Coalescent process with fluctuating population size and its effective size

We consider a Wright-Fisher model whose population size is a finite Markov chain. We introduce a sequence of two-dimensional discrete time Markov chains whose components describe the coalescent process and the fluctuation of population size. For the limiting process of the sequence of Markov chains, the relationship of the expectation of coalescence time to the harmonic and the arithmetic means of population sizes is shown, and the Laplace transform of the distribution of coalescence time is calculated. We define the coalescence effective population size (cEPS) by the expectation of coalescence time. We show that cEPS is strictly larger (resp. smaller) than the harmonic (resp. arithmetic) mean. As the population size fluctuates more quickly (resp. slowly), cEPS is closer to the harmonic (resp. arithmetic) mean. For the case of a two-valued Markov chain, we show the explicit expression of cEPS and its dependency on the sample size.     

Evaluating methods for estimating local effective population size with and without migration

Effective population size is a fundamental parameter in population genetics, evolutionary biology, and conservation biology, yet its estimation can be fraught with difficulties. Several methods to estimate N_e from genetic data have been developed that take advantage of various approaches for inferring N_e. The ability of these methods to accurately estimate N_e, however, has not been comprehensively examined. In this study, we employ seven of the most cited methods for estimating N_e from genetic data (Colony2, CoNe, Estim, MLNe, ONeSAMP, TMVP, and NeEstimator including LDNe) across simulated datasets with populations experiencing migration or no migration. The simulated population demographies are an isolated population with no immigration, an island model metapopulation with a sink population receiving immigrants, and an isolation by distance stepping stone model of populations. We find considerable variance in performance of these methods, both within and across demographic scenarios, with some methods performing very poorly. The most accurate estimates of N_e can be obtained by using LDNe, MLNe, or TMVP; however each of these approaches is outperformed by another in a differing demographic scenario. Knowledge of the approximate demography of population as well as the availability of temporal data largely improves N_e estimates.     

Detecting populations in the 'ambiguous' zone: kinship-based estimation of population structure at low genetic divergence

Identifying population structure is one of the most common and important objectives of spatial analyses using population genetic data. Population structure is detected either by rejecting the null hypothesis of a homogenous distribution of genetic variation, or by estimating low migration rates. Issues arise with most current population genetic inference methods when the genetic divergence is low among putative populations. Low levels of genetic divergence may be as a result of either high ongoing migration or historic high migration but no current, ongoing migration. We direct attention to recent developments in the use of the tempo-spatial distribution of closely related individuals to detect population structure or estimate current migration rates. These 'kinship-based' approaches complement more traditional population-based genetic inference methods by providing a means to detect population structure and estimate current migration rates when genetic divergence is low. However, for kinship-based methods to become widely adopted, formal estimation procedures applicable to a range of species life histories are needed.     

Monitoring of the genetic structure of natural populations: change of the effective population size and inversion polymorphism in <Emphasis Type="Italic">Drosophila subobscura</Emphasis>

We analyzed changes in the genetic structure and effective population size of two ecologically distinct populations of Drosophila subobscura over several years. Population sizes of D. subobscura in beech and oak wood habitats for a period of 6 years were estimated by the capture-mark-release-recapture method. Inversion polymorphism parameters were also assessed in the same populations for a period of 3 years. Significant differences in the numbers of individuals were observed between sexes. This affected the effective population sizes between particular years. The ratio of the effective size over the cenzus dropped significantly in beech wood in 2 years. Although overall heterozygosity remained unchanged during the years in both habitats, frequencies of gene arrangements on five chromosomes show variability. After the bottleneck, some complex chromosomal arrangements appeared for the first time in both populations. Standard gene arrangements of chromosome A increased in frequency over the years in each habitat, while the complex arrangements remain rather stable and specific for each population. The results obtained indicate that the population structure may significantly change if the effective size of D. subobscura population is reduced, which is mostly related to microclimatic changes in habitats. Based on the results to date, monitoring of microevolutionary changes by using D. subobscura and its relatives seems a promising way to study the effects of global climate changes.     

A Schistosoma mansoni tri- and tetramer microsatellite catalog for genetic population diversity and differentiation

All Schistosoma mansoni tri- and tetranucleotide repeat microsatellites published as of December 2018 were identified. All 52 were evaluated for autosomal location, strength of amplification, scorability and behavior as single-copy loci by polyacrylamide and capillary gel electrophoresis. Of these, 27 were unique, autosomal, polymorphic, easily scored and single copy as assessed on pooled adult worm DNA from two different continental origins and adult worm clones. These microsatellites were distributed across all seven autosomal chromosomes. On laboratory strains their heterozygosity ranged from 0.22 to 0.77. Individual markers had 5–13 alleles, allelic richness of 2–10 and an effective allele number of 1.3–8.14. Those infected by Schistosoma mansoni carry many genetically distinct, sexually reproducing parasites, therefore, for an individual infection the complete allele frequency profile of their progeny consists of a pool of DNA from multiple diploid eggs. Using a set of 25 microsatellites, we calculated allele frequency profiles of eggs in fecal samples from people in two Brazilian communities separated by 6 km: Jenipapo (n = 80) and Volta do Rio (n = 38). There were no a priori characteristics that could predict the performance of markers in natural infections based on their performance with laboratory strains. Increasing marker number did not change accuracy for differentiation and diversity but did improve precision. Our data suggest that using a random set of 10–20 microsatellites appears to result in values that exhibit low standard deviations for diversity and differentiation indices. All identified microsatellites as well as PCR conditions, allele size, primer sequences and references for all tri- and tetramer microsatellites markers presented in this work are available at: https://sites.google.com/case.edu/cwru-and-fiocruz-wdrc/home.     

Reduced genetic diversity and low effective size in peripheral northern European catfish Silurus glanis populations

Using 10 polymorphic microsatellites and 1251 individual samples (some dating back to the early 1980s), genetic structure and effective population size in all native and introduced Swedish populations of the European wels catfish or Silurus glanis were studied. Levels of genetic variability and phylogeographic relationships were compared with data from a previous study of populations in other parts of Europe. The genetically distinct Swedish populations displayed comparably low levels of genetic variability and according to one-sample estimates based on linkage disequilibrium and sib ship-reconstruction, current local effective population sizes were lower than minimum levels recommended for short-term genetic conservation. In line with a previous suggestion of postglacial colonisation from a single refugium, all Swedish populations were assembled on a common branch in a star-shaped dendrogram together with other European populations. Two distinct subpopulations were detected in upper and lower habitats of River Emån, indicating that even minor dispersal barriers may restrict gene flow for wels in running waters. Genetic assignment of specimens encountered in the brackish Baltic Sea and in lakes where the species does not occur naturally indicated presence of long-distance sea dispersal and confirmed unauthorised translocations, respectively.     

Effective population size,genetic diversity,and coalescence time in subdivided populations

A formula for the effective population size for the finite island model of subdivided populations is derived. The formula indicates that the effective size can be substantially greater than the actual number of individuals in the entire population when the migration rate among subpopulations is small. It is shown that the mean nucleotide diversity, coalescence time, and heterozygosity for genes sampled from the entire population can be predicted fairly well from the theory for randomly mating populations if the effective population size for the finite island model is used.     

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.     

Accounting for missing data in the estimation of contemporary genetic effective population size (Ne)

Theoretical models are often applied to population genetic data sets without fully considering the effect of missing data. Researchers can deal with missing data by removing individuals that have failed to yield genotypes and/or by removing loci that have failed to yield allelic determinations, but despite their best efforts, most data sets still contain some missing data. As a consequence, realized sample size differs among loci, and this poses a problem for unbiased methods that must explicitly account for random sampling error. One commonly used solution for the calculation of contemporary effective population size (N_e) is to calculate the effective sample size as an unweighted mean or harmonic mean across loci. This is not ideal because it fails to account for the fact that loci with different numbers of alleles have different information content. Here we consider this problem for genetic estimators of contemporary effective population size (N_e). To evaluate bias and precision of several statistical approaches for dealing with missing data, we simulated populations with known N_e and various degrees of missing data. Across all scenarios, one method of correcting for missing data (fixed‐inverse variance‐weighted harmonic mean) consistently performed the best for both single‐sample and two‐sample (temporal) methods of estimating N_e and outperformed some methods currently in widespread use. The approach adopted here may be a starting point to adjust other population genetics methods that include per‐locus sample size components.     

Effects of population characteristics and structure on estimates of effective population size in a house sparrow metapopulation

Effective population size (N_e) is a key parameter to understand evolutionary processes and the viability of endangered populations as it determines the rate of genetic drift and inbreeding. Low N_e can lead to inbreeding depression and reduced population adaptability. In this study, we estimated contemporary N_e using genetic estimators (LDNE, ONeSAMP, MLNE and CoNe) as well as a demographic estimator in a natural insular house sparrow metapopulation. We investigated whether population characteristics (population size, sex ratio, immigration rate, variance in population size and population growth rate) explained variation within and among populations in the ratio of effective to census population size (N_e/N_c). In general, N_e/N_c ratios increased with immigration rates. Genetic N_e was much larger than demographic N_e, probably due to a greater effect of immigration on genetic than demographic processes in local populations. Moreover, although estimates of genetic N_e seemed to track N_c quite well, the genetic N_e‐estimates were often larger than N_c within populations. Estimates of genetic N_e for the metapopulation were however within the expected range (<N_c). Our results suggest that in fragmented populations, even low levels of gene flow may have important consequences for the interpretation of genetic estimates of N_e. Consequently, further studies are needed to understand how N_e estimated in local populations or the total metapopulation relates to actual rates of genetic drift and inbreeding.     

Implications of the variance effective population size on the genetic conservation of monoecious species

The concept of variance effective population size [Ne_(v)] and other expressions are reviewed and described for specific sampling steps in germplasm collection and regeneration of monoecious species. Special attention is given to procedures for computing the variance of the number of contributed gametes [V(k)] to the next generation. Drift, as it occurs between generations, was considered to contain a component due to the sampling of parents and a subsequent component due to the sampling of gametes. This demonstrates that drift, caused by reduction of seed viability, damages the genetic integrity of accessions stored in germplasm banks. The study shows how mating designs, such as plant-to-plant or chain crossings with additional female gametic control, can partially alleviate this problem. Optimal procedures for increasing Ne_(v) when collecting germplasm in the field are also discussed. The effect of different female and male gametic control strategies on Ne_(v) is considered under several situations. Practical examples illustrating the use of V(k) and Ne_(v) expressions are given.     

Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N _e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988     

The effective number of a population that varies cyclically in size. II. Overlapping generations

We consider haploid and dioecious age-structured populations that vary over time in cycles of length k. Results are obtained for both autosomal and sex-linked loci if the population is dioecious. It is assumed that k is small in comparison with numbers of haploid individuals (or of numbers of males and females) in any generation of a cycle. The inbreeding effective population size N(e) is then approximately given by the expression [T summation operator (k-1)(j=0)1/[N(e)(j)T(j)]](-1), where N(e)(j) and T(j) are, respectively, the effective population size and generation interval that would hold if the population was at all times generated in the same way as at time j. The constant T, which is the effective overall generation interval, is defined to be k times the harmonic mean of the quantities T(j). Our expressions for T and N(e), in terms of N(e)(j) and T(j), are general, but the N(e)(j)s are derived under the assumption that offspring are produced according to Poisson distributions.     

Multiple estimates of effective population size for monitoring a long‐lived vertebrate: an application to Yellowstone grizzly bears

Effective population size (N_e) is a key parameter for monitoring the genetic health of threatened populations because it reflects a population's evolutionary potential and risk of extinction due to genetic stochasticity. However, its application to wildlife monitoring has been limited because it is difficult to measure in natural populations. The isolated and well‐studied population of grizzly bears (Ursus arctos) in the Greater Yellowstone Ecosystem provides a rare opportunity to examine the usefulness of different N_e estimators for monitoring. We genotyped 729 Yellowstone grizzly bears using 20 microsatellites and applied three single‐sample estimators to examine contemporary trends in generation interval (GI), effective number of breeders (N_b) and N_e during 1982–2007. We also used multisample methods to estimate variance (N_eV) and inbreeding N_e (N_eI). Single‐sample estimates revealed positive trajectories, with over a fourfold increase in N_e (≈100 to 450) and near doubling of the GI (≈8 to 14) from the 1980s to 2000s. N_eV (240–319) and N_eI (256) were comparable with the harmonic mean single‐sample N_e (213) over the time period. Reanalysing historical data, we found N_eV increased from ≈80 in the 1910s–1960s to ≈280 in the contemporary population. The estimated ratio of effective to total census size (N_e/N_c) was stable and high (0.42–0.66) compared to previous brown bear studies. These results support independent demographic evidence for Yellowstone grizzly bear population growth since the 1980s. They further demonstrate how genetic monitoring of N_e can complement demographic‐based monitoring of N_c and vital rates, providing a valuable tool for wildlife managers.     

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.     

Formulation and estimation of the effective size of stage-structured populations in Fritillaria camtschatcensis, a perennial herb with a complex life history

The effective population size (Ne) is formulated based on a stage-structured population model and is estimated for two populations of Fritillaria camtschatcensis (L.) Ker-Gawl. (Liliaceae), a perennial, mainly clonally reproducing herb. Plants in these populations change life-history stages year by year, either upward or downward across three unambiguously identifiable stages: one-leaf, nonflowering; multileaf nonflowering; and multileaf, flowering stages. Plants of all stages produce clonal progeny (bulblets) each year, and death of plants occurs only in the first stage. The populations are nearly at equilibrium in both population size and stage structure. Ne is estimated to be 20-30% of the census population size (N), leading to the prediction that a population size of about 20,000 or more will be needed to conserve the normal level of the gene diversity (Ne > or = 5000). With the current demographic pattern of this species, accelerated growth of the first-stage plants with reduced survival of the second- and third-stage plants will increase both the annual (Ny/N) and generation time (Ne/N) effective sizes of population.     

Estimating effective population size using RADseq: Effects of SNP selection and sample size

Effective population size (N_e) is a key parameter of population genetics. However, N_e remains challenging to estimate for natural populations as several factors are likely to bias estimates. These factors include sampling design, sequencing method, and data filtering. One issue inherent to the restriction site‐associated DNA sequencing (RADseq) protocol is missing data and SNP selection criteria (e.g., minimum minor allele frequency, number of SNPs). To evaluate the potential impact of SNP selection criteria on N_e estimates (Linkage Disequilibrium method) we used RADseq data for a nonmodel species, the thornback ray. In this data set, the inbreeding coefficient F_IS was positively correlated with the amount of missing data, implying data were missing nonrandomly. The precision of N_eestimates decreased with the number of SNPs. Mean N_e estimates (averaged across 50 random data sets with2000 SNPs) ranged between 237 and 1784. Increasing the percentage of missing data from 25% to 50% increased N_e estimates between 82% and 120%, while increasing the minor allele frequency (MAF) threshold from 0.01 to 0.1 decreased estimates between 71% and 75%. Considering these effects is important when interpreting RADseq data‐derived estimates of effective population size in empirical studies.     

The genetic effective and adult census size of an Australian population of tiger prawns (Penaeus esculentus)

This study compares estimates of the census size of the spawning population with genetic estimates of effective current and long-term population size for an abundant and commercially important marine invertebrate, the brown tiger prawn (Penaeus esculentus). Our aim was to focus on the relationship between genetic effective and census size that may provide a source of information for viability analyses of naturally occurring populations. Samples were taken in 2001, 2002 and 2003 from a population on the east coast of Australia and temporal allelic variation was measured at eight polymorphic microsatellite loci. Moments-based and maximum-likelihood estimates of current genetic effective population size ranged from 797 to 1304. The mean long-term genetic effective population size was 9968. Although small for a large population, the effective population size estimates were above the threshold where genetic diversity is lost at neutral alleles through drift or inbreeding. Simulation studies correctly predicted that under these experimental conditions the genetic estimates would have non-infinite upper confidence limits and revealed they might be overestimates of the true size. We also show that estimates of mortality and variance in family size may be derived from data on average fecundity, current genetic effective and census spawning population size, assuming effective population size is equivalent to the number of breeders. This work confirms that it is feasible to obtain accurate estimates of current genetic effective population size for abundant Type III species using existing genetic marker technology.     

The effect of a population bottleneck on the evolution of genetic variance/covariance structure

It is well known that standard population genetic theory predicts decreased additive genetic variance (V(a) ) following a population bottleneck and that theoretical models including interallelic and intergenic interactions indicate such loss may be avoided. However, few empirical data from multicellular model systems are available, especially regarding variance/covariance (V/CV) relationships. Here, we compare the V/CV structure of seventeen traits related to body size and composition between control (60 mating pairs/generation) and bottlenecked (2 mating pairs/generation; average F = 0.39) strains of mice. Although results for individual traits vary considerably, multivariate analysis indicates that V(a) in the bottlenecked populations is greater than expected. Traits with patterns and amounts of epistasis predictive of enhanced V(a) also show the largest deviations from additive expectations. Finally, the correlation structure of weekly weights is not significantly different between control and experimental lines but correlations between necropsy traits do differ, especially those involving the heart, kidney and tail length.     

Patterns of protein evolution in Tetrahymena thermophila: implications for estimates of effective population size

High levels of synonymous substitutions among alleles of the surface antigen SerH led to the hypothesis that Tetrahymena thermophila has a tremendously large effective population size, one that is greater than estimated for many prokaryotes (Lynch, M., and J. S. Conery. 2003. Science 302:1401-1404.). Here we show that SerH is unusual as there are substantially lower levels of synonymous variation at five additional loci (four nuclear and one mitochondrial) characterized from T. thermophila populations. Hence, the effective population size of T. thermophila, a model single-celled eukaryote, is lower and more consistent with estimates from other microbial eukaryotes. Moreover, reanalysis of SerH polymorphism data indicates that this protein evolves through a combination of vertical transmission of alleles and concerted evolution of repeat units within alleles. SerH may be under balancing selection due to a mechanism analogous to the maintenance of antigenic variation in vertebrate immune systems. Finally, the dual nature of ciliate genomes and particularly the amitotic divisions of processed macronuclear genomes may make it difficult to estimate accurately effective population size from synonymous polymorphisms. This is because selection and drift operate on processed chromosomes in macronuclei, where assortment of alleles, disruption of linkage groups, and recombination can alter the genetic landscape relative to more canonical eukaryotic genomes.