Genetic variability at five microsatellite loci was analysed in three hatchery-propagated populations of the flat oyster, Ostrea edulis. These populations were part of a selection programme for resistance to the protozoan parasite Bonamia ostreae and were produced by mass spawns, without control of the genealogy. Evidence for population bottlenecks and inbreeding was sought. A reduction in the number of alleles, mainly due to the loss of rare alleles, was observed in all selected populations, relative to the natural population from which they were derived. Heterozygote excesses were observed in two populations, and were attributed to substructuring of the population into a small number of families. Pedigree reconstruction showed that these two populations were produced by at most two spawning events involving a limited number of parents. Most individuals within these populations are half or full-sib, as shown by relatedness coefficients. The occurrence of population bottlenecks was supported by estimates of effective number of breeders derived by three methods: temporal variance in allelic frequencies, heterozygote excess, and a new method based on reduction in the number of alleles. The estimates from the different methods were consistent. The evidence for bottleneck and small effective number of breeders are expected to lead to increasing inbreeding, and have important consequences for the future management of the three O. edulis selected populations.

The rate and distance of instantaneous pollen flow in a population are parameters of considerable current interest for plant population geneticists and conservation biologists. We have recently developed an estimator (Φft) of differentiation between the inferred pollen clouds that fertilize several females, sampled within a single population. We have shown that there is a simple relation between Φft and the average pollen dispersal distance (δ) for the case of a population with no geographic structure. Though forest trees usually show considerable pollen flow, assuming an absence of spatially distributed genetic structure is not always wise. Here, we develop analytical theory for the relation between Φft and δ, for the case where the probability of Identity by Descent (IBD) for two individuals decreases with the physical distance between them. This analytical theory allows us to provide an effective method for estimating pollen dispersal distance in a population with adult genetic structure. Using real examples, we show that estimation errors can be large if genetic structure is not taken into account, so it is wise to evaluate adult genetic structure simultaneously with estimation of Φft for the pollen clouds. We show that the results are only moderately affected by changes in the decay function, a result of some importance since no completely established theory is available for this function.

The advancements made in molecular technology coupled with statistical methodology have led to the successful detection and location of genomic regions (quantitative trait loci; QTL) associated with quantitative traits. Binary traits (e.g. susceptibility/resistance), while not quantitative in nature, are equally important for the purpose of detecting and locating significant associations with genomic regions. Existing interval regression methods used in binary trait analysis are adapted from quantitative trait analysis and the tests for regression coefficients are tests of effect, not detection. Additionally, estimates of recombination that fail to take into account varying penetrance perform poorly when penetrance is incomplete. In this work a complete probability model for binary trait data is developed allowing for unbiased estimation of both penetrance and recombination between a genetic marker locus and a binary trait locus for backcross and F2 experimental designs. The regression model is reparameterized allowing for tests of detection. Extensive simulations were conducted to assess the performance of estimation and testing in the proposed parameterization. The proposed parameterization was compared with interval regression via simulation. The results indicate that our parameterization shows equivalent estimation capabilities, requires less computational effort and works well with only a single marker.

We reconsider deterministic models of mutation and selection acting on populations of sequences, or, equivalently, multilocus systems with complete linkage. Exact analytical results concerning such systems are few, and we present recent and new ones obtained with the help of methods from quantum statistical mechanics. We consider a continuous-time model for an infinite population of haploids (or diploids without dominance), with N sites each, two states per site, symmetric mutation and arbitrary fitness function. We show that this model is exactly equivalent to a so-called Ising quantum chain. In this picture, fitness corresponds to the interaction energy of spins, and mutation to a temperature-like parameter. The highly elaborate methods of statistical mechanics allow one to find exact solutions for non-trivial examples. These include quadratic fitness functions, as well as ‘Onsager's landscape’. The latter is a fitness function which captures some essential features of molecular evolution, such as neutrality, compensatory mutations and flat ridges. We investigate the mean number of mutations, the mutation load, and the variance in fitness under mutation–selection balance. This also yields some insight into the ‘error threshold’ phenomenon, which occurs in some, but not all, examples.

A method for estimating genotypic and identity-by-descent probabilities in complex pedigrees is described. The method consists of an algorithm for drawing independent genotype samples which are consistent with the pedigree and observed genotype. The probability distribution function for samples obtained using the algorithm can be evaluated up to a normalizing constant, and combined with the likelihood to produce a weight for each sample. Importance sampling is then used to estimate genotypic and identity-by-descent probabilities. On small but complex pedigrees, the genotypic probability estimates are demonstrated to be empirically unbiased. On large complex pedigrees, while the algorithm for obtaining genotype samples is feasible, importance sampling may require an infeasible number of samples to estimate genotypic probabilities with accuracy.

The transmission disequilibrium test (TDT) customarily uses affected children and their parents (often case–parent trios, TDTD). Control–parent trios are necessary to guard against spurious significant results due to segregation distortion but are not generally utilized in the identification of disease susceptibility loci (DSL). Controls are often easy to recruit and the TDT can easily be extended to include control–parent trios into the analyses with unrelated case–parent trios. We present an extension of the TDT (TDTDC) that incorporates unrelated cases and controls and their parents into a single analysis. We develop a simple and accurate analytical method for computing the statistical power of various TDT (e.g. the TDTD, TDTDC, TDTDC and TDTC that employ control–parent trios only) under any genetic model. We investigated the power of these TDT, and particularly compared the relative power of the TDTD and TDTDC. We found that the TDTDC is almost always more powerful than the TDTC and TDTD. The relative power of the TDTDC and TDTD depends largely upon a number of parameters identified in the study. This study provides a basis for efficient use of control–parent trios in DSL identification.

Most QTL mapping methods assume that phenotypes follow a normal distribution, but many phenotypes of interest are not normally distributed, e.g. bacteria counts (or colony-forming units, CFU). Such data are extremely skewed to the right and can present a high amount of zero values, which are ties from a statistical point of view. Our objective is therefore to assess the efficiency of four QTL mapping methods applied to bacteria counts: (1) least-squares (LS) analysis, (2) maximum-likelihood (ML) analysis, (3) non-parametric (NP) mapping and (4) nested ANOVA (AN). A transformation based on quantiles is used to mimic observed distributions of bacteria counts. Single positions (1 marker, 1 QTL) as well as chromosome scans (11 markers, 1 QTL) are simulated. When compared with the analysis of a normally distributed phenotype, the analysis of raw bacteria counts leads to a strong decrease in power for parametric methods, but no decrease is observed for NP. However, when a mathematical transformation (MT) is applied to bacteria counts prior to analysis, parametric methods have the same power as NP. Furthermore, parametric methods, when coupled with MT, outperform NP when bacteria counts have a very high proportion of zeros (70·8%). Our results show that the loss of power is mainly explained by the asymmetry of the phenotypic distribution, for parametric methods, and by the existence of ties, for the non-parametric method. Therefore, mapping of QTL for bacterial diseases, as well as for other diseases assessed by a counting process, should focus on the occurrence of ties in phenotypes before choosing the appropriate QTL mapping method.