Optimal size of progeny groups for progeny-testing programs by artificial insemination firms

A semi-stochastic model for the simulation of genetic improvement in a dairy cattle population was used to evaluate and optimize progeny-testing programs for AI firms that operate in a competitive market for semen from progeny-tested bulls with regard to number of bulls sampled and size of progeny groups. The population was serviced by four firms. The competition for market share and semen sales was determined by the relative rank of progeny-tested bulls from a firm based on EBV for a trait with a heritability of 25%. For a fixed total number of daughters from young bulls for an AI program (test capacity), optimal size of the progeny groups was highly dependent on the objective to be maximized. The rate of genetic gain was maximized with a progeny group of 57 to 61 daughters per bull, but was relatively robust to changes in size of progeny groups. The number of marketable bulls was maximized with progeny groups between 20 and 40 daughters, depending on the test capacity. However, when a relationship between price per dose of semen and EBV of marketable bulls was considered, returns from semen sales were maximized at 49 and 82 daughters per bull, respectively, for linear and quadratic functions for semen price. The critical objective, net returns from semen sales, subtracting costs of sampling bulls, was maximized for progeny groups of between 95 and 105 daughters. Optimal size of progeny groups was robust to changes in economic parameters and the breeding programs of competitors. For economic parameters that were typical for Canadian AI firms, net returns per annual cohort of young bulls were 40% higher for the optimal size of the progeny groups than for sampling with 60 daughters per bull.