Optimisation of contribution of candidate parents to maximise genetic gain and restricting inbreeding using semidefinite programming (Open Access publication)

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

Response to mass selection when an identified major gene is segregating

International audienc

Validating statistical properties of resilience indicators derived from simulated longitudinal performance measures of farmed animals

Resilience is commonly defined as the ability of an individual to be minimally affected or to quickly recover from a challenge. Improvement of animals’ resilience is a vital component of sustainable livestock production but has so far been hampered by the lack of established quantitative resilience measures. Several studies proposed that summary statistics of the deviations of an animal's observed performance from its target performance trajectory (i.e., performance in the absence of challenge) may constitute suitable quantitative resilience indicators. However, these statistical indicators require further validation. The aim of this study was to obtain a better understanding of these resilience indicators in their ability to discriminate between different response types and their dependence on different response characteristics of animals, and data recording features. To this purpose, milk-yield trajectories of individual dairy cattle differing in resilience, without and when exposed to a short-term challenge, were simulated. Individuals were categorised into three broad response types (with individual variation within each type): Fully Resilient animals, which experience no systematic perturbation in milk yield after challenge, Non-Resilient animals whose milk yield permanently deviates from the target trajectory after challenge and Partially Resilient animals that experience temporary perturbations but recover. The following statistical resilience indicators previously suggested in the literature were validated with respect to their ability to discriminate between response types and their sensitivity to various response features and data characteristics: logarithm of mean of squares (LMS), logarithm of variance (LV), skewness (S), lag-1 autocorrelation (AC1), and area under the curve (AUC) of deviations. Furthermore, different methods for estimating unknown target trajectories were evaluated. All of the considered resilience indicators could distinguish between the Fully Resilient response type and either of the other two types when target trajectories were known or estimated using a parametric method. When the comparison was between Partially Resilient and Non-Resilient, only LMS, LV, and AUC could correctly rank the response types, provided that the observation period was at least twice as long as the perturbation period. Skewness was in general the least reliable indicator, although all indicators showed correct dependency on the amplitude and duration of the perturbations. In addition, all resilience indicators except for AC1 were robust to lower frequency of measurements. In general, parametric methods (quantile or repeated regression) combined with three resilience indicators (LMS, LV and AUC) were found the most reliable techniques for ranking animals in terms of their resilience.</p

Regional Heritability Mapping to identify loci underlying genetic variation of complex traits

BACKGROUND: Genome-wide association studies can have limited power to identify QTL, partly due to the stringent correction for multiple testing and low linkage-disequilibrium between SNPs and QTL. Regional Heritability Mapping (RHM) has been advanced as an alternative approach to capture underlying genetic effects. In this study, RHM was used to identify loci underlying variation in the 16(th )QTLMAS workshop simulated traits. METHODS: The method was implemented by fitting a mixed model where a genomic region and the overall genetic background were added as random effects. Heritabilities for the genetic regional effects were estimated, and the presence of a QTL in the region was tested using a likelihood ratio test (LRT). Several region sizes were considered (100, 50 and 20 adjacent SNPs). Bonferroni correction was used to calculate the LRT thresholds for genome-wide (p < 0.05) and suggestive (i.e., one false positive per genome scan) significance. RESULTS: Genomic heritabilities (0.31, 0.32 and 0.48, respectively) and genetic correlations (0.80, -0.42 and 0.19, between trait-pairs 1&2, 1&3 and 2&3) were similar to the simulated ones. RHM identified 7 QTL (4 at genome-wide and 3 at suggestive level) for Trait1; 4 (2 genome-wide and 2 suggestive) for Trait2; and 7 (6 genome-wide and 1 suggestive) for Trait3. Only one of the identified suggestive QTL was a false-positive. The position of these QTL tended to coincide with the position where the largest QTL (or several of them) were simulated. Several signals were detected for the simulated QTL with smaller effect. A combined analysis including all significant regions showed that they explain more than half of the total genetic variance of the traits. However, this might be overestimated, due to Beavis effect. All QTL affecting traits 1&2 and 2&3 had positive correlations, following the trend of the overall correlation of both trait-pairs. All but one QTL affecting traits 1&3 were negatively correlated, in agreement with the simulated situation. Moreover, RHM identified extra loci that were not found by association and linkage analysis, highlighting the improved power of this approach. CONCLUSIONS: RHM identified the largest QTL among the simulated ones, with some signals for the ones with small effect. Moreover, RHM performed better than association and linkage analysis, in terms of both power and resolution

Behaviour of the additive finite locus model

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