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.     

Effect of population structure on the amount of polymorphism and the fixation probability under overdominant selection

Under overdominant selection, mutants substantially contribute to increase the amount of polymorphism. It is also known that under neutrality as the migration rates among demes decrease in a subdivided population, the amount of polymorphism increases along with the increase of the effective population size, N(e). In this study, under overdominant selection the effect of population subdivision on the amount of polymorphism was investigated using the diffusion approximation and the low migration approximation. It was shown that if selection is medium or strong (e.g., N(T)s > 1, where N(T) is the population size and s is the selective advantage of heterozygotes), the nucleotide diversity, pi, decreases along with the decrease of Nm against the increase of N(e), where N is the size of demes and m is the migration rate per deme. In addition, the ratio of the nucleotide diversity to the evolutionary rate also decreases along with the decrease of Nm. In some cases the ratio becomes smaller than that expected under neutrality as Nm decreases.     

Monitoring the effective population size of a brown bear (Ursus arctos) population using new single-sample approaches

The effective population size (N(e) ) could be the ideal parameter for monitoring populations of conservation concern as it conveniently summarizes both the evolutionary potential of the population and its sensitivity to genetic stochasticity. However, tracing its change through time is difficult in natural populations. We applied four new methods for estimating N(e) from a single sample of genotypes to trace temporal change in N(e) for bears in the Northern Dinaric Mountains. We genotyped 510 bears using 20 microsatellite loci and determined their age. The samples were organized into cohorts with regard to the year when the animals were born and yearly samples with age categories for every year when they were alive. We used the Estimator by Parentage Assignment (EPA) to directly estimate both N(e) and generation interval for each yearly sample. For cohorts, we estimated the effective number of breeders (N(b) ) using linkage disequilibrium, sibship assignment and approximate Bayesian computation methods and extrapolated these estimates to N(e) using the generation interval. The N(e) estimate by EPA is 276 (183-350 95% CI), meeting the inbreeding-avoidance criterion of N(e) > 50 but short of the long-term minimum viable population goal of N(e) > 500. The results obtained by the other methods are highly consistent with this result, and all indicate a rapid increase in N(e) probably in the late 1990s and early 2000s. The new single-sample approaches to the estimation of N(e) provide efficient means for including N(e) in monitoring frameworks and will be of great importance for future management and conservation.     

Large global effective population sizes in Paramecium

The genetic effective population size (N(e)) of a species is an important parameter for understanding evolutionary dynamics because it mediates the relative effects of selection. However, because most N(e) estimates for unicellular organisms are derived either from taxa with poorly understood species boundaries or from host-restricted pathogens and most unicellular species have prominent phases of clonal propagation potentially subject to strong selective sweeps, the hypothesis that N(e) is elevated in single-celled organisms remains controversial. Drawing from observations on well-defined species within the genus Paramecium, we report exceptionally high levels of silent-site polymorphism, which appear to be a reflection of large N(e).     

The effective size of mixed sexually and asexually reproducing populations

Using the transition matrix of inbreeding and coancestry coefficients, the inbreeding (N(eI)), variance (N(eV)), and asymptotic (N(e lambda)) effective sizes of mixed sexual and asexual populations are formulated in terms of asexuality rate (delta), variance of asexual (C) and sexual (K) reproductive contributions of individuals, correlation between asexual and sexual contributions (rho(ck)), selfing rate (beta), and census population size (N). The trajectory of N(eI) toward N(e lambda) changes crucially depending on delta, N, and beta, whereas that of N(eV) is rather consistent. With increasing asexuality, N(e lambda) either increases or decreases depending on C, K, and rho(ck). The parameter space in which a partially asexual population has a larger N(e lambda) than a fully sexual population is delineated. This structure is destroyed when N(1 - delta) < 1 or delta > 1 - 1/N. With such a high asexuality, tremendously many generations are required for the asymptotic size N(e lambda) to be established, and N(e lambda) is extremely large with any value of C, K, and rho(ck) because the population is dominated eventually by individuals of the same genotype and the allelic diversity within the individuals decays quite slowly. In reality, the asymptotic state would occur only occasionally, and instantaneous rather than asymptotic effective sizes should be practical when predicting evolutionary dynamics of highly asexual populations.     

Comparative evaluation of a new effective population size estimator based on approximate bayesian computation

We describe and evaluate a new estimator of the effective population size (N(e)), a critical parameter in evolutionary and conservation biology. This new "SummStat" N(e) estimator is based upon the use of summary statistics in an approximate Bayesian computation framework to infer N(e). Simulations of a Wright-Fisher population with known N(e) show that the SummStat estimator is useful across a realistic range of individuals and loci sampled, generations between samples, and N(e) values. We also address the paucity of information about the relative performance of N(e) estimators by comparing the SummStat estimator to two recently developed likelihood-based estimators and a traditional moment-based estimator. The SummStat estimator is the least biased of the four estimators compared. In 32 of 36 parameter combinations investigated using initial allele frequencies drawn from a Dirichlet distribution, it has the lowest bias. The relative mean square error (RMSE) of the SummStat estimator was generally intermediate to the others. All of the estimators had RMSE > 1 when small samples (n = 20, five loci) were collected a generation apart. In contrast, when samples were separated by three or more generations and N(e) < or = 50, the SummStat and likelihood-based estimators all had greatly reduced RMSE. Under the conditions simulated, SummStat confidence intervals were more conservative than the likelihood-based estimators and more likely to include true N(e). The greatest strength of the SummStat estimator is its flexible structure. This flexibility allows it to incorporate any potentially informative summary statistic from population genetic data.     

Effective size of fluctuating salmon populations

Pacific salmon are semelparous but have overlapping year classes, which presents special challenges for the application of standard population genetics theory to these species. This article examines the relationship between the effective number of breeders per year (N(b)) and single-generation and multigeneration effective population size (N(e)) in salmon populations that fluctuate in size. A simple analytical model is developed that allows calculation of N(e) on the basis of the number of spawners in individual years and their reproductive contribution (productivity) to the next generation. Application of the model to a 36-year time series of data for a threatened population of Snake River chinook salmon suggests that variation in population dynamic processes across years reduced the multigeneration N(e) by approximately 40-60%, and reductions may have been substantially greater within some generations. These reductions are comparable in magnitude to, and in addition to, reductions in N(b) within a year due to unequal sex ratio and nonrandom variation in reproductive success. Computer simulations suggest that the effects of variable population dynamics on N(e) observed in this dataset are not unexpected for species with a salmon life history, as random variation in productivity can lead to similar results.     

Spatial-temporal stratifications in natural populations and how they affect understanding and estimation of effective population size

The concept of effective population size (N(e) ) is based on an elegantly simple idea which, however, rapidly becomes very complex when applied to most real-world situations. In natural populations, spatial and temporal stratifications create different classes of individuals with different vital rates, and this in turn affects (generally reduces) N(e) in complex ways. I consider how these natural stratifications influence our understanding of effective size and how to estimate it, and what the consequences are for conservation and management of natural populations. Important points that emerge include the following: 1 The relative influences of local vs metapopulation N(e) depend on a variety of factors, including the time frame of interest. 2 Levels of diversity in local populations are strongly influenced by even low levels of migration, so these measures are not reliable indicators of local N(e) . 3 For long-term effective size, obtaining a reliable estimate of mutation rate is the most important consideration; unless this is accomplished, estimates can be biased by orders of magnitude. 4 At least some estimators of contemporary N(e) appear to be robust to relatively high (approximately 10%) equilibrium levels of migration, so under many realistic scenarios they might yield reliable estimates of local N(e) . 5 Age structure probably has little effect on long-term estimators of N(e) but can strongly influence contemporary estimates. 6 More research is needed in several key areas: (i) to disentangle effects of selection and drift in metapopulations connected by intermediate levels of migration; (ii) to elucidate the relationship between N(b) (effective number of breeders per year) and N(e) per generation in age-structured populations; (iii) to perform rigorous sensitivity analyses of new likelihood and coalescent-based methods for estimating demographic and evolutionary histories.     

Temporal genetic stability and high effective population size despite fisheries-induced life-history trait evolution in the North Sea sole

Heavy fishing and other anthropogenic influences can have profound impact on a species' resilience to harvesting. Besides the decrease in the census and effective population size, strong declines in mature adults and recruiting individuals may lead to almost irreversible genetic changes in life-history traits. Here, we investigated the evolution of genetic diversity and effective population size in the heavily exploited sole (Solea solea), through the analysis of historical DNA from a collection of 1379 sole otoliths dating back from 1957. Despite documented shifts in life-history traits, neutral genetic diversity inferred from 11 microsatellite markers showed a remarkable stability over a period of 50 years of heavy fishing. Using simulations and corrections for fisheries induced demographic variation, both single-sample estimates and temporal estimates of effective population size (N(e) ) were always higher than 1000, suggesting that despite the severe census size decrease over a 50-year period of harvesting, genetic drift is probably not strong enough to significantly decrease the neutral diversity of this species in the North Sea. However, the inferred ratio of effective population size to the census size (N(e) /N(c) ) appears very small (10(-5) ), suggesting that overall only a low proportion of adults contribute to the next generation. The high N(e) level together with the low N(e) /N(c) ratio is probably caused by a combination of an equalized reproductive output of younger cohorts, a decrease in generation time and a large variance in reproductive success typical for marine species. Because strong evolutionary changes in age and size at first maturation have been observed for sole, changes in adaptive genetic variation should be further monitored to detect the evolutionary consequences of human-induced selection.     

Bottleneck Effect on Evolutionary Rate in the Nearly Neutral Mutation Model

Variances of evolutionary rates among lineages in some proteins are larger than those expected from simple Poisson processes. This phenomenon is called overdispersion of the molecular clock. If population size N is constant, the overdispersion is observed only in a limited range of 2Nσ under the nearly neutral mutation model, where σ represents the standard deviation of selection coefficients of new mutants. In this paper, we investigated effects of changing population size on the evolutionary rate by computer simulations assuming the nearly neutral mutation model. The size was changed cyclically between two numbers, N(1) and N(2) (N(1) > N(2)), in the simulations. The overdispersion is observed if 2N(2)σ is less than two and the state of reduced size (bottleneck state) continues for more than ~0.1/u generations, where u is the mutation rate. The overdispersion results mainly because the average fitnesses of only a portion of populations go down when the population size is reduced and only in these populations subsequent advantageous substitutions occur after the population size becomes large. Since the fitness reduction after the bottleneck is stochastic, acceleration of the evolutionary rate does not necessarily occur uniformly among loci. From these results, we argue that the nearly neutral mutation model is a candidate mechanism to explain the overdispersed molecular clock.     

How does the 50/500 rule apply to MVPs?

The 50/500 rule has been used as a guiding principle in conservation for assessing minimum viable effective population size (N(e)). There is much confusion in the recent literature about how the 500 value should be applied to assess extinction risk and set priorities in conservation biology. Here, we argue that the confusion arises when the genetic basis for a short-term N(e) of 50 to avoid inbreeding depression is used to justify a long-term N(e) of 500 to maintain evolutionary potential. This confusion can result in misleading conclusions about how genetic arguments alone are sufficient to set minimum viable population (MVP) thresholds for assessing the extinction risk of threatened species, especially those that emphasize that MVPs should be in the thousands to maintain evolutionary potential.     

Genetic monitoring reveals temporal stability over 30 years in a small, lake-resident brown trout population

Knowledge of the degree of temporal stability of population genetic structure and composition is important for understanding microevolutionary processes and addressing issues of human impact of natural populations. We know little about how representative single samples in time are to reflect population genetic constitution, and we explore the temporal genetic variability patterns over a 30-year period of annual sampling of a lake-resident brown trout (Salmo trutta) population, covering 37 consecutive cohorts and five generations. Levels of variation remain largely stable over this period, with no indication of substructuring within the lake. We detect genetic drift, however, and the genetically effective population size (N(e)) was assessed from allele-frequency shifts between consecutive cohorts using an unbiased estimator that accounts for the effect of overlapping generation. The overall mean N(e) is estimated as 74. We find indications that N(e) varies over time, but there is no obvious temporal trend. We also estimated N(e) using a one-sample approach based on linkage disequilibrium (LD) that does not account for the effect of overlapping generations. Combining one-sample estimates for all years gives an N(e) estimate of 76. This similarity between estimates may be coincidental or reflecting a general robustness of the LD approach to violations of the discrete generations assumption. In contrast to the observed genetic stability, body size and catch per effort have increased over the study period. Estimates of annual effective number of breeders (N(b)) correlated with catch per effort, suggesting that genetic monitoring can be used for detecting fluctuations in abundance.     

Patterns of inbreeding depression and architecture of the load in subdivided populations

Inbreeding depression is a general phenomenon that is due mainly to recessive deleterious mutations, the so-called mutation load. It has been much studied theoretically. However, until very recently, population structure has not been taken into account, even though it can be an important factor in the evolution of populations. Population subdivision modifies the dynamics of deleterious mutations because the outcome of selection depends on processes both within populations (selection and drift) and between populations (migration). Here, we present a general model that permits us to gain insight into patterns of inbreeding depression, heterosis, and the load in subdivided populations. We show that they can be interpreted with reference to single-population theory, using an appropriate local effective population size that integrates the effects of drift, selection, and migration. We term this the "effective population size of selection" (NS(e)). For the infinite island model, for example, it is equal to NS(e) = N1 + m/hs, where N is the local population size, m the migration rate, and h and s the dominance and selection coefficients of deleterious mutation. Our results have implications for the estimation and interpretation of inbreeding depression in subdivided populations, especially regarding conservation issues. We also discuss the possible effects of migration and subdivision on the evolution of mating systems.     

The role of despotism and heritability in determining settlement patterns in the colonial lesser kestrel

Avian colony size variation is an evolutionary puzzle in terms of unequal fitness payoffs. We used a long-term marked lesser kestrel (Falco naumanni) population, where individual fitness increases with colony size, to test whether subordinates are evicted despotically from the largest colonies. Yearlings were smaller and lighter, were more attacked than expected, and lost most disputes over nest holes with older birds. Agonistic interactions increased with colony size; consequently, most first breeders recruited in colonies smaller than those at which they first tried to settle. As expected when subordination is a transient state, birds dispersed to a larger colony as they got older even after breeding successfully. The population consequences of these behavioral processes were that the relative frequency of yearlings and first breeders decreased with colony size. At the same time, breeding colony size was repeatable within individuals, so we estimated the amount of heritable variation in this trait. Estimates of heritability derived from parent-offspring and full-sib analyses were consistently high (h2=0.53) when individuals reached asymptotic morphological values and presumably overcame subordinate transient states. Age-related dominance asymmetries masked resemblance among relatives in colony size, but both phenomena seem to coexist in this population and explain a considerable proportion of colony size variation.     

Effective population sizes and migration rates in fragmented populations of an endangered insect (Coenagrion mercuriale: Odonata)

1. Effective population sizes (N(e)) and migration rates (m) are critical evolutionary parameters that impact on population survival and determine the relative influence of selection and genetic drift. While the parameter m is well-studied in animal populations, N(e) remains challenging to measure and consequently is only rarely estimated, particularly in insect taxa. 2. We used demographic and genetic methods to estimate N(e) and m in a fragmented population of the endangered damselfly Coenagrion mercuriale to better understand the contrast between genetic and field estimates of these parameters and also to identify the spatial scale over which populations may become locally adapted. 3. We found a contrast between demographic- and genetic-based estimates of these parameters, with the former apparently providing overestimates of N(e), owing to substantial underestimation of the variance in reproductive success, and the latter overestimating m, because spatial genetic structure is weak. 4. The overall N(e) of sites within the population network at Beaulieu Heath, the largest C. mercuriale site in the UK, was estimated to vary between approximately 60 and 2700. 5. While N(e) was not correlated with either the total numbers of adults (N) or the area of habitat, this parameter was always less than N, because of substantial variance in reproductive success. The ratio N(e)/N varied between 0.006 and 0.42 and was generally larger in smaller populations, possibly representing some 'genetic compensation'. 6. From a simple genetic model and these data on N(e) and m, it seems that populations of C. mercuriale have the potential to respond to localized spatial variation in selection and this would need to be considered for future genetic management of this endangered species.     

Heterozygote excess in small populations and the heterozygote-excess effective population size

It has been proposed that effective size could be estimated in small dioecious population by considering the heterozygote excess observed at neutral markers. When the number of breeders is small, allelic frequencies in males and females will slightly differ due to binomial sampling error. However, this excess of heterozygotes is not generated by dioecy but by the absence of individuals produced through selfing. Consequently, the approach can also be applied to self-incompatible monoecious species. Some inaccuracies in earlier equations expressing effective size as function of the heterozygote excess are also corrected in this paper. The approach is then extended to subdivided populations, where time of sampling becomes crucial. When adults are sampled, the effective size of the entire population can be estimated, whereas when juveniles are sampled, the average effective number of breeders per subpopulations can be estimated. The main limitation of the heterozygote excess method is that it will only perform satisfactorily for populations with a small number of reproducing individuals. While this situation is unlikely to happen frequently at the scale of the entire population, structured populations with small subpopulations are likely to be common. The estimation of the average number of breeders per subpopulations is thus expected to be applicable to many natural populations. The approach is straightforward to compute and independent of equilibrium assumptions. Applications to simulated data suggest the estimation of the number of breeders to be robust to mutation and migration rates, and to specificities of the mating system.     

Large variance in reproductive success and the Ne/N ratio

The ratio of the effective population size to adult (or census) population size (Ne/N) is an indicator of the extent of genetic variation expected in a population. It has been suggested that this ratio may be quite low for highly fecund species in which there is a sweepstakes-like chance of reproductive success, known as the Hedgecock effect. Here I show theoretically how the ratio may be quite small when there are only a few successful breeders (Nb) and that in this case, the Ne/N ratio is approximately Nb/N. In other words, high variance in reproductive success within a generation can result in a very low effective population size in an organism with large numbers of adults and consequently a very low Ne/N ratio. This finding appears robust when there is a large proportion of families with exactly two progeny or when there is random variation in progeny numbers among these families.     

Strong artificial selection in the wild results in predicted small evolutionary change

Estimates of genetic variation and selection allow for quantitative predictions of evolutionary change, at least in controlled laboratory experiments. Natural populations are, however, different in many ways, and natural selection on heritable traits does not always result in phenotypic change. To test whether we were able to predict the evolutionary dynamics of a complex trait measured in a natural, heterogeneous environment, we performed, over an 8-year period, a two-way selection experiment on clutch size in a subdivided island population of great tits (Parus major). Despite strong artificial selection, there was no clear evidence for evolutionary change at the phenotypic level. Environmentally induced differences in clutch size among years are, however, large and can mask evolutionary changes. Indeed, genetic changes in clutch size, inferred from a statistical model, did not deviate systematically from those predicted. Although this shows that estimates of genetic variation and selection can indeed provide quantitative predictions of evolutionary change, also in the wild, it also emphasizes that demonstrating evolution in wild populations is difficult, and that the interpretation of phenotypic trends requires great care.     

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

Effects of potyvirus effective population size in inoculated leaves on viral accumulation and the onset of symptoms

Effective population size (N(e)) is a key parameter for understanding evolutionary processes, but it is generally not considered in epidemiological studies or in studying infections of individual hosts. Whether N(e) has an effect on the onset of symptoms and viral accumulation in Tobacco etch virus (TEV) infection of Nicotiana tabacum plants is considered here. Using mixtures of TEV variants carrying fluorescent markers, the dose dependence of N(e) was confirmed, and the inoculation procedure was found to be the main source of variation in these experiments. Whereas the onset of symptoms was independent of N(e), there was less and more variable accumulation at 6 days postinoculation for small N(e) values (N(e) < 5). The observed variation in accumulation was not heritable, however, suggesting that this variation was not due to the fixation of deleterious mutations in the small founder populations. On the other hand, virus-induced fluorescence and accumulation in the inoculated leaf were strongly N(e) dependent. Systemic accumulation was independent of N(e), although removal of the inoculated leaf led to a small reduction in systemic accumulation for small N(e) values. For whole plants, N(e)-dependent effects on accumulation were no longer observed at 9 days postinoculation. Therefore, the effects of N(e) on accumulation are due mainly to limited expansion in the inoculated leaf and are transient. In this system, N(e)-dependent effects will be strongest at low doses and early in infection. We conclude that N(e) can have implications for epidemiology and infection at the individual host level, beyond determining the rate of mixed-genotype infection.