Minimising inbreeding in small populations by rotational mating with frozen semen

Mating plans are investigated in order to minimize inbreeding in small populations when frozen semen is available. For a single dam line it was found that specific sire rotations minimized the asymptotic level of inbreeding when semen is used repeatedly from certain generations. When semen of N foundation (G0) sires is used rotationally over generations it is shown that the inbreeding level asymptotes to 1/(2(N+1) - 2). However, if only G0 sires are used then all genes will eventually descend from the founder sires. Inbreeding can be reduced further by using sires from generation one (G1) and later as this retains genes from the founder dams in the long-term gene pool. If semen from NG0 sires and N unrelated G1 sons is used rotationally then inbreeding asymptotes to (2(N-1) + 1)/(2(2N+1) - 2). When there are more founder dams than sires, the asymptotic inbreeding can be reduced even further by using the semen of half-sib G1 sires in rotation. Optimal rotations using full-sib G1 sires or generation 2 (or later) sires will lower the asymptotic inbreeding also, but generally not by much. It was found that when unlimited frozen semen from a specified group of sires was available, the optimal mating plan was achieved by selecting each generation the sire with the least co-ancestry with the current female of the dam line.     

Minimizing inbreeding by managing genetic contributions across generations

Here we present the strategy that achieves the lowest possible rate of inbreeding (DeltaF) for a population with unequal numbers of sires and dams with random mating. This new strategy results in a DeltaF as much as 10% lower than previously achieved. A simple and efficient approach to reducing inbreeding in small populations with sexes of unequal census number is to impose a breeding structure where parental success is controlled in each generation. This approach led to the development of strategies for selecting replacements each generation that were based upon parentage, e.g., a son replacing its sire. This study extends these strategies to a multigeneration round robin scheme where genetic contributions of ancestors to descendants are managed to remove all uncertainties about breeding roles over generations; i.e., male descendants are distributed as equally as possible among dams. In doing so, the sampling variance of genetic contributions within each breeding category is eliminated and consequently DeltaF is minimized. Using the concept of long-term genetic contributions, the asymptotic DeltaF of the new strategy for random mating, M sires and d dams per sire, is phi/(12M), where phi = [1 + 2((1)/(4))(d)]. Predictions were validated using Monte Carlo simulations. The scheme was shown to achieve the lowest possible DeltaF using pedigree alone and showed that further reductions in DeltaF below that obtained from random mating arise from preferential mating of relatives and not from their avoidance.     

Sustainable long-term conservation of rare cattle breeds using rotational AI sires

The development of inbreeding in rotation breeding schemes, sequentially using artificial insemination (AI) sires over generations, was investigated for a full AI scheme. Asymptotic prediction formulae of inbreeding coefficients were established when the first rotation list of AI sires (possibly related) was in use. Simulated annealing provided the optimal rotation order of sires within this list, when the sires were related. These methods were also used for subsequent rotation lists, needed by the exhaustion of semen stores for the first bulls. Simulation was carried out starting with groups of independent sires, with different sizes. To generate a yearly inbreeding rate substantially lower than 0.05% (considered to be within reach by conventional conservation schemes using frequent replacements), the results obtained showed that the number of sires should be at least 10–15 and that the same sires should be used during at least 50 years. The ultimate objective was to examine the relevance of implementing rotation in breeding schemes on the actual rare French cattle breeds under conservation. The best candidate for such a test was the Villard-de-Lans breed (27 bulls and 73 000 doses for only 340 females) and it turned out to be the best performer with an inbreeding coefficient of only 7.4% after 500 years and five different sire lists. Due to the strong requirements on semen stores and on the stability of population size, actual implementation of this kind of conservation scheme was recommended only in special (''niche'') cattle populations.     

Inbreeding and reproduction in mice divergently selected for response to a dietary toxin

This study was conducted to determine whether inbreeding coefficients of selected parents or of progeny differed between lines of mice selected for increased or decreased responsiveness to a nutritional toxicosis. A second objective was to determine whether the influence of inbreeding of parents and/or progeny on reproductive traits differed between those lines. Mice were selected divergently for 8 generations for the effect on post-weaning growth of endophyte-infected fescue seed in their diet. Forty pairs (or in Generation 7, 20 pairs) were selected and mated per generation in each line. Inbreeding increased 0.5 to 0.6% per generation in both lines, a rate close to that predicted from genetic theory. Inbreeding coefficients of selected parents were not higher in the susceptible than in the resistant line. A difference would have been expected if the inbreeding coefficient had been correlated with susceptibility to toxicosis. The magnitudes of inbreeding depression for reproductive traits did not differ significantly between lines. The average inbreeding coefficient of the potential litter tended to be higher in nonfertile than fertile matings (P = 0.10), but inbreeding coefficients of sires and dams did not differ between successful and unsuccessful matings. Inbred litters tended to be born earlier than noninbred litters (P = 0.10). Inbred dams produced smaller litters than noninbred dams (main effect P < 0.05) but only when the litter also was inbred (interaction P < 0.01). Sex ratio was not influenced by inbreeding of sire, dam or litter, but there was a higher proportion of male progeny in the susceptible than in the resistant line (P = 0.01). To avoid reduced reproductive fitness, laboratory animal populations should be managed to minimize inbreeding of progeny and dam.     

Pedigree and marker information requirements to monitor genetic variability

There are several measures available to describe the genetic variability of populations. The average inbreeding coefficient of a population based on pedigree information is a frequently chosen option. Due to the developments in molecular genetics it is also possible to calculate inbreeding coefficients based on genetic marker information. A simulation study was carried out involving ten sires and 50 dams. The animals were mated over a period of 20 discrete generations. The population size was kept constant. Different situations with regard to the level of polymorphism and initial allele frequencies and mating scheme (random mating, avoidance of full sib mating, avoidance of full sib and half sib mating) were considered. Pedigree inbreeding coefficients of the last generation using full pedigree or 10, 5 and 2 generations of the pedigree were calculated. Marker inbreeding coefficients based on different sets of microsatellite loci were also investigated. Under random mating, pedigree-inbreeding coefficients are clearly more closely related to true autozygosity (i.e., the actual proportion of loci with alleles identical by descent) than marker-inbreeding coefficients. If mating is not random, the demands on the quality and quantity of pedigree records increase. Greater attention must be paid to the correct parentage of the animals.     

Evaluation of genetic variation in the international Brown Swiss population

The international Brown Swiss cattle population pedigree was studied to measure genetic variations and to identify the most influential animals. Twenty-two countries provided pedigree information on 71 497 Brown Swiss bulls used for artificial insemination (AI). The total number of animals with the pedigree is 181 094. The mean inbreeding coefficient for the pedigree population was 0.77%. There was, in most cases, an increase in the mean inbreeding coefficient, with the highest value at 2.89% during the last 5-year period (2000 to 2004). The mean average relatedness for the pedigree population was 1.1%. The effective population size in 2004 was 204. There was notable variation between average generation intervals for the four parental pathways. The longest average generation interval, at 8.73 years, was observed in the sire–son pathway. The average generation interval for the whole population was 6.53 years. Most genetically influential individuals were sires. The highest contributing founder was a sire with a 3.22% contribution, and the highest contributing founder dam made a contribution of 1.75%. The effective number of founders and the effective number of ancestors were 141 and 88, respectively. The study showed that genetic variation within the pedigree population has been decreasing over recent years. Increasing the number of AI bulls with a low individual coefficient of inbreeding could help to maintain a good level of genetic variation in the Brown Swiss population.     

Prediction of rates of inbreeding in selected populations

A method is presented for the prediction of rate of inbreeding for populations with discrete generations. The matrix of Wright's numerator relationships is partitioned into 'contribution' matrices which describe the contribution of the Mendelian sampling of genes of ancestors in a given generation to the relationship between individuals in later generations. These contributions stabilize with time and the value to which they stabilize is shown to be related to the asymptotic rate of inbreeding and therefore also the effective population size, Ne approximately 2N/(mu 2r + sigma 2r), where N is the number of individuals per generation and mu r and sigma 2r are the mean and variance of long-term relationships or long-term contributions. These stabilized values are then predicted using a recursive equation via the concept of selective advantage for populations with hierarchical mating structures undergoing mass selection. Account is taken of the change in genetic parameters as a consequence of selection and also the increasing 'competitiveness' of contemporaries as selection proceeds. Examples are given and predicted rates of inbreeding are compared to those calculated in simulations. For populations of 20 males and 20, 40, 100 or 200 females the rate of inbreeding was found to increase by as much as 75% over the rate of inbreeding in an unselected population depending on mating ratio, selection intensity and heritability of the selected trait. The prediction presented here estimated the rate of inbreeding usually within 5% of that calculated from simulation.     

Testing alternative captive breeding strategies with the subsequent release into the wild

We used the housefly (Musca domestica L.) as an experimental model to compare two strategies for the captive breeding of an endangered species: a strategy to minimize inbreeding and balance founder contributions (termed “MAI” for “maximum avoidance of inbreeding”) versus a scheme to select against less fit individuals (disregarding relatedness). By balancing the initial founder contributions, the MAI protocol was analogous to methods for minimizing kinship. In both breeding strategies, the population growth rate was limited to a maximum increase of 50% per generation. Five replicate populations, each starting with five male–female pairs, were subjected to five generations of captive breeding. Six generations of simulated “release into the wild” allowed ad lib breeding with less restrictive population growth potential, in either a benign or stressful environment (i.e., constant or variable temperature). Population size, fecundity, and fertility were assayed throughout the experiment, with juvenile‐to‐adult survival assayed in the second phase of the project. Allozyme assays determined the resultant inbreeding coefficients from the captive breeding schemes. The MAI breeding scheme resulted in significantly lower inbreeding coefficients and higher fitness, with qualitatively reduced extinction potential, most notable in the stressful environment. Spontaneous fitness rebounds suggested that the MAI strategy facilitated some form of purging of inbreeding depression effects. Importantly, the advantages of the MAI strategy were difficult to detect during the captive breeding phase, suggesting that the long‐term advantages of the MAI approach could be underestimated in actual breeding programs. We concur with the common recommendation of maximum avoidance of inbreeding at least for systems with low reproductive potential. Zoo Biol 0:1–18, 2005. © 2005 Wiley‐Liss, Inc.     

Minimization of rate of inbreeding for small populations with overlapping generations

We propose a method that minimizes the rate of inbreeding (delta F) for small unselected populations with overlapping generations and several reproductive age classes. It minimizes the increase in coancestry of parents and optimizes the contribution of each selection candidate. The carrying capacity of the population is limited to a fixed number of animals per year. When survival rate equalled 100%, only animals from the oldest age class were selected, which maximized the number of parents per generation, slowed down the turnover of generations and minimized the increase of coancestry across sublines. However, the population became split into sublines separated by age classes, which substantially increased inbreeding within sublines. Sublines were prevented by a restriction of selecting at least one sire and one dam from the second-oldest age class, which resulted in an L times lower delta F, where L equals the average generation interval of sires and dams. Minimum coancestry mating resulted in lower levels of inbreeding than random mating, but delta F was approximately the same. For schemes where the oldest animals were selected, delta F increased by 18-52% compared with the proposed method.     

Pyridine nucleosidase in bull semen I. Breed and sire differences in enzyme concentration.

The concentration of pyridine nucleosidase which cleaves the nicotinamide-ribose bond in NAD and related compounds was assayed using the cyanide addition reaction in semen samples collected by artificial vagina from 246 bulls. Among the 205 sires of recognized dairy breeds the nucleosidase concentration ranged from 0 to 1470 units/ml semen. Of the dairy sires 18% produced semen containing no nucleosidase activity. Among the 41 sires of recognized beef breeds 54% had no nucleosidase and the highest concentration was 630 units/ml semen. Among 20 sires from each of which 5-17 collections were assayed, there were significant differences in average nucleosidase concentration. There was a discontinuous distribution in nucleosidase concentration among the 169 dairy sires producing semen with measurable enzyme activity. Results for 18 dairy sires each with from 4 to 16 sons showed that sires with no seminal nucleosidase produced more sons with no enzyme or lower concentrations of enzyme than sires with higher nucleosidase concentrations. It is suggested that the concentration of the nucleosidase in bull semen is simply inherited.     

Possible negative effects of inbreeding on semen quality in Shetland pony stallions

Inbreeding is widely believed to negatively affect reproductive performance. Indeed, in some species, high levels of inbreeding are thought to be the major cause of poor semen quality. It is, however, not clear whether inbreeding affects fertility in horses. In this study, the relationship between inbreeding and semen quality was examined in 285 immature Shetland pony stallions submitted for breeding soundness examination in March-April of the years 1992-1997. The majority of stallions examined were 3 years old (85%) and their coefficients of inbreeding ranged from 0 to 25% (mean+/-S.D.: 3+/-4.6%). For the purpose of analysis, stallions were divided into six inbreeding classes (0-1, 1-2, 2-5, 5-8, 8-12 and >12%) containing 132, 40, 42, 27, 25 and 19 animals, respectively. The degree of inbreeding significantly affected many aspects of sperm production and quality, based on a standard examination of two ejaculates collected at a 1.5-3h interval. In particular, coefficients of inbreeding above 2% were associated with lower percentages of motile (p<0.01) and morphologically normal sperm (p<0.001). When the data set was used to estimate heritability of semen characteristics, the high values calculated for sperm progressive motility (0.46) and concentration (0.24) suggested that these traits could be improved by phenotypic selection. These findings support the hypothesis that inbreeding has a detrimental effect on semen quality in Shetland ponies, although examination of multiple ejaculates after repeated semen collection to bring the animals to daily sperm output is needed to confirm this conclusion. Nevertheless, the results support previous suggestions that inbreeding is an important cause of reduced semen quality.     

Incidence of 1/29 translocation in Bolivian Creole and Brahman Yacumeño cattle

In Bolivia, four different Creole cattle breeds can be found, as well as other European and Zebu breeds adapted to local environments. The relationship between the occurrence of the 1/29 translocation and subfertility is well known, and analysis of Y chromosome morphology is useful to determine a possible introgression with Bos indicus. The incidence of the 1/29 translocation was analyzed in four Bolivian Creole cattle breeds and the Brahman Yacume?o population, as well as on four farms with phenotypical Creole-type cattle. In 259 (164 dams and 95 sires) Bolivian Creole cattle, 10.42% of the individuals demonstrated the 1/29 translocation, with a variation from 0 to 28.20% between the breeds. In contrast, 43 (19 dams and 24 sires) Yacume?o Brahman and the Creole-type cattle did not show the centric fusion. The highly significant differences between Creole cattle breeds in relation to the incidence of 1/29 translocation could be a consequence of factors such as founder group, genetic drift, and selection. The low frequency observed in the Saavedre?io Creole dairy cattle might be explained by its breeding under a more intensive system, and selection according to milk yield and fertility traits. Finally, no relation between acrocentric Y chromosomes and 1/29 translocation was observed.     

A genetic interpretation of the variation in inbreeding depression

Inbreeding depression is expected to play an important but complicated role in evolution. If we are to understand the evolution of inbreeding depression (i.e., purging), we need quantitative genetic interpretations of its variation. We introduce an experimental design in which sires are mated to multiple dams, some of which are unrelated to the sire but others are genetically related owing to an arbitrary number of prior generations of selfing or sib-mating. In this way we introduce the concept of "inbreeding depression effect variance," a parameter more relevant to selection and the purging of inbreeding depression than previous measures. We develop an approach for interpreting the genetic basis of the variation in inbreeding depression by: (1) predicting the variation in inbreeding depression given arbitrary initial genetic variance and (2) estimating genetic variance components given half-sib covariances estimated by our experimental design. As quantitative predictions of selection depend upon understanding genetic variation, our approach reveals the important difference between how inbreeding depression is measured experimentally and how it is viewed by selection.     

Variance of prediction error with mixed model equations when relationships are ignored

Summary Formulas are presented to illustrate the calculation of correct variances of prediction error (PEV) and the correlation between true and predicted values (r_TI) when the incorrect variance-covariance matrix for the random effects is used in mixed-model equations (MME). The example with progeny records of highly related and inbred sires showed that PEV were underestimated from the diagonals of the inverse of the coefficient matrix of the MME when sires were assumed unrelated and not inbred and were overestimated when relationships among sires were calculated with Henderson's simple rules for the inverse of the numerator relationship matrix, A^-1, which do not consider inbreeding. When Quaas' rules for A^-1, which do consider inbreeding, are used, the correct PEV are obtained. In the example, calculations of r_TI from the diagonals of the inverse of the coefficient matrix were too large when relationships and inbreeding were ignored and were obviously wrong when the approximation to the numerator relationship matrix, A, was based on the simple rules for calculating A^-1. If the correct A is used in the MME, the calculation of r_TI may be incorrect if inbreeding of the evaluated individual is not considered. If inbreeding is known, adjustment for inbreeding is easy for calculation of r_TI.Published as paper no. 9947, Journal Ser, Nebraska Agric Res Div, University of Nebraska, Lincoln, Neb.     

Inbreeding in reintroduced populations: the effects of early reintroduction history and contemporary processes

Maintaining genetic variation and minimizing inbreeding are central goals of conservation genetics. It is therefore crucial to understand the important population parameters that affect inbreeding, particularly in reintroduction programs. Using data from 41 reintroduced Alpine ibex (Capra ibex ibex) populations we estimated inbreeding since the beginning of reintroductions using population-specific Fst, and inbreeding over the last few generations with contemporary effective population sizes. Total levels of inbreeding since reintroduction of ibex were, on average, close to that from one generation of half-sib mating. Contemporary effective population sizes did not reflect total inbreeding since reintroduction, but 16% of variation in contemporary effective population sizes among populations was due to variation in current population sizes. Substantial variation in inbreeding levels among populations was explained by founder group sizes and the harmonic mean population sizes since founding. This study emphasizes that, in addition to founder group sizes, early population growth rates are important parameters determining inbreeding levels in reintroduced populations.     

Indirect genetic effects and inbreeding: consequences of BLUP selection for socially affected traits on rate of inbreeding

Background

Social interactions often occur among living organisms, including aquatic animals. There is empirical evidence showing that social interactions may genetically affect phenotypes of individuals and their group mates. In this context, the heritable effect of an individual on the phenotype of another individual is known as an Indirect Genetic Effect (IGE). Selection for socially affected traits may increase response to artificial selection, but also affect rate of inbreeding.

Methods

A simulation study was conducted to examine the effect of Best Linear Unbiased Prediction (BLUP) selection for socially affected traits on the rate of inbreeding. A base scenario without IGE and three alternative scenarios with different magnitudes of IGE were simulated. In each generation, 25 sires and 50 dams were mated, producing eight progeny per dam. The population was selected for 20 generations using BLUP. Individuals were randomly assigned to groups of eight members in each generation, with two families per group, each contributing four individuals. “Heritabilities” (for both direct and indirect genetic effects) were equal to 0.1, 0.3 or 0.5, and direct–indirect genetic correlations were −0.8, −0.4, 0, 0.4, or 0.8. The rate of inbreeding was calculated from generation 10 to 20.

Results

For the base scenario, the rates of inbreeding were 4.09, 2.80 and 1.95% for “heritabilities” of 0.1, 0.3 and 0.5, respectively. Overall, rates of inbreeding for the three scenarios with IGE ranged from 2.21 to 5.76% and were greater than for the base scenarios. The results show that social interaction within groups of two families increases the resemblance between estimated breeding values of relatives, which, in turn, increases the rate of inbreeding.

Conclusion

BLUP selection for socially affected traits increased the rate of inbreeding. To maintain inbreeding at an acceptable rate, a selection algorithm that restricts the increase in mean kinship, such as optimum contribution selection, is required.     

Curvilinear inbreeding effects on some performance traits in laying hens

Quadratic partial regression coefficients were estimated for the inbreeding level on five performance traits (body weight, average egg weight, age at first egg, percentage of fertilized eggs, and hatchability of set eggs) of two strains of laying hens. Data on 5631 of H77 layers and 3563 of N88 layers from nine consecutive generations were analysed. Only dams were accounted for. Partial regression coefficients were estimated by REML with a single-trait animal model, which included fixed effects (generation and hatching period) and random effects (additive genetic and error effects). The mean inbreeding level was 0.87% in strain H77 and 1.08% in strain N88. The inbreeding effects were analysed based on the quadratic partial regression equations. A slight inbreeding depression was found for all the traits analysed in N88. In strain H77, negative effects of inbreeding were only noted for body weight and average egg weight. The small inbreeding effects shown here resulted from a relatively low level of homozygosity in the populations studied. The strains were found to differ in the effects of inbreeding. It is worth pointing out that differences were noted both between the inbreeding depression estimated from the partial linear regression equation and the quadratic partial regression equation, as well as different inbreeding levels.     

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.     

Incorporation of new founders into captive populations

This report describes preliminary studies intended to develop generalizations for the optimal incorporation of newcomers into breeding pools. Small populations, which grow from four to a stable size of 16 animals per generation, were simulated on a computer. New founders were introduced and various breeding schemes tried and evaluated for their effect on inbreeding coefficients and founder representation. Two variables were examined for their effects on inbreeding and founder representation: number of progeny produced by crossing new founders with the established population, and number of mates the new founder had from the established population. Increasing the value of these variables to the point at which new-founder representation was equal to the original founders' representations decreased inbreeding. Beyond this point, inbreeding increased.