Evaluating the effect of stage-specific survivorship on the N(e)/N ratio

Evaluating effective population size (Ne) and the effective size to census size ratio (Ne/N) in species with Type III survivorship curves is complicated when key demographic parameters [mean (k macro) and variance (V(k)) of family size] are measured during early life stages. The method of Crow & Morton (1955) for scaling demographic data collected at a juvenile stage to expected values at adulthood is extended to consider sequential episodes of random and family correlated survival. Results show the following: (i) The order in which the episodes of random and family-correlated survival occur does not affect N(e) or N(e)/N; (ii) If a population experiences an episode of family-correlated survival, N(e)/N scaled to its expected value in a population of constant size (k macro= 2) is simply the survival rate during the family-correlated stage. If multiple such stages occur, scaled N(e)/N is the product of the survivals during all family-correlated life stages; (iii) Under the assumption of random post-enumeration survival, adjusting the variance effective size to its expected value at k macro= 2 is equivalent to computing the inbreeding effective size at the earlier life stage. Application to experimental data for hatchery populations of Pacific salmon (Oncorhynchus spp.) indicates that nonrandom survival during the marine phase led to estimated reductions in effective size of 0-62 (mean 19) in 12 different cohorts. This approach can provide insights into N(e)/N in highly fecund species, including some marine species in which N(e) has been estimated to be several orders of magnitude less than N.     

Reproductive success and effective population size in woodrats (Neotoma macrotis)

Discrepancies between the census size and the genetically effective size of populations (N(e)) can be caused by a number of behavioural and demographic factors operating within populations. Specifically, strong skew in male reproductive success, as would be expected in a polygynous mating system, could cause a substantial decrease in N(e) relative to census size. Because the mating system of Neotoma macrotis had previously been described as one nearing harem polygyny, I examined the distribution of reproductive success and genetic variation within a population of this species. Combining genetic data and three years of field observations, I show that variance in reproductive success does not deviate from poisson expectations within either sex and variance in success is similar between the sexes. Furthermore, both males and females had multiple partners across litters in addition to some evidence of multiple paternity within litters. Despite a lack of strong skew in reproductive success, an estimate of N(e) based on a number of demographic parameters suggests that the ratio of N(e)/N in this population is 0.48. Although the ratio of N(e)/N suggests that the population is experiencing higher rates of genetic drift than would be expected based on census size alone, the population maintains high levels of genetic diversity. Estimates of neighbourhood size and patterns of recruitment to the study site suggest that immigration plays an important role in this population and may contribute to the maintenance of high levels of genetic diversity.     

Effective population size associated with self-fertilization: lessons from temporal changes in allele frequencies in the selfing annual Medicago truncatula

Despite its significance in evolutionary and conservation biology, few estimates of effective population size (N(e)) are available in plant species. Self-fertilization is expected to affect N(e), through both its effect on homozygosity and population dynamics. Here, we estimated N(e) using temporal variation in allele frequencies for two contrasted populations of the selfing annual Medicago truncatula: a large and continuous population and a subdivided population. Estimated N(e) values were around 5-10% of the population census size suggesting that other factors than selfing must contribute to variation in allele frequencies. Further comparisons between monolocus allelic variation and changes in the multilocus genotypic composition of the populations show that the local dynamics of inbred lines can play an important role in the fluctuations of allele frequencies. Finally, comparing N(e) estimates and levels of genetic variation suggest that H(e) is a poor estimator of the contemporaneous variance effective population size.     

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.     

Genetic effective size is three orders of magnitude smaller than adult census size in an abundant,Estuarine-dependent marine fish (Sciaenops ocellatus)

Using eight microsatellite loci and a variety of analytical methods, we estimated genetic effective size (N(e)) of an abundant and long-lived marine fish species, the red drum (Sciaenops ocellatus), in the northern Gulf of Mexico (Gulf). The ratio N(e)/N, where short-term variance N(e) was estimated via the temporal method from shifts in allele-frequency data over four cohorts and where N reflected a current estimate of adult census size in the northern Gulf, was approximately 0.001. In an idealized population, this ratio should approximate unity. The extraordinarily low value of N(e)/N appears to arise from high variance in individual reproductive success and perhaps more importantly from variance in productivity of critical spawning and nursery habitats located in spatially discrete bays and estuaries throughout the northern Gulf. An estimate of N(e) based on a coalescent approach, which measures long-term, inbreeding effective size, was four orders of magnitude lower than the estimate of current census size, suggesting that factors presently driving N(e)/N to low values among red drum in the northern Gulf may have operated similarly in the past. Models that predict N(e)/N exclusively from demographic and life-history features will seriously overestimate N(e) if variance in reproductive success and variance in productivity among spatially discrete demes is underestimated. Our results indicate that these variances, especially variance in productivity among demes, must be large for red drum. Moreover, our study indicates that vertebrate populations with enormous adult census numbers may still be at risk relative to decline and extinction from genetic factors.     

Effective size of subpopulations in early-run sockeye salmon Oncorhynchus nerka from Azabach'e Lake (Kamchatka): the effect of relative reproductive success of different-year cohorts

The effect of variation in reproductive success of cohorts of different year of birth (within generation) on the effective subpopulation (breeding group) size in early-run sockeye salmon Oncorhynchus nerka from Azabach'e Lake (Kamchatka). The annual variation in census size and overlapping of year classes reduced the ratio of the effective subpopulation size to the census size by 7 to 88% in different subpopulations. The total effect of the variance of reproductive success in individual years and the variance of reproductive success of different cohorts reduced the effective size/census size ratio by 68-96%.     

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

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

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.     

Large variance in reproductive success and the Ne/N ratio

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

Determinants of effective population size for loci with different modes of inheritance

Here we report an assessment of the determinants of effective population size (N(e)) in species with overlapping generations. Specifically, we used a stochastic demographic model to investigate the influence of different life-history variables on N(e)/N (where N = population census number) and the influence of sex differences in life-history variables on N(e) for loci with different modes of inheritance. We applied an individual-based modeling approach to two datasets: one from a natural population of savannah baboons (Papio cynocephalus) in the Amboseli basin of southern Kenya and one from a human tribal population (the Gainj of Papua New Guinea). Simulation-based estimates of N(e)/N averaged 0.329 for the Amboseli baboon population (SD = 0.116, 95% CI = 0.172 - 0.537) and 0.786 for the Gainj (SD = 0.184, 95% CI = 0.498 - 1.115). Although variance in male fitness had a substantial impact on N(e)/N in each of the two primate populations, ratios of N(e) values for autosomal and sex-linked loci exhibited no significant departures from Poisson-expected values. In each case, similarities in sex-specific N(e) values were attributable to the unexpectedly high variance in female fitness. Variance in male fitness resulted primarily from age-dependent variance in reproductive success, whereas variance in female fitness resulted primarily from stochastic variance in survival during the reproductive phase.     

Regional differences in responses of chinook salmon populations to large-scale climatic patterns

Aim To quantitatively explore the extent to which many different populations of the same species (chinook salmon, Oncorhynchus tshawytscha) respond cohesively to a common large‐scale climatic trend. Location The Columbia River basin of the northwestern US. Methods I used regression analyses to describe the downward trend in population growth (number of recruits per spawning adult) for thirteen populations of chinook salmon distributed among three geographical regions: Snake River, Upper Columbia River and Middle Columbia River. I then used residuals from these regressions to characterize per capita productivity for each brood year. Positive residuals indicated productivity higher than that predicted by the time series, while negative residuals revealed years in which productivity was lower than predicted. I next used analysis of covariance (ancova ) to test the null hypothesis that associations between ocean/climate conditions and deviations from predicted population growth did not vary among geographical regions. All ancova s used residuals generated from the regressions as the response variable, geographical region as the main effect, and climatic condition [characterized by the Pacific Decadal Oscillation index (PDO)] as the covariate. A major climate shift occurred in 1977, and because the association of the PDO with salmon productivity varied between the pre‐ and post‐1977 climate regimes, I analysed data from the two regimes separately. Results There were marked impacts of climate on salmon production that varied among geographical regions and between decade‐scale climate regimes. During the pre‐1977 climate regime, productivity of salmon populations from the Snake River tended to exceed expectations (i.e. residuals were positive) when values of the PDO were negative. In contrast, this pattern was not evident in populations from the upper or middle Columbia Rivers. During the post‐1977 regime when ocean productivity was generally lower, the association of the PDO with salmon productivity changed – productivity tended to fall short of expectations (i.e. residuals were negative) when values of the PDO were negative. Main conclusions Understanding the linkages between salmon populations and climate is critical as managers attempt to preserve threatened salmon populations in the face of both natural or human‐induced climate variation and the litany of human activities affecting salmon. An important step in this understanding is the recognition that the response to ocean/climate change by salmon populations of the same species and river basin is not necessarily homogeneous.     

Census (N C) and genetically effective (N e) population size in a lake-resident population of brown trout Salmo trutta

Census (N(C)) and effective population size (N(e)) were estimated for a lake-resident population of brown trout Salmo trutta as 576 and 63, respectively. The point estimate of the ratio of effective to census population size (N(e):N(C)) for this population is 0.11 with a range of 0.06-0.26, suggesting that N(e):N(C) ratio for lake-resident populations agree more with estimates for fishes with anadromous life histories than the small ratios observed in many marine fishes.     

Mitochondrial mutations may drive Y chromosome evolution

The human Y chromosome contains very low levels of nucleotide variation. It has been variously hypothesized that this invariance reflects historic reductions in the human male population, a very recent common ancestry, a slow rate of molecular evolution, an inability to evolve adaptively, or frequent selective sweeps acting on genes borne on the Y chromosome. We propose an alternative theory in which human Y chromosome evolution is driven by mutations in the maternally inherited mitochondrial genome, which impair male fertility and ultimately lead to a reduction in the effective population size (N(e)) and consequently the variability of the Y chromosome.     

Effective size of a wild salmonid population is greatly reduced by hatchery supplementation

Many declining and commercially important populations are supplemented with captive-born individuals that are intentionally released into the wild. These supplementation programs often create large numbers of offspring from relatively few breeding adults, which can have substantial population-level effects. We examined the genetic effects of supplementation on a wild population of steelhead (Oncorhynchus mykiss) from the Hood River, Oregon, by matching 12 run-years of hatchery steelhead back to their broodstock parents. We show that the effective number of breeders producing the hatchery fish (broodstock parents; N(b)) was quite small (harmonic mean N(b)=25 fish per brood-year vs 373 for wild fish), and was exacerbated by a high variance in broodstock reproductive success among individuals within years. The low N(b) caused hatchery fish to have decreased allelic richness, increased average relatedness, more loci in linkage disequilibrium and substantial levels of genetic drift in comparison with their wild-born counterparts. We also documented a substantial Ryman-Laikre effect whereby the additional hatchery fish doubled the total number of adult fish on the spawning grounds each year, but cut the effective population size of the total population (wild and hatchery fish combined) by nearly two-thirds. We further demonstrate that the Ryman-Laikre effect is most severe in this population when (1) >10% of fish allowed onto spawning grounds are from hatcheries and (2) the hatchery fish have high reproductive success in the wild. These results emphasize the trade-offs that arise when supplementation programs attempt to balance disparate goals (increasing production while maintaining genetic diversity and fitness).     

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.     

Comparative estimation of effective population sizes and temporal gene flow in two contrasting population systems

Estimation of effective population sizes (N(e)) and temporal gene flow (N(e)m, m) has many implications for understanding population structure in evolutionary and conservation biology. However, comparative studies that gauge the relative performance of N(e), N(e)m or m methods are few. Using temporal genetic data from two salmonid fish population systems with disparate population structure, we (i) evaluated the congruence in estimates and precision of long- and short-term N(e), N(e)m and m from six methods; (ii) explored the effects of metapopulation structure on N(e) estimation in one system with spatiotemporally linked subpopulations, using three approaches; and (iii) determined to what degree interpopulation gene flow was asymmetric over time. We found that long-term N(e) estimates exceeded short-term N(e) within populations by 2-10 times; the two were correlated in the system with temporally stable structure (Atlantic salmon, Salmo salar) but not in the highly dynamic system (brown trout, Salmo trutta). Four temporal methods yielded short-term N(e) estimates within populations that were strongly correlated, and these were higher but more variable within salmon populations than within trout populations. In trout populations, however, these short-term N(e) estimates were always lower when assuming gene flow than when assuming no gene flow. Linkage disequilibrium data generally yielded short-term N(e) estimates of the same magnitude as temporal methods in both systems, but the two were uncorrelated. Correlations between long- and short-term geneflow estimates were inconsistent between methods, and their relative size varied up to eightfold within systems. While asymmetries in gene flow were common in both systems (58-63% of population-pair comparisons), they were only temporally stable in direction within certain salmon population pairs, suggesting that gene flow between particular populations is often intermittent and/or variable. Exploratory metapopulation N(e) analyses in trout demonstrated both the importance of spatial scale in estimating N(e) and the role of gene flow in maintaining genetic variability within subpopulations. Collectively, our results illustrate the utility of comparatively applying N(e), N(e)m and m to (i) tease apart processes implicated in population structure, (ii) assess the degree of continuity in patterns of connectivity between population pairs and (iii) gauge the relative performance of different approaches, such as the influence of population subdivision and gene flow on N(e) estimation. They further reiterate the importance of temporal sampling replication in population genetics, the value of interpreting N(e)or m in light of species biology, and the need to address long-standing assumptions of current N(e), N(e)m or m models more explicitly in future research.     

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.     

Genetic effective size of a wild primate population: influence of current and historical demography

A comprehensive assessment of the determinants of effective population size (N(e)) requires estimates of variance in lifetime reproductive success and past changes in census numbers. For natural populations, such information can be best obtained by combining longitudinal data on individual life histories and genetic marker-based inferences of demographic history. Independent estimates of the variance effective size (N(ev), obtained from life-history data) and the inbreeding effective size (N((eI), obtained from genetic data) provide a means of disentangling the effects of current and historical demography. The purpose of this study was to assess the demographic determinants of N(e) in one of the most intensively studied natural populations of a vertebrate species: the population of savannah baboons (Papio cynocephalus) in the Amboseli Basin, southern Kenya. We tested the hypotheses that N(eV) < N < N(eI) (where N = population census number) due to a recent demographic bottleneck. N(eV) was estimated using a stochastic demographic model based on detailed life-history data spanning a 28-year period. Using empirical estimates of age-specific rates of survival and fertility for both sexes, individual-based simulations were used to estimate the variance in lifetime reproductive success. The resultant values translated into an N(eV)/N estimate of 0.329 (SD = 0.116, 95% CI = 0.172-0.537). Historical N(eI), was estimated from 14-locus microsatellite genotypes using a coalescent-based simulation model. Estimates of N(eI) were 2.2 to 7.2 times higher than the contemporary census number of the Amboseli baboon population. In addition to the effects of immigration, the disparity between historical N(eI) and contemporary N is likely attributable to the time lag between the recent drop in census numbers and the rate of increase in the average probability of allelic identity-by-descent. Thus, observed levels of genetic diversity may primarily reflect the population's prebottleneck history rather than its current demography.     

Annual changes in the population size of the salmon louse Lepeophtheirus salmonis (Copepoda: Caligidae) on high-seas Pacific Salmon (Oncorhynchus spp.), and relationship to host abundance

The population size of the salmon louse, Lepeophtheirus salmonis, was monitored annually in the summers of 1991–1997 by examining six species of Pacific salmon (Oncorhynchus spp.) caught by surface long-lines in oceanic offshore waters of the North Pacific Ocean and Bering Sea. The annual copepod population size on all salmonids caught was estimated by combining the calculated number of copepods carrying on each salmonid species. The copepod population fluctuated markedly from year to year, which resulted largely from marked annual changes in abundance of pink salmon (O. gorbuscha). Since pink salmon were most frequently and heavily infected and since their abundance changed every year, the copepod population was high in the years when this salmonid species was abundant, but low when it was rare. On the contrary, chum salmon (O. keta) did not show high prevalence and intensity of infection, but the annual abundance of this host species was consistently high, i.e. chum salmon carried many copepods every year. Copepods on other salmonid species (sockeye salmon O. nerka, coho salmon O. kisutch, chinook salmon O. tshawytscha, and steelhead trout O. mykiss) constantly formed a small percentage of the total copepod population. Both chum and pink salmon are the most important hosts in terms of their substantial contribution to support the copepod population, but the importance as hosts of each species is definitely different between the species. Chum salmon is a stable important host supporting the copepod population at a relatively high level every year, while the number of copepods on pink salmon annually exhibits marked fluctuations, and this salmonid species is regarded as an unstable important host.     

The context-dependent effect of multiple paternity on effective population size

Effective population size (N(e)) is important because it describes how evolutionary forces will affect a population. The effect of multiple sires per female on N(e) has been the subject of some debate, at the crux of which is the effects of monandry and multiple-paternity (MP) on male variance in reproductive success. In both mating systems, females mate with several males over their lifetimes, but sire offspring with one male at a time in the former and have several sires per clutch in the latter. First, I theoretically show that whether the annual male variance in reproductive success in an MP population is greater or less than that of a monandrous population depends on the distributions of within-clutch paternity. Then, I simulated different distributions of within-clutch paternity under a range of parameters that characterize natural populations to show that an MP population can have an N(e) smaller or larger than that of a monandrous population with otherwise equal dynamics. The N(e(MP)):N(e(Monandry)) ratio increased with mating frequency and female variance in reproductive success, was equalized by long generation times, and was affected by the distribution of within-clutch paternities. The results of this model provide a unifying framework for the debate.