Variance effective population size is affected by census size in sub-structured populations

Measurement of allele frequency shifts between temporally spaced samples has long been used for assessment of effective population size (N_e), and this ‘temporal method’ provides estimates of N_e referred to as variance effective size (N_eV). We show that N_eV of a local population that belongs to a sub-structured population (a metapopulation) is determined not only by genetic drift and migration rate (m), but also by the census size (N_c). The realized N_eV of a local population can either increase or decrease with increasing m, depending on the relationship between N_e and N_c in isolation. This is shown by explicit mathematical expressions for the factors affecting N_eV derived for an island model of migration. We verify analytical results using high-resolution computer simulations, and show that the phenomenon is not restricted to the island model migration pattern. The effect of N_c on the realized N_eV of a local subpopulation is most pronounced at high migration rates. We show that N_c only affects local N_eV, whereas N_eV for the metapopulation as a whole, inbreeding (N_eI), and linkage disequilibrium (N_eLD) effective size are all independent of N_c. Our results provide a possible explanation to the large variation of N_e/N_c ratios reported in the literature, where N_e is frequently estimated by N_eV. They are also important for the interpretation of empirical N_e estimates in genetic management where local N_eV is often used as a substitute for inbreeding effective size, and we suggest an increased focus on metapopulation N_eV as a proxy for N_eI.     

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.     

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 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.     

Effective/census population size ratio estimation: a compendium and appraisal

With an ecological-evolutionary perspective increasingly applied toward the conservation and management of endangered or exploited species, the genetic estimation of effective population size (N_e) has proliferated. Based on a comprehensive analysis of empirical literature from the past two decades, we asked: (i) how often do studies link N_e to the adult census population size (N)? (ii) To what extent is N_e correctly linked to N? (iii) How readily is uncertainty accounted for in both N_e and N when quantifying N_e/N ratios? and (iv) how frequently and to what degree might errors in the estimation of N_e or N affect inferences of N_e/N ratios? We found that only 20% of available N_e estimates (508 of 2617; 233 studies) explicitly attempted to link N_e and N; of these, only 31% (160 of 508) correctly linked N_e and N. Moreover, only 7% (41 of 508) of N_e/N ratios (correctly linked or not) reported confidence intervals for both N_e and N; for those cases where confidence intervals were reported for N_e only, 31% of N_e/N ratios overlapped with 1, of which more than half also reached below N_e/N = 0.01. Uncertainty in N_e/N ratios thus sometimes spanned at least two orders of magnitude. We conclude that the estimation of N_e/N ratios in natural populations could be significantly improved, discuss several options for doing so, and briefly outline some future research directions.     

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.     

Mitochondrial DNA variation, effective female population size and population history of the endangered Chinese sturgeon, Acipenser sinensis

The anadromous Chinese sturgeon (Acipenser sinensis), mainly endemic to the Yangtze River in China, is an endangered fish species. The natural population has declined since the Gezhouba Dam blocked its migratory route to the spawning grounds in 1981. In the near future, the completion of the Three Gorges Dam, the world's largest hydroelectric project, may further impact this species by altering the water flow of the Yangtze River. Little is currently known about the population genetic structure of the Chinese sturgeon. In this study, DNA sequence data were determined from the control region (D-loop) of the mitochondrial genome of adult sturgeons (n = 106) that were collected between 1995–2000. The molecular data were used to investigate genetic variation, effective female population size and population history of the Chinese sturgeon in the Yangtze River. Our results indicate that the reduction in abundance did not change genetic variation of the Chinese sturgeon, and that the population underwent an expansion in the past. AMOVA analysis indicated that 98.7% of the genetic variability occurred within each year's spawning populations, the year of collection had little influence on the diversity of annual temporary samples. The relative large effective female population size (N _ef) indicates that good potential exists for the recovery of this species in the future. Strikingly, the ratio of N _ef to the census female population size (N _f) is unusually high (0.77–0.93). This may be the result of a current bottleneck in the population of the Chinese sturgeon that is likely caused by human intervention. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

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.     

Spatial scaling of population synchrony in marine fish depends on their life history

The synchrony of population dynamics in space has important implications for ecological processes, for example affecting the spread of diseases, spatial distributions and risk of extinction. Here, we studied the relationship between spatial scaling in population dynamics and species position along the slow‐fast continuum of life history variation. Specifically, we explored how generation time, growth rate and mortality rate predicted the spatial scaling of abundance and yearly changes in abundance of eight marine fish species. Our results show that population dynamics of species' with ‘slow’ life histories are synchronised over greater distances than those of species with ‘fast’ life histories. These findings provide evidence for a relationship between the position of the species along the life history continuum and population dynamics in space, showing that the spatial distribution of abundance may be related to life history characteristics.     

Habitat use and life history of brown trout (Salmo trutta) and Arctic charr (Salvelinus alpinus) in some low acidity lakes in central Norway

Habitat utilization and the life history of browntrout Salmo trutta and Arctic charr Salvelinus alpinus were investigated in fivesympatric populations and five allopatric brown troutpopulations in Høylandet catchment, a atmosphaericlow deposition area in Mid Norway. There was asignificant inverse correlation in abundance ofepibenthic Arctic charr and brown trout in theselakes, indicating that the latter species is dominant.The largest numbers of sympatric brown trout andArctic charr were caught in epibenthic habitat. In twolakes, brown trout to some extent also occurredpelagically, while pelagic individuals of Arctic charrwere found in all five lakes. The main food items forboth epibenthic and pelagic brown trout wereterrestrial surface insects and chironomid pupae.Zooplankton was the primary food item for Arctic charrin both habitats. Although the age distribution wasvery different in the populations, neither speciesseem to suffer from recruitment failure. There was nosignificant difference in survival rates betweensympatric populations of brown trout and Arctic charr.We found a significant inverse correlation betweenepibenthic catches of brown trout and the mean weightof 4+ fish, the most abundant age group. However, ifusing weight data for three-year-old fish, no suchrelationship was found for Arctic charr. Brown troutand Arctic charr reached asymptotic lengths of197–364 mm and 259–321 mm, respectively. Both speciestypically reached sexual maturity at age 2–3, and nomaturation-induced mortality was evident. We concludethat fish populations in Høylandet lakes areregulated throughout their lifes by inter- andintraspecific competition.     

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.     

Exploring the structure of genetic variation and the influences of demography on effective population size in the gag grouper Mycteroperca microlepi (Goode & Bean)

Using 11 microsatellite markers, genetic analyses of three successive year-classes of gag Mycteroperca microlepis juveniles across the north-eastern Gulf of Mexico revealed a lack of spatial structure and very little temporal variation between year-classes. These results are consistent with long-term effective population sizes on the order of 30 000 adults. The importance of reproductive-style and sex-ratio variation is discussed as an important influence on long-term effective sizes.     

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.     

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.     

Estimating effective population size from linkage disequilibrium: severe bias in small samples

Effective population size (N _e) is a central concept in evolutionary biology and conservation genetics. It predicts rates of loss of neutral genetic variation, fixation of deleterious and favourable alleles, and the increase of inbreeding experienced by a population. A method exists for the estimation of N _e from the observed linkage disequilibrium between unlinked loci in a population sample. While an increasing number of studies have applied this method in natural and managed populations, its reliability has not yet been evaluated. We developed a computer program to calculate this estimator of N _e using the most widely used linkage disequilibrium algorithm and used simulations to show that this estimator is strongly biased when the sample size is small (<‰100) and below the true N _e. This is probably due to the linkage disequilibrium generated by the sampling process itself and the inadequate correction for this phenomenon in the method. Results suggest that N _e estimates derived using this method should be regarded with caution in many cases. To improve the method’s reliability and usefulness we propose a way to determine whether a given sample size exceeds the population N _e and can therefore be used for the computation of an unbiased estimate.     

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.     

Mature male parr contribution to the effective size of an anadromous Atlantic salmon (Salmo salar) population over 30 years

We describe temporal changes in the genetic composition of a small anadromous Atlantic salmon (Salmo salar) population from South Newfoundland, an area where salmon populations are considered threatened (COSEWIC 2010). We examined the genetic variability (13 microsatellite loci) in 869 out‐migrating smolt and post‐spawning kelt samples, collected from 1985 to 2011 for a total of 22 annual collections and a 30 year span of assigned cohorts. We estimated the annual effective number of breeders (N_b) and the generational effective population size (N_e) through genetic methods and demographically using the adult sex ratio. Comparisons between genetic and demographic estimates show that the adult spawners inadequately explain the observed N_e estimates, suggesting that mature male parr are significantly increasing N_b and N_e over the study period. Spawning as parr appears to be a viable and important strategy in the near absence of adult males.     

Ontogenetic variation in density‐dependent growth of brown trout through habitat competition

1. Density‐dependent growth has been widely reported in freshwater fishes, but the ontogenetic evolution of competition and its subsequent effects on growth through a life span remains unclear. 2. Patterns of competition can be described by integrating population abundance data with habitat‐modelling results. Weighted usable area (WUA; m² WUA ha^?1) curves are obtained for each flow value and are then coupled with demographic data to obtain the occupancy rates (trout m^?2 WUA, the density of a given age class related to its suitable habitat) of the WUA for every age class, year and site. 3. We examined a long‐term data series searching for temporal variation in the influence of habitat occupancy rate on the growth of brown trout Salmo trutta. We tested whether (i) mean cohort mass (mean mass of the cohort during the first 3 years of life) is affected by the occupancy rate experienced across a life span; and (ii) the occupancy rate experienced at different ages influenced mean body size. 4. We observed a consistent negative power relationship between average cohort mass and mean occupancy rate through a life span, indicating that stronger cohorts were related to a reduced growth, with likely consequences for individual fitness. 5. The effects of occupancy rate on size‐at‐age were mainly detected in the size attained at the second year of life, but they were because of the competition at different times. Thus, the level of competition varied through ontogeny, in some of the rivers affecting growth since the first year of life, whereas in most of the rivers the main effects on body size resulted from the competition during the second year of life. 6. Occupancy rate appears more appropriate than density for assessing the occurrence of habitat competition in freshwater fishes, since it encompasses the differences in quantity and quality of suitable habitat for each age class. 7. Our study highlights the importance of density‐dependent growth as a key process in the dynamics of brown trout populations, its temporal variation depending on the temporal changes of density and the variation of competition associated with the habitat capacity for each life stage.