INTERMITTENT BREEDING AND CONSTRAINTS ON LITTER SIZE: CONSEQUENCES FOR EFFECTIVE POPULATION SIZE PER GENERATION (Ne) AND PER REPRODUCTIVE CYCLE (Nb)

Estimates of Effective Number of Breeders Identify Drivers of Decline in Mid-Atlantic Brook Trout Populations

Brook Trout (Salvelinus fontinalis) populations have experienced marked declines throughout their native range and are presently threatened due to isolation in small habitat fragments, land use changes, and climate change. The existence of numerous, spatially distinct populations poses substantial challenges for monitoring population status (e.g., abundance, recruitment, or occupancy). Genetic monitoring with estimates of effective number of breeders (N b) provides a potentially powerful metric to complement existing population monitoring, assessment, and prioritization. We estimated N b for 71 Brook Trout habitat units in mid-Atlantic region of the United States and obtained a mean N b of 73.2 (range 6.90-493). Our modeling approach tested whether N b estimates were sensitive to differences in habitat size, presence of non-native salmonids, base flow index, temperature, acidic precipitation, and indices of anthropogenic disturbance. We found significant support for three of our hypotheses including the positive influences of available habitat and base flow index and negative effect of temperature. Our results are consistent with presently observed and predicted future impacts of climate change on populations of this cold-water fish. Importantly, these findings support the use of N b in population assessments as an index of relative population status.

Estimation of effective number of breeders and effective population size in an abundant and heavily exploited marine teleost

Obtaining reliable estimates of the effective number of breeders (N b) and generational effective population size (N e) for fishery-important species is challenging because they are often iteroparous and highly abundant, which can lead to bias and imprecision. However, recent advances in understanding of these parameters, as well as the development of bias correction methods, have improved the capacity to generate reliable estimates. We utilized samples of both single-cohort young of the year and mixed-age adults from two geographically and genetically isolated stocks of the Australasian snapper (Chrysophrys auratus) to investigate the feasibility of generating reliable N b and N e estimates for a fishery species. Snapper is an abundant, iteroparous broadcast spawning teleost that is heavily exploited by recreational and commercial fisheries. Employing neutral genome-wide SNPs and the linkage-disequilibrium method, we determined that the most reliable N b and N e estimates could be derived by genotyping at least 200 individuals from a single cohort. Although our estimates made from the mixed-age adult samples were generally lower and less precise than those based on a single cohort, they still proved useful for understanding relative differences in genetic effective size between stocks. The correction formulas applied to adjust for biases due to physical linkage of loci and age structure resulted in substantial upward modifications of our estimates, demonstrating the importance of applying these bias corrections. Our findings provide important guidelines for estimating N b and N e for iteroparous species with large populations. This work also highlights the utility of samples originally collected for stock structure and stock assessment work for investigating genetic effective size in fishery-important species.

Consequences of domestication in eastern oyster: Insights from whole genomic analyses

Selective breeding for production traits has yielded relatively rapid successes with high-fecundity aquaculture species. Discovering the genetic changes associated with selection is an important goal for understanding adaptation and can also facilitate better predictions about the likely fitness of selected strains if they escape aquaculture farms. Here, we hypothesize domestication as a genetic change induced by inadvertent selection in culture. Our premise is that standardized culture protocols generate parallel domestication effects across independent strains. Using eastern oyster as a model and a newly developed 600K SNP array, this study tested for parallel domestication effects in multiple independent selection lines compared with their progenitor wild populations. A single contrast was made between pooled selected strains (1-17 generations in culture) and all wild progenitor samples combined. Population structure analysis indicated rank order levels of differentiation as [wild - wild] < [wild - cultured] < [cultured - cultured]. A genome scan for parallel adaptation to the captive environment applied two methodologically distinct outlier tests to the wild versus selected strain contrast and identified a total of 1174 candidate SNPs. Contrasting wild versus selected strains revealed the early evolutionary consequences of domestication in terms of genomic differentiation, standing genetic diversity, effective population size, relatedness, runs of homozygosity profiles, and genome-wide linkage disequilibrium patterns. Random Forest was used to identify 37 outlier SNPs that had the greatest discriminatory power between bulked wild and selected oysters. The outlier SNPs were in genes enriched for cytoskeletal functions, hinting at possible traits under inadvertent selection during larval culture or pediveliger setting at high density. This study documents rapid genomic changes stemming from hatchery-based cultivation of eastern oysters, identifies candidate loci responding to domestication in parallel among independent aquaculture strains, and provides potentially useful genomic resources for monitoring interbreeding between farm and wild oysters.

Partitioning variance in reproductive success, within years and across lifetimes

Variance in reproductive success (s k 2 , with k = number of offspring) plays a large role in determining the rate of genetic drift and the scope within which selection acts. Various frameworks have been proposed to parse factors that contribute to s k 2 , but none has focused on age-specific values of ϕ = s k 2 / k ¯ , which indicate the degree to which reproductive skew is overdispersed (compared to the random Poisson expectation) among individuals of the same age and sex. Instead, within-age effects are generally lumped with residual variance and treated as "noise." Here, an ANOVA sums-of-squares framework is used to partition variance in annual and lifetime reproductive success into between-group and within-group components. For annual reproduction, the between-age effect depends on age-specific fecundity (b x), but relatively few empirical data are available on the within-age effect, which depends on ϕ x. By defining groups by age-at-death rather than age, the same ANOVA framework can be used to partition variance in lifetime reproductive success (LRS) into between-group and within-group components. Analytical methods are used to develop null-model expectations for random contributions to within-group and between-group components. For analysis of LRS, random variation in longevity appears as part of the between-group variance, and effects (if any) of skip breeding and persistent individual differences contribute to the within-group variance. Simulations are used to show that the methods for variance partitioning are asymptotically unbiased. Practical application is illustrated with empirical data for annual reproduction in American black bears and lifetime reproduction in Dutch great tits. Results show that overdispersed within-age variance (1) dominates annual s k 2 in both male and female black bears, (2) is the primary factor that reduces annual effective size to a fraction of the number of adults, and (3) represents most of the opportunity for selection. In contrast, about a quarter of the variance in LRS in great tits can be attributed to random variation in longevity, and most of the rest is due to modest differences in fecundity with age estimated for a single cohort of females. R code is provided that reads generic input files for annual and lifetime reproductive success and allows users to conduct variance partitioning with their own data.

Evaluating the utility of effective breeding size estimates for monitoring sea lamprey spawning abundance

Sea lamprey (Petromyzon marinus) is an invasive species that is a significant source of mortality for populations of valued fish species across the North American Great Lakes. Large annual control programs are needed to reduce the species' impacts; however, the number of successfully spawning adults cannot currently be accurately assessed. In this study, effective breeding size (N b) and the minimum number of spawning adults (N s) were estimated for larval cohorts from 17 tributaries across all five Great Lakes using single nucleotide polymorphisms (SNP) genotyped via RAD-capture sequencing. Reconstructed larval pedigrees showed substantial variability in the size and number of full- and half-sibling groups, N b (<1-367), and N s (5-545) among streams. Generalized linear models examining the effects of stream environmental characteristics and aspects of sampling regimes on N b and N s estimates identified sample size, the number of sampling sites, and drainage area as important factors predicting N b and N s. Correlations between N b, N s, and capture-mark-recapture estimates of adult census size (N c) increased when streams with small sample sizes (n < 50) were removed. Results collectively indicate that parameters estimated from genetic data can provide valuable information on spawning adults in a river system, especially if sampling regimes are standardized and physical stream covariates are included.

Alternative life-history strategy contributions to effective population size in a naturally spawning salmon population

Alternative life-history tactics are predicted to affect within-population genetic processes but have received little attention. For example, the impact of precocious males on effective population size (N e) has not been quantified directly in Pacific salmon Oncorhynchus spp., even though they can make up a large percentage of the total male spawners. We investigated the contribution of precocial males ("jacks") to N e in a naturally spawning population of Coho Salmon O. kisutch from the Auke Creek watershed in Juneau, Alaska. Mature adults that returned from 2009 to 2019 (~8000 individuals) were genotyped at 259 single-nucleotide polymorphism (SNP) loci for parentage analysis. We used demographic and genetic methods to estimate the effective number of breeders per year (N b). Jack contribution to N b was assessed by comparing values of N b calculated with and without jacks and their offspring. Over a range of N b values (108-406), the average jack contribution to N b from 2009 to 2015 was 12.9% (SE = 3.8%). Jacks consistently made up over 20% of the total male spawners. The presence of jacks did not seem to influence N b/N. The linkage disequilibrium N e estimate was lower than the demographic estimate, possibly due to immigration effects on population genetic processes: based on external marks and parentage data, we estimated that immigrant spawners produced 4.5% of all returning offspring. Our results demonstrate that jacks can influence N b and N e and can make a substantial contribution to population dynamics and conservation of threatened stocks.

Effective population size in a partially clonal plant is not predicted by the number of genetic individuals

Estimating effective population size (N _e) is important for theoretical and practical applications in evolutionary biology and conservation. Nevertheless, estimates of N _e in organisms with complex life-history traits remain scarce because of the challenges associated with estimation methods. Partially clonal plants capable of both vegetative (clonal) growth and sexual reproduction are a common group of organisms for which the discrepancy between the apparent number of individuals (ramets) and the number of genetic individuals (genets) can be striking, and it is unclear how this discrepancy relates to N _e. In this study, we analysed two populations of the orchid Cypripedium calceolus to understand how the rate of clonal versus sexual reproduction affected N _e. We genotyped >1000 ramets at microsatellite and SNP loci, and estimated contemporary N _e with the linkage disequilibrium method, starting from the theoretical expectation that variance in reproductive success among individuals caused by clonal reproduction and by constraints on sexual reproduction would lower N _e. We considered factors potentially affecting our estimates, including different marker types and sampling strategies, and the influence of pseudoreplication in genomic data sets on N _e confidence intervals. The magnitude of N _e/N _ramets and N _e/N _genets ratios we provide may be used as reference points for other species with similar life-history traits. Our findings demonstrate that N _e in partially clonal plants cannot be predicted based on the number of genets generated by sexual reproduction, because demographic changes over time can strongly influence N _e. This is especially relevant in species of conservation concern in which population declines may not be detected by only ascertaining the number of genets.

Learning mitigates genetic drift

Genetic drift is a basic evolutionary principle describing random changes in allelic frequencies, with far-reaching consequences in various topics ranging from species conservation efforts to speciation. The conventional approach assumes that genetic drift has the same effect on all populations undergoing the same changes in size, regardless of different non-reproductive behaviors and history of the populations. However, here we reason that processes leading to a systematic increase of individuals` chances of survival, such as learning or immunological memory, can mitigate loss of genetic diversity caused by genetic drift even if the overall mortality rate in the population does not change. We further test this notion in an agent-based model with overlapping generations, monitoring allele numbers in a population of prey, either able or not able to learn from successfully escaping predators' attacks. Importantly, both these populations start with the same effective size and have the same and constant overall mortality rates. Our results demonstrate that even under these conditions, learning can mitigate loss of genetic diversity caused by drift, by creating a pool of harder-to-die individuals that protect alleles they carry from extinction. Furthermore, this effect holds regardless if the population is haploid or diploid or whether it reproduces sexually or asexually. These findings may be of importance not only for basic evolutionary theory but also for other fields using the concept of genetic drift.

Demographic resilience of brook trout populations subjected to experimental size-selective harvesting

Sustainable management of exploited populations benefits from integrating demographic and genetic considerations into assessments, as both play a role in determining harvest yields and population persistence. This is especially important in populations subject to size-selective harvest, because size selective harvesting has the potential to result in significant demographic, life-history, and genetic changes. We investigated harvest-induced changes in the effective number of breeders (N ^ b ) for introduced brook trout populations (Salvelinus fontinalis) in alpine lakes from western Canada. Three populations were subject to 3 years of size-selective harvesting, while three control populations experienced no harvest. TheN ^ c decreased consistently across all harvested populations (on average 60.8%) but fluctuated in control populations. There were no consistent changes inN ^ b between control or harvest populations, but one harvest population experienced a decrease inN ^ b of 63.2%. TheN ^ b /N ^ c ratio increased consistently across harvest lakes; however we found no evidence of genetic compensation (where variance in reproductive success decreases at lower abundance) based on changes in family evenness (FE ^ ) and the number of full-sibling families (N ^ fam ). We found no relationship betweenFE ^ andN ^ c or betweenN ^ fam /N ^ c andFE ^ . We posit that change inN ^ b was buffered by constraints on breeding habitat prior to harvest, such that the same number of breeding sites were occupied before and after harvest. These results suggest that effective size in harvested populations may be resilient to considerable changes in Nc in the short-term, but it is still important to monitor exploited populations to assess the risk of inbreeding and ensure their long-term survival.

Evaluating sources of bias in pedigree-based estimates of breeding population size

Applications of genetic-based estimates of population size are expanding, especially for species for which traditional demographic estimation methods are intractable due to the rarity of adult encounters. Estimates of breeding population size (N_S ) are particularly amenable to genetic-based approaches as the parameter can be estimated using pedigrees reconstructed from genetic data gathered from discrete juvenile cohorts, therefore eliminating the need to sample adults in the population. However, a critical evaluation of how genotyping and sampling effort influence bias in pedigree reconstruction, and how these biases subsequently influence estimates of N_S , is needed to evaluate the efficacy of the approach under a range of scenarios. We simulated a model system to understand the interactive effects of genotyping and sampling effort on error in genetic pedigrees reconstructed from the program COLONY. We then evaluated how errors in pedigree reconstruction influenced bias and precision in estimates of N_S using three different rarefaction estimators. Results indicated that pedigree error can be minimal when adequate genetic data are available, such as when juvenile sample sizes are large and/or individuals are genotyped at many informative loci. However, even in cases for which data are limited, using results of the simulation analysis to understand the magnitude and sources of bias in reconstructed pedigrees can still be informative when estimating N_S . We applied results of the simulation analysis to evaluate N ̂ $$ \hat{N} $$ _S for a population of federally endangered Atlantic sturgeon (Acipenser oxyrinchus oxyrinchus) in the Delaware River, USA. Our results indicated that N_S is likely to be three orders of magnitude lower compared with historic breeding population sizes, which is a considerable advancement in our understanding of the population status of Atlantic sturgeon in the Delaware River. Our analyses are broadly applicable in the design and interpretation of studies seeking to estimate N_S and can help to guide conservation decisions when ecological uncertainty is high. The utility of these results is expected to grow as rapid advances in genetic technologies increase the popularity of genetic population monitoring and estimation.

Population abundance in arctic grayling using genetics and close-kin mark-recapture

Arctic Grayling (Thymallus arcticus) are among the most widely distributed and abundant freshwater fish in the Yukon Territory of Canada, yet little information exists regarding their broad and fine-scale population structures or the number and size of these populations. The estimation of population abundance is fundamental for robust management and conservation, yet estimating abundance in the wild is often difficult. Here, we estimated abundance of an Arctic Grayling population using multiple genetic markers and the close-kin mark-recapture (CKMR) method. A total of N = 1,104 Arctic Grayling collected from two systems in Yukon were genotyped at 38 sequenced microsatellites. We first identified structure and assessed genetic diversity (effective population size,N ^ e ). Collections from one of the systems (Lubbock River) comprised adults and young-of-the-year sampled independently allowing the identification of parent-offspring pairs (POPs), and thus, the estimation of abundance using CKMR. We used COLONY and CKMRsim to identify POPs and both provided similar results leading to indistinguishable estimates (95% CI) of census size, that is,N ^ c ( C O L O N Y ) = 1858 (1259-2457) andN ^ c ( C K M R s i m ) = 1812 (1229-2389). The accuracy of the population abundance estimates can in the future be improved with temporal sampling and more precise age or size-specific fecundity estimates for Arctic Grayling. Our study demonstrates that the method can be used to inform management and conservation policy for Arctic Grayling and likely also for other fish species for which the assumption of random and independent sampling of adults and offspring can be assured.

Effective number of white shark (Carcharodon carcharias, Linnaeus) breeders is stable over four successive years in the population adjacent to eastern Australia and New Zealand

Population size is a central parameter for conservation; however, monitoring abundance is often problematic for threatened marine species. Despite substantial investment in research, many marine species remain data-poor presenting barriers to the evaluation of conservation management outcomes and the modeling of future solutions. Such is the case for the white shark (Carcharodon carcharias), a highly mobile apex predator for whom recent and substantial population declines have been recorded in many globally distributed populations. Here, we estimate the effective number of breeders that successfully contribute offspring in one reproductive cycle (Nb) to provide a snapshot of recent reproductive effort in an east Australian-New Zealand population of white shark. Nb was estimated over four consecutive age cohorts (2010, 2011, 2012, and 2013) using two genetic estimators (linkage disequilibrium; LD and sibship assignment; SA) based on genetic data derived from two types of genetic markers (single nucleotide polymorphisms; SNPs and microsatellite loci). While estimates of Nb using different marker types produced comparable estimates, microsatellite loci were the least precise. The LD and SA estimates of Nb within cohorts using SNPs were comparable; for example, the 2013 age cohort Nb(SA) was 289 (95% CI 200-461) and Nb(LD) was 208.5 (95% CI 116.4-712.7). We show that over the time period studied, Nb was stable and ranged between 206.1 (SD ± 45.9) and 252.0 (SD ± 46.7) per year using a combined estimate of Nb(LD+SA) from SNP loci. In addition, a simulation approach showed that in this population the effective population size (Ne) per generation can be expected to be larger than Nb per reproductive cycle. This study demonstrates how breeding population size can be monitored over time to provide insight into the effectiveness of recovery and conservation measures for the white shark, where the methods described here may be applicable to other data-poor species of conservation concern.

AgeStrucNb: Software for Simulating and Detecting Changes in the Effective Number of Breeders (Nb)

Estimation of the effective number of breeders per reproductive event (Nb) using single sample DNA-marker-based methods has rapidly grown in recent years. However, estimating Nb is difficult in age-structured populations because the performance of estimators is influenced by the Nb / Ne ratio, which varies among species with different life histories. We provide a computer program, AgeStrucNb, to simulate age-structured populations (including life history) and also estimate Nb. The AgeStrucNb program is composed of 4 major components to simulate, subsample, estimate, and then visualize Nb time series data. AgeStrucNb allows users to also quantify the precision and accuracy of any set of loci or sample size to estimate Nb for many species and populations. AgeStrucNb allows users to conduct power analysis to evaluate sensitivity to detect changes in Nb or the power to detect a correlation between trends in Nb and environmental variables (e.g., temperature, habitat quality, predator or pathogen abundance) that could be driving changes in Nb. The software provides Nb estimates for empirical data sets using the LDNe (linkage disequilibrium) method, includes publication-quality output graphs, and outputs genotype files in Genepop format for use in other programs. AgeStrucNb will help advance the application of genetic markers for monitoring Nb, which will help biologists to detect population declines and growth, which is crucial for research and conservation of natural and managed populations.

An estimator of the Opportunity for Selection that is independent of mean fitness

Variation among individuals in number of offspring (fitness, k) sets an upper limit to the evolutionary response to selection. This constraint is quantified by Crow's Opportunity for Selection (I), which is the variance in relative fitness (I = σ² _k /(u_k )² ). Crow's I has been widely used but remains controversial because it depends on mean offspring number in a sample ( k ¯ ). Here, I used a generalized Wright-Fisher model that allows for unequal probabilities of producing offspring to evaluate behavior of Crow's I and related indices under a wide range of sampling scenarios. Analytical and numerical results are congruent and show that rescaling the sample variance (s² _k ) to its expected value at a fixed k ¯ 2 removes dependence of I on mean offspring number, but the result still depends on choice of k ¯ 2 . A new index is introduced, Δ_I = Π- E(Î_drift ) = Π- 1/ k ¯ , which makes Î independent of sample k ¯ without the need for variance rescaling. Δ_I has a straightforward interpretation as the component of variance in relative fitness that exceeds that expected under a null model of random reproductive success. Δ_I can be used to directly compare estimates of the Opportunity for Selection for samples from different studies, different sexes, and different life stages.

Accounting for Age Structure and Spatial Structure in Eco-Evolutionary Analyses of a Large, Mobile Vertebrate

The idealized concept of a population is integral to ecology, evolutionary biology, and natural resource management. To make analyses tractable, most models adopt simplifying assumptions, which almost inevitably are violated by real species in nature. Here, we focus on both demographic and genetic estimates of effective population size per generation (Ne), the effective number of breeders per year (Nb), and Wright's neighborhood size (NS) for black bears (Ursus americanus) that are continuously distributed in the northern lower peninsula of Michigan, United States. We illustrate practical application of recently developed methods to account for violations of 2 common, simplifying assumptions about populations: 1) reproduction occurs in discrete generations and 2) mating occurs randomly among all individuals. We use a 9-year harvest dataset of >3300 individuals, together with genetic determination of 221 parent-offspring pairs, to estimate male and female vital rates, including age-specific survival, age-specific fecundity, and age-specific variance in fecundity (for which empirical data are rare). We find strong evidence for overdispersed variance in reproductive success of same-age individuals in both sexes, and we show that constraints on litter size have a strong influence on results. We also estimate that another life-history trait that is often ignored (skip breeding by females) has a relatively modest influence, reducing Nb by 9% and increasing Ne by 3%. We conclude that isolation by distance depresses genetic estimates of Nb, which implicitly assume a randomly mating population. Estimated demographic NS (100, based on parent-offspring dispersal) was similar to genetic NS (85, based on regression of genetic distance and geographic distance), indicating that the >36000 km2 study area includes about 4-5 black-bear neighborhoods. Results from this expansive data set provide important insight into effects of violating assumptions when estimating evolutionary parameters for long-lived, free-ranging species. In conjunction with recently developed analytical methodology, the ready availability of nonlethal DNA sampling methods and the ability to rapidly and cheaply survey many thousands of molecular markers should facilitate eco-evolutionary studies like this for many more species in nature.

Robust estimates of a high Ne/N ratio in a top marine predator, southern bluefin tuna

Genetic studies of several marine species with high fecundity have produced "tiny" estimates (≤10-3) of the ratio of effective population size (Ne) to adult census size (N), suggesting that even very large populations might be at genetic risk. A recent study using close-kin mark-recapture methods estimated adult abundance at N ≈ 2 × 106 for southern bluefin tuna (SBT), a highly fecund top predator that supports a lucrative (~$1 billion/year) fishery. We used the same genetic and life history data (almost 13,000 fish collected over 5 years) to generate genetic and demographic estimates of Ne per generation and Nb (effective number of breeders) per year and the Ne/N ratio. Demographic estimates, which accounted for age-specific vital rates, skip breeding, variation in fecundity at age, and persistent individual differences in reproductive success, suggest that Ne/N is >0.1 and perhaps about 0.5. The genetic estimates supported this conclusion. Simulations using true Ne = 5 × 105 (Ne/N = 0.25) produced results statistically consistent with the empirical genetic estimates, whereas simulations using Ne = 2 × 104 (Ne/N = 0.01) did not. Our results show that robust estimates of Ne and Ne/N can be obtained for large populations, provided sufficiently large numbers of individuals and genetic markers are used and temporal replication (here, 5 years of adult and juvenile samples) is sufficient to provide a distribution of estimates. The high estimated Ne/N ratio in SBT is encouraging and suggests that the species will not be compromised by a lack of genetic diversity in responding to environmental change and harvest.

Effective population size and the genetic consequences of commercial whaling on the humpback whales (Megaptera novaeangliae) from Southwestern Atlantic Ocean

Genotypes of 10 microsatellite loci of 420 humpback whales from the Southwestern Atlantic Ocean population were used to estimate for the first time its contemporary effective (N_e) and census (N_c) population sizes and to test the genetic effect of commercial whaling. The results are in agreement with our previous studies that found high genetic diversity for this breeding population. Using an approximate Bayesian computation approach, the scenario of constant N_e was significantly supported over scenarios with moderate to strong size changes during the commercial whaling period. The previous generation N_c (N_e multiplied by 3.6), which should corresponds to the years between around 1980 and 1990, was estimated between ~2,600 and 6,800 whales (point estimate ~4,000), and is broadly compatible with the recent abundance surveys extrapolated to the past using a growth rate of 7.4% per annum. The long-term N_c in the constant scenario (point estimate ~15,000) was broadly compatible (considering the confidence interval) with pre-whaling catch records estimates (point estimate ~25,000). Overall, our results shown that the Southwestern Atlantic Ocean humpback whale population is genetically very diverse and resisted well to the strong population reduction during commercial whaling.

Genetic substructure and admixture as important factors in linkage disequilibrium-based estimation of effective number of breeders in recovering wildlife populations

The number of effective breeders (Nb ) and effective population size (Ne ) are population parameters reflective of evolutionary potential, susceptibility to stochasticity, and viability. We have estimated these parameters using the linkage disequilibrium-based approach with LDNE through the latest phase of population recovery of the brown bears (Ursus arctos) in Finland (1993-2010; N = 621). This phase of the recovery was recently documented to be associated with major changes in genetic composition. In particular, differentiation between the northern and the southern genetic cluster declined rapidly within 1.5 generations. Based on this, we have studied effects of the changing genetic structure on Nb and Ne , by comparing estimates for whole Finland with the estimates for the two genetic clusters. We expected a potentially strong relationship between estimate sizes and genetic differentiation, which should disappear as the population recovers and clusters merge. Consistent with this, our estimates for whole Finland were lower than the sum of the estimates of the two genetic clusters and both approaches produced similar estimates in the end. Notably, we also found that admixed genotypes strongly increased the estimates. In all analyses, our estimates for Ne were larger than Nb and likely reflective for brown bears of the larger region of Finland and northwestern Russia. Conclusively, we find that neglecting genetic substructure may lead to a massive underestimation of Nb and Ne . Our results also suggest the need for further empirical analysis focusing on individuals with admixed genotypes and their potential high influence on Nb and Ne .

Reliable effective number of breeders/adult census size ratios in seasonal-breeding species: Opportunity for integrative demographic inferences based on capture-mark-recapture data and multilocus genotypes

The ratio of the effective number of breeders (Nb) to the adult census size (Na), Nb/Na, approximates the departure from the standard capacity of a population to maintain genetic diversity in one reproductive season. This information is relevant for assessing population status, understanding evolutionary processes operating at local scales, and unraveling how life-history traits affect these processes. However, our knowledge on Nb/Na ratios in nature is limited because estimation of both parameters is challenging. The sibship frequency (SF) method is adequate for reliable Nb estimation because it is based on sibship and parentage reconstruction from genetic marker data, thereby providing demographic inferences that can be compared with field-based information. In addition, capture-mark-recapture (CMR) robust design methods are well suited for Na estimation in seasonal-breeding species. We used tadpole genotypes of three pond-breeding amphibian species (Epidalea calamita, Hyla molleri, and Pelophylax perezi, n = 73-96 single-cohort tadpoles/species genotyped at 15-17 microsatellite loci) and candidate parental genotypes (n = 94-300 adults/species) to estimate Nb by the SF method. To assess the reliability of Nb estimates, we compared sibship and parentage inferences with field-based information and checked for the convergence of results in replicated subsampled analyses. Finally, we used CMR data from a 6-year monitoring program to estimate annual Na in the three species and calculate the Nb/Na ratio. Reliable ratios were obtained for E. calamita (Nb/Na = 0.18-0.28) and P. perezi (0.5), but in H. molleri, Na could not be estimated and genetic information proved insufficient for reliable Nb estimation. Integrative demographic studies taking full advantage of SF and CMR methods can provide accurate estimates of the Nb/Na ratio in seasonal-breeding species. Importantly, the SF method provides results that can be readily evaluated for reliability. This represents a good opportunity for obtaining robust demographic inferences with wide applications for evolutionary and conservation research.

A critical assessment of estimating census population size from genetic population size (or vice versa) in three fishes

Technological and methodological advances have facilitated the use of genetic data to infer census population size (Nc) in natural populations, particularly where traditional mark-and-recapture is challenging. The effective number of breeders (Nb) describes how many adults effectively contribute to a cohort and is often correlated with Nc. Predicting Nc from Nb or vice versa in species with overlapping generations has important implications for conservation by permitting (i) estimation of the more difficult to quantify variable and (ii) inferences of Nb/Nc relationships in related species lacking data. We quantitatively synthesized Nb/Nc relationships in three salmonid fishes where sufficient data have recently accumulated. Mixed-effects models were analysed in which each variable was included as a dependent variable or predictor term (Nb from Nc and vice versa). Species-dependent Nb/Nc slope estimates were significantly positive in two of three species. Variation in species slopes was likely due to varying life histories and reinforce caution when inferring Nb/Nc from taxonomically related species. Models provided maximum probable estimates for Nb and Nc for two species. However, study, population and year effects explained substantial amounts of variation (39%-57%). Consequently, prediction intervals were wide and included or were close to zero for all population sizes and species; model predictive utility was limited. Cost-benefit trade-offs when estimating Nb and/or Nc were also discussed using a real-world system example. Our findings based on salmonids suggest that no short cuts currently exist when estimating population size and researchers should focus on quantifying the variable of interest or be aware of caveats when inferring the desired variable because of cost or logistics. We caution that the salmonid species examined share life-history traits that may obscure relationships between Nb and Nc. Sufficient data on other taxa were unavailable; additional research examining Nb/Nc relationships in species with potentially relevant life-history trait differences (e.g., differing survival curves) is needed.

Ecological and evolutionary consequences of alternative sex-change pathways in fish

Sequentially hermaphroditic fish change sex from male to female (protandry) or vice versa (protogyny), increasing their fitness by becoming highly fecund females or large dominant males, respectively. These life-history strategies present different social organizations and reproductive modes, from near-random mating in protandry, to aggregate- and harem-spawning in protogyny. Using a combination of theoretical and molecular approaches, we compared variance in reproductive success (V_k*) and effective population sizes (N_e) in several species of sex-changing fish. We observed that, regardless of the direction of sex change, individuals conform to the same overall strategy, producing more offspring and exhibiting greater V_k* in the second sex. However, protogynous species show greater V_k*, especially pronounced in haremic species, resulting in an overall reduction of N_e compared to protandrous species. Collectively and independently, our results demonstrate that the direction of sex change is a pivotal variable in predicting demographic changes and resilience in sex-changing fish, many of which sustain highly valued and vulnerable fisheries worldwide.

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.

Tiny estimates of the Ne /N ratio in marine fishes: Are they real?

Theory and empirical estimates agree that the ratio of effective size (N_e ) to census size (N) falls roughly in the range 0·1-0·5 for most populations. In a number of marine species, however, genetic estimates of contemporary N_e /N are as much as 5-6 orders of magnitude lower. Although some mechanisms that could produce such tiny N_e /N ratios have been proposed, the subject remains controversial. This issue is important to resolve: if N_e /N can be 10^-3 or smaller, marine fish populations that are quite large could be at genetic risk. Based on a recently-improved understanding of factors that influence N_e and N_e /N in species with overlapping generations, this paper evaluates conditions necessary to produce tiny N_e /N ratios in actual populations. These analyses show that although increased longevity, fecundity and variance in reproductive success that increase with age, and increased egg quality with age [the big old fat fecund female fish (BOFFFF) hypothesis] all reduce N_e /N, extreme scenarios are required to reduce N_e /N below about 0·01. Therefore, tiny N_e /N ratios require some version of Hedgecock's 'sweepstakes' hypothesis, whereby only a few families reproduce successfully. Simulations using common genetically-based estimators show that, when true N_e is very large (≥10⁶ ), a substantial fraction of point estimates of N_e /N can be 10^-3 or smaller. These results mean that tiny, genetically-based point estimates of N_e /N in large marine populations are expected to be quite common, even when the true N_e /N ratio is 'normal' (∼0·1 or higher). Very large samples of individuals can reduce, but not eliminate, this problem. The simulation results also emphasize the importance of considering deviations from model assumptions (e.g. non-random sampling; weak selection or migration) that may be relatively small (and hence can generally be ignored when the signal is strong) but can lead to substantial biases when the drift signal is weak, as is likely for large marine populations. Empirical studies of this topic need to be able to distinguish between episodes of sweepstakes reproductive success that are ephemeral and lead to chaotic genetic patchiness, and those that are consistent enough across space and time to produce persistent evolutionary consequences.

Life-history traits and effective population size in species with overlapping generations revisited: the importance of adult mortality

The relationship between life-history traits and the key eco-evolutionary parameters effective population size (Ne) and Ne/N is revisited for iteroparous species with overlapping generations, with a focus on the annual rate of adult mortality (d). Analytical methods based on populations with arbitrarily long adult lifespans are used to evaluate the influence of d on Ne, Ne/N and the factors that determine these parameters: adult abundance (N), generation length (T), age at maturity (α), the ratio of variance to mean reproductive success in one season by individuals of the same age (φ) and lifetime variance in reproductive success of individuals in a cohort (Vk•). Although the resulting estimators of N, T and Vk• are upwardly biased for species with short adult lifespans, the estimate of Ne/N is largely unbiased because biases in T are compensated for by biases in Vk• and N. For the first time, the contrasting effects of T and Vk• on Ne and Ne/N are jointly considered with respect to d and φ. A simple function of d and α based on the assumption of constant vital rates is shown to be a robust predictor (R(2)=0.78) of Ne/N in an empirical data set of life tables for 63 animal and plant species with diverse life histories. Results presented here should provide important context for interpreting the surge of genetically based estimates of Ne that has been fueled by the genomics revolution.

Prediction and estimation of effective population size

Effective population size (Ne) is a key parameter in population genetics. It has important applications in evolutionary biology, conservation genetics and plant and animal breeding, because it measures the rates of genetic drift and inbreeding and affects the efficacy of systematic evolutionary forces, such as mutation, selection and migration. We review the developments in predictive equations and estimation methodologies of effective size. In the prediction part, we focus on the equations for populations with different modes of reproduction, for populations under selection for unlinked or linked loci and for the specific applications to conservation genetics. In the estimation part, we focus on methods developed for estimating the current or recent effective size from molecular marker or sequence data. We discuss some underdeveloped areas in predicting and estimating Ne for future research.

Harvest-induced evolution and effective population size

Much has been written about fishery‐induced evolution (FIE) in exploited species, but relatively little attention has been paid to the consequences for one of the most important parameters in evolutionary biology—effective population size (N_e). We use a combination of simulations of Atlantic cod populations experiencing harvest, artificial manipulation of cod life tables, and analytical methods to explore how adding harvest to natural mortality affects N_e, census size (N), and the ratio N_e/N. We show that harvest‐mediated reductions in N_e are due entirely to reductions in recruitment, because increasing adult mortality actually increases the N_e/N ratio. This means that proportional reductions in abundance caused by harvest represent an upper limit to the proportional reductions in N_e, and that in some cases N_e can even increase with increased harvest. This result is a quite general consequence of increased adult mortality and does not depend on harvest selectivity or FIE, although both of these influence the results in a quantitative way. In scenarios that allowed evolution, N_e recovered quickly after harvest ended and remained higher than in the preharvest population for well over a century, which indicates that evolution can help provide a long‐term buffer against loss of genetic variability.

Improved confidence intervals for the linkage disequilibrium method for estimating effective population size

The linkage disequilibrium method is currently the most widely used single sample estimator of genetic effective population size. The commonly used software packages come with two options, referred to as the parametric and jackknife methods, for computing the associated confidence intervals. However, little is known on the coverage performance of these methods, and the published data suggest there may be some room for improvement. Here, we propose two new methods for generating confidence intervals and compare them with the two in current use through a simulation study. The new confidence interval methods tend to be conservative but outperform the existing methods for generating confidence intervals under certain circumstances, such as those that may be encountered when making estimates using large numbers of single-nucleotide polymorphisms.

Evaluation of the linkage-disequilibrium method for the estimation of effective population size when generations overlap: an empirical case

BACKGROUND

Within the genetic methods for estimating effective population size (N e ), the method based on linkage disequilibrium (LD) has advantages over other methods, although its accuracy when applied to populations with overlapping generations is a matter of controversy. It is also unclear the best way to account for mutation and sample size when this method is implemented. Here we have addressed the applicability of this method using genome-wide information when generations overlap by profiting from having available a complete and accurate pedigree from an experimental population of Iberian pigs. Precise pedigree-based estimates of N e were considered as a baseline against which to compare LD-based estimates.

METHODS

We assumed six different statistical models that varied in the adjustments made for mutation and sample size. The approach allowed us to determine the most suitable statistical model of adjustment when the LD method is used for species with overlapping generations. A novel approach used here was to treat different generations as replicates of the same population in order to assess the error of the LD-based N e estimates.

RESULTS

LD-based N e estimates obtained by estimating the mutation parameter from the data and by correcting sample size using the 1/2n term were the closest to pedigree-based estimates. The N e at the time of the foundation of the herd (26 generations ago) was 20.8 ± 3.7 (average and SD across replicates), while the pedigree-based estimate was 21. From that time on, this trend was in good agreement with that followed by pedigree-based N e.

CONCLUSIONS

Our results showed that when using genome-wide information, the LD method is accurate and broadly applicable to small populations even when generations overlap. This supports the use of the method for estimating N e when pedigree information is unavailable in order to effectively monitor and manage populations and to early detect population declines. To our knowledge this is the first study using replicates of empirical data to evaluate the applicability of the LD method by comparing results with accurate pedigree-based estimates.

Effects of overlapping generations on linkage disequilibrium estimates of effective population size

Use of single-sample genetic methods to estimate effective population size has skyrocketed in recent years. Although the underlying models assume discrete generations, they are widely applied to age-structured species. We simulated genetic data for 21 iteroparous animal and plant species to evaluate two untested hypotheses regarding performance of the single-sample method based on linkage disequilibrium (LD): (1) estimates based on single-cohort samples reflect the effective number of breeders in one reproductive cycle (Nb), and (2) mixed-age samples reflect the effective size per generation (Ne). We calculated true Ne and Nb, using the model species' vital rates, and verified these with individual-based simulations. We show that single-cohort samples should be equally influenced by Nb and Ne and confirm this with simulated results: [Formula: see text] was a linear (r(2) = 0.98) function of the harmonic mean of Ne and Nb. We provide a quantitative bias correction for raw [Formula: see text] based on the ratio Nb/Ne, which can be estimated from two or three simple life history traits. Bias-adjusted estimates were within 5% of true Nb for all 21 study species and proved robust when challenged with new data. Mixed-age adult samples produced downwardly biased estimates in all species, which we attribute to a two-locus Wahlund effect (mixture LD) caused by combining parents from different cohorts in a single sample. Results from this study will facilitate interpretation of rapidly accumulating genetic estimates in terms of both Ne (which influences long-term evolutionary processes) and Nb (which is more important for understanding eco-evolutionary dynamics and mating systems).