Estimating the prevalence of inbreeding from incomplete pedigrees

A previous review of inbreeding in natural populations suggested that close inbreeding (inbreeding coefficient f = 0.25) is generally rare in wild birds and mammals. However, the review did not assess rates of moderate inbreeding (f = 0.125), which may make a rather larger contribution to overall inbreeding in a population. Furthermore, previous studies may have underestimated the prevalence of inbreeding in wild populations with incomplete pedigrees. By categorizing inbreeding events by the relationship of the parental pair, we suggest a simple method for estimating rates of close and moderate inbreeding from incomplete pedigree data. We applied this method to three wild populations of ruminants: red deer on Rum, Scotland, Soay sheep on Hirta, Scotland and reintroduced Arabian oryx on the Jiddat-al-Harasis, Oman. Although paternal half-sib pairs were the most common category of inbreeding in all three populations, there was considerable variation among populations in the frequencies of the various categories of inbreeding. This variation may be largely explained by differences in population size and dynamics, in maternal and paternal sibship size and in the overlap of reproductive lifespan of consecutive generations. Close and moderate inbreeding appear to be a routine part of breeding behaviour in these ruminant populations.     

Two-locus inbreeding measures for recurrent selection

Summary For a population undergoing recurrent selection, a method is presented for determining the average inbreeding coefficients at the end of each breeding cycle. The coefficients are derived in terms of probability measures that genes are identical by descent. For the one-locus case, two digametic measures are defined and employed in the derivation of a recurrence formula for the inbreeding coefficient. Two further classes of measures, trigametic and quadrigametic, are required for transition from one cycle to the previous one to allow the calculation of the inbreeding function for the two-locus case. Numerical values of the average probability of double identity by descent for populations with various imposed assumptions are listed to illustrate the effects of linkage and population size on the accrual of inbreeding and hence of homozygosity.Paper number 5018 of the Journal Series of the North Carolina Agricultural Experiment Station, Raleigh, North Carolina. This investigation was supported in part by NIH research grant number GM 11546 from the National Institute of General Medical Sciences.     

Inbreeding in Japanese quail estimated by pedigree and microsatellite analyses

Accurately estimating inbreeding is important because inbreeding reduces fitness and production traits in populations. We analyzed information from pedigrees and from microsatellite markers to estimate inbreeding in a line of Japanese quail derived from a randombred line (QO) and maintained for 17 generations by pedigreed matings of brothers to groups of sisters. Pedigree data were used to calculate the inbreeding coefficient (F(IT)), which is the level of inbreeding based on a reference ancestor. Data from analysis of 14 microsatellite markers in the inbred and QO lines were used to calculate the population differentiation (F(ST)) of the lines caused by inbreeding. The F(IT) was then calculated as F(IT) = F(IS) + (1 - F(IS)) x F(ST), where F(IS) is the level of inbreeding in the inbred line. Observed heterozygosity from analysis of the microsatellite markers of the QO and inbred lines was 0.43 and 0.21, respectively, and the number of alleles was 3.29 and 1.93, demonstrating a reduction of genetic diversity in the inbred line. The F(IT) of the inbred line calculated from the pedigree and microsatellite marker analyses was 0.69 +/- 0.07 and 0.57 +/- 0.33, respectively. These data suggest that pedigree analysis was more accurate than microsatellite marker analyses for estimating inbreeding in this line of Japanese quail.     

THE EFFECTS OF FIVE GENERATIONS OF ENFORCED SELFING ON POTENTIAL MALE AND FEMALE FUNCTION IN MIMULUS GUTTATUS

In prior work we detected no significant inbreeding depression for pollen and ovule production in the highly selfing Mimulus micranthus, but both characters showed high inbreeding depression in the mixed-mating M. guttatus. The goal of this study was to determine if the genetic load for these traits in M. guttatus could be purged in a program of enforced selfing. These characters should have been under much stronger selection in our artificial breeding program than previously reported characters such as biomass and total flower production because, for example, plants unable to produce viable pollen could not contribute to future generations. Purging of genetic load was investigated at the level of both the population and the individual maternal line within two populations of M. guttatus. Mean ovule number, pollen number, and pollen viability declined significantly as plants became more inbred. The mean performance of outcross progeny generated from crosses between pairs of maternal inbred lines always exceeded that of self progeny and was fairly constant for each trait through all five generations. The consistent performance of outcross progeny and the universally negative relationships between performance and degree of inbreeding are interpreted as evidence for the weakness of selection relative to the quick fixation of deleterious alleles due to drift during the inbreeding process. The selective removal (purging) of deleterious alleles from our population would have been revealed by an increase in performance of outcross progeny or an attenuation of the effects of increasing homozygosity. The relationships between the mean of each of these traits and the expected inbreeding coefficient were linear, but one population displayed a significant negative curvilinear relationship between the log of male fertility (a function of pollen number and viability) and the inbreeding coefficient. The generally linear form of the responses to inbreeding were taken as evidence consistent with an additive model of gene action, but the negative curvilinear relationship between male fertility and the inbreeding coefficient suggested reinforcing epistasis. Within both populations there was significant genetic variation among maternal lineages for the response to inbreeding in all traits. Although all inbred lineages declined at least somewhat in performance, several maternal lines maintained levels of performance just below outcross means even after four or five generations of selfing. We suggest that selection among maternal lines will have a greater effect than selecting within lines in lowering the genetic load of populations.     

EFFECTS OF DIFFERENT LEVELS OF INBREEDING ON PROGENY FITNESS IN PLANTAGO CORONOPUS

Inbreeding depression (δ) is a major selective force favoring outcrossing in flowering plants. Many phenotypic and genetic models of the evolution of selfing conclude that complete outcrossing should evolve whenever inbreeding depression is greater than one-half, otherwise selfing should evolve. Recent theoretical work, however, has challenged this view and emphasized (1) the importance of variation in inbreeding depression among individuals within a population; and (2) the nature of gene action between deleterious mutations at different loci (epistasis) as important determinants for the evolution of plant mating systems. The focus of this study was to examine the maintenance of inbreeding depression and the relationship between inbreeding level and inbreeding depression at both the population and the individual level in one population of the partially self-fertilizing plant Plantago coronopus (L.). Maternal plants, randomly selected from an area of about 50 m² in a natural population, were used to establish lines with expected inbreeding coefficients (f) of 0, 0.25, 0.50, 0.75, and 0.875. Inbreeding depression was estimated both in the greenhouse and at the site of origin of the maternal plants by comparing growth, survival, flowering, and seed production of the progeny with different inbreeding coefficients. No significant inbreeding depression for these fitness traits was detected in the greenhouse after 16 weeks. This was in strong contrast to the field, where the traits all displayed significant inbreeding depression and declined with increased inbreeding. The results were consistent with the view that mutation to mildly deleterious alleles is the primary cause of inbreeding depression. At the family level, significantly different maternal line responses (maternal parent × inbreeding level interaction) provide a mechanism for the invasion of a selfing variant into the population through any maternal line exhibiting purging of its genetic load. At the population level, evidence for synergistic epistasis was detected for the probability of flowering, but not for total seed production. At the family level, however, a significant interaction between inbreeding level and maternal families for both traits was observed, indicating that epistasis could play a role in the expression of inbreeding depression among maternal lines.     

Reduction of inbreeding in commercial females by rotational mating with several sire lines

A mating system to reduce the inbreeding of commercial females in the lower level was examined theoretically, assuming a hierarchical breed structure, in which favorable genes are accumulated in the upper level by artificial selection and the achieved genetic progress is transferred to the lower level through migration of males. The mating system examined was rotational mating with several closed sire lines in the upper level. Using the group coancestry theory, we derived recurrence equations for the inbreeding coefficient of the commercial females. The asymptotic inbreeding coefficient was also derived. Numerical computations showed that the critical factor for determining the inbreeding is the number of sire lines, and that the size of each sire line has a marginal effect. If four or five sire lines were available, rotational mating was found to be quite an effective system to reduce the short- and long-term inbreeding of the commercial females, irrespective of the effective size of each sire line. Oscillation of the inbreeding coefficient under rotational mating with initially related sire lines could be minimized by avoiding the consecutive use of highly related lines. Extensions and perspectives of the system are discussed in relation to practical application.     

Heterozygosity, inbreeding and neonatal traits in Soay sheep on St Kilda

We investigated whether birth weight and neonatal survival, a period within which 24% of all mortalities occur, were correlated with levels of inbreeding in St Kilda Soay sheep, using pedigree inbreeding coefficients and four marker-based estimators of inbreeding. None of the inbreeding estimators, either of the offspring, or of their mothers, explained significant variation in a lamb's birth weight or probability of surviving the neonatal period, suggesting low inbreeding depression for these traits. We evaluated the correlation between the marker-based measures of inbreeding and inbreeding coefficients obtained from the Soay pedigree, where paternal links were inferred using the same panel of microsatellite markers. Even when using a relatively complete portion of the pedigree, in which all individuals had known maternal and paternal grandparents, the correlation was found to be weak (r = -0.207, where mean f = 0.0168). These results add support to the recent prediction that when the mean and variance in inbreeding are low in a population, heterozygosity-fitness correlations can be very weak or even undetectable. The pursuit of more detailed pedigrees offers the best prospect for identifying inbreeding depression within this study population.     

A Bayesian method for the joint estimation of outcrossing rate and inbreeding depression

The population outcrossing rate (t) and adult inbreeding coefficient (F) are key parameters in mating system evolution. The magnitude of inbreeding depression as expressed in the field can be estimated given t and F via the method of Ritland (1990). For a given total sample size, the optimal design for the joint estimation of t and F requires sampling large numbers of families (100–400) with fewer offspring (1–4) per family. Unfortunately, the standard inference procedure (MLTR) yields significantly biased estimates for t and F when family sizes are small and maternal genotypes are unknown (a common occurrence when sampling natural populations). Here, we present a Bayesian method implemented in the program BORICE (Bayesian Outcrossing Rate and Inbreeding Coefficient Estimation) that effectively estimates t and F when family sizes are small and maternal genotype information is lacking. BORICE should enable wider use of the Ritland approach for field-based estimates of inbreeding depression. As proof of concept, we estimate t and F in a natural population of Mimulus guttatus. In addition, we describe how individual maternal inbreeding histories inferred by BORICE may prove useful in studies of inbreeding and its consequences.     

Effects of population structures and selection strategies on the purging of inbreeding depression due to deleterious mutations

Stochastic simulations were run to compare the effects of nine breeding schemes, using full-sib mating, on the rate of purging of inbreeding depression due to mutations with equal deleterious effect on viability at unlinked loci in an outbred population. A number of full-sib mating lines were initiated from a large outbred population and maintained for 20 generations (if not extinct). Selection against deleterious mutations was allowed to occur within lines only, between lines or equal within and between lines, and surviving lines were either not crossed or crossed following every one or three generations of full-sib mating. The effectiveness of purging was indicated by the decreased number of lethal equivalents and the increased fitness of the purged population formed from crossing surviving lines after 20 generations under a given breeding scheme. The results show that the effectiveness of purging, the survival of the inbred lines and the inbreeding level attained are generally highest with between-line selection and lowest with within-line selection. Compared with no crossing, line crossing could lower the risk of extinction and the inbreeding coefficient of the purged population substantially with little loss of the effectiveness of purging. Compromising between the effectiveness of purging, and the risk of extinction and inbreeding coefficient, the breeding scheme with equal within- and between-line selection and crossing alternatively with full-sib mating is generally the most desirable scheme for purging deleterious mutations. Unless most deleterious mutations have relatively large effects on fitness in species with reproductive ability high enough to cope with the depressed fitness and thus increased risk of extinction with inbreeding, it is not justified to apply a breeding programme aimed at purging inbreeding depression by inbreeding and selection to a population of conservation concern.     

Inbreeding, coancestry, and covariance between relatives for X-chromosomal loci

Knowledge about the relationships between relatives for X-chromosomal loci is necessary to compute genetic variances and covariances for the genetic evaluation of individuals for economically important traits in livestock and poultry. Using a unified approach, we derived explicitly the coefficient of inbreeding for individuals and the coefficient of coancestry between collateral and lineal relatives of the same or different sex, assuming that the male is heterogametic and the female is homogametic. Collateral relatives include full sibs, paternal and maternal half-sibs, paternal and maternal single first cousins, and double first cousins. Lineal relatives include parent-offspring, paternal and maternal grandparent-grandoffspring, and aunt- or uncle-niece or -nephew. We also defined additive and dominance relationships to compute genetic covariance between relatives, assuming random mating equilibrium, and clarified misinterpretations and corrected errors in the literature. Our results are also applicable to organisms that have few autosomal loci, such as Drosophila, in which X-chromosomal loci can account for a large amount of genetic variance, and to haplodiploid organisms, such as the honeybee, in which the entire genome is equivalent to being X-chromosomal.     

Heterozygosity–fitness correlations in a wild mammal population: accounting for parental and environmental effects

HFCs (heterozygosity–fitness correlations) measure the direct relationship between an individual's genetic diversity and fitness. The effects of parental heterozygosity and the environment on HFCs are currently under‐researched. We investigated these in a high‐density U.K. population of European badgers (Meles meles), using a multimodel capture–mark–recapture framework and 35 microsatellite loci. We detected interannual variation in first‐year, but not adult, survival probability. Adult females had higher annual survival probabilities than adult males. Cubs with more heterozygous fathers had higher first‐year survival, but only in wetter summers; there was no relationship with individual or maternal heterozygosity. Moist soil conditions enhance badger food supply (earthworms), improving survival. In dryer years, higher indiscriminate mortality rates appear to mask differential heterozygosity‐related survival effects. This paternal interaction was significant in the most supported model; however, the model‐averaged estimate had a relative importance of 0.50 and overlapped zero slightly. First‐year survival probabilities were not correlated with the inbreeding coefficient (f); however, small sample sizes limited the power to detect inbreeding depression. Correlations between individual heterozygosity and inbreeding were weak, in line with published meta‐analyses showing that HFCs tend to be weak. We found support for general rather than local heterozygosity effects on first‐year survival probability, and g2 indicated that our markers had power to detect inbreeding. We emphasize the importance of assessing how environmental stressors can influence the magnitude and direction of HFCs and of considering how parental genetic diversity can affect fitness‐related traits, which could play an important role in the evolution of mate choice.     

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.     

Inbreeding depression in fecundity and inbred line extinction in the bulb mite,Rhizoglyphus robini

This study investigated the magnitude of inbreeding depression in fecundity, and whether the depression is purged during six generations of sib mating in the bulb mite, Rhizoglyphus robini. The progeny resulting from a single generation of brother-sister mating suffered significant inbreeding depression in fecundity. During the following six generations of continuous sib-mating, 58% lines were lost, 45% because of sterility and 13% because of preadult mortality. The lines were then outcrossed, and their inbreeding depression compared with that of the base population. The inbreeding depression for the outcrossed population was 0.15, and for the base population 0.19, but the difference was not significant. The lack of significant purging of inbreeding depression indicates that it was caused either by detrimental genes of small effect, or by the breaking down of overdominant relations between alleles. However, the large proportion of extinct lines points to the former mechanism as a predominant cause of inbreeding depression. Theory predicts that the probability of line extinction with inbreeding increases with its load of mutations. If phenotypic variation in fecundity was partly because of differences in numbers of mutations carried by individuals, the fecundity of the line founder could be expected to correlate with the probability that the line derived from it will survive long-term inbreeding. Indeed, fecundity of founder females was significantly associated with line survival, which suggests that line extinction rate may be used as a method to study individual mutational loads, for example, in studies of sexual selection.     

Transmission of paternal chloroplasts in tobacco (Nicotiana tabacum)

Medgyesy et al. (1986, Mol. Gen. Genet. 204, 195–198) have described in Nicotiana plumbaginifolia and in an interspecific cross involving N. plumbaginifolia and N. tabacum a procedure for selecting cell lines derived from seedlings carrying paternal chloroplasts by taking advantage of a plastid-encoded mutation which confers resistance to streptomycin. We have extended their demonstration of occasional transmission of chloroplasts through pollen to the case of an intraspecific cross in N. tabacum. The line used as maternal parent, ITB19(sua), displayed a cytoplasmic male sterility due to the presence of a cytoplasm originating from N. suaveolens. The line used as paternal parent, SR1, was fertile and possessed mutant chloroplasts conferring resistance to streptomycin. From cell lines derived from 204 seedlings, three were regenerated into streptomycin-resistant buds. The plants derived from these three clones were male-sterile. Their progeny, after crossing with a wild type tobacco line, XHFD8, was resistant to streptomycin. Tests of resistance of the seedlings to tentoxin and restriction analyses of the chloroplast DNA indicated that two clones still had the maternal chloroplasts and were thus probably new streptomycin-resistant mutants, whereas the third one had acquired the chloroplasts of the paternal parent, but had retained the mitochondria of the maternal parent.Abbreviations cp-DNA chloroplast DNA - mt-DNA mitochondrial DNA - Np Nicotiana plumbaginifolia - Nt Nicotiana tabacum     

The names of Spain: a study of the isonymy structure of Spain

In order to estimate the isonymy structure of Spain, we studied surname distribution in 283 Spanish towns based on 3.625 million telephone users selected from 6.328 million users, downloaded from a commercial CD-ROM which contains all 13 million users in the country. Since in Spain the surname is made by the paternal and the maternal surname, it was possible to classify surnames according to parental origin. Two matrices of isonymy distances, one for paternal and one for maternal surnames, were constructed and tested for correlation with geographic distance. For the whole of Spain, Euclidean distance was significantly but weakly correlated with geographic distance both for paternal and maternal surnames, with r = 0.205 +/- 0.013 and r = 0.263 +/- 0.012, respectively. Two dendrograms of the 283 sampled towns were built from the two matrices of Euclidean distance. They are largely colinear. Four main clusters identified by the dendrograms are correlated with geography. Given the surname structure of Spain, we were able to calculate from isonymy and for each town 1). total or expressed inbreeding, 2). random or expected inbreeding, and 3). local inbreeding. Total inbreeding, F(IT), was highest in the North Atlantic regions and lowest along the Mediterranean Coast. The lowest levels were found in Andalusia, Catalunyia, Valencia, and Navarra. Random inbreeding, F(ST), had a similar geographical pattern. Local inbreeding, F(IS), was relatively uniform in the whole of Spain. In towns, random inbreeding dominates over local inbreeding. From the analysis, it emerges that the northwestern area of Spain is the most inbred.     

Ranked Set Sampling and the Line Intercept Method: A More Efficient Procedure

Ranked set sampling is a method which may be used to increase the efficiency of the estimator of the mean of a population. Ranked set sampling with size biased probability of selection (i.e., the items are selected with probability proportion to its size) is combined with the line intercept method to increase the efficency of estimating cover, density and total amount of some variable of interest (e.g. biomass). A two-stage sampling plan is suggested with line intercept sampling in the first stage. Simple random sampling and ranked set sampling are compared in the second stage to show that the unbiased estimators of density, cover and total amount of some variable of interest based on ranked set sampling have smaller variances than the usual unbiased estimator based on simple random sampling. Efficiency is increased by reducing the number of items which are measured on a transect or by increasing the number of independent transects utilized in a study area. An application procedure is given for estimation of coverage, density and number of stems of mountain mahogany (Cercocarpus montanus) in a study area east of Laramie, Wyoming.     

Microsatellite DNA markers: evaluating their potential for estimating the proportion of hatchery-reared offspring in a stock enhancement programme

We describe a statistical method for estimating the effectiveness of a stock enhancement programme using nuclear DNA loci. It is based on knowing the population allele frequencies and the genotypes of the hatchery parents (mother only, or mother and father), and on determining the probability that a wild-born animal will by chance have a genotype consistent with hatchery origin. We show how to estimate the proportion of released animals in the wild population, and its standard error. The method is applied to a data set of eight microsatellite loci in brown tiger prawns (Penaeus esculentus), prior to the start of a possible enhancement programme. We conclude that, for this particular data set, the effectiveness of such an enhancement programme could be quantified accurately if both maternal and paternal genotypes are known, but not if maternal genotypes only are known. Full paternal genotyping would require offspring genotyping and thus would be expensive, but a partly typed paternal genotype from a mass homogenate of offspring would be almost as effective and much cheaper. The experiment would become feasible based on maternal genotypes alone, if a further three typical microsatellite loci could be found to add to the existing panel of eight. The methods detailed should be of interest to any enhancement project that relies on nuclear DNA markers to provide tags.     

Genetic Analysis of Esterase Polymorphism in the Soybean Cyst Nematode, Heterodera glycines

The genetic basis of esterase polymorphism in Heterodera glycines was investigated through controlled matings and analysis of F₁ and F₂ progeny. Three nematode lines, each fixed for a different esterase phenotype, were isolated and purified through repeated directional selection and inbreeding. Each phenotype was characterized by its distinct pair of closely spaced bands of esterase activity. Single-female single-male crosses were conducted according to a modified agar-plate mating technique. F₁ progeny were homogeneous, exhibiting both parental esterase phenotypes (codominant heterozygotes) but no hybrid bands. Approximately 1,500 F₂ progeny segregated in a 1:2:1 ratio for expression of the esterase phenotypes of the female parental line, the heterozygote, and the male parental line. Apparently the three esterase phenotypes correspond to three codominant alleles of a single esterase locus. Reciprocal crosses gave similar results, suggesting no maternal inheritance.     

藉遗传标记评价动物个体近交程度

目的评价动物个体近交程度所需的遗传标记数量。方法通过计算机模拟动物近交系的建立过程,比较不同数量遗传标记估计的个体纯合度与相应世代近交系数的差异。结果 1000次模拟中各世代10个个体不同数量的标记组合计算的纯合度平均值与该世代个体的近交系数都存在差异,使用75个标记所获得的个体纯合度与相应近交系数差异最小的有8个世代,其他组合差异最小的世代为0～3个。随着标记数量的增加,单次模拟所获得标记基因纯合度的最大值和最小值逐渐向真实近交系数接近。结论使用少量的标记评价个体近交程度将存在较大的偏差,标记数量越少,偏差越大,当选用多态性丰富标记数接近75万个时,这种偏差会降到最低,标记数量进一步增大并不能提高评价的准确性。     

Using genetic markers to directly estimate male selection gradients

We present an analysis of Raphanus raphanistrum and simulations illustrating the utility of directly estimating male phenotypic selection gradients using genetic markers. The method offers a much more refined characterization of selection than attempting to assign paternity to individual progeny. Our analysis of R. raphanistrum reveals selection on remarkably fine features of floral morphology, including anther exsertion, that were opaque to previous approaches. The new results also undermine a previous conclusion that selection on wild radish floral morphology acts primarily through female fitness. Simulation results show that selection gradients on the order of beta = 0.1-0.2 can be readily detected with allozyme markers in moderate-sized (< 200 paternal individuals) populations. Highly polymorphic (e.g., microsatellite) markers will likely detect fine scale selection (beta < 0.1) in larger populations (> or = 400 individuals). Increased progeny sample size, by sampling either additional maternal families or more progeny per maternal parent, partly compensates for low exclusion probability. Increasing the number of possible fathers without changing progeny sample size decreases the ability to detect selection, especially at lower exclusion probabilities. Sampling only some male genotypes reduces the power to detect selection and biases (underestimates) the magnitude of the selection gradient estimate.