Estimating the ratio of effective to actual size of an age‐structured population from individual demographic data

The effective population size is a central concept for understanding evolutionary processes in a finite population. We employ Fisher's reproductive value to estimate the ratio of effective to actual population size for an age‐structured population with two sexes using random samples of individual vital rates. The population may be subject to environmental stochasticity affecting the vital rates. When the mean sex ratio at birth is known, improved efficiency is obtained by utilizing the records of total number of offspring rather than considering separately female and male offspring. We also show how to incorporate uncertain paternity.     

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 size of two feral domestic cat populations (Felis catus L): effect of the mating system

A variety of behavioural traits have substantial effects on the gene dynamics and genetic structure of local populations. The mating system is a plastic trait that varies with environmental conditions in the domestic cat (Felis catus) allowing an intraspecific comparison of the impact of this feature on genetic characteristics of the population. To assess the potential effect of the heterogenity of males' contribution to the next generation on variance effective size, we applied the ecological approach of Nunney & Elam (1994) based upon a demographic and behavioural study, and the genetic 'temporal methods' of Waples (1989) and Berthier et al. (2002) using microsatellite markers. The two cat populations studied were nearly closed, similar in size and survival parameters, but differed in their mating system. Immigration appeared extremely restricted in both cases due to environmental and social constraints. As expected, the ratio of effective size to census number (Ne/N) was higher in the promiscuous cat population (harmonic mean = 42%) than in the polygynous one (33%), when Ne was calculated from the ecological method. Only the genetic results based on Waples' estimator were consistent with the ecological results, but failed to evidence an effect of the mating system. Results based on the estimation of Berthier et al. (2002) were extremely variable, with Ne sometimes exceeding census size. Such low reliability in the genetic results should retain attention for conservation purposes.     

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.     

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

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

Sensitivity analysis of effective population size to demographic parameters in house sparrow populations

The ratio between the effective and the census population size, , is an important measure of the long‐term viability and sustainability of a population. Understanding which demographic processes that affect most will improve our understanding of how genetic drift and the probability of fixation of alleles is affected by demography. This knowledge may also be of vital importance in management of endangered populations and species. Here, we use data from 13 natural populations of house sparrow (Passer domesticus) in Norway to calculate the demographic parameters that determine . Using the global variance‐based Sobol’ method for the sensitivity analyses, we found that was most sensitive to demographic variance, especially among older individuals. Furthermore, the individual reproductive values (that determine the demographic variance) were most sensitive to variation in fecundity. Our results draw attention to the applicability of sensitivity analyses in population management and conservation. For population management aiming to reduce the loss of genetic variation, a sensitivity analysis may indicate the demographic parameters towards which resources should be focused. The result of such an analysis may depend on the life history and mating system of the population or species under consideration, because the vital rates and sex–age classes that is most sensitive to may change accordingly.     

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.     

Monitoring the effective population size of a brown bear (Ursus arctos) population using new single-sample approaches

The effective population size (N(e) ) could be the ideal parameter for monitoring populations of conservation concern as it conveniently summarizes both the evolutionary potential of the population and its sensitivity to genetic stochasticity. However, tracing its change through time is difficult in natural populations. We applied four new methods for estimating N(e) from a single sample of genotypes to trace temporal change in N(e) for bears in the Northern Dinaric Mountains. We genotyped 510 bears using 20 microsatellite loci and determined their age. The samples were organized into cohorts with regard to the year when the animals were born and yearly samples with age categories for every year when they were alive. We used the Estimator by Parentage Assignment (EPA) to directly estimate both N(e) and generation interval for each yearly sample. For cohorts, we estimated the effective number of breeders (N(b) ) using linkage disequilibrium, sibship assignment and approximate Bayesian computation methods and extrapolated these estimates to N(e) using the generation interval. The N(e) estimate by EPA is 276 (183-350 95% CI), meeting the inbreeding-avoidance criterion of N(e) > 50 but short of the long-term minimum viable population goal of N(e) > 500. The results obtained by the other methods are highly consistent with this result, and all indicate a rapid increase in N(e) probably in the late 1990s and early 2000s. The new single-sample approaches to the estimation of N(e) provide efficient means for including N(e) in monitoring frameworks and will be of great importance for future management and conservation.     

Genetic consequences of polygyny and social structure in an Indian fruit bat, Cynopterus sphinx. II. Variance in male mating success and effective population size

Variance in reproductive success is a primary determinant of genetically effective population size (Ne), and thus has important implications for the role of genetic drift in the evolutionary dynamics of animal taxa characterized by polygynous mating systems. Here we report the results of a study designed to test the hypothesis that polygynous mating results in significantly reduced Ne in an age-structured population. This hypothesis was tested in a natural population of a harem-forming fruit bat, Cynopterus sphinx (Chiroptera: Pteropodidae), in western India. The influence of the mating system on the ratio of variance Ne to adult census number (N) was assessed using a mathematical model designed for age-structured populations that incorporated demographic and genetic data. Male mating success was assessed by means of direct and indirect paternity analysis using 10-locus microsatellite genotypes of adults and progeny from two consecutive breeding periods (n = 431 individually marked bats). Combined results from both analyses were used to infer the effective number of male parents in each breeding period. The relative proportion of successfully reproducing males and the size distribution of paternal sibships comprising each offspring cohort revealed an extremely high within-season variance in male mating success (up to 9.2 times higher than Poisson expectation). The resultant estimate of Ne/N for the C. sphinx study population was 0.42. As a result of polygynous mating, the predicted rate of drift (1/2Ne per generation) was 17.6% higher than expected from a Poisson distribution of male mating success. However, the estimated Ne/N was well within the 0.25-0.75 range expected for age-structured populations under normal demographic conditions. The life-history schedule of C. sphinx is characterized by a disproportionately short sexual maturation period scaled to adult life span. Consequently, the influence of polygynous mating on Ne/N is mitigated by the extensive overlap of generations. In C. sphinx, turnover of breeding males between seasons ensures a broader sampling of the adult male gamete pool than expected from the variance in mating success within a single breeding period.     

An empirical test of the estimation of historical effective population size using Drosophila melanogaster

The availability of a large number of high-density markers (SNPs) allows the estimation of historical effective population size (N_e) from linkage disequilibrium between loci. A recent refinement of methods to estimate historical N_e from the recent past has been shown to be rather accurate with simulation data. The method has also been applied to real data for numerous species. However, the simulation data cannot encompass all the complexities of real genomes, and the performance of any estimation method with real data is always uncertain, as the true demography of the populations is not known. Here, we carried out an experimental design with Drosophila melanogaster to test the method with real data following a known demographic history. We used a population maintained in the laboratory with a constant census size of about 2800 individuals and subjected the population to a drastic decline to a size of 100 individuals. After a few generations, the population was expanded back to the previous size and after a few further generations again expanded to twice the initial size. Estimates of historical N_e were obtained with the software GONE both for autosomal and X chromosomes from samples of 17 individuals sequenced for the whole genome. Estimates of the historical effective size were able to infer the patterns of changes that occurred in the populations showing generally good performance of the method. We discuss the limitations of the method and the application of the software carried out so far.     

Inbreeding effective population size under some artificial selection schemes

Summary It is well known that truncation selection is the most efficient form of directional selection in terms of changing gene frequency. In this paper we show circumstances where truncation selection followed by a balanced mating generates inbreeding effective population size smaller than that generated by a selection that assigns mating frequencies to individuals according to their breeding values, where both selection schemes give the same expected performance of selected individuals (selection differential). Breeding values of selected individuals and the weight used to determine mating frequencies are assumed to be linearly distributed on a performance scales, x. To assign mating frequencies to the individuals in the weighting system, the selected individuals are grouped using a constant , and ith group in the interval x_i, x_i + . With small number of groups, say 2 or 3, the weighting system in general generates inbreeding effective population size that is larger than that generated by a truncation selection. As the number of the groups increases, truncation selection generates larger effective numbers.     

Effective size of density‐dependent two‐sex populations: the effect of mating systems

Density dependence in vital rates is a key feature affecting temporal fluctuations of natural populations. This has important implications for the rate of random genetic drift. Mating systems also greatly affect effective population sizes, but knowledge of how mating system and density regulation interact to affect random genetic drift is poor. Using theoretical models and simulations, we compare N_e in short‐lived, density‐dependent animal populations with different mating systems. We study the impact of a fluctuating, density‐dependent sex ratio and consider both a stable and a fluctuating environment. We find a negative relationship between annual N_e/N and adult population size N due to density dependence, suggesting that loss of genetic variation is reduced at small densities. The magnitude of this decrease was affected by mating system and life history. A male‐biased, density‐dependent sex ratio reduces the rate of genetic drift compared to an equal, density‐independent sex ratio, but a stochastic change towards male bias reduces the N_e/N ratio. Environmental stochasticity amplifies temporal fluctuations in population size and is thus vital to consider in estimation of effective population sizes over longer time periods. Our results on the reduced loss of genetic variation at small densities, particularly in polygamous populations, indicate that density regulation may facilitate adaptive evolution at small population sizes.     

Population genetic structure and effective population size of ayu (Plecoglossus altivelis), an amphidromous fish

The temporal and spatial population genetic structure of ayu Plecoglossus altivelis (Salmoniformes: Plecoglossidae), an amphidromous fish, was examined using analysis of variation at six microsatellite DNA loci. Intracohort genetic diversities, as measured by the number of alleles and heterozygosity, were similar among six cohorts (2001–2006) within a population (Nezugaseki River), with the mean number of alleles per cohort ranging from 11·0 to 12·5 and the expected heterozygosity ranging from 0·74 to 0·77. Intrapopulational genetic diversities were also similar across the three studied populations along the 50 km coast, with the mean number of alleles and the expected heterozygosity ranging from 11·33 to 11·67 and from 0·75 to 0·76, respectively. The authors observed only one significant difference in pair-wise population differentiation ( F _ST-value) between the cohorts within a population and among three populations. Estimates of the effective population size ( N _e) based on maximum-likelihood method yielded small values (ranging from 94·8 to 135·5), whereas census population size ranged from c. 4800 to 24 000. As a result, the ratio of annual effective population sizes to census population size ( N _e/ N ) ranged from 0·004 to 0·023. These estimates of N _e/ N agree more closely with estimates for marine fishes than that of the larger estimates for freshwater fishes. The present study suggests that ayu which is highly fecund and shows low survival during the early life stages is also characterized by having low value of N _e/ N , similar to marine species with a pelagic life cycle.     

Small effective population size in the long-toed salamander

The effective population sizes (Ne) of six populations of the long-toed salamander (Ambystoma macrodactylum) from Montana and Idaho, USA were estimated from allozyme data from samples collected in 1978, 1996 and 1997 using the temporal allele frequency method. Five of the six estimates ranged from 23 to 207 (mean = 123 +/- 79); one estimate was indistinguishable from infinity. In order to infer the actual Ne of salamander populations, we compared the frequency distribution of our observed Ne estimates with distributions obtained from simulated populations of known Ne. Our observed Ne estimate distribution was consistent with distributions from simulated populations with Ne values of 10, 25, and 50, suggesting an actual Ne for each of the six salamander populations of less than 100. This Ne estimate agrees with most other Ne estimates for amphibians. We conclude by discussing the conservation implications of small Ne values in amphibians in the context of increasing isolation of populations due to habitat fragmentation.     

Gene genealogies when the sample size exceeds the effective size of the population

We study the properties of gene genealogies for large samples using a continuous approximation introduced by R. A. Fisher. We show that the major effect of large sample size, relative to the effective size of the population, is to increase the proportion of polymorphisms at which the mutant type is found in a single copy in the sample. We derive analytical expressions for the expected number of these singleton polymorphisms and for the total number of polymorphic, or segregating, sites that are valid even when the sample size is much greater than the effective size of the population. We use simulations to assess the accuracy of these predictions and to investigate other aspects of large-sample genealogies. Lastly, we apply our results to some data from Pacific oysters sampled from British Columbia. This illustrates that, when large samples are available, it is possible to estimate the mutation rate and the effective population size separately, in contrast to the case of small samples in which only the product of the mutation rate and the effective population size can be estimated.     

Interannual variation in effective number of breeders and estimation of effective population size in long‐lived iteroparous lake sturgeon (Acipenser fulvescens)

Quantifying interannual variation in effective adult breeding number (N_b) and relationships between N_b, effective population size (N_e), adult census size (N) and population demographic characteristics are important to predict genetic changes in populations of conservation concern. Such relationships are rarely available for long‐lived iteroparous species like lake sturgeon (Acipenser fulvescens). We estimated annual N_b and generational N_e using genotypes from 12 microsatellite loci for lake sturgeon adults (n = 796) captured during ten spawning seasons and offspring (n = 3925) collected during larval dispersal in a closed population over 8 years. Inbreeding and variance N_b estimated using mean and variance in individual reproductive success derived from genetically identified parentage and using linkage disequilibrium (LD) were similar within and among years (interannual range of N_b across estimators: 41–205). Variance in reproductive success and unequal sex ratios reduced N_b relative to N on average 36.8% and 16.3%, respectively. Interannual variation in N_b/N ratios (0.27–0.86) resulted from stable N and low standardized variance in reproductive success due to high proportions of adults breeding and the species' polygamous mating system, despite a 40‐fold difference in annual larval production across years (437–16 417). Results indicated environmental conditions and features of the species' reproductive ecology interact to affect demographic parameters and N_b/N. Estimates of N_e based on three single‐sample estimators, including LD, approximate Bayesian computation and sibship assignment, were similar to annual estimates of N_b. Findings have important implications concerning applications of genetic monitoring in conservation planning for lake sturgeon and other species with similar life histories and mating systems.     

Generation time and effective population size in Polar Eskimos

North Greenland Polar Eskimos are the only hunter-gatherer population, to our knowledge, who can offer precise genealogical records spanning several generations. This is the first report from Eskimos on two key parameters in population genetics, namely, generation time (T) and effective population size (Ne). The average mother-daughter and father-son intervals were 27 and 32 years, respectively, roughly similar to the previously published generation times obtained from recent agricultural societies across the world. To gain an insight for the generation time in our distant ancestors, we calculated maternal generation time for two wild chimpanzee populations. We also provide the first comparison among three distinct approaches (genealogy, variance and life table methods) for calculating Ne, which resulted in slightly differing values for the Eskimos. The ratio of the effective to the census population size is estimated as 0.6-0.7 for autosomal and X-chromosomal DNA, 0.7-0.9 for mitochondrial DNA and 0.5 for Y-chromosomal DNA. A simulation of alleles along the genealogy suggested that Y-chromosomal DNA may drift a little faster than mitochondrial DNA in this population, in contrast to agricultural Icelanders. Our values will be useful not only in prehistoric population inference but also in understanding the shaping of our genome today.     

Spatiotemporal relationship between adult census size and genetic population size across a wide population size gradient

Adult census population size (N) and effective number of breeders (N_b) are highly relevant for designing effective conservation strategies. Both parameters are often challenging to quantify, however, making it of interest to determine whether one parameter can be generalized from the other. Yet, the spatiotemporal relationship between N and N_b has not been well characterized empirically in many taxa. We analysed this relationship for 5–7 consecutive years in twelve brook trout populations varying greatly in N (49‐10032) and N_b (3‐567) and identified major environmental variables affecting the two parameters. N or habitat size alone explained 47–57% of the variance in N_b, and N_b was strongly correlated with effective population size. The ratio N_b/N ranged from 0.01 to 0.45 and increased at small N or following an annual decrease in N, suggesting density‐dependent constraints on N_b. We found no evidence for a consistent, directional difference between variability in N_b and/or N_b/N among small and large populations; however, small populations had more varying temporal variability in N_b/N ratios than large populations. Finally, N_b and N_b/N were 2.5‐ and 2.3‐fold more variable among populations than temporally within populations. Our results demonstrate a clear linkage between demographic and evolutionary parameters, suggesting that N_b could be used to approximate N (or vice versa) in natural populations. Nevertheless, using one variable to infer the other to monitor trends within populations is less recommended, perhaps even less so in small populations given their less predictable N_b vs. N dynamics.     

The influence of persistent individual differences and age at maturity on effective population size

Ratios of effective populations size, N(e), to census population size, N, are used as a measure of genetic drift in populations. Several life-history parameters have been shown to affect these ratios, including mating system and age at sexual maturation. Using a stochastic matrix model, we examine how different levels of persistent individual differences in mating success among males may affect N(e)/N, and how this relates to generation time. Individual differences of this type are shown to cause a lower N(e)/N ratio than would be expected when mating is independent among seasons. Examining the way in which age at maturity affects N(e)/N, we find that both the direction and magnitude of the effect depends on the survival rate of juveniles in the population. In particular, when maturation is delayed, lowered juvenile survival causes higher levels of genetic drift. In addition, predicted shifts in N(e)/N with changing age at maturity are shown to be dependent on which of the commonly used definitions of census population size, N, is employed. Our results demonstrate that patterns of mating success, as well as juvenile survival probabilities, have substantial effects on rates of genetic drift.