On the robustness of regular systems of inbreeding.

Half-sib, first cousin, half nth cousin, and nth cousin mating systems are robust in that small deviations from the mating structure will not significantly alter the levels of genetic identity or effect qualitative distinctions between the models. Substitution of nearest kin in matings may either increase or decrease the level of homozygosity depending on the mating structure; the effect of a single error in the mating structure is not an accurate indicator of the equilibrium resulting from recurrent errors. Models of mixed half nth cousin or nth cousin mating show that the relative frequency of the lowest order inbred mating essentially determines the level of homozygosity. Any positive relative frequency of more distant matings will reduce the probability of identity by descent under half-sib or first cousin mating to less than 1.     

Half-sib mating structures

All ways in which all matings in a population can be between half-sibs under a generalization of regular systems of inbreeding are characterized for both finite and infinite populations. A model of random half-sib mating is developed and analyzed, and the asymptotic configuration of populations subject to it is described. The classical model of half-sib mating which ensues from the standard definition of regular systems of inbreeding is only one of many ways a population can propagate by half-sib mating, and a wide range of genetic identity is possible dependent on which half-sib mating structure governs a population.     

Mating structure and the cost of deleterious mutation: I. Postponing inbreeding

Mating structure governs the distribution of alleles in populations and thus the extent to which the phenotypes associated with the alleles are manifested. A mating system which initially achieves more genetic identity within individuals than between individuals enhances the probability that a finite population without reproductive excess will become extinct from a recessive lethal or semidominant lethal mutation; however, such a mating system decreases the number of deaths that will ensue if the population size is maintained by replacement of inviable progeny with individuals engendered from the entire mating pool. This is illustrated with Markov chain models for half-sib and double-first-cousin mating in populations of four individuals and by various techniques for analogous large populations. An appropriate choice of mating strategy can mitigate the effect of deleterious mutations, but the determination of which strategy is appropriate depends on how much reproductive excess is available and on the relative costs assigned to individual deaths and the extinction of a population.     

The efficiency of close inbreeding to reduce genetic adaptation to captivity

Although ex situ conservation is indispensable for thousands of species, captive breeding is associated with negative genetic changes: loss of genetic variance and genetic adaptation to captivity that is deleterious in the wild. We used quantitative genetic individual-based simulations to model the effect of genetic management on the evolution of a quantitative trait and the associated fitness of wild-born individuals that are brought to captivity. We also examined the feasibility of the breeding strategies under a scenario of a large number of loci subject to deleterious mutations. We compared two breeding strategies: repeated half-sib mating and a method of minimizing mean coancestry (referred to as gc/mc). Our major finding was that half-sib mating is more effective in reducing genetic adaptation to captivity than the gc/mc method. Moreover, half-sib mating retains larger allelic and adaptive genetic variance. Relative to initial standing variation, the additive variance of the quantitative trait increased under half-sib mating during the sojourn in captivity. Although fragmentation into smaller populations improves the efficiency of the gc/mc method, half-sib mating still performs better in the scenarios tested. Half-sib mating shows two caveats that could mitigate its beneficial effects: low heterozygosity and high risk of extinction when populations are of low fecundity and size and one of the following conditions are met: (i) the strength of selection in captivity is comparable with that in the wild, (ii) deleterious mutations are numerous and only slightly deleterious. Experimental validation of half-sib mating is therefore needed for the advancement of captive breeding programs.     

Genetic relatedness in open-pollinated families of two leguminous tree species,Robinia pseudoacacia L. and Gleditsia triacanthos L.

Summary When conducting tree breeding experiments, geneticists often assume that individuals from open-pollinated families are halfsibs. The reliability of this assumption was tested using data from enzyme electrophoresis to estimate the genetic relatedness among progeny within 22 open-pollinated families of Robinia pseudoacacia L. (black locust) and 34 open-pollinated families of Gleditsia triacanthos L. (honey locust) from natural stands. An algorithm employing population estimates of fixation indices, pollen allele frequencies, and selfing rates was used to calculate the mean expected number of alleles in common across loci under assumptions of either full-sib (i.e., a single pollen parent) or half-sib (i.e., random mating) relationships. For each open-pollinated family, the average coefficient of relationship among progeny was calculated by linear interpolation from the observed number of alleles in common. For most families of both species, coefficients were significantly higher than 0.25 (half-sib relation), but were significantly lower than 0.50 (full-sib relation). These results suggest that the assumption of a half-sib relationship among progeny of open-pollinated families is violated for these tree species. More critical to the estimation of heritabilities and the prediction of genetic gains was the observation that estimates of the coefficient of relationship varied widely among open-pollinated families (for R. pseudoacacia r ₀=0.20–0.43, mean=0.34; for G. triacanthos r ₀=0.29–0.55, mean=0.36).     

Modifiers of mutation rate: a general reduction principle

A deterministic two-locus population genetic model with random mating is studied. The first locus, with two alleles, is subject to mutation and arbitrary viability selection. The second locus, with an arbitrary number of alleles, controls the mutation at the first locus. A class of viability-analogous Hardy-Weinberg equilibria is analyzed in which the selected gene and the modifier locus are in linkage equilibrium. It is shown that at these equilibria a reduction principle for the success of new mutation-modifying alleles is valid. A new allele at the modifier locus succeeds if its marginal average mutation rate is less than the mean mutation rate of the resident modifier allele evaluated at the equilibrium. Internal stability properties of these equilibria are also described.     

Use of microsatellite loci to classify individuals by relatedness

This study investigates the use of microsatellite loci for estimating relatedness between individuals in wild, outbred, vertebrate populations. We measured allele frequencies at 20 unlinked, dinucleotide-repeat microsatellite loci in a population of wild mice ( Mus musculus ), and used these observed frequencies to generate the expected distributions of pairwise relatedness among full sib, half sib, and unrelated pairs of individuals, as would be estimated from the microsatellite data. In this population one should be able to discriminate between unrelated and full-sib dyads with at least 97% accuracy, and to discriminate half-sib pairs from unrelated pairs or from full-sib pairs with better than 80% accuracy. If one uses the criterion that parent-offspring pairs must share at least one allele per locus, then only 15% of full-sib pairs, 2% of half-sib pairs, and 0% of unrelated pairs in this population would qualify as potential parent-offspring pairs. We verified that the simulation results (which assume a random mating population in Hardy-Weinberg and linkage equilibrium) accurately predict results one would obtain from this population in real life by scoring laboratory-bred full- and half-sib families whose parents were wild-caught mice from the study population. We also investigated the effects of using different numbers of loci, or loci of different average heterozygosities ( He ), on misclassification frequencies. Both variables have strong effects on misclassification rate. For example, it requires almost twice as many loci of He = 0.62 to achieve the same accuracy as a given number of loci of He = 0.75. Finally, we tested the ability of UPGMA clustering to identify family groups in our population. Clustering of allele matching scores among the offspring of four sets of independent maternal half sibships (four females, each mated to two different males) perfectly recovered the true family relationships.     

Heritability and Y-chromosome influence in the jack male life history of chinook salmon (Oncorhynchus tshawytscha)

Jacking in chinook salmon (Oncorhynchus tshawytscha) is an alternative reproductive strategy in which males sexually mature at least 1 year before other members of their year class. We characterize the genetic component of this reproductive strategy using two approaches; hormonal phenotypic sex manipulation, and a half-sib breeding experiment. We 'masculinized' chinook salmon larvae with testosterone, reared them to first maturation, identified jacks and immature males based on phenotype, and genotyped all fish as male ('XY') or female ('XX') using PCR-based Y-chromosome markers. The XY males had a much higher incidence of jacking than the XX males (30.8% vs 9.9%). There was no difference in body weight, gonad weight, and plasma concentrations of testosterone and 17beta-estradiol between the two jack genotypes, although XY jacks did have a higher gonadosomatic index (GSI) than XX jacks. In the second experiment, we bred chinook salmon in two modified half-sib mating designs, and scored the number of jacks and immature fish at first maturation. Heritability of jacking was estimated using two ANOVA models: dams nested within sires, and sires nested within dams with one-half of the half-sib families common to the two models. The sire component of the additive genetic variance yielded a high heritability estimate and was significantly higher than the dam component (h(2)(sire) = 0.62 +/- 0.21; h(2)(dam) = -0.14 +/- 0.12). Our experiments both indicated a strong sex-linked component (Y-chromosome) to jacking in chinook salmon, although evidence for at least some autosomal contribution was also observed.     

Joint Frequencies of Alleles Determined by Separate Formulations for the Mating and Mutation Systems

A method to calculate joint gene frequencies, which are the probabilities that two neutral genes taken at random from a population have certain allelic states, is developed taking into account the effects of the mating system and the mutation scheme. We assume that the mutation rates are constant in the population and that the mating system does not depend on allelic states. Under either--the condition that mutation rates are symmetric or that the mating unit is large and the mutation rate is small--the general formula is represented by two terms, one for the mating system and the other for the mutation scheme. The term for the mating system is expressed using the coancestry coefficient in the infinite allele model, and the term for the mutation scheme is a function of the eigenvalues and the eigenvectors of the mutation matrix. Several examples are presented as applications of the method, including homozygosity in a stepping-stone model with a symmetric mutation scheme.     

Role of the ABC transporter Ste6 in cell fusion during yeast conjugation

Though early stages of yeast conjugation are well-mimicked by treatment with pheromones, the final degradation of the cell wall and membrane fusion of mating that leads to cytoplasmic mixing may require separate signals. Mutations that blocked cell fusion during mating in Saccharomyces cerevisiae were identified in a multipartite screen. The three tightest mutations proved to be partial-function alleles of the ABC-transporter gene STE6 required for transport of a-factor. The ste6(cefl-1) allele was recovered and sequenced. The ste6(cefl-1) allele contained a stop codon predicted to truncate Ste6 at amino acid residue 862 (of 1290). The ste6(cef) mutations reduced, but did not eliminate, expression of a-factor. Light and electron microscopy revealed that unlike ste6 null mutations which block mating before the formation of mating pairs, the ste6(cef) (cell fusion) alleles permitted early steps in mating to proceed normally but blocked at a late stage in conjugation where mating partners were encased by a single cell wall and separated by only a thin layer of cell wall material we term the fusion wall. Morphologically the prezygotes appeared symmetrical with successful cell wall fusion at the periphery of the region of cell contact. Responses to a-factor were efficiently induced in partner cells under mating conditions as expected given the symmetric appearance of the prezygotes. A strain expressing a ste6(K1093A) mutation that conferred export of a twofold to fourfold higher level of a-factor than ste6(cef) did not accumulate prezygotes during mating which could indicate a tight threshold of a-factor signaling required for mating. However, mating to an sst2 partner which has a greatly increased sensitivity to a-factor did not suppress the fusion defect of a ste6(cef) strain. Overexpression of the structural gene for a-factor also did not suppress the fusion defect. It is possible that a-factor or STE6 play more complex roles in cell fusion.     

Complete amino acid sequence of the human alpha 5 (IV) collagen chain and identification of a single-base mutation in exon 23 converting glycine 521 in the collagenous domain to cysteine in an Alport syndrome patient.

We have generated and characterized cDNA clones providing the complete amino acid sequence of the human type IV collagen chain whose gene has been shown to be mutated in X chromosome-linked Alport syndrome. The entire translation product has 1,685 amino acid residues. There is a 26-residue signal peptide, a 1,430-residue collagenous domain starting with a 14-residue noncollagenous sequence, and a Gly-Xaa-Yaa-repeat sequence interrupted at 22 locations, and a 229-residue carboxyl-terminal noncollagenous domain. The calculated molecular weight of the mature alpha 5(IV) chain is 158,303. Analysis of genomic DNA from members of a kindred with Alport syndrome revealed a new HindIII cleavage site within the coding sequence of one of the cDNA clones characterized. The proband had a new 1.25-kilobase HindIII fragment and a lack of a 1.35-kilobase fragment, and his mildly affected female cousin had both alleles. The mutation which was located to exon 23 was sequenced from a polymerase chain reaction-amplified product, and shown to be a G----T change in the coding strand. The mutation changed the GGT codon of glycine 521 to cysteine. The same mutation was found in one allele of the female cousin. The results were confirmed by allele-specific hybridization analyses.     

Effect of selection against deleterious mutations on the decline in heterozygosity at neutral loci in closely inbreeding populations.

Transition matrices for selfing and full-sib mating were derived to investigate the effect of selection against deleterious mutations on the process of inbreeding at a linked neutral locus. Selection was allowed to act within lines only (selection type I) or equally within and between lines (type II). For selfing lines under selection type I, inbreeding is always retarded, the retardation being determined by the recombination fraction between the neutral and selected loci and the inbreeding depression from the selected locus, irrespective of the selection coefficient (s) and dominance coefficient (h) of the mutant allele. For selfing under selection type II or full-sib mating under both selection types, inbreeding is delayed by weak selection (small s and sh), due to the associative overdominance created at the neutral locus, and accelerated by strong selection, due to the elevated differential contributions between alternative alleles at the neutral locus within individuals and between lines (for selection type II). For multiple fitness loci under selection, stochastic simulations were run for populations with selfing, full-sib mating, and random mating, using empirical estimates of mutation parameters and inbreeding load in Drosophila. The simulations results are in general compatible with empirical observations.     

A very rare association of three mutations of the HFE gene for hemochromatosis

In the present paper, we describe a patient who is a compound heterozygote for three mutations in the HFE gene: C282Y, H63D, and E168Q. The patient's mother carries two copies of H63D and one copy of E168Q; the patient's father is heterozygous for C282Y. The family study indicates that the patient, as well as his sister, a maternal uncle, and a first cousin, all have inherited a single HFE allele that contains two mutations H63D and E168Q. The clinical symptoms and laboratory findings of the patient and his relatives are consistent with the conclusion that the E168Q mutation by itself is unlikely to result in hemochromatosis.     

EVALUATING A SIMPLE APPROXIMATION TO MODELING THE JOINT EVOLUTION OF SELF‐FERTILIZATION AND INBREEDING DEPRESSION

A comprehensive understanding of plant mating system evolution requires detailed genetic models for both the mating system and inbreeding depression, which are often intractable. A simple approximation assuming that the mating system evolves by small infrequent mutational steps has been proposed. We examine its accuracy by comparing the evolutionarily stable selfing rates it predicts to those obtained from an explicit genetic model of the selfing rate, when inbreeding depression is caused by partly recessive deleterious mutations at many loci. Both models also include pollen limitation and pollen discounting. The approximation produces reasonably accurate predictions with a low or moderate genomic mutation rate to deleterious alleles, on the order of U = 0.02–0.2. However, for high mutation rates, the predictions of the full genetic model differ substantially from those of the approximation, especially with nearly recessive lethal alleles. This occurs because when a modifier allele affecting the selfing rate is rare, homozygous modifiers are produced mainly by selfing, which enhances the opportunity for purging nearly recessive lethals and increases the marginal fitness of the allele modifying the selfing rate. Our results confirm that explicit genetic models of selfing rate and inbreeding depression are required to understand mating system evolution.     

Multiple paternity occurs with low frequency in the territorial roe deer, Capreolus capreolus

An explanation for female multiple mating when males offer no material benefits but sperm remains elusive, largely because of a lack of empirical support for the genetic benefits hypothesis. We used 21 microsatellite markers to test for multiple paternities among 88 litters of roe deer, Capreolus capreolus , and to investigate the inbreeding avoidance hypothesis as a potential mechanism for the evolution of female multiple mating. From paternity analyses, we found that 13.5% of polytocous litters were sired by more than one male. We also found that a half-sib relationship was more likely than a full-sib relationship for 20.5% of all litters. This is the first report of multiple paternities in a territorial ungulate species. In support of the inbreeding avoidance hypothesis, we found that parents who were strongly related produced offspring with lower individual heterozygosity that survived less well during their first summer than fawns with unrelated parents. In addition, fawns from multiple paternity litters survived their first summer better than fawns from single paternity litters. However, it remains unclear whether all female multiple paternity events in this species are provoked by an initial consanguineous mating.  © 2009 The Linnean Society of London, Biological Journal of the Linnean Society 2009, 97 , 128–139.     

The Inbreeding Effective Population Number and the Expected Homozygosity for an X-Linked Locus

Assuming random mating and discrete nonoverlapping generations, the inbreeding effective population number, (see PDF), is calculated for an X-linked locus. For large populations, the result agrees with the variance effective population number. As an application, the maintenance of genetic variability by the joint action of mutation and random drift is investigated. It is shown that, if every allele mutates at rate u to new types, then the probabilities of identity in state (and hence the expected homozygosity of females) converge to the approximate value (see PDF) at the approximate asymptotic rate (see PDF).     

Confidence intervals for heritability for two-factor mating design single environment linear models

Summary Precision measurement is an essential part of heritability estimate interpretation. Approximate standard errors are commonly used as measures of precision for heritability on a progeny mean basis (H). Their derivation, however, is not inferred from the distribution theory for H. F-distribution based exact confidence intervals have been derived for some onefactor mating design H estimators. Extension of the confidence interval results from one-factor to twofactor mating designs is reported in this paper. Functions of heritability on a full-sib or half-sib progeny mean basis from nested or factorial mating design parameters were distributed according to the F-distribution. Exact confidence intervals were derived for heritability on a full-sib progeny mean basis. Exact confidence intervals for heritability on a half-sib progeny basis were adapted from previous results. Maize (Zea mays L.) data were used to estimate confidence intervals. Complete equations were given for interpolation in F-tables.Oregon Agricultural Experiment Station Technical Paper No. 7659     

Allele Frequencies at Microsatellite Loci: The Stepwise Mutation Model Revisited

We summarize available data on the frequencies of alleles at microsatellite loci in human populations and compare observed distributions of allele frequencies to those generated by a simulation of the stepwise mutation model. We show that observed frequency distributions at 108 loci are consistent with the results of the model under the assumption that mutations cause an increase or decrease in repeat number by one and under the condition that the product Nu, where N is the effective population size and u is the mutation rate, is larger than one. We show that the variance of the distribution of allele sizes is a useful estimator of Nu and performs much better than previously suggested estimators for the stepwise mutation model. In the data, there is no correlation between the mean and variance in allele size at a locus or between the number of alleles and mean allele size, which suggests that the mutation rate at these loci is independent of allele size.     

Male reproductive behavior in Drosophila melanogaster strains with different alleles of the flamenco gene

The allelic state of gene flamenco has been determined in a number of Drosophila melanogaster strains using the ovoD test. The presence of an active copy of gypsy in these strains was detected by restriction analysis. Then male reproduction behavior was studied in the strains carrying a mutation in gene flamenco. In these experiments mating success has been experimentally estimated in groups of flies. It has been demonstrated that the presence of mutant allele flamMS decreases male mating activity irrespective of the presence or absence of mutation white. The active copy of gypsy does not affect mating activity in the absence of the mutation in gene flamenco. Individual analysis has demonstrated that that mutation flamMS results in characteristic changes in courtship: flamMS males exhibit a delay in the transition from the orientation stage to the vibration stage (the so-called vibration delay). The role of locus flamenco in the formation of male mating behavior in Drosophila is discussed.     

A Bayesian Approach to Inferring Rates of Selfing and Locus-Specific Mutation

We present a Bayesian method for characterizing the mating system of populations reproducing through a mixture of self-fertilization and random outcrossing. Our method uses patterns of genetic variation across the genome as a basis for inference about reproduction under pure hermaphroditism, gynodioecy, and a model developed to describe the self-fertilizing killifish Kryptolebias marmoratus. We extend the standard coalescence model to accommodate these mating systems, accounting explicitly for multilocus identity disequilibrium, inbreeding depression, and variation in fertility among mating types. We incorporate the Ewens sampling formula (ESF) under the infinite-alleles model of mutation to obtain a novel expression for the likelihood of mating system parameters. Our Markov chain Monte Carlo (MCMC) algorithm assigns locus-specific mutation rates, drawn from a common mutation rate distribution that is itself estimated from the data using a Dirichlet process prior model. Our sampler is designed to accommodate additional information, including observations pertaining to the sex ratio, the intensity of inbreeding depression, and other aspects of reproduction. It can provide joint posterior distributions for the population-wide proportion of uniparental individuals, locus-specific mutation rates, and the number of generations since the most recent outcrossing event for each sampled individual. Further, estimation of all basic parameters of a given model permits estimation of functions of those parameters, including the proportion of the gene pool contributed by each sex and relative effective numbers.