Effective population size associated with self-fertilization: lessons from temporal changes in allele frequencies in the selfing annual Medicago truncatula

Despite its significance in evolutionary and conservation biology, few estimates of effective population size (N(e)) are available in plant species. Self-fertilization is expected to affect N(e), through both its effect on homozygosity and population dynamics. Here, we estimated N(e) using temporal variation in allele frequencies for two contrasted populations of the selfing annual Medicago truncatula: a large and continuous population and a subdivided population. Estimated N(e) values were around 5-10% of the population census size suggesting that other factors than selfing must contribute to variation in allele frequencies. Further comparisons between monolocus allelic variation and changes in the multilocus genotypic composition of the populations show that the local dynamics of inbred lines can play an important role in the fluctuations of allele frequencies. Finally, comparing N(e) estimates and levels of genetic variation suggest that H(e) is a poor estimator of the contemporaneous variance effective population size.     

Estimating Effective Population Size from Temporally Spaced Samples with a Novel,Efficient Maximum-Likelihood Algorithm

The effective population size N_e is a key parameter in population genetics and evolutionary biology, as it quantifies the expected distribution of changes in allele frequency due to genetic drift. Several methods of estimating N_e have been described, the most direct of which uses allele frequencies measured at two or more time points. A new likelihood-based estimator NB^ for contemporary effective population size using temporal data is developed in this article. The existing likelihood methods are computationally intensive and unable to handle the case when the underlying N_e is large. This article tries to work around this problem by using a hidden Markov algorithm and applying continuous approximations to allele frequencies and transition probabilities. Extensive simulations are run to evaluate the performance of the proposed estimator NB^, and the results show that it is more accurate and has lower variance than previous methods. The new estimator also reduces the computational time by at least 1000-fold and relaxes the upper bound of N_e to several million, hence allowing the estimation of larger N_e. Finally, we demonstrate how this algorithm can cope with nonconstant N_e scenarios and be used as a likelihood-ratio test to test for the equality of N_e throughout the sampling horizon. An R package “NB” is now available for download to implement the method described in this article.     

Change in genetic size of small-closed populations: Lessons from a domestic mammal population

The aim of this study was to monitor changes in genetic size of a small-closed population of Iranian Zandi sheep, by using pedigree information from animals born between 1991 and 2005. The genetic size was assessed by using measures based on the probability of identity-by-descend of genes (coancestry, f, and effective population size, N(e) ), as well as measures based on probability of gene origin (effective number of founders, f(e) , effective number of founder genomes, f(g) , and effective number of non-founder genomes, f(ne) ). Average coancestry, or the degree of genetic similarity of individuals, increased from 0.81% to 1.44% during the period 1993 to 2005, at the same time that N(e) decreased from 263 to 93. The observed trend for f(e) was irregular throughout the experiment in a way that f(e) was 68, 87, 77, 92, and 80 in 1993, 1996, 1999, 2002, and 2005, respectively. Simultaneously, f(g) , the most informative effective number, decreased from 61 to 35. The index of genetic diversity (GD) which was obtained from estimates of f(g) , decreased about 2% throughout the period studied. In addition, a noticeable reduction was observed in the estimates of f(ne) from 595 in 1993 to 61 in 2005. The higher than 1 ratio of f(e) to f(g) indicated the presence of bottlenecks and genetic drift in the development of this population of Zandi sheep. From 1993 to 1999, f(ne) was much higher than f(e) , thereby indicating that with respect to loss of genetic diversity, the unequal contribution of founders was more important than the random genetic drift in non-founder generations. Subsequently, random genetic drift in non-founder generations was the major reason for f(e) > f(ne) . The minimization of average coancestry in new reproductive individuals was recommended as a means of preserving the population against a further loss in genetic diversity.     

Estimating the ratio of effective to actual size of an age‐structured population from individual demographic data

The effective population size is a central concept for understanding evolutionary processes in a finite population. We employ Fisher's reproductive value to estimate the ratio of effective to actual population size for an age‐structured population with two sexes using random samples of individual vital rates. The population may be subject to environmental stochasticity affecting the vital rates. When the mean sex ratio at birth is known, improved efficiency is obtained by utilizing the records of total number of offspring rather than considering separately female and male offspring. We also show how to incorporate uncertain paternity.     

Drift load in populations of small size and low density

According to theory, drift load in randomly mating populations is determined by past population size, because enhanced genetic drift in small populations causes accumulation and fixation of recessive deleterious mutations of small effect. In contrast, segregating load due to mutations of low frequency should decline in smaller populations, at least when mutations are highly recessive and strongly deleterious. Strong local selection generally reduces both types of load. We tested these predictions in 13 isolated, outcrossing populations of Arabidopsis lyrata that varied in population size and plant density. Long-term size was estimated by expected heterozygosity at 20 microsatellite loci. Segregating load was assessed by comparing performance of offspring from selfings versus within-population crosses. Drift load was the heterosis effect created by interpopulation outbreeding. Results showed that segregating load was unrelated to long-term size. However, drift load was significantly higher in populations of small effective size and low density. Drift load was mostly expressed late in development, but started as early as germination and accumulated thereafter. The study largely confirms predictions of theory and illustrates that mutation accumulation can be a threat to natural populations.     

Effects of habitat size and quality on equilibrium density and extinction time of Sorex araneus populations

1. The effects of changes in habitat size and quality on the expected population density and the expected time to extinction of Sorex araneus are studied by means of mathematical models that incorporate demographic stochasticity.
2. Habitat size is characterized by the number of territories, while habitat quality is represented by the expected number of offspring produced during the lifetime of an individual.
3. The expected population density of S. araneus is shown to be mainly influenced by the habitat size. The expected time to extinction of S. araneus populations due to demographic stochasticity, on the other hand, is much more affected by the habitat quality.
4. In a more general setting we demonstrate that, irrespective of the actual species under consideration, the likelihood of extinction as a consequence of demographic stochasticity is more effectively countered by increasing the reproductive success and survival of individuals then by increasing total population size.     

The effects of cyclic dynamics and mating system on the effective size of an island mouflon population

The Haute Island mouflon (Ovis aries) population is isolated on one small (6.5 km2) island of the remote Kerguelen archipelago. Given a promiscuous mating system, a cyclic demography and a strong female-biased sex ratio after population crashes, we expected a low effective population size (Ne). We estimated Ne using demographic and temporal genetic approaches based on genetic information at 25 microsatellite loci from 62 and 58 mouflons sampled in 1988 and 2003, respectively. Genetic Ne estimates were higher than expected, varying between 104 and 250 depending on the methods used. Both demographic and genetic approaches show the Haute Island Ne is buffered against population crashes. The unexpectedly high Ne likely results from the cyclic winter crashes that allow young males to reproduce, limiting the variance of male reproductive success. Based on individual-based simulations, we suggest that despite a strongly female-biased sex ratio, the effects of the mating system on the effective population size more closely resemble random mating or weak polygyny.     

Consequences of the founder effect in the genetic structure of introduced island coral reef fish populations

Between 1955 and 1961, the Division of Fish and Game of the State of Hawaii (USA) undertook an introduction program which brought 11 species of families Serranidae and Lutjanidae (Pisces) from French Polynesia to the coral reefs off Oahu and Big Island in Hawaii. Only three— Cephalopholis argus, Lutjanus fulvus and Lutjanus kasmira —for which we have records of locations and number offish released, are known to have become established. Comparison of allozyme distribution of C. argus and L. kasmira between individuals collected in Hawaiian and Polynesian populations provided a unique opportunity to estimate the impact of genetic drift and selection processes caused by a founder event. We used temporal variance of allelic frequencies to estimate and validate effective population size within marine fish populations. Despite the fact that only 571 C. argus and 2435 L. kasmira were released, we did not observe major changes in polymorphism and heterozygosity. Using different models to estimate effective population size from temporal variance in allelic frequencies and the number of generations, we estimate that the effective population size is about 1–5% of the total population size. Such reduced effective population size explains why most of the species introduced in Hawaii (8/11) failed to become established. Our results have implications for conservation biology because they emphasize that in spite of the fact that only a few individuals bequeathed their characteristics to subsequent generations, no significant change in genetic diversity was observed; success of introduced species is therefore limited by the number of fish released.     

Effective size in management and conservation of subdivided populations

A numerical method for computing the eigenvalue variance effective size of a subdivided population connected by any fixed pattern of migration is described. Using specific examples it is shown that total effective size of a subdivided population can become less than the sum of the subpopulation sizes as a result of directionalities in the pattern of migration. For an extension of the model with threshold harvesting and local deterministic logistic population dynamic we consider the problem of maximizing the total harvesting yield with constraints on the total effective size. For some simple source-sink systems and more complicated population structures where subpopulations differ in their degree of isolation, it is shown to be optimal, for a given total effective size, to raise the harvesting thresholds relatively more in small and in isolated populations. Finally, we show how the method applies to populations which are supplemented, either intentionally or unintentionally. It is shown that the total effective size can be reduced by several orders of magnitude if the captive component of a population is much smaller than the wild component, even with symmetric backward migration.     

Do females adjust the sex of their offspring in relation to the breeding sex ratio?

When the adult sex ratio differs between years in local populations, but still is predictable between adjacent years, it has been proposed that the best strategy would be to bias the offspring sex ratio in favour of the rare sex. We tested this hypothesis using a data set of great reed warbler offspring, sexed by molecular techniques, that were collected over 11 breeding seasons at two adjacent reed marshes. Three important assumptions for this hypothesis are fulfilled in the studied great reed warbler population. First, a substantial proportion of great reed warblers are living in small local populations where sex ratio distortions would be sufficiently large and common. Second, breeding adults and their offspring return to breed in the local population to a high degree. Third, females have a possibility to assess the breeding sex ratio before laying their eggs. At our study site, the breeding sex ratio was positively correlated between successive years. However, contrary to our prediction, female great reed warblers seemed not to adjust their offspring sex ratio in relation to the local breeding sex ratio.     

Effective population size and the rate and pattern of nucleotide substitutions

Both the overall rate of nucleotide substitution and the relative proportions of synonymous and non-synonymous substitutions are predicted to vary between species that differ in effective population size (N_e). Our understanding of the genetic processes underlying these lineage-specific differences in molecular evolution is still developing. Empirical analyses indicate that variation in substitution rates and patterns caused by differences in N_e is often substantial, however, and must be accounted for in analyses of molecular evolution.     

Analysis of genetic diversity for the management of conserved subdivided populations

Recent studies in the literature have appliedphylogenetic methods based on genetic distancesto set priorities for conservation of domesticanimal breeds. While these methods may beappropriate for between-species conservation,they are clearly inappropriate forwithin-species breed conservation, because theyignore within-breed variation. In this paper weshow the basic tools to analyse geneticdiversity in subdivided populations withinspecies, and illustrate the errors incurred byapplying methods based exclusively on geneticdistances. We also show that maximisation ofgenetic diversity (minimisation of coancestryor kinship) is equivalent to maximisation ofeffective population size, as in undividedpopulations, and derive a generalisation ofprevious equations for the prediction ofeffective size. Finally, we discuss thestrategies for conservation in the light of thetheory.     

Effects of habitat quality and size on extinction in experimental populations

Stochastic population theory makes clear predictions about the effects of reproductive potential and carrying capacity on characteristic time-scales of extinction. At the same time, the effects of habitat size and quality on reproduction and regulation have been hotly debated. To trace the causal relationships among these factors, we looked at the effects of habitat size and quality on extinction time in experimental populations of Daphnia magna. Replicate model systems representative of a broad-spectrum consumer foraging on a continuously supplied resource were established under crossed treatments of habitat size (two levels) and habitat quality (three levels) and monitored until eventual extinction of all populations. Using statistically derived estimates of key parameters, we related experimental treatments to persistence time through their effect on carrying capacity and the population growth rate. We found that carrying capacity and the intrinsic rate of increase were each influenced similarly by habitat size and quality, and that carrying capacity and the intrinsic rate of increase were in turn both correlated with time to population extinction. We expected habitat quality to have a greater influence on extinction. However, owing to an unexpected effect of habitat size on reproductive potential, habitat size and quality were similarly important for population persistence. These results support the idea that improving the population growth rate or carrying capacity will reduce extinction risk and demonstrate that both are possible by improving habitat quality or increasing habitat size.     

Estimating fluctuating selection in age-structured populations

In age-structured populations, viability and fecundity selection of varying strength may occur in different age classes. On the basis of an original idea by Fisher of weighting individuals by their reproductive value, we show that the combined effect of selection on traits at different ages acts through the individual reproductive value defined as the stochastic contribution of an individual to the total reproductive value of the population the following year. The selection differential is a weighted sum of age-specific differentials that are the covariances between the phenotype and the age-specific relative fitness defined by the individual reproductive value. This enables estimation of weak selection on a multivariate quantitative character in populations with no density regulation by combinations of age-specific linear regressions of individual reproductive values on the traits. Demographic stochasticity produces random variation in fitness components in finite samples of individuals and affects the statistical inference of the temporal average directional selection as well as the magnitude of fluctuating selection. Uncertainties in parameter estimates and test power depend strongly on the demographic stochasticity. Large demographic variance results in large uncertainties in yearly estimates of selection that complicates detection of significant fluctuating selection. The method is illustrated by an analysis of age-specific selection in house sparrows on a fitness-related two-dimensional morphological trait, tarsus length and body mass of fledglings.