Temporal estimates of effective population size in species with overlapping generations

The standard temporal method for estimating effective population size (N(e)) assumes that generations are discrete, but it is routinely applied to species with overlapping generations. We evaluated bias in the estimates N(e) caused by violation of this assumption, using simulated data for three model species: humans (type I survival), sparrow (type II), and barnacle (type III). We verify a previous proposal by Felsenstein that weighting individuals by reproductive value is the correct way to calculate parametric population allele frequencies, in which case the rate of change in age-structured populations conforms to that predicted by discrete-generation models. When the standard temporal method is applied to age-structured species, typical sampling regimes (sampling only newborns or adults; randomly sampling the entire population) do not yield properly weighted allele frequencies and result in biased N(e). The direction and magnitude of the bias are shown to depend on the sampling method and the species' life history. Results for populations that grow (or decline) at a constant rate paralleled those for populations of constant size. If sufficient demographic data are available and certain sampling restrictions are met, the Jorde-Ryman modification of the temporal method can be applied to any species with overlapping generations. Alternatively, spacing the temporal samples many generations apart maximizes the drift signal compared to sampling biases associated with age structure.     

Effective population size and temporal genetic change in stream resident brown trout (Salmo trutta, L.)

Temporal genetic data may be used forestimating effective population size (N _e) and for addressing the `temporal stability' of population structure, two issues of central importance for conservation and management. In this paper we assess the amount of spatio-temporal genetic variation at 17 di-allelic allozyme loci and estimate current N _e in two populations of stream resident brown trout (Salmo trutta) using data collected over 20 years. The amount ofpopulation divergence was found to bereasonably stable over the studied time period.There was significant temporal heterogeneitywithin both populations, however, and N _e was estimated as 19 and 48 for the twopopulations. Empirical estimates of theprobability of detecting statisticallysignificant allele frequency differencesbetween samples from the same populationseparated by different numbers of years wereobtained. This probability was found to befairly small when comparing samples collectedonly a few years apart, even for theseparticular populations that exhibit quiterestricted effective sizes. We discuss someimplications of the present results for browntrout population genetics and conservation, andfor the analysis of temporal genetic change inpopulations with overlapping generations ingeneral.     

Demographic Genetics of Brown Trout (Salmo Trutta) and Estimation of Effective Population Size from Temporal Change of Allele Frequencies

We studied temporal allele frequency shifts over 15 years and estimated the genetically effective size of four natural populations of brown trout (Salmo trutta L.) on the basis of the variation at 14 polymorphic allozyme loci. The allele frequency differences between consecutive cohorts were significant in all four populations. There were no indications of natural selection, and we conclude that random genetic drift is the most likely cause of temporal allele frequency shifts at the loci examined. Effective population sizes were estimated from observed allele frequency shifts among cohorts, taking into consideration the demographic characteristics of each population. The estimated effective sizes of the four populations range from 52 to 480 individuals, and we conclude that the effective size of natural brown trout populations may differ considerably among lakes that are similar in size and other apparent characteristics. In spite of their different effective sizes all four populations have similar levels of genetic variation (average heterozygosity) indicating that excessive loss of genetic variability has been retarded, most likely because of gene flow among neighboring populations.     

Estimating genetic drift and effective population size from temporal shifts in dominant gene marker frequencies

Measurement of temporal change in allele frequencies represents an indirect method for estimating the genetically effective size of populations. When allele frequencies are estimated for gene markers that display dominant gene expression, such as, e.g. random amplified polymorphic DNA (RAPD) and amplified fragment length polymorphism (AFLP) markers, the estimates can be seriously biased. We quantify bias for previous allele frequency estimators and present a new expression that is generally less biased and provides a more precise assessment of temporal allele frequency change. We further develop an estimator for effective population size that is appropriate when dealing with dominant gene markers. Comparison with estimates based on codominantly expressed genes, such as allozymes or microsatellites, indicates that about twice as many loci or sampled individuals are required when using dominant markers to achieve the same precision.     

Short-term genetic changes: evaluating effective population size estimates in a comprehensively described brown trout (Salmo trutta) population

The effective population size (N(e)) is notoriously difficult to accurately estimate in wild populations as it is influenced by a number of parameters that are difficult to delineate in natural systems. The different methods that are used to estimate N(e) are affected variously by different processes at the population level, such as the life-history characteristics of the organism, gene flow, and population substructure, as well as by the frequency patterns of genetic markers used and the sampling design. Here, we compare N(e) estimates obtained by different genetic methods and from demographic data and elucidate how the estimates are affected by various factors in an exhaustively sampled and comprehensively described natural brown trout (Salmo trutta) system. In general, the methods yielded rather congruent estimates, and we ascribe that to the adequate genotyping and exhaustive sampling. Effects of violating the assumptions of the different methods were nevertheless apparent. In accordance with theoretical studies, skewed allele frequencies would underestimate temporal allele frequency changes and thereby upwardly bias N(e) if not accounted for. Overlapping generations and iteroparity would also upwardly bias N(e) when applied to temporal samples taken over short time spans. Gene flow from a genetically not very dissimilar source population decreases temporal allele frequency changes and thereby acts to increase estimates of N(e). Our study reiterates the importance of adequate sampling, quantification of life-history parameters and gene flow, and incorporating these data into the N(e) estimation.     

TEMPORAL ALLOZYME FREQUENCY CHANGES IN DENSITY FLUCTUATING POPULATIONS OF WILLOW GROUSE (LAGOPUS LAGOPUS L.)

The population density of willow grouse (Lagopus lagopus L.) in northern Scandinavia changes in synchrony with the cyclic density variations in populations of microtine rodents. To assess the genetic changes accompanying the variations in population number, allozyme variation was studied at 23 loci in 640 willow grouse, representing four mainland and one island locality sampled during high and low population density. The average heterozygosity (H = 8.3%) and proportion of polymorphic loci (P = 26%) is not lower in willow grouse than in avian species with a more stable demography; the recurrent population density changes do not appear to affect drastically the long term effective population size, presumably because of extensive migration. Significant allele frequency differences were found both between populations and between different density phases. The genetic distance (D; Nei, 1972) was, in about 50% of the cases, larger between two consecutive time periods than between two localities in a certain year. Spatial and temporal allele frequency variation each represented around 3% of the gene diversity. The temporal heterogeneity may be caused by nonrandom sampling of family groups, rather than drift of allele frequencies between generations due to small effective population size, as has been suggested for microtine species.     

Temporal Stability of Genetic Variability and Differentiation in the Three-Spined Stickleback (Gasterosteus aculeatus)

Temporal variation in allele frequencies, whether caused by deterministic or stochastic forces, can inform us about interesting demographic and evolutionary phenomena occurring in wild populations. In spite of the continued surge of interest in the genetics of three-spined stickleback (Gasterosteus aculeatus) populations, little attention has been paid towards the temporal stability of allele frequency distributions, and whether there are consistent differences in effective size (N_e) of local populations. We investigated temporal stability of genetic variability and differentiation in 15 microsatellite loci within and among eight collection sites of varying habitat type, surveyed twice over a six-year time period. In addition, N_es were estimated with the expectation that they would be lowest in isolated ponds, intermediate in larger lakes and largest in open marine sites. In spite of the marked differences in genetic variability and differentiation among the study sites, the temporal differences in allele frequencies, as well as measures of genetic diversity and differentiation, were negligible. Accordingly, the N_e estimates were temporally stable, but tended to be lower in ponds than in lake or marine habitats. Hence, we conclude that allele frequencies in putatively neutral markers in three-spined sticklebacks seem to be temporally stable – at least over periods of few generations – across a wide range of habitat types differing markedly in levels of genetic variability, effective population size and gene flow.     

managedpop: a computer simulation to project allelic diversity in managed populations with overlapping generations

We present a Monte Carlo simulation, managedpop , to project the loss of allelic diversity in a population with overlapping generations supported (or invaded) by a prodigious subpopulation. Input parameters allow the user to account for complex life histories and critical management practices, such as the frequency at which supportive breeding stocks are replaced. The simulation could also be used to examine the threat of species or population level extinction via hybridization. managedpop merges theoretical formulations on the effective size of supported populations and of populations with overlapping generations using easily measured life history traits.     

Samples from subdivided populations yield biased estimates of effective size that overestimate the rate of loss of genetic variation

Many empirical studies estimating effective population size apply the temporal method that provides an estimate of the variance effective size through the amount of temporal allele frequency change under the assumption that the study population is completely isolated. This assumption is frequently violated, and the magnitude of the resulting bias is generally unknown. We studied how gene flow affects estimates of effective size obtained by the temporal method when sampling from a population system and provide analytical expressions for the expected estimate under an island model of migration. We show that the temporal method tends to systematically underestimate both local and global effective size when populations are connected by gene flow, and the bias is sometimes dramatic. The problem is particularly likely to occur when sampling from a subdivided population where high levels of gene flow obscure identification of subpopulation boundaries. In such situations, sampling in a manner that prevents biased estimates can be difficult. This phenomenon might partially explain the frequently reported unexpectedly low effective population sizes of marine populations that have raised concern regarding the genetic vulnerability of even exceptionally large populations.     

Archival genetic analysis suggests recent immigration has altered a population of Chinook salmon in an unsupplemented wilderness area

Detecting genetic population shifts (i.e. allele frequency differences) through time is a primary function of effective conservation monitoring, but it is equally vital to understand the underlying causative factors of change which may be revealed through analyses of long-term, temporal trends. We compared archival and contemporary Chinook salmon (Oncorhynchus tshawytscha) collections from the John Day River in Oregon, USA, to evaluate the temporal relationships among four primary spawning areas over a span of 28 years (1978–2006). Although it lies amid many hatchery-supplemented salmon populations of the Columbia River, the John Day River has itself experienced no directed supplementation. Using a combined panel of 13 microsatellite and 92 single nucleotide polymorphism loci, we observed significant temporal heterogeneity across sample sites and tested for two likely evolutionary influences: stochastic processes (i.e. genetic drift) and gene flow via immigration. Based on abundance and effective population size estimates, we found no evidence indicating a recent bottleneck. We observed a sharp temporal decline in probability of self-assignment of John Day River fish, particularly for the North Fork tributary. There was a corresponding increase in assignment to distant Snake River populations, attributed to accumulating introgression from out-of-basin sources over time. Our study demonstrates that low level immigration sustained over multiple generations can alter the genetic composition of natural populations, and while immigration may help maintain genetic population diversity, it risks reducing adaptive advantages in local ecosystems.     

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.     

利用全基因组连锁不平衡估计中国荷斯坦牛有效群体大小

有效群体大小是群体遗传学研究的一个重要内容,有助于我们更清楚地了解群体的遗传变异、进化和复杂性状的遗传机制等。随着高密度SNP标记的出现,越来越多的研究利用SNP标记间连锁不平衡估计有效群体大小。文章采集北京地区中国荷斯坦牛2 093个样本,并利用牛SNP芯片(Illumina BovineSNP50,含5 4001 SNPs)进行基因型测定,估计不同世代中国荷斯坦牛的有效群体大小。质量控制标准设定为SNP检出率0.95,最小等位基因频率>0.05,样本检出率0.95,哈代温伯格平衡检验显著性水平P<0.0001。经过质量控制,共1 968个样本和38 796个SNPs用于连锁不平衡分析。文章选取SNP间距0.1、0.2、0.5、1、2、5、10、15(Mb),估计中国荷斯坦牛在4世代之前有效群体大小。结果表明,中国荷斯坦牛的有效群体呈逐代下降趋势,至4世代前,中国荷斯坦牛平均有效群体为45头左右。     

Stability of population structure and genetic diversity across generations assessed by microsatellites among sympatric populations of landlocked Atlantic salmon (Salmo salar L.)

It may often be necessary to perform genetic analyses of temporal replicates to estimate the significance of spatial variation independently from that of temporal variation in order to ensure the reliability of estimates of a defined population structure. Nevertheless, temporal studies of genetic diversity remain scarce in the literature relative to the plethora of empirical studies of population structure. In vertebrates, a limited number of studies have specifically assessed the temporal stability of population structure for more than one generation. In this study, we performed a microsatellite analysis of DNA obtained from archived scales to compare the population structure among four sympatric landlocked populations of Atlantic salmon ( Salmo salar ) over a time frame of three to five generations. The same patterns of allele frequency distribution, θ, R _ST and genetic distance estimates were observed among populations for two time periods, confirming the temporal stability of the population structure. Despite population declines and stocking during this period, no statistically significant changes in intrapopulation genetic diversity were apparent. This study illustrates the feasibility and usefulness of microsatellite analysis of temporal samples, not only to infer changes of intrapopulation genetic diversity, but also to assess the stability of population structure over a time frame of several generations.     

How old is the most recent ancestor of two copies of an allele?

An important clue to the evolutionary history of an allele is the structure of the neighboring region of the genome, which we term the genomic background of the allele. Consider two copies of the allele. How similar we expect their genomic background to be is strongly influenced by the age of their most recent common ancestor (MRCA). We apply diffusion theory, first used by Motoo Kimura as a tool for predicting the changes in allele frequencies over time and developed by him in many articles in this journal, to prove a variety of new results on the age of the MRCA under the simplest demographic assumptions. In particular, we show that the expected age of the MRCA of two copies of an allele with population frequency f is just 2Nf generations, where N is the effective population size. Our results are a first step in running exact coalescent simulations, where we also simulate the history of the population frequency of an allele.     

ESTIMATION OF PARAMETERS OF INBREEDING AND GENETIC DRIFT IN POPULATIONS WITH OVERLAPPING GENERATIONS

Many long‐lived plant and animal species have nondiscrete overlapping generations. Although numerous models have been developed to predict the effective sizes (N_e) of populations with overlapping generations, they are extremely difficult to apply to natural populations because of the large array of unknown and elusive life‐table parameters involved. Unfortunately, little work has been done to estimate the N_e of populations with overlapping generations from marker data, in sharp contrast to the situation of populations with discrete generations for which quite a few estimators are available. In this study, we propose an estimator (EPA, estimator by parentage assignments) of the current N_e of populations with overlapping generations, using the sex, age, and multilocus genotype information of a single sample of individuals taken at random from the population. Simulations show that EPA provides unbiased and accurate estimates of N_e under realistic sampling and genotyping effort. Additionally, it yields estimates of other interesting parameters such as generation interval, the variances and covariances of lifetime family size, effective number of breeders of each age class, and life‐table variables. Data from wild populations of baboons and hihi (stitchbird) were analyzed by EPA to demonstrate the use of the estimator in practical sampling and genotyping situations.     

TEMPORAL CHANGE OF MITOCHONDRIAL DNA HAPLOTYPE FREQUENCIES AND FEMALE EFFECTIVE SIZE IN A BROWN TROUT (SALMO TRUTTA) POPULATION

We report data on genetic drift of mitochondrial DNA (mtDNA) haplotypes in a natural brown trout (Salmo trutta) population in Sweden. Large temporal frequency shifts were observed over the 14 consecutive year classes studied. The observed rate of drift was used to estimate the effective size of the population. This effective size applies to the female segment of the population as mtDNA is maternally inherited. The magnitude of mtDNA haplotype frequency change is compared with the corresponding allele frequency changes at 14 allozyme loci in the same population. The female effective size is estimated as 58, which is approximately half the effective size of 97 for the total population (both sexes) previously obtained from the shifts of allozyme allele frequencies.     

Effective population sizes and temporal stability of genetic structure in Rana pipiens, the northern leopard frog

Although studies of population genetic structure are very common, whether genetic structure is stable over time has been assessed for very few taxa. The question of stability over time is particularly interesting for frogs because it is not clear to what extent frogs exist in dynamic metapopulations with frequent extinction and recolonization, or in stable patches at equilibrium between drift and gene flow. In this study we collected tissue samples from the same five populations of leopard frogs, Rana pipiens, over a 22-30 year time interval (11-15 generations). Genetic structure among the populations was very stable, suggesting that these populations were not undergoing frequent extinction and colonization. We also estimated the effective size of each population from the change in allele frequencies over time. There exist few estimates of effective size for frog populations, but the data available suggest that ranid frogs may have much larger ratios of effective size (Ne) to census size (Nc) than toads (bufonidae). Our results indicate that R. pipiens populations have effective sizes on the order of hundreds to at most a few thousand frogs, and Ne/Nc ratios in the range of 0.1-1.0. These estimates of Ne/Nc are consistent with those estimated for other Rana species. Finally, we compared the results of three temporal methods for estimating Ne. Moment and pseudolikelihood methods that assume a closed population gave the most similar point estimates, although the moment estimates were consistently two to four times larger. Wang and Whitlock's new method that jointly estimates Ne and the rate of immigration into a population (m) gave much smaller estimates of Ne and implausibly large estimates of m. This method requires knowing allele frequencies in the source of immigrants, but was thought to be insensitive to inexact estimates. In our case the method may have failed because we did not know the true source of immigrants for each population. The method may be more sensitive to choice of source frequencies than was previously appreciated, and so should be used with caution if the most likely source of immigrants cannot be identified clearly.     

Census vs. effective population size in chinook salmon: large- and small-scale environmental perturbation effects

Population viability has often been assessed by census of reproducing adults. Recently this method has been called into question and estimation of the effective population size (Ne) proposed as a complementary method to determine population health. We examined genetic diversity in five populations of chinook salmon (Oncorhynchus tshawytscha) from the upper Fraser River watershed (British Columbia, Canada) at 11 microsatellite loci over 20 years using DNA extracted from archived scale samples. We tested for changes in genetic diversity, calculated the ratio of the number of alleles to the range in allele size to give the statistic M, calculated Ne from the temporal change in allele frequency, used the maximum likelihood method to calculate effective population size (NeM), calculated the harmonic mean of population size, and compared these statistics to annual census estimates. Over the last two decades population size has increased in all five populations of chinook examined; however, Ne calculated for each population was low (81-691) and decreasing over the time interval measured. Values of NeM were low, but substantially higher than Ne calculated using the temporal method. The calculated values for M were generally low (M < 0.70), indicating recent population reductions for all five populations. Large-scale historic barriers to migration and development activities do not appear to account for the low values of Ne; however, available spawning area is positively correlated with Ne. Both Ne and M estimates indicate that these populations are potentially susceptible to inbreeding effects and may lack the ability to respond adaptively to stochastic events. Our findings question the practice of relying exclusively on census estimates for interpreting population health and show the importance of determining genetic diversity within populations.     

Controlling for P‐value inflation in allele frequency change in experimental evolution and artificial selection experiments

Experimental evolution studies can be used to explore genomic response to artificial and natural selection. In such studies, loci that display larger allele frequency change than expected by genetic drift alone are assumed to be directly or indirectly associated with traits under selection. However, such studies report surprisingly many loci under selection, suggesting that current tests for allele frequency change may be subject to P‐value inflation and hence be anticonservative. One factor known from genomewide association (GWA) studies to cause P‐value inflation is population stratification, such as relatedness among individuals. Here, we suggest that by treating presence of an individual in a population after selection as a binary response variable, existing GWA methods can be used to account for relatedness when estimating allele frequency change. We show that accounting for relatedness like this effectively reduces false‐positives in tests for allele frequency change in simulated data with varying levels of population structure. However, once relatedness has been accounted for, the power to detect causal loci under selection is low. Finally, we demonstrate the presence of P‐value inflation in allele frequency change in empirical data spanning multiple generations from an artificial selection experiment on tarsus length in two free‐living populations of house sparrow and correct for this using genomic control. Our results indicate that since allele frequencies in large parts of the genome may change when selection acts on a heritable trait, such selection is likely to have considerable and immediate consequences for the eco‐evolutionary dynamics of the affected populations.     

A Generalized Approach for Estimating Effective Population Size from Temporal Changes in Allele Frequency

The temporal method for estimating effective population size (Ne) from the standardized variance in allele frequency change (F) is presented in a generalized form. Whereas previous treatments of this method have adopted rather limiting assumptions, the present analysis shows that the temporal method is generally applicable to a wide variety of organisms. Use of a revised model of gene sampling permits a more generalized interpretation of Ne than that used by some other authors studying this method. It is shown that two sampling plans (individuals for genetic analysis taken before or after reproduction) whose differences have been stressed by previous authors can be treated in a uniform way. Computer simulations using a wide variety of initial conditions show that different formulas for computing F have much less effect on Ne than do sample size (S), number of generations between samples (t), or the number of loci studied (L). Simulation results also indicate that (1) bias of F is small unless alleles with very low frequency are used; (2) precision is typically increased by about the same amount with a doubling of S, t, or L; (3) confidence intervals for Ne computed using a chi 2 approximation are accurate and unbiased under most conditions; (4) the temporal method is best suited for use with organisms having high juvenile mortality and, perhaps, a limited effective population size.