Estimating demographic contributions to effective population size in an age-structured wild population experiencing environmental and demographic stochasticity.

[ Proc. R. Soc. B 281 , 20132976. (22 February 2014; Published online 8 January 2014) ([doi:10.1098/rspb.2013.2976][2])][2] Concerns with the original article [[1][2]] were originally brought to light by Prof Einar Arnason and his concerns are outlined here [[2][3]]. Moreover, there were errors in

The genetically unique population of muskellunge Esox masquinongy inhabiting Shoepack Lake in Voyageurs National Park, Minnesota, is potentially at risk for loss of genetic variability and long-term viability. Shoepack Lake has been subject to dramatic surface area changes from the construction of an outlet dam by beavers Castor canadensis and its subsequent failure. We simulated the long-term dynamics of this population in response to recruitment variation, increased exploitation, and reduced habitat area. We then estimated the effective population size of the simulated population and evaluated potential threats to long-term viability, based on which we recommend management actions to help preserve the long-term viability of the population. Simulations based on the population size and habitat area at the beginning of a companion study resulted in an effective population size that was generally above the threshold level for risk of loss of genetic variability, except when fishing mortality was increased. Simulations based on the reduced habitat area after the beaver dam failure and our assumption of a proportional reduction in population size resulted in an effective population size that was generally below the threshold level for risk of loss of genetic variability. Our results identified two potential threats to the long-term viability of the Shoepack Lake muskellunge population, reduction in habitat area and exploitation. Increased exploitation can be prevented through traditional fishery management approaches such as the adoption of no-kill, barbless hook, and limited entry regulations. Maintenance of the greatest possible habitat area and prevention of future habitat area reductions will require maintenance of the outlet dam built by beavers. Our study should enhance the long-term viability of the Shoepack Lake muskellunge population and illustrates a useful approach for other unique populations.

We calculated a genetically based minimum viable population size of the red-cockaded woodpecker (Picoides borealis) using a formula derived from Hill (1972) and life history data from a long-term study. Based on published criteria for maintenance of genetic variability, a red-cockaded woodpecker population must contain 509 breeding pairs to be considered viable. It is likely that no existing population contains 509 breeding pairs. Genetically based estimates of population viability may not be valid, but if they are adopted as in the recovery plan for the red-cockaded woodpecker, the area required for a viable population would be >25,450 ha. The estimates of population size and area required for a viable population are considerably higher than those contained in the species' recovery plan (U.S. Fish and Wildl. Serv. 1985). J. WILDL. MANAGE. 52(3):385-391 A viable population is self-sustaining over a long period. Population viability is a critical issue in conservation, but how viability should be assessed is unclear. The most commonly used methods are (1) determining the probability, based on demography and population size, that a population will become extinct over a predetermined number of years (Shaffer 1983, Shaffer and Samson 1985); (2) determining the size of naturally occurring, stable populations of a species (Shaffer 1981); and (3) determining if a population is large enough to maintain its genetic variability (Franklin 1980, Lehmkuhl 1984). These 3 methods address different aspects of viability and are not interchangeable. Genetic variability contributes to viability because it provides potential for populations to adapt to changing environments. An excessive loss of genetic variability therefore reduces the chances of a population persisting. In small populations, loss of genetic variability may be caused by inbreeding (Ballou and Rails 1982, Ralls and Ballou 1983) or genetic drift (Wright 1931, 1948). Franklin (1980) suggested that an effective population size (N,) of 50 would be adequate to avoid losses from inbreeding and an N, of 500 would avoid loss of genetic variability caused by drift. Frankel and Soule (1981) and Frankel (1983) provided further support for these recommendations. There are, however, serious problems in determining viable population size using genetic criteria. Although the relationship between N, and loss of genetic variability is fairly well understood, the relationship between genetic variability and population viability is not. Franklin's (1980) recommendations are based on the former relationship. Moreover, N, required to maintain genetic variability may vary from the standard of 500 individuals because of differences in inherent variability among species, demographic constraints, or evolutionary history of a population's structure (Frankel 1983, Lande and Barrowclough 1987). Therefore, Franklin's (1980) estimate of 500 should be considered an approximation subject to a variety of errors in any application. Furthermore, maintainin a certain N, does not guarantee the longterm preservation of genetic variability. Consider a s ochastic event, such as a hurricane or severe winter, that kills a large portion of the breeding population and causes poor reproduction the following year. Even if the population recovers to its original size within 2 years, the loss of genetic variability caused by the stochastic event is not recovered immediately (Franklin 1980). Such rare events are unlikely to be incorporated into calculations of N,. These considerations lead some to favor demographically based estimates of minimum viable popl ion size over genetically based estimates (Shaffer 1983), and to argue against the use of genetic models of population viability in conse vation (W. R. Dawson et al., Report of the advisory panel on the spotted owl, Natl. Audubon Soc., unpubl. rep., 1986). Although we share these reservations about genetic models of population viability, we recognize certain realities. Genetically based estimates of minimum viable population size are already being incorporated into recovery plans for endangered species. Because the National

Genetic methods for estimating effective population size ( Ne) or the effective number of breeders ( Nb) have become popular, but comparisons of these estimates with demographic estimates of Ne and Nb are rare, especially in anurans. We used three genetic (linkage disequilibrium, temporal moments, Bayesian coalescent-based method) and three demographic models, the latter considering number of breeding individuals, sex ratio, reproductive skew, and other demographic data, to estimate Ne and Nb in two subarctic populations (T and P) of the common frog Rana temporaria, subject to long-term capture-recapture studies. Demographic estimates of Ne based on total population size ( Ne ([T])= 44.5-56.9; Ne ([P])= 68.8-93.7) deviated markedly from the genetic estimates obtained using the linkage disequilibrium method ( Ne ([T])= 97.1; Ne ([P])= 13.2). The demographic estimates of Nb, taking into consideration sex ratio and variance in reproductive success ( Nb ([T])= 10.1-39.7; Nb ([P])= 3.9-21.3), were higher than the genetic estimates ( Nb ([T])= 3.7-5.4; Nb ([P])= 3.5-3.9). The main factors affecting the effective size estimates were sex ratio and reproductive skew. The discrepancies between corresponding Ne and Nb estimates highlight the sensitivity of both demographic and genetic estimates on their underlying assumptions. Yet the ratios of effective or breeding effective size to the census population size were similar to those reported earlier for anurans, reinforcing the view that the discrepancy between actual and effective breeding sizes in anuran populations is typically very large.

Conservation genetic techniques and considerations of the evolutionary potential of a species are increasingly being applied to species conservation. For example, effective population size (Ne) estimates are useful for determining the conservation status of species, yet accurate estimates of current Ne remain difficult to obtain. The effective population size can contribute to setting federal delisting criteria, as was done for the southern sea otter (Enhydra lutris nereis). After being hunted to near extinction during the North Pacific fur trade, the southern sea otter has recovered over part of its former range, but remains at relatively low numbers, making it desirable to obtain accurate and consistent estimates of Ne. Although theoretical papers have compared the validity of several methods, comparisons of estimators using empirical data in applied conservation settings are limited. We combined thirteen years of demographic and genetic data from 1,006 sea otters to assess multiple Ne estimators, as well as temporal trends in genetic diversity and population genetic structure. Genetic diversity was low and did not increase over time. There was no evidence for distinct genetic units, but some evidence for genetic isolation by distance. In particular, estimates of Ne based on demographic data were much larger than genetic estimates when computed for the entire range of the population, but were similar at smaller spatial scales. The discrepancy between estimates at large spatial scales could be driven by cryptic population structure and/or individual differences in reproductive success. We recommend the development of new delisting criteria for the southern sea otter. We advise the use of multiple estimates of Ne for other wide‐ranging species, species with overlapping generations, or with sex‐biased dispersal, as well as the development of improved metrics of genetic assessments of populations.

By the mid-1900s the guanaco (Lama guanicoe) approached extinction in southern South America due to habitat destruction and hunting. In order to maintain the ecological prominence of this iconic species, as well as assist in the management of populations that are emerging economically while increasing in conservation value, accurate and potentially rapid estimates of effective population size (Ne) (demographic and/or genetic) are essential. Estimates of Ne generally focus on the genetic effective population size; however, we posited that both parameters may be necessary to provide more accurate and timely estimates. Therefore, we examined the performance of three demographic and four genetic estimators of Ne of guanacos in Torres del Paine National Park, Chile, at different years and time intervals between 1987 and 1997. We compared our estimates with census estimates of the adult population size (Nac) during the same time period. Average Ne/Nac ratios of demographic estimates varied between 0.04 and 0.99 of the adult census size. Genetic estimates varied between 0.02 and 0.08 of the adult census size. Based upon group composition and population size (n = 82) of guanacos in 1975, the number of breeding adults was 44 animals. Mean Ne of the single-sample and temporal genetic estimators was 43.1, and 34.3, respectively; estimated Ne of one of the demographic estimators was 41. Our findings suggest that intermittent genetic estimates of Ne (via fecal samples, carcasses, blood collection during capture, and/or other non-invasive methods) can provide crucial information regarding the genetic integrity of increasingly isolated populations of wild South American camelids. Considering the overall performance of these estimators, and differences in how each functions, we recommend an integrative approach using both genetic and demographic estimators, to evaluate Ne for the wild South American camelids and other species with polygynous mating systems.

A procedure is described to estimate viable population size and the area of habitat needed to support an endangered stream fish population. Monte Carlo simulations were used to evaluate population fates with stochastic demography and random variation simulated to cause age class 0 failures in some years. Viable population was defined in this paper to be large enough to have less than a 10% chance of extinction in 100 years and to have a long‐term effective size of at least 500 breeding adults, although the method could be applied for any assumed extinction rate and effective size. Using data for Rio Grande cutthroat trout (Oncorhynchus clarkii virginalis) in an age class model, it was inferred from simulations that minimum viable population size was 2750 fish, which would require 2.2 ha of habitat at median density of the subspecies in New Mexico streams. Minimum viable population size occurred at the highest survival rate of young of year and no population‐wide year class failures. Viable population size, and hence required habitat size, increased as the failure rate for age class 0 increased or when the survival rate from age 0 to 1 declined. This suggested that managers should avoid managing for smallest possible viable population size and instead plan for much larger population sizes to accommodate temporal variation in demography and habitat quality. Decreased survival rate of young of year caused the stable age class distribution to be skewed toward the age class 0, which profoundly reduced effective population size. This suggested that habitat restoration that improves survival of young of year would be a good strategy to increase effective size over the long term. Estimating required habitat size could improve introductions of fish to create new populations. Although requiring time‐consuming simulations, the procedure can be used to estimate required habitat size for any species for which population and demographic data are available. Copyright © 2007 John Wiley & Sons, Ltd.

Effective population size (Ne) determines the rate of genetic drift and the relative influence of selection over random genetic changes. While free-living protist populations characteristically consist of huge numbers of cells (N), the absence of any estimates of contemporary Ne raises the question whether protist effective population sizes are comparably large. Using microsatellite genotype data of strains derived from revived cysts of the marine dinoflagellate Pentapharsodinium dalei from sections of a sediment record that spanned some 100 years, we present the first estimates of contemporary Ne for a local population in a free-living protist. The estimates of Ne are relatively small, of the order of a few 100 individuals, and thus are similar in magnitude to values of Ne reported for multicellular animals: the implications are that Ne of P. dalei is of many orders of magnitude lower than the number of cells present (Ne/N ∼ 10(-12)) and that stochastic genetic processes may be more prevalent in protist populations than previously anticipated.

Levels of random genetic drift are influenced by demographic factors, such as mating system, sex ratio and age structure. The effective population size (Ne ) is a useful measure for quantifying genetic drift. Evaluating relative contributions of different demographic factors to Ne is therefore important to identify what makes a population vulnerable to loss of genetic variation. Until recently, models for estimating Ne have required many simplifying assumptions, making them unsuitable for this task. Here, using data from a small, harvested moose population, we demonstrate the use of a stochastic demographic framework allowing for fluctuations in both population size and age distribution to estimate and decompose the total demographic variance and hence the ratio of effective to total population size (Ne /N) into components originating from sex, age, survival and reproduction. We not only show which components contribute most to Ne /N currently, but also which components have the greatest potential for changing Ne /N. In this relatively long-lived polygynous system we show that Ne /N is most sensitive to the demographic variance of older males, and that both reproductive autocorrelations (i.e., a tendency for the same individuals to be successful several years in a row) and covariance between survival and reproduction contribute to decreasing Ne /N (increasing genetic drift). These conditions are common in nature and can be caused by common hunting strategies. Thus, the framework presented here has great potential to increase our understanding of the demographic processes that contribute to genetic drift and viability of populations, and to inform management decisions.

Mutation can critically affect the viability of small populations by causing inbreeding depression, by maintaining potentially adaptive genetic variation in quantitative characters, and through the erosion of fitness by accumulation of mildly detrimental mutations. I review and integrate recent empirical and theoretical work on spontaneous mutation and its role in population viability and conservation planning. I analyze both the maintenance of potentially adaptive genetic variation in quantitative characters and the role of detrimental mutations in increasing the extinction risk of small populations. Recent experiments indicate that the rate of production of quasineutral, potentially adaptive genetic variance in quantitative characters is an order of magnitude smaller than the total mutational variance because mutations with large phenotypic effects tend to be strongly detrimental. This implies that, to maintain normal adaptive potential in quantitative characters under a balance between mutation and random genetic drift (or among mutation, drift, and stabilizing natural selection), the effective population size should be about 5000 rather than 500 (the Franklin‐Soulé number). Recent theoretical results suggest that the risk of extinction due to the fixation of mildly detrimental mutations may be comparable in importance to environmental stochasticity and could substantially decrease the long‐term viability of populations with effective sizes as large as a few thousand. These findings suggest that current recovery goals for many threatened and endangered species are inadequate to ensure long‐term population viability.

Reliable estimates of effective population size Ne are of central importance in population genetics and evolutionary biology. For populations that fluctuate in size, harmonic mean population size is commonly used as a proxy for (multi-) generational effective size. This assumes no effects of density dependence on the ratio between effective and actual population size, which limits its potential application. Here, we introduce density dependence on vital rates in a demographic model of variance effective size. We derive an expression for the ratio Ne/N in a density-regulated population in a fluctuating environment. We show by simulations that yearly genetic drift is accurately predicted by our model, and not proportional to 1/(2N) as assumed by the harmonic mean model, where N is the total population size of mature individuals. We find a negative relationship between Ne/N and N. For a given N, the ratio depends on variance in reproductive success and the degree of resource limitation acting on the population growth rate. Finally, our model indicate that environmental stochasticity may affect Ne/N not only through fluctuations in N, but also for a given N at a given time. Our results show that estimates of effective population size must include effects of density dependence and environmental stochasticity.

Conservation and the genetics of populations

Previous theories on the effective size of age-structured populations assumed a constant environment and, usually, a constant population size and age structure. We derive formulas for the variance effective size of populations subject to fluctuations in age structure and total population size produced by a combination of demographic and environmental stochasticity. Haploid and monoecious or dioecious diploid populations are analyzed. Recent results from stochastic demography are employed to derive a two-dimensional diffusion approximation for the joint dynamics of the total population size, N, and the frequency of a selectively neutral allele, p. The infinitesimal variance for p, multiplied by the generation time, yields an expression for the effective population size per generation. This depends on the current value of N, the generation time, demographic stochasticity, and genetic stochasticity due to Mendelian segregation, but is independent of environmental stochasticity. A formula for the effective population size over longer time intervals incorporates deterministic growth and environmental stochasticity to account for changes in N.

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.

Effective population size (Ne) is a fundamental concept that links population structure to the evolutionary processes that shape genetic variation. Demographic estimates of Ne may be influenced by a number of factors, including adult sex ratio and variance in individual reproductive success. Genetic estimates of Ne are influenced not only by these variables but also by neighborhood size, degree of population substructure, and historical changes in population size. Hence, comparisons of demographic and genetic estimates of Ne may yield important insights into the parameters that determine effective size. To explore interactions between demography and Ne, we compared estimates of effective population size/census size (Ne/N) for 2 demographically distinct populations of the talar tuco-tuco (Ctenomys talarum), a subterranean rodent from Buenos Aires Province, Argentina. Examination of data on adult sex ratios and reproductive success obtained from long-term field studies of C. talarum at Mar de Cobo ...