Overview

MateSel uses a frontier graph and OCS (Optimal Contributions Selection) to provide breeders a mechanism to balance short-term genetic gain and long-term diversity.

What is the Frontier?

This graph shows the most extreme responses possible when all emphasis is shared by just two component objectives:

• Progeny Index (xG)
• Parental Coancestry (xAx/2).

It is the frontier of Optimal Contributions Selection (OCS). The favourable direction is towards the top-left. The frontier line is drawn between points that are found by running the MateSel algorithms multiple times, each with a different relative emphasis on each of these issues. In fact it is run to target solutions that are graphically closest to calculated points on the graph. The “origin” is at the bottom right, and a web of 10-degree spacing is drawn for orientation.

In the diagram below, the current solution indicator (blue cross-hair) is sitting on the frontier at 25 degrees. The red trail shows the pathway that the algorithm has made during convergence.

In the next diagram, extremely strong emphasis has been placed on progeny inbreeding, and some compromise has resulted in both lower Progeny Index and higher Coancestry:

What is Parental Coancestry?

Parental Coancestry is the average relationship among all parents to be mated in the current mating list solution, appropriately weighted by the number of matings allocated to each parent. This includes the relationships of each individual to itself, because a single allele in an individual can be inherited down different pedigree paths and be joined together “identical by descent” in a different individual in a future generation. This is the simple definition of inbreeding. If you have few parents then a much bigger proportion of the relationships are high self-relationships, and average Parental Coancestry is much higher, as is long term inbreeding.

For illustration: Driving the breeding program by mating a single elite bull with many oocytes from a single unrelated elite cow gives no inbreeding in the progeny generation – but this is a recipe for inbreeding disaster in the longer term.

Behaviour when using Target Degrees (TD)

MateSel provides a number of different Balance Strategies to control the Frontier graph. This section relates only to the balance strategies that involve Target Degrees.

For Target Degrees less than 45 degrees, the Target Degrees line is green in color, as shown in these diagrams, when using the Hard or Soft Constraint on Target Degrees Balance Strategy, these aim to increase gain while keeping the solution above the chosen Target Degrees (to the left/below the Target Degree line, as in the diagram above).

For Target Degrees above 45 degrees a magenta color is shown to illustrate that Hard and Soft Constraint on Target Degrees Balance Strategies operate differently – here they aim to minimise coancestry while keeping the solution below the chosen Target Degrees (to the right/above the Target Degree line).

At TD=0 (or maximum Gain), negative degrees (to right of green line) is permitted. Likewise, at TD=90, >90 degrees is permitted (below the magenta line). When the solution is off the scale, the current solution indicator stays on the nearest axis and it displays an arrow pointing to where the current solution lies.

Tip

In the absence of other objective function components (i.e. there are no trait/marker/inbreeding targets or constraints), the 0 target degrees scenario is equivalent to performing selection entirely based on the index.

Theory behind OCS and the Frontier Graph

Because of the need to balance genetic gain and inbreeding rate, for which there’s no objective optimum, the results of OCS are often presented as a gain-diversity frontier (Pareto front) of possible outcomes for varying importance attributed to these two factors, as applied through weightings or constraints. The focus of OCS is on selection of males and females for breeding and optimizing their contributions to the next generation, but this does not cover mate allocation. While OCS has a major role to play in balancing genetic gains with maintenance of genetic diversity, in some circumstances appropriate attention to mate allocation can further improve long-term gain and diversity outcomes (Kinghorn and Kinghorn, 2023).