Using parametric models that describe the increase in mortality rates with age, we demonstrate that environmentally induced heterogeneity among genetically identical individuals is sufficient to generate biased estimates of age-specific genetic variance. Although the magnitude of the bias may change with age, one general trend emerges: the true genetic variance at the oldest ages is likely to be dramatically underestimated. Our results are robust to different manifestations of heterogeneity and suggest that such a bias is a general feature of these models. We note that age-dependent estimates of genetic variance for characters that are correlated with mortality (either genetically or environmentally) can be expected to be similarly affected. The results are independent of sample size and suggest that the bias may be more widespread in the literature than is currently appreciated. Our results are discussed with reference to existing data on mortality variance in Drosophila melanogaster.

Genetic parameters widely used to monitor genetic variation in conservation programmes, such as effective number of founders, founder genome equivalents and effective population size, are interrelated in terms of coancestries and variances of contributions from ancestors to descendants. A new parameter, the effective number of non-founders, is introduced to describe the relation between effective number of founders and founder genome equivalents. Practical recommendations for the maintenance of genetic variation in small captive populations are discussed. To maintain genetic diversity, minimum coancestry among individuals should be sought. This minimizes the variances of contributions from ancestors to descendants in all previous generations. The method of choice of parents and the system of mating should be independent of each other because a clear-cut recommendation cannot be given on the latter.

Selection for high or low daily food intake (DFI) in Large White pigs resulted in higher serum leptin concentration, fat deposition and food intake in the high DFI line. The response in serum leptin concentration indicated that the higher fat deposition of the high DFI line was not due to insufficient leptin production, as in the Lepob/Lepob mouse. Serum leptin was more highly correlated with fat deposition than with food intake indicating that the response in serum leptin was primarily due to increased fat deposition rather than to higher energy intake per se. The low correlations between serum leptin measured at 30 kg and performance test traits indicate that serum leptin would not be efficient for selection of animals prior to performance test. However, the consistent positive correlations between serum leptin and a measure of fat deposition suggest that serum leptin could usefully be incorporated in selection criteria for genetic improvement of carcass lean content in pigs.

We studied the effects of population size on the inbreeding depression and genetic load caused by deleterious mutations at a single locus. Analysis shows how the inbreeding depression decreases as population size becomes smaller and/or the rate of inbreeding increases. This pattern contrasts with that for the load, which increases as population size becomes smaller but decreases as inbreeding rate goes up. The depression and load both approach asymptotic limits when the population size becomes very large or very small. Numerical results show that the transition between the small and the large population regimes is quite rapid, and occurs largely over a range of population sizes that vary by a factor of 10. The effects of drift on inbreeding depression may bias some estimates of the genomic rate of deleterious mutation. These effects could also be important in the evolution of breeding systems in hermaphroditic organisms and in the conservation of endangered populations.

Lande's equation for predicting the response of trait means to a shift in optimal trait values is tested using a stochastic simulation model. The simulated population is finite, and each individual has a finite number of loci. Therefore, selection may cause allele frequencies and distributions to change over time. Since the equation assumes constant genetic parameters, the degree to which such allelic changes affect predictions can be examined. Predictions are based only on information available at generation zero of directional selection. The quality of the predictions depends on the nature of allelic distributions in the original population. If allelic effects are approximately normally distributed, as assumed in Lande's Gaussian approximation to the continuum-of-alleles model, the predictions are very accurate, despite small changes in the G matrix. If allelic effects have a leptokurtic distribution, as is likely in Turelli's ‘house-of-cards’ approximation, the equation underestimates the rate of response and correlated response, and overestimates the time required for the trait means to reach their equilibrium values. Models with biallelic loci have limits as to the amount of trait divergence possible, since only two allelic values are available at each of a finite set of loci. If the new optimal trait values lie within these limits, predictions are good. if not, singularity in the G matrix results in suboptimal equilibria, despite the presence of genetic variance for each individual trait.

In the interspecific cross of Populus trichocarpa × P. deltoides, unexpected simultaneous occurrence of diploid hybrids and triploid hybrids (with two alleles from the female parent and one from the male parent at each locus) led us to examine the evolutionary genetic significance of this phenomenon. As expected, leaf size and shape of the triploid progeny are closer to the female P. trichocarpa than male P. deltoides parent. Although the pure triploid progeny population did not have higher genetic variance in leaf traits than the pure diploid population, the former appears to hide much non-additive genetic variance and display strong genetic control over the phenotypic plasticity of leaf traits. It is suggested that the cryptic non-additive variance, especially epistasis, can be released when a population is disturbed by changes in the environment. A mixed diploid and triploid progeny population combines phenotypic and genetic characteristics of both pure hybrids and is considered to be of adaptive significance for poplars to survive and evolve in a fluctuating environment. The significant effect due to general and specific combining ability differences at the population level suggests that the population divergence of these two species is under additive and non-additive genetic control.

Most current statistical methods developed for mapping quantitative trait loci (QTL) based on inbred line designs apply to crosses from two inbred lines. Analysis of QTL in these crosses is restricted by the parental genetic differences between lines. Crosses from multiple inbred lines or multiple families are common in plant and animal breeding programmes, and can be used to increase the efficiency of a QTL mapping study. A general statistical method using mixture model procedures and the EM algorithm is developed for mapping QTL from various cross designs of multiple inbred lines. The general procedure features three cross design matrices, W, that define the contribution of parental lines to a particular cross and a genetic design matrix, D, that specifies the genetic model used in multiple line crosses. By appropriately specifying W matrices, the statistical method can be applied to various cross designs, such as diallel, factorial, cyclic, parallel or arbitrary-pattern cross designs with two or multiple parental lines. Also, with appropriate specification for the D matrix, the method can be used to analyse different kinds of cross populations, such as F2 backcross, four-way cross and mixed crosses (e.g. combining backcross and F2). Simulation studies were conducted to explore the properties of the method, and confirmed its applicability to diverse experimental designs.

We address various statistical aspects of biological parentage in multi-offspring broods that arise via multiple paternity or multiple maternity and, hence, consist of mixtures of full- and half-sibs. Conditioned on population genetic parameters, computer simulations described herein permit estimation of: (1) the mean number of offspring needed to detect all parental gametes in a brood and (2) the relationship between the number of distinct parental gametes found in a brood and the number of parents. Results are relevant to the design of empirical studies employing molecular markers to assess genetic parentage in polygynous or polyandrous species with large broods, such as are found in many fishes, amphibians, insects, plants and other groups. The utility of this approach is illustrated using two empirical data sets.

Data on osteochondrosis and femur dimensions from 195 F2 pigs from a wild boar × Large White intercross were analysed with the aim of detecting quantitative trait loci (QTLs) for normal and disturbed bone formation. The information from numerous recorded traits was summarized by principal component analysis and analysed by least-squares interval mapping. An increase in the proportion of wild boar alleles across the genome increased length versus width of femur and reduced the prevalence of osteochondrosis. The presence of QTLs with an impact on femur dimensions was indicated on chromosomes 2, 4, 16 and 17 and on osteochondrosis on chromosomes 5, 13 and 15. A substantial effect of the chromosome 5 QTL calls for further studies within commercial populations to evaluate whether marker-assisted selection could be used to reduce the prevalence of osteochondrosis.

We studied the efficiency of recurrent selection based solely on marker genotypes (marker-based selection), in order to increase favourable allele frequency at 50 previously detected quantitative trait loci (QTLs). Two selection procedures were investigated, using computer simulations: (1) Truncation Selection (MTS), in which individuals are ranked based on marker score, and best individuals are selected for recombination; and (2) QTL Complementation Selection (QCS), in which individuals are selected such that their QTL composition complements those individuals already selected. Provided QTL locations are accurate, marker-based selection with a population size of 200 was very effective in rapidly increasing frequencies of favourable QTL alleles. QCS methods were more effective than MTS for improving the mean frequency and fixation of favourable QTL alleles. Marker-based selection was not very sensitive to a reduction in population size, and appears valuable to optimize the use of molecular markers in recurrent selection programmes.

Standard theory provides a simple prediction for the frequency of a recessive lethal allele conferring heterozygous protection against an infectious disease (the best-known example being sickle cell protection against malaria). This relationship allows historic disease mortality rates to be estimated. There are, however, hidden biases in this approach. Reproductively active human females in archaic societies normally produce children at intervals of around 4 years. If death of the fetus or young infant (less than around 3 years of age) occurs, then the mother re-enters oestrus and produces another child. This ‘reproductive compensation’ reduces selection against the agent causing early mortality (the recessive allele or infective agent) and biases our estimates of historic mortality rates. The magnitude of these biases is investigated. Re-conception also constitutes a demographic selective pressure acting alongside natural selection: lethal genetic diseases (or tightly linked loci) will be selected to become ever more virulent, killing at ever decreasing ages, to allow the mother to re-enter oestrus and re-conceive a (hopefully unaffected) sibling; this effect also invalidates statistical tests using the number of alleles to distinguish overdominance from drift as explanations for high allele frequency. The same bias affects calculations of mutation/selection balance: for any given mutation rate, syndromes which kill early in life will reach much higher frequencies than those killing at later ages. An intriguing consequence is that lethal recessive disorders in humans will increase in frequency by up to 45% as a consequence of the recent demographic transition to planned family size.

A Bayesian approach is presented for mapping a quantitative trait locus (QTL) using the ‘Fernando and Grossman’ multivariate Normal approximation to QTL inheritance. For this model, a Bayesian implementation that includes QTL position is problematic because standard Markov chain Monte Carlo (MCMC) algorithms do not mix, i.e. the QTL position gets stuck in one marker interval. This is because of the dependence of the covariance structure for the QTL effects on the adjacent markers and may be typical of the ‘Fernando and Grossman’ model. A relatively new MCMC technique, simulated tempering, allows mixing and so makes possible inferences about QTL position based on marginal posterior probabilities. The model was implemented for estimating variance ratios and QTL position using a continuous grid of allowed positions and was applied to simulated data of a standard granddaughter design. The results showed a smooth mixing of QTL position after implementation of the simulated tempering sampler. In this implementation, map distance between QTL and its flanking markers was artificially stretched to reduce the dependence of markers and covariance. The method generalizes easily to more complicated applications and can ultimately contribute to QTL mapping in complex, heterogeneous, human, animal or plant populations.

We present a general regression-based method for mapping quantitative trait loci (QTL) by combining different populations derived from diallel designs. The model expresses, at any map position, the phenotypic value of each individual as a function of the specific-mean of the population to which the individual belongs, the additive and dominance effects of the alleles carried by the parents of that population and the probabilities of QTL genotypes conditional on those of neighbouring markers. Standard linear model procedures (ordinary or iteratively reweighted least-squares) are used for estimation and test of the parameters.

Pedigree and marker data from a multiple-generation pig selection experiment have been analysed to screen for loci affecting quantitative traits (QTL). Pigs from a base population were selected either for low backfat thickness at fixed live weight (L-line) or high live weight at fixed age (F-line). Selection was based on single-trait own performance and DNA was available on selected individuals only. Genotypes for three marker loci with known positions on chromosome 4 were available. The transmission/disequilibrium test (TDT) was originally described in human genetics to test for linkage between a genetic marker and a disease-susceptibility locus, in the presence of association. Here, we adapt the TDT to test for linkage between a marker and QTL favoured by selection, and for linkage disequilibrium between them in the base population. The a priori unknown distribution of the test statistic under the null hypothesis, no linkage, was obtained via Monte Carlo simulation. Significant TDT statistics were found for markers AFABP and SW818 in the F-line, indicating the presence of a closely linked QTL affecting growth performance. In the L-line, none of the markers studied showed significance. This study emphasizes the potential of the TDT as a quick and simple approach to screen for QTL in situations where marker genotypes are available on selected individuals. The results suggest that previously identified QTL in crosses of genetically diverse breeds may also segregate in commercial selection lines.

In crosses between inbred lines, linear regression can be used to estimate the correlation of markers with a trait of interest; these marker effects then allow marker assisted selection (MAS) for quantitative traits. Usually a subset of markers to include in the model must be selected: no completely satisfactory method of doing this exists. We show that replacing this selection of markers by ridge regression can improve the mean response to selection and reduce the variability of selection response.