A test of quantitative genetic theory using Drosophila- effects of inbreeding and rate of inbreeding on heritabilities and variance components

Inbreeding is expected to decrease the heritability within populations. However, results from empirical studies are inconclusive. In this study, we investigated the effects of three breeding treatments (fast and slow rate of inbreeding - inbred to the same absolute level - and a control) on heritability, phenotypic, genetic and environmental variances of sternopleural bristle number in Drosophila melanogaster. Heritability, and phenotypic, genetic and environmental variances were estimated in 10 replicate lines within each of the three treatments. Standard least squares regression models and Bayesian methods were used to analyse the data. Heritability and additive genetic variance within lines were higher in the control compared with both inbreeding treatments. Heritabilities and additive genetic variances within lines were higher in slow compared with fast inbred lines, indicating that slow inbred lines retain more evolutionary potential despite the same expected absolute level of inbreeding. The between line variance was larger with inbreeding and more than twice as large in the fast than in the slow inbred lines. The different pattern of redistribution of genetic variance within and between lines in the two inbred treatments cannot be explained invoking the standard model based on selective neutrality and additive gene action. Environmental variances were higher with inbreeding, and more so with fast inbreeding, indicating that inbreeding and the rate of inbreeding affect environmental sensitivity. The phenotypic variance decreased with inbreeding, but was not affected by the rate of inbreeding. No inbreeding depression for mean sternopleural bristle number was observed in this study. Considerable variance between lines in additive genetic variance within lines was observed, illustrating between line variation in evolutionary potential.     

Analysis of genetic diversity for the management of conserved subdivided populations

Recent studies in the literature have appliedphylogenetic methods based on genetic distancesto set priorities for conservation of domesticanimal breeds. While these methods may beappropriate for between-species conservation,they are clearly inappropriate forwithin-species breed conservation, because theyignore within-breed variation. In this paper weshow the basic tools to analyse geneticdiversity in subdivided populations withinspecies, and illustrate the errors incurred byapplying methods based exclusively on geneticdistances. We also show that maximisation ofgenetic diversity (minimisation of coancestryor kinship) is equivalent to maximisation ofeffective population size, as in undividedpopulations, and derive a generalisation ofprevious equations for the prediction ofeffective size. Finally, we discuss thestrategies for conservation in the light of thetheory.     

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

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

Pedigree analysis of the Turkish Arab horse population: structure,inbreeding and genetic variability

The aim of this study was to evaluate genetic variability in the Turkish Arab horse population using pedigree information. This study is the first detailed pedigree analysis of the breed in Turkey. Pedigree data were collected from the National Studbook. The pedigree data for 23 668 horses, born between 1904 and 2014, were used in the analysis. From this data set, a reference population (RP) of 14 838 animals symbolising the last generation was defined. Demographic parameters, the inbreeding level (F), the average relatedness (AR), the effective population size (N_e), the effective number of founders (f_e), the effective number of ancestors (f_a) and the number of founder genome equivalents (f_g) were calculated for the population. The average generation interval for the RP was 12.2±4.6 years, whereas the calculated pedigree completeness levels were 98.2%, 96.6% and 95.0% for the first, second and third known generations. The mean equivalent generations (t), the average complete generations and the mean maximum generations for the RP were 7.8, 5.4 and 12.2, respectively, whereas the meanFand AR were 4.6% and 9.5% for the RP. The rate of inbred animals was 94.2% for the RP, whereas the number of founders, the number of ancestors and thef_e,f_aandf_gwere 342, 223, 40, 22 and 9.6 for the RP. The large differences observed betweenf_e, and the number of founders demonstrates that genetic diversity decreased between the founder and the RP. Contribution of the 14 most influential founder to the RP was 50.0%, whereas just eight ancestral horses can account for 50% of the genetic variability.N_eestimated via an individual increase in inbreeding per generation (${\overline{N}}_{\text{e}}$), and paired increase in coancestry$\left(\text{}{\overline{N}}_{eC}\right)$, were 74.4±3.9 and 73.5±0.58, respectively. The inbreeding increases with the pedigree knowledge. In addition, the decrease in inbreeding in last years is more noticeable.     

Associative overdominance: Evaluating the effects of inbreeding and linkage disequilibrium

Expressions are obtained for the expected phenotypic values of homozygous and heterozygous genotypes for a neutral marker locus linked to a locus segregating for a recessive deleterious gene. The phenotypic values are functions of the allele frequencies at the marker locus, the inbreeding coefficient and the degree of association of the deleterious gene with the marker alleles. The analysis is extended to more than two alleles at the marker locus. Either linkage disequilibrium or inbreeding alone can produce an apparent superiority of heterozygotes for the marker locus (unless specified otherwise, the terms ‘homozygote’ and ‘heterozygote’ will refer to the marker locus). The effect of linkage disequilibrium on the difference between the heterozygote and homozygote values can be positive (associative overdominance) or negative (associative underdominance), depending on the frequencies of the marker alleles and the degree of their association with the deleterious gene. Inbreeding has always a positive effect. In general, the expected value of a homozygote is a positive function of its allele frequency. When the various homozygous genotypes are combined into one class and the various heterozygous genotypes into another, the phenotypic difference of the two classes is a function of the evenness of the allelic frequency distribution. Inbreeding is a more likely explanation of associative overdominance if the frequency of the deleterious gene is low, but its effect on the character high. Conversely, linkage disequilibrium is more likely if the frequency is high and the effect low. The degrees of association between marker alleles and the deleterious gene can, in principle, be estimated from the observed phenotypic scores and used to calculate expected multi-locus genotype scores. This could provide the basis for statistical tests of the associative overdominance hypothesis as an explanation of observed correlations between multi-locus heterozygosity and phenotypic traits.     

Genetic variability in the European bison (Bison bonasus) population from Białowieża forest over 50 years

The aim of this study was to assess potential post-bottleneck temporal genetic differentiation following the reintroduction of the species into the Białowieża Forest. Variability of 12 polymorphic microsatellite markers was analysed for 178 individuals born between 1955 and 2005, divided by birth year into five temporal groups. Low overall allelic richness (AR) per locus (AR = 2.0) and a low overall expected heterozygosity (H_E = 0.28) were observed. The overall F _IS was not significantly different from zero. The mean F _IS values were, however, significantly different from zero for individuals born between 1955 and 1965 ( F _IS = 0.19). A Bayesian computation was used to estimate effective population size (N_e) for each temporal group. We observed relatively small values of N_e ranging from 7.9 to 28.4. The low N_e values confirm that, despite a rapid growth of the bison population following the founder event, N_e increased only slowly.  © 2009 The Linnean Society of London, Biological Journal of the Linnean Society , 2009, 97 , 801–809.     

Pedigree analysis and inbreeding effects over morphological traits in Campolina horse population

Genetic improvement, without control of inbreeding, can go to loss of genetic variability, reducing the potential for genetic gains in the domestic populations. The aim of this study was to analyze the population structure and the inbreeding depression in Campolina horses. Phenotype information from 43 465 individuals was analyzed, data provided by the Campolina Breeders Association. A pedigree file containing 107 951 horses was used to connected the phenotyped individuals. The inbreeding coefficient was performed by use of the diagonal of the relationship matrix and the genealogical parameters were computed using proper softwares. The effective population size was estimated based on the rate of inbreeding and census information, and the stratification of the population was verified by the average relationship coefficient between animals born in different regions of Brazil. The effects of inbreeding on morphological traits were made by the use of inbreeding coefficient as a covariate in the model of random regression. The inbreeding coefficient increased from 1990 on, impacting effective population size and, consequently, shrinking genetic variability. The paternal inbreeding was greater than maternal, which may be attributed to the preference for inbred animals in reproduction. The average genetic relationship coefficient of animals born in different states was lower than individuals born within the same state. The increase in the inbreeding coefficient was negatively associated with all studied traits, showing the importance to avoid genetic losses in the long term. Although results do not indicate a severe narrowing of the population until the present date, the average relationship coefficient shows signs of increase, which could cause a drastic reduction in genetic variability if inbred mating is not successfully controlled in the Campolina horse population.     

Individual increase in inbreeding allows estimating effective sizes from pedigrees

We present here a simple approach to obtain reliable estimates of the effective population size in real world populations via the computation of the increase in inbreeding for each individual (delta F_i) in a given population. The values of delta F_i are computed as t-root of 1 - (1 - F_i) where F_i is the inbreeding coefficient and t is the equivalent complete generations for each individual. The values of delta F computed for a pre-defined reference subset can be averaged and used to estimate effective size. A standard error of this estimate of N_e can be further computed from the standard deviation of the individual increase in inbreeding. The methodology is demonstrated by applying it to several simulated examples and to a real pedigree in which other methodologies fail when considering reference subpopulations. The main characteristics of the approach and its possible use are discussed both for predictive purposes and for analyzing genealogies.     

Joint effect of selection, linkage and partial inbreeding on additive genetic variance in an infinite population

Under the inifinitesimal model of gene effects, selection reduces the additive genetic variance by inducing negative linkage disequilibrium among selected genes. If the selected genes are linked, the decay of linkage disequilibrium is delayed, and the reduction of additive genetic variance is enhanced. Inbreeding in an infinite population also alters the additive genetic variance through the generation of positive association among genes within a locus. In the present study, the joint effect of selection, linkage and partial inbreeding (partial selfing or partial full-sib mating) on the additive genetic variance was modeled. The recurrence relations of the additive genetic variance between successive generations and the prediction equation of the asymptotic additive genetic variance were derived. Numerical computation showed that although partially inbred populations initially maintain larger genetic variances, the accumulated effect of selection overrides the effect of inbreeding. Stochastic simulation was carried out to check the precision of prediction, showing that the obtained equations give a satisfactory prediction during initial generations. However, the predicted values always overestimate the simulated values, especially in later generations. Based on these results, possible extensions and perspectives of the assumed model were discussed.     

The efficiency of purifying selection in Mammals vs. Drosophila for metabolic genes

The nearly neutral theory of molecular evolution states that the efficiency of natural selection depends on the effective population size. By using a wide range of multispecies data on nucleotide polymorphism, we have tried to ascertain whether there are any differences in the level of selective constraints of metabolic process genes between Mammals and Drosophila species. The results are consistent with a higher selective constraint in Drosophila than in Mammals, according to the expected under the nearly neutral model: purifying selection seems to be more efficient in species with a larger effective population size.     

An explicit model for the inbreeding load in the evolutionary analysis of selfing

I present analytical predictions for the equilibrium inbreeding load expected in a population under mutation, selection, and a regular mating system for any population size and for any magnitude and recessivity of the deleterious effects. Using this prediction, I deduce the relative fitness of mutant alleles with small effect on selfing to explore the situations where selfing or outcrossing are expected to evolve. The results obtained are in agreement with previous literature, showing that natural selection is expected to lead to stable equilibria where populations show either complete outcrossing or complete selfing, and that selfing is promoted by large deleterious mutation rates. I find that the evolution of selfing is favored by a large recessivity of deleterious effects, while the magnitude of homozygous deleterious effects only becomes relevant in relatively small populations. This result contradicts the standard assumption that purging in large populations will only promote selfing when homozygous deleterious effects are large, and implies that previously published results obtained assuming lethal mutations in large populations can be extrapolated to nonlethal alleles of similar recessivity. This conclusion and the general approach used in this analysis can be useful in the study of the evolution of mating systems.     

A comparison of single‐sample estimators of effective population sizes from genetic marker data

In molecular ecology and conservation genetics studies, the important parameter of effective population size (N_e) is increasingly estimated from a single sample of individuals taken at random from a population and genotyped at a number of marker loci. Several estimators are developed, based on the information of linkage disequilibrium (LD), heterozygote excess (HE), molecular coancestry (MC) and sibship frequency (SF) in marker data. The most popular is the LD estimator, because it is more accurate than HE and MC estimators and is simpler to calculate than SF estimator. However, little is known about the accuracy of LD estimator relative to that of SF and about the robustness of all single‐sample estimators when some simplifying assumptions (e.g. random mating, no linkage, no genotyping errors) are violated. This study fills the gaps and uses extensive simulations to compare the biases and accuracies of the four estimators for different population properties (e.g. bottlenecks, nonrandom mating, haplodiploid), marker properties (e.g. linkage, polymorphisms) and sample properties (e.g. numbers of individuals and markers) and to compare the robustness of the four estimators when marker data are imperfect (with allelic dropouts). Extensive simulations show that SF estimator is more accurate, has a much wider application scope (e.g. suitable to nonrandom mating such as selfing, haplodiploid species, dominant markers) and is more robust (e.g. to the presence of linkage and genotyping errors of markers) than the other estimators. An empirical data set from a Yellowstone grizzly bear population was analysed to demonstrate the use of the SF estimator in practice.     

The change in quantitative genetic variation with inbreeding

Inbreeding is known to reduce heterozygosity of neutral genetic markers, but its impact on quantitative genetic variation is debated. Theory predicts a linear decline in additive genetic variance (V(A)) with increasing inbreeding coefficient (F) when loci underlying the trait act additively, but a nonlinear hump-shaped relationship when dominance and epistasis are important. Predictions for heritability (h2) are similar, although the exact shape depends on the value of h2 in the absence of inbreeding. We located 22 published studies in which the level of genetic variation in experimentally inbred populations (measured by V(A) or h2) was compared with that in outbred control populations. For life-history traits, the data strongly supported a nonlinear change in genetic variation with increasing F. V(A) and h2 were, respectively, 244% and 50% higher at F = 0.4 than in outbred populations, and dominance plus epistatic variance together exceeded additive variance by a factor of four. For nonfitness traits the decline was linear and estimates of nonadditive variance were small. These results confirm that population bottlenecks frequently increase V(A) in some traits, and imply that life-history traits are underlain by substantial dominance or epistasis. However, the importance of drift-induced genetic variation in conservation or evolutionary biology is questionable, in part because inbreeding depression usually accompanies inbreeding.     

Effective size of populations under partial inbreeding and selection on a set of linked additive genes

The prediction theory of effective population size (Ne) is extended to cover selection on a set of linked additive genes and partial inbreeding (partial selfing or partial full-sib mating). Ne under selection is generally expressed as a function of the cumulative change in frequency of a neutral gene due to the random association between the neutral and selected genes generated by finite sampling. In this study, the association under partial selfing was classified into two types, the association between the neutral and selected genes on the same gamete, and the association between the neutral and selected genes each on the different gametes in the same parent. For partial full-sib mating, an additional association, i.e., the association between the neutral and selected genes each in the different parents in the same family, was included in the model. According to this classification of the association, the coefficient accounting for the cumulative change in frequency of the neutral gene was partitioned into two or three components. A method for computing the partitioned coefficients was obtained from the transition matrix approach, in which the joint effect of linkage, selection and partial inbreeding was taken into account. To assess the joint effects of linkage, selection and partial inbreeding on Ne, numerical computations with the obtained expressions were carried out. The effect of linkage on Ne was generally small, except for an extremely small genome size, while the partial inbreeding resulted in a drastic reduction in Ne. For a given genome size, Ne was essentially independent of the length and number of chromosomes. Some of these results were verified by stochastic simulations.     

Estimating relatedness and inbreeding using molecular markers and pedigrees: the effect of demographic history

Estimates of inbreeding and relatedness are commonly calculated using molecular markers, although the accuracy of such estimates has been questioned. As a further complication, in many situations, such estimates are required in populations with reduced genetic diversity, which is likely to affect their accuracy. We investigated the correlation between microsatellite‐ and pedigree‐based coefficients of inbreeding and relatedness in laboratory populations of Drosophila melanogaster that had passed through bottlenecks to manipulate their genetic diversity. We also used simulations to predict expected correlations between marker‐ and pedigree‐based estimates and to investigate the influence of linkage between loci and null alleles. Our empirical data showed lower correlations between marker‐ and pedigree‐based estimates in our control (nonbottleneck) population than were predicted by our simulations or those found in similar studies. Correlations were weaker in bottleneck populations, confirming that extreme reductions in diversity can compromise the ability of molecular estimates to detect recent inbreeding events. However, this result was highly dependent on the strength of the bottleneck and we did not observe or predict any reduction in correlations in our population that went through a relatively severe bottleneck of N = 10 for one generation. Our results are therefore encouraging, as molecular estimates appeared robust to quite severe reductions in genetic diversity. It should also be remembered that pedigree‐based estimates may not capture realized identity‐by‐decent and that marker‐based estimates may actually be more useful in certain situations.     

INCREASED PROBABILITY OF EXTINCTION DUE TO DECREASED GENETIC EFFECTIVE POPULATION SIZE: EXPERIMENTAL POPULATIONS OF CLARKIA PULCHELLA

We established replicated experimental populations of the annual plant Clarkia pulchella to evaluate the existence of a causal relationship between loss of genetic variation and population survival probability. Two treatments differing in the relatedness of the founders, and thus in the genetic effective population size (N_e), were maintained as isolated populations in a natural environment. After three generations, the low N_e treatment had significantly lower germination and survival rates than did the high N_e treatment. These lower germination and survival rates led to decreased mean fitness in the low N_e populations: estimated mean fitness in the low N_e populations was only 21% of the estimated mean fitness in the high N_e populations. This inbreeding depression led to a reduction in population survival: at the conclusion of the experiment, 75% of the high N_e populations were still extant, whereas only 31% of the low N_e populations had survived. Decreased genetic effective population size, which leads to both inbreeding and the loss of alleles by genetic drift, increased the probability of population extinction over that expected from demographic and environmental stochasticity alone. This demonstrates that the genetic effective population size can strongly affect the probability of population persistence.     

INBREEDING AND VARIANCE EFFECTIVE SIZES FOR NONRANDOM MATING POPULATIONS

Following an inbreeding approach and assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, I have derived expressions for the inbreeding effective size, N_eI, for a finite diploid population with variable census sizes for three cases: monoecious populations with partial selfing; dioecious populations of equal numbers of males and females with partial sib mating; and unequal numbers of males and females with random mating. For the first two cases, recurrence equations for the inbreeding coefficient are also obtained, which allow inbreeding coefficients to be predicted exactly in both early and late generations. Following the variance of change in gene frequency approach, a general expression for variance effective size, N_eV, is obtained for a population with unequal numbers of male and female individuals, arbitrary family size distribution, and nonrandom mating. All the parameters involved are allowed to change over generations. For some special cases, the equation reduces to the simple expressions approximately as derived by previous authors. Comparisons are made between equations derived by the present study and those obtained by previous authors. Some of the published equations for N_eI and N_eV are shown to be incomplete or incorrect. Stochastic simulations are run to check the results where disagreements with others are involved.     

A comparison of pedigree‐ and DNA‐based measures for identifying inbreeding depression in the critically endangered Attwater's Prairie‐chicken

The primary goal of captive breeding programmes for endangered species is to prevent extinction, a component of which includes the preservation of genetic diversity and avoidance of inbreeding. This is typically accomplished by minimizing mean kinship in the population, thereby maintaining equal representation of the genetic founders used to initiate the captive population. If errors in the pedigree do exist, such an approach becomes less effective for minimizing inbreeding depression. In this study, both pedigree‐ and DNA‐based methods were used to assess whether inbreeding depression existed in the captive population of the critically endangered Attwater's Prairie‐chicken (Tympanuchus cupido attwateri), a subspecies of prairie grouse that has experienced a significant decline in abundance and concurrent reduction in neutral genetic diversity. When examining the captive population for signs of inbreeding, variation in pedigree‐based inbreeding coefficients (f_pedigree) was less than that obtained from DNA‐based methods (f_DNA). Mortality of chicks and adults in captivity were also positively correlated with parental relatedness (r_DNA) and f_DNA, respectively, while no correlation was observed with pedigree‐based measures when controlling for additional variables such as age, breeding facility, gender and captive/release status. Further, individual homozygosity by loci (HL) and parental r_DNA values were positively correlated with adult mortality in captivity and the occurrence of a lethal congenital defect in chicks, respectively, suggesting that inbreeding may be a contributing factor increasing the frequency of this condition among Attwater's Prairie‐chickens. This study highlights the importance of using DNA‐based methods to better inform management decisions when pedigrees are incomplete or errors may exist due to uncertainty in pairings.