The effective population size of some age-structured populations

It was shown in a previous paper that if generations are discrete, then the effective population size of a large population can be derived from the theory of multitype branching processes. It turns out to be proportional to the reciprocal of a term that appears in the denominator of expressions for survival probabilities when there is a supercritical positively regular branching process for which the dominant positive eigenvalue of the first moment matrix is slightly larger than 1. If there is an age-structured population with unchanging proportions among sexes and age groups, then the effective population size is shown to be also obtainable from the theory of multitype branching processes. The expression for this parameter has the same form as in the corresponding model for discrete generations, multiplied by an appropriate measure of the average length of a generation. Results are obtained for dioecious random mating populations, populations reproducing partly by selfing, and populations reproducing partly by full-sib mating.     

Ancient mtDNA haplogroups: a new insight into the genetic history of European populations

In the present work, DNA was extracted from 63 skeletal samples recovered at the Neolithic site of San Juan ante Portam Latinam (SJAPL) (Araba, Basque Country). These samples have proved useful as genetic material for the performance of population studies. To achieve this it was necessary to overcome the methodological problems arising when working with damaged DNA molecules. We succeeded in performing an amplification and restriction analysis of the polymorphisms present in the mtDNA. Ninety seven percent of the samples were classified as belonging to one of the nine mtDNA haplogroups described in Caucasians. This work shows that restriction analysis is a useful methodological tool to perform reliable population genetic analysis on archaeological remains. Tha analysis of ancient and modern haplogroup distribution can shed more light on the genetic evolution of human populations. Moreover, a more exhaustive data on prehistoric populations will allow to build stronger hypothesis on the genetic relationships among human populations.     

Testing single-sample estimators of effective population size in genetically structured populations

The effective population size (N _e ) is a key parameter in evolutionary and population genetics. Single-sample N _e estimation provides an alternative to traditional approaches requiring two or more samples. Single-sample methods assume that the study population has no genetic sub-structure, which is unlikely to be true in wild populations. Here we empirically investigated two single-sample estimators (onesamp and L d N e) in replicated and controlled genetically structured populations of Drosophila melanogaster. Using experimentally controlled population parameters, we calculated the Wright–Fisher expected N _e for the structured population ( ^Total N _e ) and demonstrated that the loss of heterozygosity did not significantly differ from Wright’s model. We found that disregarding the population substructure resulted in ^Total N _e estimates with a low coefficient of variation but these estimates were systematically lower than the expected values, whereas hierarchical estimates accounting for population structure were closer to the expected values but had a higher coefficient of variation. Analysis of simulated populations demonstrated that incomplete sampling, initial allelic diversity and balancing selection may have contributed to deviations from the Wright–Fisher model. Overall the approximate-Bayesian onesamp method performed better than L d N e (with appropriate priors). Both methods performed best when dispersal rates were high and the population structure was approaching panmixia.     

Genetic diversity, population structure, effective population size and demographic history of the Finnish wolf population

The Finnish wolf population (Canis lupus) was sampled during three different periods (1996-1998, 1999-2001 and 2002-2004), and 118 individuals were genotyped with 10 microsatellite markers. Large genetic variation was found in the population despite a recent demographic bottleneck. No spatial population subdivision was found even though a significant negative relationship between genetic relatedness and geographic distance suggested isolation by distance. Very few individuals did not belong to the local wolf population as determined by assignment analyses, suggesting a low level of immigration in the population. We used the temporal approach and several statistical methods to estimate the variance effective size of the population. All methods gave similar estimates of effective population size, approximately 40 wolves. These estimates were slightly larger than the estimated census size of breeding individuals. A Bayesian model based on Markov chain Monte Carlo simulations indicated strong evidence for a long-term population decline. These results suggest that the contemporary wolf population size is roughly 8% of its historical size, and that the population decline dates back to late 19th century or early 20th century. Despite an increase of over 50% in the census size of the population during the whole study period, there was only weak evidence that the effective population size during the last period was higher than during the first. This may be caused by increased inbreeding, diminished dispersal within the population, and decreased immigration to the population during the last study period.     

Genetic variation and effective population size in isolated populations of coastal cutthroat trout

Following glacial recession in southeast Alaska, waterfalls created by isostatic rebound have isolated numerous replicate populations of coastal cutthroat trout (Oncorhynchus clarkii clarkii) in short coastal streams. These replicate isolated populations offer an unusual opportunity to examine factors associated with the maintenance of genetic diversity. We used eight microsatellites to examine genetic variation within and differentiation among 12 population pairs sampled from above and below these natural migration barriers. Geological evidence indicated that the above-barrier populations have been isolated for 8,000–12,500 years. Genetic differentiation among below-barrier populations (F _ST = 0.10, 95% C.I. 0.08–0.12) was similar to a previous study of more southern populations of this species. Above-barrier populations were highly differentiated from adjacent below-barrier populations (mean pairwise F _ST = 0.28; SD 0.18) and multiple lines of evidence were consistent with asymmetric downstream gene flow that varied among streams. Each above-barrier population had reduced within-population genetic variation when compared to the adjacent below-barrier population. Within-population genetic diversity was significantly correlated with the amount of available habitat in above-barrier sites. Increased genetic differentiation of above-barrier populations with lower genetic diversity suggests that genetic drift has been the primary cause of genetic divergence. Long-term estimates of N _e based on loss of heterozygosity over the time since isolation were large (3,170; range 1,077–7,606) and established an upper limit for N _e if drift were the only evolutionary process responsible for loss of genetic diversity. However, it is likely that a combination of mutation, selection, and gene flow have also contributed to the genetic diversity of above-barrier populations. Contemporary above-barrier N _e estimates were much smaller than long-term N _e estimates, not correlated with within-population genetic diversity, and not consistent with the amount of genetic variation retained, given the approximate 10,000-year period of isolation. The populations isolated by waterfalls in this study that occur in larger stream networks have retained substantial genetic variation, which suggests that the amount of habitat in headwater streams is an important consideration for maintaining the evolutionary potential of isolated populations.     

Estimation of effective population size in continuously distributed populations: there goes the neighborhood

Use of genetic methods to estimate effective population size (N_e) is rapidly increasing, but all approaches make simplifying assumptions unlikely to be met in real populations. In particular, all assume a single, unstructured population, and none has been evaluated for use with continuously distributed species. We simulated continuous populations with local mating structure, as envisioned by Wright''s concept of neighborhood size (NS), and evaluated performance of a single-sample estimator based on linkage disequilibrium (LD), which provides an estimate of the effective number of parents that produced the sample (N_b). Results illustrate the interacting effects of two phenomena, drift and mixture, that contribute to LD. Samples from areas equal to or smaller than a breeding window produced estimates close to the NS. As the sampling window increased in size to encompass multiple genetic neighborhoods, mixture LD from a two-locus Wahlund effect overwhelmed the reduction in drift LD from incorporating offspring from more parents. As a consequence, never approached the global N_e, even when the geographic scale of sampling was large. Results indicate that caution is needed in applying standard methods for estimating effective size to continuously distributed populations.     

Empirical Bayes procedure for estimating genetic distance between populations and effective population size

We developed an empirical Bayes procedure to estimate genetic distances between populations using allele frequencies. This procedure makes it possible to describe the skewness of the genetic distance while taking full account of the uncertainty of the sample allele frequencies. Dirichlet priors of the allele frequencies are specified, and the posterior distributions of the various composite parameters are obtained by Monte Carlo simulation. To avoid overdependence on subjective priors, we adopt a hierarchical model and estimate hyperparameters by maximizing the joint marginal-likelihood function. Taking advantage of the empirical Bayesian procedure, we extend the method to estimate the effective population size using temporal changes in allele frequencies. The method is applied to data sets on red sea bream, herring, northern pike, and ayu broodstock. It is shown that overdispersion overestimates the genetic distance and underestimates the effective population size, if it is not taken into account during the analysis. The joint marginal-likelihood function also estimates the rate of gene flow into island populations.     

Interrelations between effective population size and other pedigree tools for the management of conserved populations

Genetic parameters widely used to monitor genetic variation in conservation programmes, such as effective number of founders, founder genome equivalents and effective population size, are interrelated in terms of coancestries and variances of contributions from ancestors to descendants. A new parameter, the effective number of non-founders, is introduced to describe the relation between effective number of founders and founder genome equivalents. Practical recommendations for the maintenance of genetic variation in small captive populations are discussed. To maintain genetic diversity, minimum coancestry among individuals should be sought. This minimizes the variances of contributions from ancestors to descendants in all previous generations. The method of choice of parents and the system of mating should be independent of each other because a clear-cut recommendation cannot be given on the latter.     

The effective size of annual plant populations: the interaction of a seed bank with fluctuating population size in maintaining genetic variation

Many annual plant populations undergo dramatic fluctuations in size. Such fluctuations can result in the loss of genetic variability. Here I formalize the potential for a seed bank to buffer against such genetic loss. The average time to seed germination (T) defines the generation time of "annuals" with a seed bank, and assuming random seed germination, I show that, under otherwise ideal conditions, a population's effective size (Ne) equals NT, where N is the number of adult plants. This result supports the general principle that lengthening the prereproductive period increases Ne. When adult numbers vary, Ne at any time depends on N and on the numbers contributing to the seed bank in previous seasons. Averaging these effects over time gives Ne approximately Nh + (T - 1)Na, where Nh and Na are the harmonic and arithmetic means of the adult population. Thus if T > 1, Ne is determined primarily by Na. Simulations showed that until fluctuations in N are large (>25x) this relationship is accurate. I extended the theory to incorporate a selfing rate (S) and reproductive variance (I) through seed production (k), outcrossed pollen (m), and variation in selfing rate: Ne = NT(1 -S/2)/(1 + I) = NT/[1 + FIS)(1 + I)]. Reproductive variance (I) equals [Ik(1 + S)2 + IM(1 - S)2 + 2(1 - S2)Ikm = S2IS(1 + Ik)]/4, , where Ij is the standardized variance (Vj/j2) of factor j and Ikm is the standardized covariance between k and m. These results are applicable to other organisms with a similar life history, such as freshwater crustaceans with diapausing eggs (e.g., tadpole shrimp, clam shrimp, and fairy shrimp) and other semelparous species with discrete breeding seasons and a variable maturation time (e.g., Pacific salmon).     

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.     

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 variation in genetic diversity and effective population size of Mediterranean and subalpine Arabidopsis thaliana populations

Currently, there exists a limited knowledge on the extent of temporal variation in population genetic parameters of natural populations. Here, we study the extent of temporal variation in population genetics by genotyping 151 genome-wide SNP markers polymorphic in 466 individuals collected from nine populations of the annual plant Arabidopsis thaliana during 4 years. Populations are located along an altitudinal climatic gradient from Mediterranean to subalpine environments in NE Spain, which has been shown to influence key demographic attributes and life cycle adaptations. Genetically, A. thaliana populations were more variable across space than over time. Common multilocus genotypes were detected several years in the same population, whereas low-frequency multilocus genotypes appeared only 1 year. High-elevation populations were genetically poorer and more variable over time than low-elevation populations, which might be caused by a higher overall demographic instability at higher altitudes. Estimated effective population sizes were low but also showed a significant decreasing trend with increasing altitude, suggesting a deeper impact of genetic drift at high-elevation populations. In comparison with single-year samplings, repeated genotyping over time captured substantially higher amount of genetic variation contained in A. thaliana populations. Furthermore, repeated genotyping of populations provided novel information on the genetic properties of A. thaliana populations and allowed hypothesizing on their underlying mechanisms. Therefore, including temporal genotyping programmes into traditional population genetic studies can significantly increase our understanding of the dynamics of natural populations.     

Low effective population size and survivorship in a grassland grouse

Assessments of census size (N _c) and effective population size (N _e) are necessary for the conservation of species exhibiting population declines. We examined two populations (Oklahoma and New Mexico) of the lesser prairie-chicken (Tympanuchus pallidicinctus), a declining lek-breeding bird, in which one population (Oklahoma) has larger clutch size and more nesting attempts per year but lower survival caused by human changes to the landscape. We estimated demographic and genetic estimates of N _e for each population and found that both populations have low N _e estimates with a risk of inbreeding depression. Although Oklahoma females produce a larger number of offspring, the proportion of females successfully reproducing is not higher than in New Mexico. Higher reproductive effort has likely reached a physiological limit in Oklahoma prairie-chickens but has not led to a higher N _e or even a larger N _c than New Mexico. We propose that future conservation efforts focus on maximizing survivorship and decreasing the variance in reproductive success because these factors are more likely than increasing reproductive output alone to yield population persistence in lek-breeding species.     

Mitochondrial DNA variation, effective female population size and population history of the endangered Chinese sturgeon, Acipenser sinensis

The anadromous Chinese sturgeon (Acipenser sinensis), mainly endemic to the Yangtze River in China, is an endangered fish species. The natural population has declined since the Gezhouba Dam blocked its migratory route to the spawning grounds in 1981. In the near future, the completion of the Three Gorges Dam, the world's largest hydroelectric project, may further impact this species by altering the water flow of the Yangtze River. Little is currently known about the population genetic structure of the Chinese sturgeon. In this study, DNA sequence data were determined from the control region (D-loop) of the mitochondrial genome of adult sturgeons (n = 106) that were collected between 1995–2000. The molecular data were used to investigate genetic variation, effective female population size and population history of the Chinese sturgeon in the Yangtze River. Our results indicate that the reduction in abundance did not change genetic variation of the Chinese sturgeon, and that the population underwent an expansion in the past. AMOVA analysis indicated that 98.7% of the genetic variability occurred within each year's spawning populations, the year of collection had little influence on the diversity of annual temporary samples. The relative large effective female population size (N _ef) indicates that good potential exists for the recovery of this species in the future. Strikingly, the ratio of N _ef to the census female population size (N _f) is unusually high (0.77–0.93). This may be the result of a current bottleneck in the population of the Chinese sturgeon that is likely caused by human intervention. This revised version was published online in July 2006 with corrections to the Cover Date.     

Predicting the annual effective size of livestock populations

Effective population size (Ne) is an important parameter determining the genetic structure of small populations. In natural populations, the number of adults (N) is usually known and Ne can be estimated on the basis of an assumed ratio Ne/N, usually found to be close to 0.5. In farm animal populations, apart from using pedigrees or genetic marker information, Ne can be estimated from the number N of breeding animals, and a value of 1 is commonly assumed for the ratio Ne/N. The purpose of this paper is to show the relation between effective population size and breeding herd size in livestock species. With overlapping generations, Ne can be predicted knowing the number of individuals entering the population per generation and the variance of family size, the latter being directly related to the survival pattern (or replacement policy) in the breeding herd. Assuming an ideal survivorship leading to a geometric age distribution, it can be shown that the number of breeding animals tends to overestimate effective size, particularly in early-maturing species. The ratio of annual effective size to the number of breeding animals is shown to be equal to [1 + (a- 1)(1 - s)]2/(1 - s2), where a is the age at first offspring and s is the survival rate (including culling) of the parents between successive births. This expression shows to what extent inbreeding may be determined by demography or culling policy independently of the actual herd size. In many situations a fast replacement or an early culling will increase annual effective size. Consequences for the management of small populations are discussed.     

Quantifying the variation in the effective population size within a genome

The effective population size (N(e)) is one of the most fundamental parameters in population genetics. It is thought to vary across the genome as a consequence of differences in the rate of recombination and the density of selected sites due to the processes of genetic hitchhiking and background selection. Although it is known that there is intragenomic variation in the effective population size in some species, it is not known whether this is widespread or how much variation in the effective population size there is. Here, we test whether the effective population size varies across the genome, between protein-coding genes, in 10 eukaryotic species by considering whether there is significant variation in neutral diversity, taking into account differences in the mutation rate between loci by using the divergence between species. In most species we find significant evidence of variation. We investigate whether the variation in N(e) is correlated to recombination rate and the density of selected sites in four species, for which these data are available. We find that N(e) is positively correlated to recombination rate in one species, Drosophila melanogaster, and negatively correlated to a measure of the density of selected sites in two others, humans and Arabidopsis thaliana. However, much of the variation remains unexplained. We use a hierarchical Bayesian analysis to quantify the amount of variation in the effective population size and show that it is quite modest in all species-most genes have an N(e) that is within a few fold of all other genes. Nonetheless we show that this modest variation in N(e) is sufficient to cause significant differences in the efficiency of natural selection across the genome, by demonstrating that the ratio of the number of nonsynonymous to synonymous polymorphisms is significantly correlated to synonymous diversity and estimates of N(e), even taking into account the obvious nonindependence between these measures.     

Life history and environmental variation interact to determine effective population to census size ratio

Successful recovery and sustainability of threatened and exploited species depends in part on retention and maintenance of genetic diversity. Theory indicates that genetic diversity is lost at a rate inversely proportional to the genetically effective population size (N(e)), which is roughly equal to one-half the adult census size (N) in many organisms. However, N(e) has been reported to be up to five orders of magnitude lower than N in species with life histories that result in type III survivorship (high fecundity, but heavy mortality in early life stages, e.g. bony fishes), prompting speculation that low values of N(e) may be a general feature of such organisms despite sometimes vast abundances. Here, we compared N(e) and the ratio N(e)/N across three ecologically similar fish species from the arid southwestern United States, all with type III life histories but with differing expectations of egg and larval survivorship that correlate with the degree of human-imposed habitat fragmentation. Our study indicates that type III life history may be necessary, but this alone is insufficient to account for extraordinarily low values of N(e)/N. Rather, life history interacts with environmentally imposed mortality to determine the rate and magnitude of change in genetic diversity in these desert fish species.