The effect of multi-allelic balancing selection on nucleotide diversity at linked neutral sites was investigated by simulations of subdivided populations. The motivation is to understand the behaviour of self-recognition systems such as the MHC and plant self-incompatibility. For neutral sites, two types of subdivision are present: (1) into demes (connected by migration), and (2) into classes defined by different functional alleles at the selected locus (connected by recombination). Previous theoretical studies of each type of subdivision separately have shown that each increases diversity, and decreases the relative frequencies of low-frequency variants, at neutral sites or loci. We show here that the two types of subdivision act non-additively when sampling is at the whole population level, and that subdivision produces some non-intuitive results. For instance, in highly subdivided populations, genetic diversity at neutral sites may decrease with tighter linkage to a selected locus or site. Another conclusion is that, if there is population subdivision, balancing selection leads to decreased expected FST values for neutral sites linked to the selected locus. Finally, we show that the ability to detect balancing selection by its effects on linked variation, using tests such as Tajima's D, is reduced when genes in a subdivided population are sampled from the total population, rather than within demes.

Sponsored by: The Genetical Society, Promega (UK) Ltd and B&K Universal Group Ltd

We study genetic variation in phenotypic plasticity maintained by a balance between mutation and weak stabilizing selection. We consider linear reaction norms allowing for spatial and/or temporal variation in the environments of development and selection. We show that the overall genetic variation maintained does not depend on whether the trait is plastic or not. The genetic variances in height and slope of a linear reaction norm, and their covariance, are predicted to decrease with the variation in the environment. Non-pleiotropic loci influencing either height or slope are expected to decrease the genetic variance in slope relative to that in height. Decrease in the ratio of genetic variance in slope to genetic variance in height with increasing variation in the environment presents a test for the presence of loci that only influence the slope, and not the height. We use data on Drosophila to test the theory. In seven of eight pair-wise comparisons genetic variation in reaction norm is higher in a less variable environment than in a more variable environment, which is in accord with the model's predictions.

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.

A generalized interval mapping (GIM) method to map quantitative trait loci (QTL) for binary polygenic traits in a multi-family half-sib design is developed based on threshold theory and implemented using a Newton–Raphson algorithm. Statistical power and bias of QTL mapping for binary traits by GIM is compared with linear regression interval mapping (RIM) using simulation. Data on 20 paternal half-sib families were simulated with two genetic markers that bracketed an additive QTL. Data simulated and analysed were: (1) data on the underlying normally distributed liability (NDL) scale, (2) binary data created by truncating NDL data based on three thresholds yielding data sets with three different incidences, and (3) NDL data with polygenic and QTL effects reduced by a proportion equal to the ratio of the heritabilities on the binary versus NDL scale (reduced-NDL). Binary data were simulated with and without systematic environmental (herd) effects in an unbalanced design. GIM and RIM gave similar power to detect the QTL and similar estimates of QTL location, effects and variances. Presence of fixed effects caused differences in bias between RIM and GIM, where GIM showed smaller bias which was affected less by incidence. The original NDL data had higher power and lower bias in QTL parameter estimates than binary and reduced-NDL data. RIM for reduced-NDL and binary data gave similar power and estimates of QTL parameters, indicating that the impact of the binary nature of data on QTL analysis is equivalent to its impact on heritability.

Two groups of methods are being developed to fine-map quantitative trait loci (QTLs): identity-by-descent methods or methods using historical recombinations, and genetic chromosome dissection methods or methods utilizing current recombinations. Here we propose two methods that fall into the second group: contrast mapping and substitution mapping. A QTL has previously been detected via linkage mapping in a half-sib design (granddaughter or daughter design), and sires (grandsires) likely to be heterozygous at the QTL have been identified. A sire (grandsire) and its recombinant offspring are then genotyped for a series of ordered markers spanning the initial marker interval. Offspring are grouped by paternal multi-marker haplotype with haplotypes differing in the location of the recombination event. In the contrast method, contrasts between the phenotypic averages of haplotypes or offspring groups are calculated which correspond to marker intervals within the original interval. The expected value of the contrast for the true QTL interval is always maximum, hence the interval with maximum observed contrast is assumed to contain the QTL. Alternative statistics for determining the interval most likely to contain a QTL are presented for contrast mapping, as well as a bootstrap estimation of the probability of having identified the correct interval. For an initial marker bracket of 20 cM and 10 additional equidistant markers, the probability of assigning the QTL to the correct 2 cM marker interval or to a combined 4 cM interval was calculated. For substitution effects of 0·093, 0·232, 0·464, 0·696 and 0·928 (in additive genetic SD), power values near 0·14, 0·26, 0·48, 0·67 and 0·80 (0·25, 0·53, 0·86, 0·97 and 0·99) are achieved for a family of 200 (1000) sons, respectively. In substitution mapping, QTL segregation status of recombinant sons must be determined using daughter genotyping. Combinations of two haplotypes with their segregation status are required to assign the QTL to an interval. Probabilities of correct QTL assignment were calculated assuming absence of the mutant QTL allele in dams of sons. For a 2 cM interval and a QTL at the midpoint of an interval, power near 0·95 (0·90) is reached when the number of recombinant sons is 70 (60), or total number of sons is 424 (363). For QTL positions away from the midpoint, power decreases but can be improved by combining marker intervals. For a QTL located halfway to the midpoint, and 182 sons in a family resulting in 30 recombinant sons, probability is 0·94 for assignment to either a 2 cM or a combined 4 cM interval. Effect of type I and type II errors in segregation status determination on power of QTL assignment was found to be small. Errors in segregation status due to QTL segregation in dams have an impact if the frequency of the mutant QTL allele is intermediate to high.

Knowledge of quantitative trait locus (QTL) mapping in polyploids is almost void, albeit many exquisite strategies of QTL mapping have been proposed and extensive investigations have been carried out in diploid animals and plants. In this paper we develop a simple algorithm which uses an iteratively reweighted least square method to map QTLs in tetraploid populations. The method uses information from all markers in a linkage group to infer the probability distribution of QTL genotype under the assumption of random chromosome segregation. Unlike QTL mapping in diploid species, here we estimate and test the compound ‘gametic effect’, which consists of the composite ‘genic effect’ of alleles and higher-order gene interactions. The validity and efficiency of the proposed method are investigated through simulation studies. Results show that the method can successfully locate QTLs and separates different sources (e.g. additive and dominance) of variance components contributed by the QTLs.

Active duplicate PgiC genes in sheep's fescue, Festuca ovina, are associated with a PCR marker of specific length (about 370 bp, of which 231 are in an intron). Using this marker, the frequency of plants with duplicate genes is estimated to be about 10% in a population from southern Sweden. The close molecular similarity between the electrophoretically different duplicated genes is in accordance with the conclusion reached earlier that they are indeed alleles at the same locus.

Microsatellite mutations were studied in a set of 175 mutation accumulation lines, all of them independently derived from a completely homozygous population of Drosophila melanogaster and maintained under strong inbreeding during 80 generations. We assayed 28 microsatellites and detected two mutations. One mutation consisted of a single addition of a dinucleotide repeat and the other was a deletion of five trinucleotide repeats. The average mutation rate was 5·1 × 10−6, in full agreement with previous estimates from two different sets of mutation accumulation lines.

Sudden mobilization of transposable elements in Drosophila is a well-reported phenomenon but one that usually affects no more than a few elements (one to four). We report here the existence of a D. simulans natural population (Canberra) from Australia, which had high copy numbers for various transposable elements (transposons, LTR retrotransposons and non-LTR retrotransposons). The impact of transposable elements on the host genome and populations is discussed.

Volume 75, number 3, June 2000

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Page 328, column 2: equation (A2) should read

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Volume 76, number 2, October 2000

Page 166, column 1,

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