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.     

Prediction of Response to Selection and Inbreeding Coefficient under Assortative Mating

A method for predicting response to selection and inbreeding coefficient under the continuous use of assortative mating was derived. Using the method, numerical computation was carried out, and the utility of assortative mating in the selection programmes was evaluated. It was shown that the continuous use of assortative mating could not produce an appreciable additional increase in intermediate- or long-term selection response.     

Pedigree analysis in the Polish Red cattle population

The objective of this study was to describe the population structure and inbreeding level of the population of Polish Red Cattle (PRC). The structure of the breed was analysed in the context of the existing genetic resources conservation programme. The level of genetic diversity and the effective population size were also determined. The analyses were carried out based on pedigree records of 9 170 animals. Data and pedigree information were collected during the time period of 1950–2014. Records were collected by the National Research Institute of Animal Production in Balice, Poland. The population structure was analysed using the CFC programme. All the animals were grouped into five classes according to their inbreeding coefficient: the first class included non-inbred animals; and the next classes included inbred animals 0% < F ≤ 5%, 5% < F ≤ 10%, 10% < F ≤ 20%, 20% < F ≤ 30% or F > 30%. The average inbreeding in PRC population was 4% and there were 2 182 (23.8%) inbred animals. The study also included the determination of ancestral paths for the PRC population. The longest ancestral path (LAP) consisted of 12 generations (three animals) while only 229 animals (2.53%) had an LAP comprising at least 10 generations. Therefore, a need exists, particularly in PRC as a small local breed, to manage selection and mating decisions to control future coancestry and inbreeding, which would lead to better handling of the effective population size. The study results showed the possibility of disrupting the balance of the structure of a small population like PRC. Hence, endangered populations need to be monitored on a continuous basis.     

Inbreeding depression and mating-distance dependent offspring fitness in large and small populations of Lychnis flos-cuculi (Caryophyllaceae)

The spatial structure of four Lychnis flos-cuculi populations, varying in size and degree of isolation, was studied by comparing the fitness of offspring resulting from self-pollination and pollinations by neighbouring plants, plants within the same population, and plants from other populations. Selfed offspring had the lowest fitness of the four offspring groups. No significant difference was found between the performance of offspring from pollinations by neighbouring plants and offspring pollinated by plants further apart but within the same population. A lower fitness of offspring from pollinations between neighbours would be expected if these matings, on average, yielded inbred offspring which suffered from inbreeding depression. These results imply that either a tight neighbourhood structuring is not present, or that the inbreeding depression for offspring by neighbours is too low to detect, although these are inbred. Crossings between populations produced offspring with a significantly higher fitness than offspring sired within populations. There were no significant differences in response to inbreeding among the populations, and differences in mean fitness among populations had no clear relation to the population size or degree of isolation. A reduced fitness of small populations due to inbreeding depression or a less severe response to experimental inbreeding due to purging of deleterious alleles is therefore not supported by our results.     

Coalescent process with fluctuating population size and its effective size

We consider a Wright-Fisher model whose population size is a finite Markov chain. We introduce a sequence of two-dimensional discrete time Markov chains whose components describe the coalescent process and the fluctuation of population size. For the limiting process of the sequence of Markov chains, the relationship of the expectation of coalescence time to the harmonic and the arithmetic means of population sizes is shown, and the Laplace transform of the distribution of coalescence time is calculated. We define the coalescence effective population size (cEPS) by the expectation of coalescence time. We show that cEPS is strictly larger (resp. smaller) than the harmonic (resp. arithmetic) mean. As the population size fluctuates more quickly (resp. slowly), cEPS is closer to the harmonic (resp. arithmetic) mean. For the case of a two-valued Markov chain, we show the explicit expression of cEPS and its dependency on the sample size.     

Evaluating methods for estimating local effective population size with and without migration

Effective population size is a fundamental parameter in population genetics, evolutionary biology, and conservation biology, yet its estimation can be fraught with difficulties. Several methods to estimate N_e from genetic data have been developed that take advantage of various approaches for inferring N_e. The ability of these methods to accurately estimate N_e, however, has not been comprehensively examined. In this study, we employ seven of the most cited methods for estimating N_e from genetic data (Colony2, CoNe, Estim, MLNe, ONeSAMP, TMVP, and NeEstimator including LDNe) across simulated datasets with populations experiencing migration or no migration. The simulated population demographies are an isolated population with no immigration, an island model metapopulation with a sink population receiving immigrants, and an isolation by distance stepping stone model of populations. We find considerable variance in performance of these methods, both within and across demographic scenarios, with some methods performing very poorly. The most accurate estimates of N_e can be obtained by using LDNe, MLNe, or TMVP; however each of these approaches is outperformed by another in a differing demographic scenario. Knowledge of the approximate demography of population as well as the availability of temporal data largely improves N_e estimates.     

Response to Selection and Inbreeding Depression in a Dynamic Population for Amount of Inbreeding

A method for predicting response to selection and inbreeding depression in a dynamic population for amount of inbreeding was derived and illustrated with an example of selection under full-sib mating.     

The effective number of a population that varies cyclically in size. II. Overlapping generations

We consider haploid and dioecious age-structured populations that vary over time in cycles of length k. Results are obtained for both autosomal and sex-linked loci if the population is dioecious. It is assumed that k is small in comparison with numbers of haploid individuals (or of numbers of males and females) in any generation of a cycle. The inbreeding effective population size N(e) is then approximately given by the expression [T summation operator (k-1)(j=0)1/[N(e)(j)T(j)]](-1), where N(e)(j) and T(j) are, respectively, the effective population size and generation interval that would hold if the population was at all times generated in the same way as at time j. The constant T, which is the effective overall generation interval, is defined to be k times the harmonic mean of the quantities T(j). Our expressions for T and N(e), in terms of N(e)(j) and T(j), are general, but the N(e)(j)s are derived under the assumption that offspring are produced according to Poisson distributions.     

Pedigree analysis of the closed nucleus of Iranian Baluchi sheep

A study was conducted to characterise genetic diversity in the closed nucleus of Baluchi sheep using pedigree analysis. Herdbook information collected between 1979 and 2008, including pedigree records on 21,721 animals, was used to compute inbreeding and average generation intervals. Effective population size and parameters derived from probability of gene origin were computed for ewes born between 2005 and 2008 with both parents known (female reference population). The average complete generation equivalent of the female reference population was 5.47. The mean generation interval was 3.33 years in the studied period. From 1983 to 1994, the rate of increase in inbreeding was approximately 0.2% per year, but, after 1994, inbreeding did not increase as in the preceding years and had an approximately flat trend over time. The mean relationship coefficients among rams, among ewes and between rams and ewes in active animals were calculated to predict the future level of inbreeding. The effective number of founders, effective number of ancestors and founder genome equivalent of the reference population were 80, 47 and 19.5, respectively. The realised effective population size was 134 animals. The results of this study indicated that the population under study has fairly good genetic variability.     

Accounting for missing data in the estimation of contemporary genetic effective population size (Ne)

Theoretical models are often applied to population genetic data sets without fully considering the effect of missing data. Researchers can deal with missing data by removing individuals that have failed to yield genotypes and/or by removing loci that have failed to yield allelic determinations, but despite their best efforts, most data sets still contain some missing data. As a consequence, realized sample size differs among loci, and this poses a problem for unbiased methods that must explicitly account for random sampling error. One commonly used solution for the calculation of contemporary effective population size (N_e) is to calculate the effective sample size as an unweighted mean or harmonic mean across loci. This is not ideal because it fails to account for the fact that loci with different numbers of alleles have different information content. Here we consider this problem for genetic estimators of contemporary effective population size (N_e). To evaluate bias and precision of several statistical approaches for dealing with missing data, we simulated populations with known N_e and various degrees of missing data. Across all scenarios, one method of correcting for missing data (fixed‐inverse variance‐weighted harmonic mean) consistently performed the best for both single‐sample and two‐sample (temporal) methods of estimating N_e and outperformed some methods currently in widespread use. The approach adopted here may be a starting point to adjust other population genetics methods that include per‐locus sample size components.     

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.     

Genetic vulnerability of a remnant ant population

Ants are ecologically important species in many environments forming a big proportion of the total animal biomass. However, their special features such as sociality and complementary sex-determination system have received little attention in conservation discussions. We examined the social and genetic structure of the hairy wood ant Formica lugubris in Ireland to evaluate factors relevant to the vulnerability of small, isolated wood ant populations. We also clarified the conservation status of the species in Ireland. Our results showed that the populations are mainly monogynous (one queen per nest). Consequently the effective population size is very low (<100 individuals) in Ireland. We found extremely little genetic variation, signs of inbreeding and inbreeding depression, which can be a consequence of the small effective population size and of the restricted gene flow due to strong isolation of populations. Putatively high genetic diversity at the sex-determining locus can reflect a larger population in the past. The study shows that even though the population may seem stable because of the long life span of queen ants, sociality can impact species conservation by keeping the effective population size small. According to our results, the hairy wood ant can be considered native to Ireland. Hence it needs urgent protection and the genetic issues need to be considered in the future management strategies.     

Implications of the variance effective population size on the genetic conservation of monoecious species

The concept of variance effective population size [Ne_(v)] and other expressions are reviewed and described for specific sampling steps in germplasm collection and regeneration of monoecious species. Special attention is given to procedures for computing the variance of the number of contributed gametes [V(k)] to the next generation. Drift, as it occurs between generations, was considered to contain a component due to the sampling of parents and a subsequent component due to the sampling of gametes. This demonstrates that drift, caused by reduction of seed viability, damages the genetic integrity of accessions stored in germplasm banks. The study shows how mating designs, such as plant-to-plant or chain crossings with additional female gametic control, can partially alleviate this problem. Optimal procedures for increasing Ne_(v) when collecting germplasm in the field are also discussed. The effect of different female and male gametic control strategies on Ne_(v) is considered under several situations. Practical examples illustrating the use of V(k) and Ne_(v) expressions are given.     

The effect of sample size on estimates of genetic differentiation and effective population size for Schistosoma mansoni populations

Eradication or local extinction of the human parasite Schistosoma mansoni is a goal for many control programs. Population genetic analyses are helping to evaluate and guide these efforts, yet what to sample, how to sample and how densely to sample is not well established. We determined the S. mansoni allele frequency profile of nearly all infected inhabitants in two small Brazilian communities and created sub-samples representing 5–50% of all detected human infections (infrapopulations). Samples were selected at random with replacement, and each size class was replicated 100 times. Mean pairwise differentiation for all infrapopulations (Di) and the variance effective population size (Ne) were calculated for each sample. Prior to community-wide treatment, the true mean Di was moderate (0.095–0.123) and Ne large (>30,000). Most samples of <50% of those infected produced estimates outside of 5% of the true value. For estimates within 10%, sample sizes of >15% of all infrapopulations were required. At the 3?year follow-up after treatment, the Di increased and Ne was reduced by >15 fold. At this time sampling of >30–45% was needed to achieve the same accuracy. Following a second treatment and 4?years from baseline, the Di further increased and Ne decreased with little change in the sampling effort required. Extensive sampling is required for accurate estimates of these important population parameters. Characteristics such as population census size, infection prevalence, the community’s treatment history and the degree of infrapopulation differentiation should be taken into account. The intensity of infection was weakly correlated with the ability of a single infrapopulation to represent the component population (Dic), indicating a tendency toward random acquisition of parasite genotypes. This also suggests that targeted sampling from those most heavily infected will better represent the genetic diversity of the whole community than a random sample of infrapopulations.     

Formulation and estimation of the effective size of stage-structured populations in Fritillaria camtschatcensis, a perennial herb with a complex life history

The effective population size (Ne) is formulated based on a stage-structured population model and is estimated for two populations of Fritillaria camtschatcensis (L.) Ker-Gawl. (Liliaceae), a perennial, mainly clonally reproducing herb. Plants in these populations change life-history stages year by year, either upward or downward across three unambiguously identifiable stages: one-leaf, nonflowering; multileaf nonflowering; and multileaf, flowering stages. Plants of all stages produce clonal progeny (bulblets) each year, and death of plants occurs only in the first stage. The populations are nearly at equilibrium in both population size and stage structure. Ne is estimated to be 20-30% of the census population size (N), leading to the prediction that a population size of about 20,000 or more will be needed to conserve the normal level of the gene diversity (Ne > or = 5000). With the current demographic pattern of this species, accelerated growth of the first-stage plants with reduced survival of the second- and third-stage plants will increase both the annual (Ny/N) and generation time (Ne/N) effective sizes of population.     

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.     

WFABC: a Wright–Fisher ABC‐based approach for inferring effective population sizes and selection coefficients from time‐sampled data

With novel developments in sequencing technologies, time‐sampled data are becoming more available and accessible. Naturally, there have been efforts in parallel to infer population genetic parameters from these data sets. Here, we compare and analyse four recent approaches based on the Wright–Fisher model for inferring selection coefficients (s) given effective population size (N_e), with simulated temporal data sets. Furthermore, we demonstrate the advantage of a recently proposed approximate Bayesian computation (ABC)‐based method that is able to correctly infer genomewide average N_e from time‐serial data, which is then set as a prior for inferring per‐site selection coefficients accurately and precisely. We implement this ABC method in a new software and apply it to a classical time‐serial data set of the medionigra genotype in the moth Panaxia dominula. We show that a recessive lethal model is the best explanation for the observed variation in allele frequency by implementing an estimator of the dominance ratio (h).     

Genomic inbreeding and population structure of northern pike (Esox lucius) in Xinjiang,China

Northern pike (Esox lucius) was widely distributed in the high latitudes of the northern hemisphere. In China, northern pike was originally distributed only in the upper reaches of the Irtysh River in Xinjiang and has appeared in many water bodies outside the Irtysh River Basin in Northern Xinjiang. A total of four populations were collected from north to south in Xinjiang, including Irtysh River (RIR), Ulungu Lake (LUL), a small lake nearby Ulungu River (LJD), and Bosten Lake (LBO). We estimated population genomic parameters, performed gene flow analysis, and estimated the effective population size of each population. The proportion of individuals with high inbreeding coefficient (F ≥ 0.0625) accounted for 36.4% (44/121) of all sequenced individuals, approximately 4.5% (1/22) in LUL, 25.9% (7/27) in LBO, 42.9% (18/42) in RIR, and 60% (18/30) in LJD. RIR had the highest mean of genomic relatedness (coancestry coefficient = 0.025 ± 0.040, IBD = 0.036 ± 0.078). Gene flow results showed that the population spreading was from RIR into two branches, one was LBO, and the other continued to split into LUL and LJD, and migration signal from LBO to LUL was detected. Our results suggested that the extinction risk of northern pike was very low in Xinjiang of China, and the controlled capture fishery of northern pike could be developed reasonably.     

Large effective population sizes and high levels of gene flow between subpopulations of Lilium cernuum (Liliaceae)

The Baekdudaegan, a mountain range that runs north to south along the Korean Peninsula, has been suggested to harbor important glacial refugia for boreal and temperate plant species. A series of allozyme-based genetic studies supports this trend. A large effective population size (N_e) is suggested as one of major factors contributing to maintaining moderate or high levels of within-population genetic variation in these plant species. To test this hypothesis, we examined the levels and patterns of allozyme diversity, tested recent bottlenecks, and estimated recent migration rates in 10 subpopulations (collected within a distance of ca. 640 m) of the boreal Lilium cernuum at Mt. Deokhang, in the central part of the Baekdudaegan. We found high levels of within-population genetic variation as well as a low between-population genetic differentiation (H_e = 0.206 and F_ST = 0.019). Based on the F_ST estimate and mean recent migration rate, we approximately calculated a total effective population size of 508 across 10 subpopulations. Consistent with this, we found no evidence of recent bottlenecks in the subpopulations. This study reveals that subpopulations of L. cernuum at Mt. Deokhang are effectively large (on the order of hundreds), and that high levels of gene flow occur among them, probably due to the species' high potential for seed dispersal. These demographic and life-history traits, coupled with its high levels of genetic diversity, suggests that this cold-adapted species would have found large refugial areas in these mountains (i.e., macrorefugia) during the Last Glacial Maximum.     

Small effective population sizes of two remnant ocelot populations (<Emphasis Type="Italic">Leopardus pardalis albescens</Emphasis>) in the United States

Threatened populations are vulnerable to the effects of genetic drift and inbreeding, particularly when gene flow is low and the effective population size is small. Estimates of effective population size (N _e ) provide important information on the status of endangered populations that have experienced severe fragmentation and serve as indicators of genetic viability. Genetic data from microsatellite loci were used to estimate N _e for the 2 remaining populations of the endangered ocelot (Leopardus pardalis albescens) occurring in the United States. Several methods were used to calculate N _e , resulting in estimates ranging from N _e  = 8.0 (95% CI: 3.2–23.1) to 13.9 (95% CI: 7.7–25.1) for the population located at the Laguna Atascosa Wildlife Refuge in Cameron County, Texas. The ocelot population in Willacy County, Texas, had N _e estimates of 2.9 (95% CI: 1.7–5.6) and 3.1 (95% CI: 1.9–13.5), respectively. Estimates of N _e in both populations were below the critical value recommended for short-term viability.