Biomedical subjects

John A Woolliams

Publications and source records attributed to John A Woolliams.

11 recordsLinked to original sources

PubMed2007

Optimisation of contribution of candidate parents to maximise genetic gain and restricting inbreeding using semidefinite programming.

An approach for optimising genetic contributions of candidates to control inbreeding in the offspring generation using semidefinite programming (SDP) was proposed. Formulations were done for maximising genetic gain while restricting inbreeding to a preset value and for minimising inbreeding without regard of gain. Adaptations to account for candidates with fixed contributions were also shown. Using small but traceable numerical examples, the SDP method was compared with an alternative based upon Lagrangian multipliers (RSRO). The SDP method always found the optimum solution that maximises genetic gain at any level of restriction imposed on inbreeding, unlike RSRO which failed to do so in several situations. For these situations, the expected gains from the solution obtained with RSRO were between 1.5-9% lower than those expected from the optimum solution found with SDP with assigned contributions varying widely. In conclusion SDP is a reliable and flexible method for solving contribution problems.

Animals↗

PubMed2006

Prediction of IBD based on population history for fine gene mapping.

A novel multiple regression method (RM) is developed to predict identity-by-descent probabilities at a locus L (IBDL), among individuals without pedigree, given information on surrounding markers and population history. These IBDL probabilities are a function of the increase in linkage disequilibrium (LD) generated by drift in a homogeneous population over generations. Three parameters are sufficient to describe population history: effective population size (Ne), number of generations since foundation (T), and marker allele frequencies among founders (p). IBDL are used in a simulation study to map a quantitative trait locus (QTL) via variance component estimation. RM is compared to a coalescent method (CM) in terms of power and robustness of QTL detection. Differences between RM and CM are small but significant. For example, RM is more powerful than CM in dioecious populations, but not in monoecious populations. Moreover, RM is more robust than CM when marker phases are unknown or when there is complete LD among founders or Ne is wrong, and less robust when p is wrong. CM utilises all marker haplotype information, whereas RM utilises information contained in each individual marker and all possible marker pairs but not in higher order interactions. RM consists of a family of models encompassing four different population structures, and two ways of using marker information, which contrasts with the single model that must cater for all possible evolutionary scenarios in CM.

Alleles↗

PubMed2006

Prediction of genetic gain from quadratic optimisation with constrained rates of inbreeding.

There are selection methods available that allow the optimisation of genetic contributions of selection candidates for maximising the rate of genetic gain while restricting the rate of inbreeding. These methods imply selection on quadratic indices as the selection merit of a particular individual is a quadratic function of its estimated breeding value. This study provides deterministic predictions of genetic gain from selection on quadratic indices for a given set of resources (the number of candidates), heritability, and target rate of inbreeding. The rate of gain was obtained as a function of the accuracy of the Mendelian sampling term at the time of convergence of long-term contributions of selected candidates and the theoretical ideal rate of gain for a given rate of inbreeding after an exact allocation of long-term contributions to Mendelian sampling terms. The expected benefits from quadratic indices over traditional linear indices (i.e. truncation selection), both using BLUP breeding values, were quantified. The results clearly indicate higher gains from quadratic optimisation than from truncation selection. With constant rate of inbreeding and number of candidates, the benefits were generally largest for intermediate heritabilities but evident over the entire range. The advantage of quadratic indices was not highly sensitive to the rate of inbreeding for the constraints considered.

Animals↗

PubMed2004

On the prediction of simultaneous inbreeding coefficients at multiple loci.

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.

Data Interpretation, Statistical↗

PubMed2004

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.

Algorithms↗

PubMed2004

Impact of nonrandom mating on genetic variance and gene flow in populations with mass selection.

The mechanisms by which nonrandom mating affects selected populations are not completely understood and remain a subject of scientific debate in the development of tractable predictors of population characteristics. The main objective of this study was to provide a predictive model for the genetic variance and covariance among mates for traits subjected to directional selection in populations with nonrandom mating based on the pedigree. Stochastic simulations were used to check the validity of this model. Our predictions indicate that the positive covariance among mates that is expected to result with preferential mating of relatives can be severely overpredicted from neutral expectations. The covariance expected from neutral theory is offset by an opposing covariance between the genetic mean of an individual's family and the Mendelian sampling term of its mate. This mechanism was able to predict the reduction in covariance among mates that we observed in the simulated populations and, in consequence, the equilibrium genetic variance and expected long-term genetic contributions. Additionally, this study provided confirmatory evidence on the postulated relationships of long-term genetic contributions with both the rate of genetic gain and the rate of inbreeding (deltaF) with nonrandom mating. The coefficient of variation of the expected gene flow among individuals and deltaF was sensitive to nonrandom mating when heritability was low, but less so as heritability increased, and the theory developed in the study was sufficient to explain this phenomenon.

Genetic Variation↗

PubMed2003

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.

Animal Husbandry↗

PubMedDate not supplied

Precision of methods for calculating identity-by-descent matrices using multiple markers.

A rapid, deterministic method (DET) based on a recursive algorithm and a stochastic method based on Markov Chain Monte Carlo (MCMC) for calculating identity-by-descent (IBD) matrices conditional on multiple markers were compared using stochastic simulation. Precision was measured by the mean squared error (MSE) of the relationship coefficients in predicting the true IBD relationships, relative to MSE obtained from using pedigree only. Comparisons were made when varying marker density, allele numbers, allele frequencies, and the size of full-sib families. The precision of DET was 75-99% relative to MCMC, but was not simply related to the informativeness of individual loci. For situations mimicking microsatellite markers or dense SNP, the precision of DET was > or = 95% relative to MCMC. Relative precision declined for the SNP, but not microsatellites as marker density decreased. Full-sib family size did not affect the precision. The methods were tested in interval mapping and marker assisted selection, and the performance was very largely determined by the MSE. A multi-locus information index considering the type, number, and position of markers was developed to assess precision. It showed a marked empirical relationship with the observed precision for DET and MCMC and explained the complex relationship between relative precision and the informativeness of individual loci.

Algorithms↗

PubMedDate not supplied

Marker assisted selection with optimised contributions of the candidates to selection.

The benefits of marker assisted selection (MAS) are evaluated under realistic assumptions in schemes where the genetic contributions of the candidates to selection are optimised for maximising the rate of genetic progress while restricting the accumulation of inbreeding. MAS schemes were compared with schemes where selection is directly on the QTL (GAS or gene assisted selection) and with schemes where genotype information is not considered (PHE or phenotypic selection). A methodology for including prior information on the QTL effect in the genetic evaluation is presented and the benefits from MAS were investigated when prior information was used. The optimisation of the genetic contributions has a great impact on genetic response but the use of markers leads to only moderate extra short-term gains. Optimised PHE did as well as standard truncation GAS (i.e. with fixed contributions) in the short-term and better in the long-term. The maximum accumulated benefit from MAS over PHE was, at the most, half of the maximum benefit achieved from GAS, even with very low recombination rates between the markers and the QTL. However, the use of prior information about the QTL effects can substantially increase genetic gain, and, when the accuracy of the priors is high enough, the responses from MAS are practically as high as those obtained with direct selection on the QTL.

Genetic Markers↗

PubMedDate not supplied

The advantage of factorial mating under selection is uncovered by deterministically predicted rates of inbreeding.

Rates of inbreeding (DeltaF) in selected populations were predicted using the framework of long-term genetic contributions and validated against stochastic simulations. Deterministic predictions decomposed DeltaF into four components due to: finite population size, directional selection, covariance of genetic contribution of mates, and deviation of variance of family size from that expected from a Poisson distribution. Factorial (FM) and hierarchical (HM) mating systems were compared under mass and sib-index selection. Prediction errors were in most cases for DeltaF less than 10% and for rate of gain less than 5%. DelatF was higher with index than mass selection. DeltaF was lower with FM than HM in all cases except random selection. FM reduced the variance of the average breeding value of the mates of an individual. This reduced the impact of the covariance of contributions of mates on DeltaF. Thus, contributions of mates were less correlated with FM than HM, causing smaller deviations of converged contributions from the optimum contributions. With index selection, FM also caused a smaller variance of number of offspring selected from each parent. This reduced variance of family size reduced DeltaF further. FM increases the flexibility in breeding schemes for achieving the optimum genetic contributions.

Animals↗

PubMedDate not supplied

Genomic contributions in livestock gene introgression programmes.

The composition of the genome after introgression of a marker gene from a donor to a recipient breed was studied using analytical and simulation methods. Theoretical predictions of proportional genomic contributions, including donor linkage drag, from ancestors used at each generation of crossing after an introgression programme agreed closely with simulated results. The obligate drag, the donor genome surrounding the target locus that cannot be removed by subsequent selection, was also studied. It was shown that the number of backcross generations and the length of the chromosome affected proportional genomic contributions to the carrier chromosomes. Population structure had no significant effect on ancestral contributions and linkage drag but it did have an effect on the obligate drag whereby larger offspring groups resulted in smaller obligate drag. The implications for an introgression programme of the number of backcross generations, the population structure and the carrier chromosome length are discussed. The equations derived describing contributions to the genome from individuals from a given generation provide a framework to predict the genomic composition of a population after the introgression of a favourable donor allele. These ancestral contributions can be assigned a value and therefore allow the prediction of genetic lag.

Animals↗