is often modest, especially if some long‐distance dispersal is present.     

A TEST AND REVIEW OF THE ROLE OF EFFECTIVE POPULATION SIZE ON EXPERIMENTAL SEXUAL SELECTION PATTERNS

Experimental evolution, particularly experimental sexual selection in which sexual selection strength is manipulated by altering the mating system, is an increasingly popular method for testing evolutionary theory. Concerns have arisen regarding genetic diversity variation across experimental treatments: differences in the number and sex ratio of breeders (effective population size; N_e ) and the potential for genetic hitchhiking, both of which may cause different levels of genetic variation between treatments. Such differences may affect the selection response and confound interpretation of results. Here we use both census-based estimators and molecular marker-based estimates to empirically test how experimental evolution of sexual selection in Drosophila pseudoobscura impacts N_e and autosomal genetic diversity. We also consider effects of treatment on X-linked N_e s, which have previously been ignored. Molecular autosomal marker-based estimators indicate that neither N_e nor genetic diversity differs between treatments experiencing different sexual selection intensities; thus observed evolutionary responses reflect selection rather than any confounding effects of experimental design. Given the increasing number of studies on experimental sexual selection, we also review the census N_e s of other experimental systems, calculate X-linked N_e , and compare how different studies have dealt with the issues of inbreeding, genetic drift, and genetic hitchhiking to help inform future designs.     

SEASONAL CHANGES IN SIZE STRUCTURE OF SARGASSUM AND TURBINARIA POPULATIONS (PHAEOPHYCEAE) ON TROPICAL REEF FLATS IN THE SOUTHERN RED SEA1

Seasonal variation in density, thallus length and biomass, population size structure, and allometric length‐biomass relationships was investigated in populations of Sargassum ilicifolium (Turner) C. Agardh, Sargassum subrepandum (Forssk.) C. Agardh, and Turbinaria triquetra (J. Agardh) Kütz. (Phaeophyceae) on shallow reef flats in the southern Red Sea. Thallus length and biomass varied strongly with season, with the highest values occurring in the cooler months. Thallus densities showed no significant temporal variation. Log‐total biomass versus log‐density relationships were positive throughout the growth season without any decrease in the slope of the relationship. In two populations, biomass‐density combinations approached the interspecific biomass‐density line, but the massive annual shedding of modules occurred before self‐thinning would set in. Allometric length‐biomass relationships varied with season in all populations and were associated with seasonal module initiation, growth, and shedding. Evidence of a strong asymmetric competition was found in two high‐density populations. These populations showed a predominance of small thalli during peak development, asymmetrical Lorenz curves, increasing Gini coefficients, and increasing thallus length relative to biomass during the main growth phase. In two other less crowded populations, small thalli were absent during peak development, Lorenz curves were symmetrical, and Gini coefficients decreased during the main growth phase. In these populations, size equalization appears to be due to responses at the modular level rather than size‐dependent mortality. We conclude that changes in size structure in this highly seasonal environment are determined by module dynamics, modified by asymmetric competition in some populations, with a minor role of recruitment and no regulatory effect of self‐thinning.     

PERSISTENCE OF AMBROSIA TRIFIDA POPULATIONS IN OLD FIELDS AND RESPONSES TO SUCCESSIONAL CHANGES

A population of Ambrosia trifida L. (Asteraceae) in an annually ploughed field and an adjacent 15-year old population in an old field were compared to determine how plant responses, genotypic composition, and genetic variability change in populations over successional time. The two populations were originally part of a large contiguous population in an annually ploughed field. When individuals from the two populations were grown from seed in a common garden, they showed several significant differences in characteristics indicating different genotypic compositions in the two populations. Individuals from the old field population showed earlier emergence, lower leaf mortality, and greater numbers of leaves, biomass, seed production, and reproductive allocation relative to plants from the annually ploughed field. When sown in the field in a reciprocal transplant experiment, individuals from the two populations also differed in patterns of emergence, survivorship, yield, and fecundity. When grown together in a pairwise competition experiment, individuals from the old field population showed competitive superiority with respect to growth and seed production. This genetic differentiation between populations of different successional ages may be explained by natural selection imposed by the changing environment over successional time. However, the history and characteristics of these populations are such that founder effects may also be important in explaining the differences between them. A comparison of levels of variability in 14 different characters of individuals of the two populations showed no evidence that genetic variability in A. trifida populations declined over successional time.     

THE EFFECTIVE SIZE OF A HIERARCHICALLY STRUCTURED POPULATION

A knowledge of the effective size of a population (N_e) is important in understanding its current and future evolutionary potential. Unfortunately, the effective size of a hierarchically structured population is not, in general, equal to the sum of its parts. In particular, the inbreeding structure has a major influence on N_e. Here I link N_e to Wright's hierarchical measures of inbreeding, F_IS and F_ST, for an island-structured population (or metapopulation) of size N_T. The influence of F_ST depends strongly on the degree to which island productivity is regulated. In the absence of local regulation (the interdemic model), interdemic genetic drift reduces N_e. When such drift is combined with local inbreeding under otherwise ideal conditions, the effects of F_IS and F_ST are identical: increasing inbreeding either within or between islands reduces N_e, with N_e = N_T/[(1 + F_IS)(1 + F_ST) ? 2F_ISF_ST]. However, if islands are all equally productive because of local density regulation (the traditional island model), then N_e = N_T/[(1 + F_IS)(1 –F_ST)] and the effect of F_ST is reversed. Under the interdemic model, random variation in the habitat quality (and hence productivity) of islands act to markedly decrease N_e. This variation has no effect under the island model because, by definition, all islands are equally productive. Even when no permanent island structure exists, spatial differences in habitat quality can significantly increase the overall variance in reproductive success of both males and females and hence lower N_e. Each of these basic results holds when other nonideal factors are added to the model. These factors, deviations from a 1:1 sex ratio, greater than Poisson variance in female reproductive success, and variation in male mating success due to polygynous mating systems, all act to lower N_e. The effects of male and female variance on N_e have important differences because only females affect island productivity. Finally, it is noted that to use these relationships, F_IS and F_ST must be estimated according to Wright's definition (and corrected to have a zero expectation under the null model). A commonly used partitioning (θ, θ_g) can be biased if either island size or the number of islands is small.