Identity coefficients and covariances between relatives in a parent-offspring inbreeding system

Summary A one-locus operator for a younger parent-offspring inbreeding system is obtained by a generation matrix method in which 14 classes of matings are defined. The eigenvalues and a set of eigenvectors for the generation matrix and, also, the general solution for the frequencies of mating classes among descendants of an original mating of genotypes ab x cd are given. The operator gives the genotypic array of descendants of a given mating an arbitrary number of generations later. Using this operator, an algorithm is developed for calculating identity coefficients between any two relatives in a possibly branching younger parent-off spring mating system. Application to obtaining covariances between relatives for a one-locus model is illustrated.Journal article (74-3-73) of the Kentucky Agricultural Experiment Station published with approval of the Director.     

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.     

Effect of rate of inbreeding on inbreeding depression in Drosophila melanogaster

Summary This experiment was designed to study the relationship between rate of inbreeding and observed inbreeding depression of larval viability, adult fecundity and cold shock mortality in Drosophila melanogaster. Rates of inbreeding used were full-sib mating and closed lines of N=4 and N=20. Eight generations of mating in the N=20 lines, three generations in the N=4 lines and one generation of full-sib mating were synchronised to simultaneously produce individuals with an expected level of inbreeding coefficient (F) of approximately 0.25. Inbreeding depression for the three traits was significant at F=0.25. N=20 lines showed significantly less inbreeding depression than full-sib mated lines for larval viability at approximately the same level of F. A similar trend was observed for fecundity. No effect of rate of inbreeding depression was found for cold shock mortality, but this trait was measured with less precision than the other two. Natural selection acting on loci influencing larval viability and fecundity during the process of inbreeding could explain these results. Selection is expected to be more effective with slow rates of inbreeding because there are more generations and greater opportunity for selection to act before F=0.25 is reached. Selection intensities seem to have been different in the three traits measured. Selection was most intense for larval viability, less intense for fecundity and, perhaps, negligible at loci influencing cold shock mortality.     

Optimised parent selection and minimum inbreeding mating in small aquaculture breeding schemes: a simulation study

The effectiveness of low cost breeding scheme designs for small aquaculture breeding programmes were assessed for their ability to achieve genetic gain while managing inbreeding using stochastic simulation. Individuals with trait data were simulated over 15 generations with selection on a single trait. Combinations of selection methods, mating strategies and genetic evaluation options were evaluated with and without the presence of common environmental effects. An Optimal Parent Selection (OPS) method using semi-definite programming was compared with a truncation selection (TS) method. OPS constrains the rate of inbreeding while maximising genetic gain. For either selection method, mating pairs were assigned from the selected parents by either random mating (RM) or Minimum Inbreeding Mating (MIM), which used integer programming to determine mating pairs. Offspring were simulated for each mating pair with equal numbers of offspring per pair and these offspring were the candidates for selection of parents of the next generation. Inbreeding and genetic gain for each generation were averaged over 25 replicates. Combined OPS and MIM led to a similar level of genetic gain to TS and RM, but inbreeding levels were around 75% lower than TS and RM after 15 generations. Results demonstrate that it would be possible to manage inbreeding over 15 generations within small breeding programmes comprised of 30 to 40 males and 30 to 40 females with the use of OPS and MIM. Selection on breeding values computed using Best Linear Unbiased Prediction (BLUP) with all individuals genotyped to obtain pedigree information resulted in an 11% increase in genetic merit and a 90% increase in the average inbreeding coefficient of progeny after 15 generations compared with selection on raw phenotype. Genetic evaluation strategies using BLUP wherein elite individuals by raw phenotype are genotyped to obtain parentage along with a range of different samples of remaining individuals did not increase genetic progress in comparison to selection on raw phenotype. When common environmental effects on full-sib families were simulated, performance of small breeding scheme designs was little affected. This was because the majority of selection must anyway be applied within family due to inbreeding constraints.     

Effects of inbreeding on economic traits of channel catfish

Summary Inbred channel catfish (Ictalurus punctatus) were produced from two generations of full-sib matings to study the effect of inbreeding on reproduction, growth and survival. A randomly mated control line was propagated from the same base population to be used for the evaluation of the inbred fish. First generation inbred (I1) and control (C1) lines comprised five full-sib families each. Second generation inbred (I2) and control (C2) lines were produced by mating each male catfish from the I1 or C1 line to two females in sequence, one from the I1 and one from the C1 line. The design also produced two reciprocal outcross lines to be compared to their contemporary inbred and control lines. The coefficient of inbreeding for the inbred line increased from 0.25 in generation 1 to 0.375 in generation 2. The inbreeding coefficient was zero for all other lines. The resulting fish were performance tested in two locations, Tifton, Georgia and Auburn, Alabama and no genotype-environment interactions occurred. Results indicated that one generation of inbreeding increased number of days required for eggs to hatch by 21%, but did not significantly influence spawn weight or hatchability score. However, inbred females produced more eggs/kg body weight than control females. Two generations of full-sib mating in Georgia did not depress weight when expressed as a deviation to random controls but was depressed 13–16% when expressed as a deviation to half-sib out-crosses. Second generation inbreds produced in Alabama exhibited a 19% depression for growth rate when compared to either random or half-sib outcross controls. Survival rates at various age intervals was not decreased by inbreeding. The amount of inbreeding depression varied among families and between sexes.This study was supported by State and Hatch Funds allocated to the Georgia and Alabama Agricultural Experiment Stations     

Methods for predicting rates of inbreeding in selected populations

Summary In selected populations, families superior for the selected trait are likely to contribute more offspring to the next generation than inferior families and, as a consequence, the rate of inbreeding is likely to be higher in selected populations than in randomly mated populations of the same structure. Methods to predict rates of inbreeding in selected populations are discussed. The method of Burrows based on probabilities of coselection is reappraised in conjunction with the transition matrix method of Woolliams. The method of Latter based on variances and covariances of family size is also examined. These methods are one-generation approaches in the sense that they only account for selective advantage over a single generation, from parents to offspring. Two-generation methods are developed that account for selective advantage over two generations, from grandparent to grandoffspring as well as from parent to offspring. Predictions are compared to results from simulation. The best one-generation method was found to underpredict rates of inbreeding by 10–25%, and the two-generation methods were found to underpredict rates of inbreeding by 9–18%.     

遗传性大鼠脐疝模型的选育

目的近交繁殖先天性脐疝大鼠获得能稳定遗传的大鼠脐疝模型,大鼠脐疝结构观察及治疗。方法每代大鼠全同胞交配,记录产子数及脐疝情况,分析大鼠脐疝率;取F2代6月龄脐疝雌雄大鼠各6只,其中雌雄各2只进行解剖观察,雌雄大鼠各4只进行外科手术缝合。结果随近交系数增大,大鼠脐疝率升高,F12、F13代大鼠均为脐疝;F1代至F13代雌性大鼠总体脐疝率显著高于雄性大鼠（x2=11.1,P=0.001）;雌雄大鼠脐疝结构一致,手术后3~4周痊愈无复发。结论经连续13代全同胞交配获得了遗传性状稳定的大鼠脐疝模型。     

Is inbreeding depression more severe in a stressful environment?

Successful reintroduction of endangered species depends in part on their ability to respond to changing environmental conditions. Population genetics theory suggests that inbred populations lacking genetic variability may be unable to respond effectively to environmental stress. There have been very few studies designed explicitly to investigate the phenomenon of inbreeding depression under environmental stress, particularly in the context of conservation genetics. Three separate experiments using Drosophila melanogaster were designed to explore this issue. No increase in the magnitude of inbreeding depression was detected in laboratory lines subjected to three generations of continuous full-sib mating under temperature stress (28°C), lead stress (medium contaminated with 400 ppm Pb), or a combination of these stresses. Individual isofemale lines from a different population, however, did show significant increases in inbreeding depression when exposed to temperature stress for one generation of full-sib mating following three generations of full-sib inbreeding at 25°C. Further, chromosome-2 homozygotes showed, on average, a significant increase in inbreeding depression under lead stress when in competition with corresponding chromosome-2 heterozygotes compared to the same lines in a benign environment. Taken together, these results suggest that inbreeding depression is more severe under conditions of environmental stress and is more likely to be realized in an inter- or intraspecific competitive situation as can be experienced in the wild. Therefore, it is likely that reduced genetic variability through inbreeding is a much greater problem for recently reintroduced populations than it is for populations in a relatively benign zoo environment. © 1994 Wiley-Liss, Inc.     

Polyandrous females found fitter populations

Multiple mating by females (polyandry) requires an evolutionary explanation, because it carries fitness costs in many species. When mated females disperse alone to a new habitat, their offspring may have no option but to mate with their siblings and incur inbreeding depression. However, some of the offspring of polyandrous females may only be half siblings, reducing inbreeding depression when isolated groups of siblings only have each other as mates. We investigated this putative benefit of polyandry over monandry by initiating multiple genetically isolated populations of Callosobruchus maculatus beetles, each founded by a single female, who received a complete ejaculate from either one or two males. The early generations had comparable fitness, but the F4 and F5 descendants of doubly inseminated females were more numerous and had higher egg‐to‐adult survival than the descendants of singly inseminated females. This fitness benefit was of similar magnitude whether beetles were reared on their standard food plant, or on a less favourable food source. Our results suggest that polyandrous females produce fitter descendants in inbred founder populations and therefore that polyandry may affect movement ecology and invasion biology.     

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.     

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.     

Effects of mating system in Japanese quail

Summary A 17-generation selection experiment was conducted to study direct and correlated responses to mass selection under a mating system with alternating generations of full-sib inbreeding and wide outbreeding (population I) as compared with a mass selected, randomly mated population (population II). The selection criterion was an index of total egg mass to 78 days divided by adult female body weight. Estimates of heritabilities and genetic correlations are reported. Estimated heritabilities for the index were 0.38±0.04 and 0.29±0.05 in population I and II, respectively. Realized heritabilites were 0.10±0.05 and 0.12±0.03. For most traits studied the mean phenotypic values in the cyclic mated population decreased for inbred generations. Increased inbreeding levels also caused outbred generation means of population I to decrease through the first six or seven generations. After this period of adaptation to inbreeding selection response was positive for the index and positively correlated traits. Total response to selection under the cyclic inbred-outbred mating system did not exceed selection response made under random mating. However, the rate of response in the cyclically mated population exceeded that in the randomly mated population in later generations when the cyclically mated population had apparently adapted to inbreeding.Published with approval of the Director of the Montana Agricultural Experiment Station, Journal Series No. 1221     

Inbreeding depression in the competitive fertilization success of male crickets

Mating between close relatives generally results in offspring of decreased fitness. Inbreeding depression is generally greater for life-history traits than for morphological traits, and recent studies of traits subject to sexual selection suggest that these may suffer the greatest inbreeding depression. Sexual selection continues after mating in the form of sperm competition and cryptic female choice, imposing strong selection on male competitive fertilization success. Here, I examine the effects of a single generation of full-sib mating on competitive fertilization success in a cricket, Teleogryllus oceanicus. The estimated coefficient of inbreeding depression in competitive fertilization success was 0.37, higher than that for other life-history and morphological traits. Such intense inbreeding depression coupled with little or no additive genetic variance for this trait is consistent with strong directional selection on male competitive fertilization success generating high levels of dominance variance, and provides an adaptive explanation for the evolution of inbreeding avoidance found in this species.     

Inbreeding under a cyclical mating system

Summary General recursion formulae for the coefficient of inbreeding under a cyclical mating system were derived in which one male and one female are selected from each of the n families per generation (population size N = 2 n). Each male is given the family number of his sire in each generation, while his mate comes from another family, varying systematically in different generations. Males of the r-th family in generations 1, 2, 3,..., t = n–1 within each cycle mate with females from families r+1, r+2, r+3,..., r+t to produce generations 2, 3, 4,..., t+1=1, respectively. The change in heterozygosity shows a cyclical pattern of rises and falls, repeating in cycles of n–1 generations. The rate of inbreeding oscillates between <-3% to >6% in different generations within each cycle, irrespective of the population size. The average rate of inbreeding per generation is approximately 1/[4 N-(Log₂N+1)], which is the rate for the maximum avoidance of inbreeding. The average inbreeding effective population size is approximately 2 N–2.     

Identification at the larval stage of four Curculio species coexisting on oak trees using PCR‐RFLP

Several species in the family Cecidomyiidae (Diptera) are known by a particular reproduction mechanism called monogeny, in which all offspring of each individual female are either exclusively male or exclusively female. As a consequence, no full‐sib mating occurs in monogenous populations. So offspring of each female must inevitably mate with those of other females, and in the worst condition, mating may occur between individuals with a common sire but different mothers, where they are only half siblings. Simulation of monogenous gall midge pedigrees, calculation of inbreeding coefficients of individuals for 20 generations, and comparing the results with those of a non‐monogenous species revealed that the total average inbreeding coefficients of individuals were not dramatically different between these two populations. However, the maximum inbreeding coefficient of individuals per generation in non‐monogenous populations was significantly higher than in monogenous populations. Despite the effect of monogeny on inbreeding, it is doubted whether inbreeding avoidance is the only force that drives the evolution of monogeny in gall midges.     

Isozyme polymorphisms maintained by lethal loci in inbred strains of Aedes triseriatus

We analyzed the progeny of brother-sister matings of two inbred strains of the treehole mosquito, Aedes triseriatus, at several isozyme loci to determine which factors were maintaining heterozygosity at these loci after prolonged inbreeding. The triseriatus Kramer (TK) lines were polymorphic for the Odh and Hbd loci after 12 generations of full-sib mating, and the triseriatus Vero Beach (TV) lines were polymorphic for the Odh, Hk-4, Pgm, and Hbd loci after 14 generations of full-sib mating. Genetic analysis of 22 TK F13 matings and nine TV F15 matings showed that heterozygosity was enforced by lethal loci to which all the polymorphic isozyme loci were linked. The lethal loci formed a balanced lethal system. We determined the relative positions and map distances of lethals and enzyme loci.     

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.     

Trait mean depression for second-generation inbred strawberry populations with and without parent selection

 Strawberry genotypes selected for superior fruit yield or chosen at random from first-generation self, full-sib, and half-sib populations were crossed to provide second-generation inbred progenies and composite cross-fertilized control populations. Mean yields for inbred offspring from crosses among selected parents exceeded those from the offspring of unselected parents by 87%, 23%, and 37% for self, full-sib, and half-sib populations, respectively; yields for offspring from unrelated crosses among selected parents were 54% larger than those for crosses among unselected parents. Selection for yield also resulted in significant correlated response for fruit number and plant diameter. Mean yields for second-generation half-sib and full-sib offspring from selected parents were greater than those for offspring from the unselected but non-inbred control population. This suggests that selection can be a powerful force in counteracting most of the inbreeding depression expected in cross-fertilized strawberry breeding programs. Selection treatment× inbreeding rate interactions were non-significant for all traits; thus, selection among partially inbred offspring did not have a large effect on the rate of genetic progress. Differential realized selection intensity among individuals with differing levels of homozygosity accumulated due to inbreeding is suggested as the most likely explanation for the absence of association between pedigree inbreeding coefficients and cross performance detected previously in strawberry. Received: 21 July 1996 / Accepted: 7 March 1997     

Reduced inbreeding depression due to historical inbreeding in Drosophila melanogaster: evidence for purging

An important issue in conservation biology and the study of evolution is the extent to which inbreeding depression can be reduced or reversed by natural selection. If the deleterious recessive alleles causing inbreeding depression can be 'purged' by natural selection, outbred populations that have a history of inbreeding are expected to be less susceptible to inbreeding depression. This expectation, however, has not been realized in previous laboratory experiments. In the present study, we used Drosophila melanogaster as a model system to test for an association between inbreeding history and inbreeding depression. We created six 'purged' populations from experimental lineages that had been maintained at a population size of 10 male-female pairs for 19 generations. We then measured the inbreeding depression that resulted from one generation of full-sib mating in the purged populations and in the original base population. The magnitude of inbreeding depression in the purged populations was approximately one-third of that observed in the original base population. In contrast to previous laboratory experiments, therefore, we found that inbreeding depression was reduced in populations that have a history of inbreeding. The large purging effects observed in this study may be attributable to the rate of historical inbreeding examined, which was slower than that considered in previous experiments.     

CORRELATED INBREEDING AMONG RELATIVES: OCCURRENCE,MAGNITUDE, AND IMPLICATIONS

Understanding the magnitude and causes of genetic and phenotypic resemblance among relatives is key to understanding evolutionary processes. Contrary to basic expectation, individual coefficients of inbreeding ( f) were recently hypothesized to be intrinsically correlated across parents and offspring in structured populations, potentially creating an additional source of phenotypic resemblance in traits that show inbreeding depression. To test this hypothesis, we used individual‐based simulations to quantify the parent–offspring correlations in f arising under random mating in populations of different size, immigration rate, and mating system. Parent–offspring correlations in f were typically positive (median r≈ 0.2–0.4) in relatively small and isolated populations. Relatively inbred parents therefore produced relatively inbred offspring on average, although the magnitude of this effect varied considerably among replicate populations. Correlations were higher given more generations of random mating, greater variance in reproductive success, polygynous rather than monogamous mating, and for midparent–offspring rather than parent–offspring relationships. Furthermore, f was also positively correlated across half‐siblings, and closer relatives had more similar inbreeding coefficients across entire generations. Such intrinsic resemblance in f among relatives could provide an additional genetic benefit of mate choice and bias quantitative genetic analyses that do not account for correlated inbreeding depression.