Modem breeding programmes of livestock species have successfully led to increased genetic merit in
traits of economic relevance through accurate and intense selection. However, concomitant increased
levels of inbreeding have been also observed. Quadratic optimisation constitutes a general approach to
the joint management of the rates of genetic gain (ΔG) and inbreeding (ΔF) in selected populations.
The rate of inbreeding can be used as a measure of risk in the breeding programme. The method
optimises the genetic contributions of selection candidates for maximising ΔG while restricting ΔF to
a pre-defined value. The ΔF restriction is achieved by applying a quadratic constraint on the average
co-ancestry of selection candidates weighted by their projected use. The general objectives of this
thesis were: i) to implement and evaluate the potential benefits of quadratic optimisation in real
livestock populations; ii) to develop a deterministic framework for predicting ΔG under constrained
ΔF and iii) to evaluate the benefits of quadratic optimisation in multiple trait scenarios under mixed
The application of quadratic optimisation in two populations of beef cattle (Aberdeen Angus) and
sheep (Meatlinc) led to important increases in the expected AG. At the observed ΔF in each
population, increments per year in ΔG of 17% for Meatlinc and 30% for Aberdeen Angus were found
in comparison to the ΔG expected from conventional truncation BLUP selection. More relaxed
constraints on ΔF allowed even higher increases in expected ΔG in both populations.
Stochastic simulations have revealed that under quadratic optimisation the selective advantage of the
candidates for selection is primarily their Mendelian sampling terms rather than their breeding values
as under truncation selection. Thus, under quadratic optimisation, the contribution of candidates to the
future genetic pool is decided upon the best information on their unique superiority or inferiority with
respect to the parental mean.
A self-contained and accurate deterministic approach for predicting ΔG for pre-defined ΔF has been
developed. It requires only specification of the trait heritability, the number of selection candidates
and the target ΔF
Benefits from quadratic optimisation were also evaluated in a two-trait scenario where the trait with
lower heritability was affected by an identified quantitative trait loci (QTL). Extra gains in the
breeding goal were observed throughout the whole selection process from the combined use of both
optimised contributions and QTL information. In contrast, this scheme was not the most effective for
improving each of the traits in the breeding objective.
The design and operational tools developed in this thesis constitute a general framework for the
evaluation and realisation of the benefits from quadratic optimisation tools in practical livestock