Mate Selection History

What is Mate Selection?

Mate Selection is the process of choosing breeding animals and deciding how they are paired, producing a mating list. The purpose is to meet genetic goals (such as direction, magnitude, and pattern of genetic changes for multiple traits), avoid genetic defects and inbreeding, manage long-term genetic diversity, use reproductive technologies (e.g. superovulation), satisfy diverse customer needs, and stay within practical and logistical constraints.

Mate Selection Solutions and History

A key task for breeding programs is to balance the relative emphasis on genetic gain and maintenance of diversity. This has now been done quite widely in the context of an objective function that includes measures of genetic merit and coancestry among selected parents. Wray and Goddard (1994) and Brisbane and Gibson (1994) included negative weighting on individual relationships in selection indices in order to help control the rate of inbreeding, and hence genetic diversity. Meuwissen (1997) formalized the optimisation of individual contributions, differentiating a function that includes genetic merit and individual coancestries, accommodating individual contribution constraints in an iterative manner. Hinrichs et al. (2006) and Dagnachew and Meuwissen (2016) have improved speed in this method considerably, and Pong-Wong and Woolliams (2007, 2018) have illustrated a method that handles individual contribution constraints directly, and thus gives a guaranteed optimal solution.

The results from such methods generally give optimal contributions as proportions on a continuous scale. The practitioner uses these to help make selections and allocate numbers of matings to each breeding individual. This represents a powerful way to allocate more matings to higher-EBV individuals in a manner that properly manages genetic diversity.

Progressive breeding programs are motivated by many other issues in addition to genetic gain and diversity, including progeny inbreeding, management of genetic marker frequencies and genotypes, management of trait distributions, multi-stage selection, various types of costs, and various logistical constraints, including constraints on pattern of use of individuals across groups. For such cases, contributions can be specified in numbers of matings to be allocated, rather than proportional contributions, and indeed the actual mate allocation set (e.g. Kinghorn 2000), but the optimal solution must be discovered, rather than derived, due to the complexity of the resulting objective function.

Solving complex objective functions

Such problems can be solved using Evolutionary Computation (EC), and adaptations of Differential Evolution (DE, Storn and Price 1997) have been used for this. The central idea behind EC is to create populations of candidate solutions of a problem and evolve these populations by selection based on an objective function which emulates natural selection (eg. Bäck 2003).

The key to making this work relates to how the problem is presented to the solving algorithm. Kinghorn and Shepherd (1999) show how a vector of numbers can be transformed to derive a pattern of individual selection and mate allocation – Mate Selection. This makes the optimisation problem simple – the DE algorithm has only to find the vector of numbers that maximizes the objective function.

For each mating set tested, the component outcomes evaluated constitute the overall Mate Selection Index (MSI). Ideally, each component should be evaluated on the same scale, typically the scale of the breeding objective in units of, for example, dollars profit per breeding female per year. The MSI is a function of the selections and mate allocations chosen across all mating individuals in the population - it is used to form a mating set for the specified number of matings in the breeding program. The MSI can include predicted genetic merit in progeny, long-term inbreeding as reflected by parental coancestry, progeny inbreeding, heterosis (if relevant) and various costs and logistical constraints associated with the breeding program (Banks 2000; Kinghorn 2000). The objective function can be changed (weightings changed, or variables added or deleted) to suit the desired outcomes of the breeder.

Comprehensive use of a Mate Selection Tool (MST) involves decision making at various stages of the life cycle, including selection/culling at various juvenile and adult stages, selections for main round matings and, in some cases, selection of sires for backup matings. The MST can be made to accommodate all members of the population, across different groups, including putative embryos in utero, immature juveniles, virgin females and pregnant females, as well as candidates for active matings. An effective way to do this is to force the MST to include recent actual matings in its solution – this being preferable to including the juvenile fruits of these matings as candidates for ‘virtual matings’ that will not be acted on. These approaches help to accommodate overlapping generations, and to account for contributions already made as reflected by juveniles and embryos in the analysis – sires that have already been used extensively, and their close relatives, will be somewhat inhibited from further use.

To implement such a scheme, there is a requirement to constrain the solution such that individuals can only be allocated to members of the opposite sex (unless bisexuality is accommodated) that are in an appropriate group, with the two key groups being the male and female active mating groups (although these may be sub-grouped in turn, for example by location). One way to handle such complex grouping constraints is to penalize nonconforming solutions in the objective function. However, this has proved to result in slow computation speed, as most evolutionary pressure is used up maintaining legality of solutions. However, a method has been developed to translate a vector of numbers to a legal mate selection solution that satisfies complex constraints, not previously handled by Kinghorn and Shepherd (1999), related to grouping and mate allocation among groups. This has resulted in considerably higher speed, giving much increased flexibility (Kinghorn, 2011).

Part of the need for high speed in such MSTs relates to the need to explore the solution space to find a result that gives a satisfactory balance among the wide range of issues that can be represented in the objective function. It is difficult to be economically rational across issues such as level and cost of migration, pattern of trait distributions, marker genotype frequencies and number of mating paddocks required. Experience shows that iterations of quickly finding an optimal solution for the prevailing objective function followed by adjustments to weighting factors and/or thresholds set in the objective function gives the practitioner a good feel for the trade-offs involved in putting differential emphasis on component objectives. In decision making theory these solutions are sometimes referred to as satisficing – they are at least close to optimal given all of the information at hand. This leads to some understanding of what can be achieved, and acceptance of a final mate selection solution.

In practice, there is a trade-off between what rigorous scientific effort might determine to be the “best” overall direction, and the direction that is chosen by the practitioner. The latter has the advantage that it is in fact implemented, and not left hanging as a mere recommendation.

In addition, of course, scientific method gets well implemented ‘around’ the constraints and weightings applied by the practitioner - for example, the theory of optimal contributions (Meuwissen, 1997) is effectively invoked by default, but subject to hard and soft constraints related to issues other than genetic gain and genetic diversity.

Breeding decisions are made on a frequent basis in, for example, the pig and poultry industries, and so this discovery process needs to be captured in a manner permitting essentially automatic running of the MST with little or no user intervention. This can be achieved using algorithms to maintain certain key outcomes, such as keeping the relationship between parental coancestry and predicted progeny merit within a narrow trajectory, so that other issues cannot displace the final solution from that path. This is analogous to a desired gains selection index (e.g. Brascamp 1984), but where the ratio of gains between two traits (issues in the MST case) is softly constrained within certain bounds. Overall response surfaces can be very flat – giving good opportunity to move one issue in a favourable direction, with little compromise in other key issues.

MSTs that are available include Ani-Mate (Amer, www.abacusbio.com/projects/animate/), TGRM and X’Aim (X’Prime, www.xprime.com.au), GENCONT/OCSELECT (Meuwissen, 2002; Hinrichs et al., 2006), AlphaMate (Gorjanc/Hickey, 2018), EVA (Berg et al., 2006) and MateSel. These are now being used in breeding programs for Dairy, Beef, Pigs, Meat Sheep, Wool Sheep, Broilers, Eggs, Turkeys, Atlantic Salmon, Pacific Salmon, Rainbow Trout, Shrimp, Trees, Canola, Potatos, Chickpeas, and Beans.

Implementation level ranges from providing target numbers of matings for each candidate individual, with the aim of maximizing genetic gain at a defined rate of inbreeding, through to dictation of all stages of selection, culling, semen collection, mate allocation and backup matings, with comprehensive attention to the full prevailing range of technical and operational constraint issues. More complete implementations can take a considerable amount of setting up. However, once established they provide for routine optimal implementation of progressive breeding programs. They also constitute an appropriately competitive framework for implementation of new technical opportunities, including a range of genomic opportunities, reproductive boosting, and engineering extra genetic variation in key traits well before the physical splitting of a breeding line.

Look ahead mating strategies (Hayes et al 2002, Shepherd and Woolliams, 2004, Niehoff et al, 2024) have been proposed, aiming to exploit non-additive components some generations ahead. This includes the setting up of “investment matings” (such as F1 crosses) in order to capitalize on “realization matings” (such as 3-breed cross using F1 females). This constitutes short-term management of genetic variation for longer term gains. A simulated example has been given by Li et al. (2006) where an MST operating on cohorts rather than individuals was implemented for simultaneous decision making over generations, resulting in the setting up of divergent lines to exploit dominance at known loci. This approach has the potential to give tactical targeting of a suitable route through genotypic changes across multiple interacting loci, should we ever have sufficient understanding of the genotypic effects involved.