Genetic diversity and reproductive biology in Warea carteri (Brassicaceae), a narrowly endemic Florida scrub annual

Carter's mustard (Warea carteri) is an endangered, fire-stimulated annual endemic of the Lake Wales Ridge, Florida, USA. This species is characterized by seed banks and large fluctuations in plant numbers, with increases occurring in postdisturbance habitat. We investigated the mating system, patterns of isozyme variation, and effective population sizes of W. carteri to better understand its population biology and to comment on reserve designs and management proposals relevant to this species. Warea carteri is self-compatible and autogamous, and probably largely selfing. Measures of genetic variation in W. carteri were lower than values reported for species with similar ecological and life history traits (6.6% of loci polymorphic within populations, 1.87 alleles per polymorphic locus, and 0.026 and 0.018 expected and observed heterozygosity, respectively). The high average value for Nei's genetic identity (0.989) reflects the paucity of genetic diversity. Genetic variation within populations was not correlated with aboveground population size, effective population size estimates (N(e)), or recent disturbance history. Much of the diversity detected was found among populations (F(ST) = 0.304). A significant cline in allele frequencies at one locus and a significant negative correlation between geographic distance and Nei's genetic identity also point to spatial organization of genetic diversity. As a result we propose that reserve design should include the entire geographic range of W. carteri. We also recommend that the natural fire regime be mimicked.     

Estimation of effective population size and detection of a recent population decline coinciding with habitat fragmentation in a ground beetle

We assess the impact of habitat fragmentation on the effective size (N(e)) of local populations of the flightless ground beetle Carabus violaceus in a small (<25 ha) and a large (>80 ha) forest fragment separated by a highway. N(e) was estimated based on the temporal variation of allele frequencies at 13 microsatellite loci using two different methods. In the smaller fragment, N(e) estimates ranged between 59 and a few hundred, whereas values between 190 and positive infinity were estimated for the larger fragment. In both samples, we detected a signal of population decline, which was stronger in the small fragment. The estimated time of onset of this N(e) reduction was consistent with the hypothesis that recent road constructions have divided a continuous population into several isolated subpopulations. In the small fragment, N(e) of the local population may be so small that its long-term persistence is endangered.     

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.     

Dynamics of neutral and selected alleles when the offspring distribution is skewed

We analyze the dynamics of two alternative alleles in a simple model of a population that allows for large family sizes in the distribution of offspring number. This population model was first introduced by Eldon and Wakeley, who described the backward-time genealogical relationships among sampled individuals, assuming neutrality. We study the corresponding forward-time dynamics of allele frequencies, with or without selection. We derive a continuum approximation, analogous to Kimura's diffusion approximation, and we describe three distinct regimes of behavior that correspond to distinct regimes in the coalescent processes of Eldon and Wakeley. We demonstrate that the effect of selection is strongly amplified in the Eldon-Wakeley model, compared to the Wright-Fisher model with the same variance effective population size. Remarkably, an advantageous allele can even be guaranteed to fix in the Eldon-Wakeley model, despite the presence of genetic drift. We compute the selection coefficient required for such behavior in populations of Pacific oysters, based on estimates of their family sizes. Our analysis underscores that populations with the same effective population size may nevertheless experience radically different forms of genetic drift, depending on the reproductive mechanism, with significant consequences for the resulting allele dynamics.     

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.     

Founder events and variation at microsatellite loci in an insular passerine bird, the Laysan finch (Telespiza cantans)

Historically documented founder events provide opportunities to assess the effects of population size reductions on genetic variation, but the actual magnitude of genetic change can be measured only when direct comparisons can be made to the source or ancestral population. We assayed variation at nine microsatellite loci in the translocated population of the Laysan finch ( Telespiza cantans ) at Pearl and Hermes reef (PHR), and compared the level of variation to that in the source population on Laysan Island. Heterogeneity in allele frequencies was highly significant at eight of the nine loci, primarily as a result of fluctuations in allele frequencies in the three PHR populations. Intra- and interpopulational measures of genetic diversity generally matched predictions based on the well-documented history of three islet populations at PHR: significantly lower numbers of alleles and polymorphic loci, as well as higher pairwise F _ST values and genetic distance, were observed for the two populations that underwent severe size reductions. Changes in heterozygosity at single loci were unpredictable, as both significant increases and decreases were observed in founder populations. A significant excess of heterozygotes was found in two populations and was highly significant over all four finch populations ( P < 0.003). Estimates of effective population size from temporal changes in heterozygosity and allele frequencies were very small ( N _e≤ 30) as a result of the founding events and the constraints of islet area on population numbers. We concluded that the PHR population is not adequate as a secondary genetic reserve for T. cantans , and an alternative refuge needs to be established.     

Estimating effective population size and migration rates from genetic samples over space and time

In the past, moment and likelihood methods have been developed to estimate the effective population size (N(e)) on the basis of the observed changes of marker allele frequencies over time, and these have been applied to a large variety of species and populations. Such methods invariably make the critical assumption of a single isolated population receiving no immigrants over the study interval. For most populations in the real world, however, migration is not negligible and can substantially bias estimates of N(e) if it is not accounted for. Here we extend previous moment and maximum-likelihood methods to allow the joint estimation of N(e) and migration rate (m) using genetic samples over space and time. It is shown that, compared to genetic drift acting alone, migration results in changes in allele frequency that are greater in the short term and smaller in the long term, leading to under- and overestimation of N(e), respectively, if it is ignored. Extensive simulations are run to evaluate the newly developed moment and likelihood methods, which yield generally satisfactory estimates of both N(e) and m for populations with widely different effective sizes and migration rates and patterns, given a reasonably large sample size and number of markers.     

Divergent selection and heterogeneous migration rates across the range of Sitka spruce (Picea sitchensis)

Gene flow and effective population size (N(e)) should depend on a population's position within its range: those near the edges are expected to have smaller N(e) and lower relative emigration rates, whereas those nearer the centre should have larger N(e) and higher relative emigration rates. In species with continuous ranges, this phenomenon may limit the ability of peripheral populations to respond to divergent selection. Here, we employ Sitka spruce as a model to test these predictions. We previously genotyped 339 single nucleotide polymorphisms (SNPs) in 410 individuals from 13 populations, and used these data to identify putative targets of divergent selection, as well as to explore the extent to which central-peripheral structure may impede adaptation. Fourteen SNPs had outlier F(ST) estimates suggestive of divergent selection, of which nine were previously associated with phenotypic variation in adaptive traits (timing of autumn budset and cold hardiness). Using coalescent simulations, we show that populations from near the centre of the range have higher effective populations sizes than those from the edges, and that central populations contribute more migrants to marginal populations than the reverse. Our results suggest that while divergent selection appears to have shaped allele frequencies among populations, asymmetrical movement of alleles from the centre to the edges of the species range may affect the adaptive capacity of peripheral populations. In southern peripheral populations, the movement of cold-adapted alleles from the north represents a significant impediment to adaptation under climate change, while in the north, movement of warm-adapted alleles from the south may enhance adaptation.     

A Direct Assessment of the Role of Genetic Drift in Determining Allele Frequency Variation in Populations of EUPHYDRYAS EDITHA

Estimates of allele frequencies at six polymorphic loci were collected over eight generations in two populations of Euphydryas editha. We have estimated, in addition, the effective population size for each generation for both populations with results from mark-recapture and other field data. The variation in allele frequencies generated by random genetic drift was then studied using computer simulations and our direct estimates of effective population size. Substantial differences between observed values and computer-generated expected values assuming drift alone were found for three loci (Got, Hk, Pgi) in one population. These observations are consistent with natural selection in a variable environment.     

Long-term stability and effective population size in North Sea and Baltic Sea cod (Gadus morhua)

DNA from archived otoliths was used to explore the temporal stability of the genetic composition of two cod populations, the Moray Firth (North Sea) sampled in 1965 and 2002, and the Bornholm Basin (Baltic Sea) sampled in 1928 and 1997. We found no significant changes in the allele frequencies for the Moray Firth population, while subtle but significant genetic changes over time were detected for the Bornholm Basin population. Estimates of the effective population size ( N _e ) generally exceeded 500 for both populations when employing a number of varieties of the temporal genetic method. However, confidence intervals were very wide and N _e 's most likely range in the thousands. There was no apparent loss of genetic variability and no evidence of a genetic bottleneck for either of the populations. Calculations of the expected levels of genetic variability under different scenarios of N _e showed that the number of alleles commonly reported at microsatellite loci in Atlantic cod is best explained by N _e 's exceeding thousand. Recent fishery-induced bottlenecks can, however, not be ruled out as an explanation for the apparent discrepancy between high levels of variability and recently reported estimates of N _e  << 1000. From life history traits and estimates of survival rates in the wild, we evaluate the compatibility of the species' biology and extremely low N _e / N ratios. Our data suggest that very small N _e 's are not likely to be of general concern for cod populations and, accordingly, most populations do not face any severe threat of losing evolutionary potential due to genetic drift.     

Historical Analysis of Genetic Variation Reveals Low Effective Population Size in a Northern Pike (Esox Lucius) Population

Effective population size (N(e)) of a natural fish population was estimated from temporal changes in allele frequencies at seven microsatellite loci. Use of a historical collection of fish scales made it possible to increase the precision of estimates by increasing the time interval between samples and to use an equation developed for discrete generations without correcting for demographic parameters. Estimates of N(e) for the time intervals 1961-1977 and 1977-1993 were 35 and 72, respectively. For the entire interval, 1961-1993, the estimate of N(e) was 48 when based on a weighted mean derived from the above two estimates or 125 when calculated from 1961 and 1993 samples only. Corresponding ratios of effective size to adult census size ranged from 0.03 to 0.14. An N(e) of 48 over a 32-year period would imply that this population lost as much as 8% of its heterozygosity in that time. Results suggest the potential for using genetic methods based on microsatellite loci data to compare historical trends in N(e) with population dynamic parameters. Such comparisons will help to evaluate the relationship between genetic diversity and long-term persistence of natural populations.     

Effective population size of natural populations of Drosophila buzzatii, with a comparative evaluation of nine methods of estimation

Allozyme and microsatellite data from numerous populations of Drosophila buzzatii have been used (i) to determine to what degree N(e) varies among generations within populations, and among populations, and (ii) to evaluate the congruence of four temporal and five single-sample estimators of N(e) . Effective size of different populations varied over two orders of magnitude, most populations are not temporally stable in genetic composition, and N(e) showed large variation over generations in some populations. Short-term N(e) estimates from the temporal methods were highly correlated, but the smallest estimates were the most precise for all four methods, and the most consistent across methods. Except for one population, N(e) estimates were lower when assuming gene flow than when assuming populations that were closed. However, attempts to jointly estimate N(e) and immigration rate were of little value because the source of migrants was unknown. Correlations among the estimates from the single-sample methods generally were not significant although, as for the temporal methods, estimates were most consistent when they were small. These single-sample estimates of current N(e) are generally smaller than the short-term temporal estimates. Nevertheless, population genetic variation is not being depleted, presumably because of past or ongoing migration. A clearer picture of current and short-term effective population sizes will only follow with better knowledge of migration rates between populations. Different methods are not necessarily estimating the same N(e) , they are subject to different bias, and the biology, demography and history of the population(s) may affect different estimators differently.     

EFFECTIVE POPULATION SIZE AND GENETIC DRIFT IN TRISTYLOUS EICHHORNIA PANICULATA (PONTEDERIACEAE)

Populations of the tristylous, annual Eichhornia paniculata are markedly differentiated with respect to frequency of mating types. This variation is associated with evolutionary changes in mating system, from predominant outcrossing to high self-fertilization. To assess the potential influence of genetic drift acting on this variation, we estimated effective population size in 10 populations from northeastern Brazil using genetic and demographic methods. Effective size (N_e) was inferred from temporal changes in allele frequency at two to eight isozyme loci and also calculated using five demographic variables: 1) the number of flowering individuals (N); 2) temporal fluctuations in N; 3) variance in flower number; 4) frequency of mating types; and 5) selfing rate. Average N_e based on isozyme data was 15.8, range 3.4–70.6, and represented a fraction (mean N_e/N = 0.106) of the census number of individuals (mean N = 762.8; range: 30.5–5,040). Temporal variation in N and variance in flower number each reduced N_e to about a half of N whereas mating type frequencies and selfing rate caused only small reductions in N_e relative to N. All estimates of N_e based on demographic variables were considerably larger than those obtained from genetic data. The two kinds of estimates were in general agreement, however, when all demographic variables were combined into a single measure. Monte Carlo simulations indicated that effective size must be fewer than about 40 for drift to overcome the frequency-dependent selection that maintains the polymorphism for mating type. Applying the average N_e/N value to 167 populations censused in northeastern Brazil indicated that 72% had effective sizes below this number. This suggests that genetic drift is likely to play a dominant role in natural populations of E. paniculata.     

A potential bias in the temporal method for estimating Ne in admixed populations under natural selection

Indirect genetic methods are frequently used to estimate the effective population size (N(e)) or effective number of breeders (N(b)) in natural populations. Although assumptions behind these methods are often violated, there have been few attempts to evaluate how accurate these estimates really are in practice. Here we investigate the influence of natural selection following a population admixture on the temporal method for estimating N(e). Our analytical and simulation results suggest that N(e) is often underestimated in this method when subpopulations differ substantially in allele frequencies and in reproductive success. The underestimation is exacerbated when true N(e) and the fraction of the low-fitness group are large. As an empirical example, we compared N(b) estimated in natural populations of steelhead trout (Oncorhynchus mykiss) using the temporal method (N(b[temp])) with estimates based on direct demographic methods (N(b[demo])) and the linkage disequilibrium method (N(b[LD])). While N(b[LD]) was generally in close agreement with N(b[demo]), N(b[temp]) was much lower in sample sets that were dominated by nonlocal hatchery fish with low reproductive success, as predicted by the analytical results. This bias in the temporal method, which arises when genes associated with a particular group of parents are selected against in the offspring sample, has not been widely appreciated before. Such situations may be particularly common when artificial propagation or translocations are used for conservation. The linkage disequilibrium method, which requires data from only one sample, is robust to this type of bias, although it can be affected by other factors.     

Temporal changes in genetic variation of north European cattle breeds

Temporal changes in genetic variation within and between 13 North European cattle breeds were evaluated using erythrocyte antigen systems and transferrin protein as genetic markers. Current data on allele frequency distributions of markers in large commercial and smaller endangered native cattle breeds were compared to data published during 1956 to 1975. Intrabreed genetic variation was quantified by conventional parameters (e.g. heterozygosity, average number of alleles per locus) and migration by the effective migration rate. The neighbour-joining dendrogram of relationships between old and present cattle populations was constructed using Nei's standard genetic distance. Variance effective population size was estimated from changes in allele frequencies over time. Comparison of old and new data indicated some significant changes in allele frequencies. In six of the breeds, a few low-frequency alleles in the old data were absent in the present samples. Heterozygosity remained stable in most breeds. The harmonic means for variance effective population size ranged between 30 and 257. Current results indicate that despite marked declines in total population sizes, North European native cattle breeds have retained a reasonably high genetic diversity. However, their genes contribute less than previously to genetic variation of Nordic production breeds. Commercial breeds do not appear to have a larger effective population size than native breeds. The present effective population sizes imply that Nordic breeds could have lost from 1 to 11% of their heterozygosity over a 20-40-year period.     

GONe: software for estimating effective population size in species with generational overlap

GONe is a user-friendly, Windows-based program for estimating effective size (N(e) ) in populations with overlapping generations. It uses the Jorde-Ryman modification to the temporal method to account for age structure in populations. This method requires estimates of age-specific survival and birth rate and allele frequencies measured in two or more consecutive cohorts. Allele frequencies are acquired by reading in genotypic data from files formatted for either GENEPOP or TEMPOFS. For each interval between consecutive cohorts, N(e) is estimated at each locus and over all loci. Furthermore, N(e) estimates are output for three different genetic drift estimators (F(s) , F(c) and F(k) ). Confidence intervals are derived from a chi-square distribution with degrees of freedom equal to the number of independent alleles. GONe has been validated over a wide range of N(e) values, and for scenarios where survival and birth rates differ between sexes, sex ratios are unequal and reproductive variances differ. GONe is freely available for download at https://bcrc.bio.umass.edu/pedigreesoftware/.     

Effective number of breeding adults in Bufo bufo estimated from age-specific variation at minisatellite loci

Estimates of the effective number of breeding adults were derived for three semi-isolated populations of the common toad Bufo bufo based on temporal (i.e. adult-progeny) variance in allele frequency for three highly polymorphic minisatellite loci. Estimates of spatial variance in allele frequency among populations and of age-specific measures of genetic variability are also described. Each population was characterized by a low effective adult breeding number ( N _b) based on a large age-specific variance in mini-satellite allele frequency. Estimates of N _b (range 21–46 for population means across three loci) were ≊ 55–230-fold lower than estimates of total adult census size. The implications of low effective breeding numbers for long-term maintenance of genetic variability and population viability are discussed relative to the species' reproductive ecology, current land-use practices, and present and historical habitat modification and loss. The utility of indirect measures of population parameters such as N _b and N _e based on time-series data of minisatellite allele frequencies is discussed relative to similar measures estimated from commonly used genetic markers such as protein allozymes.     

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.     

A metapopulation perspective on genetic diversity and differentiation in partially self-fertilizing plants

Abstract.— Partial self-fertilization is common in higher plants. Mating system variation is known to have important consequences for how genetic variation is distributed within and among populations. Selfing is known to reduce effective population size, and inbreeding species are therefore expected to have lower levels of genetic variation than comparable out crossing taxa. However, several recent empirical studies have shown that reductions in genetic diversity within populations of inbreeding species are far greater than the expected reductions based on the reduced effective population size. Two different processes have been argued to cause these patterns, selective sweeps (or hitchhiking) and background selection. Both are expected to be most effective in reducing genetic variation in regions of low recombination rates. Selfing is known to reduce the effective recombination rate, and inbreeding taxa are thus thought to be particularly vulnerable to the effects of hitchhiking or background selection. Here I propose a third explanation for the lower-than-expected levels of genetic diversity within populations of selfing species; recurrent extinctions and recolonizations of local populations, also known as metapopulation dynamics. I show that selfing in a metapopulation setting can result in large reductions in genetic diversity within populations, far greater than expected based the lower effective population size inbreeding species is expected to have. The reason for this depends on an interaction between selfing and pollen migration.     

Variation in Outcrossing Rates in Eichhornia paniculata: Temporal Changes in Populations of Contrasting Style Morph Structure

Abstract Surveys of mating-system parameters in populations of the annual, self-compatible, tristylous, emergent aquatic, Eichhornia paniculata (Pontederiaceae) from N.E. Brazil and Jamaica have indicated that the species exhibits a wide range of outcrossing rates. To investigate whether temporal variation in outcrossing rate was also a feature of populations, open-pollinated families were sampled from five populations of contrasting style morph structure from N.E. Brazil over three consecutive years (1987–1989). Multilocus estimates of outcrossing rate ( t ) were obtained from assays of isozyme polymorphisms using starch gel electrophoresis. There was significant variation both among populations and between years in the frequency of outcrossing. Outcrossing in three tristylous populations was high ( t > 0.80), with relatively small fluctuations occurring over the three-year sampling period. In contrast, in a dimorphic and monomorphic population considerable self-fertilization occurred and the frequency of outcrossing declined significantly from 1987 to 1989 in both populations. In the dimorphic population, increased selfing was associated with a marked reduction in population size and an increase in the frequency of selfing variants of the mid-styled morph. The significance of temporal variation in outcrossing frequency in plant populations is discussed in relation to its effect on population genetic structure and recent models of mating-system evolution.