Selectiongain: an R package for optimizing multi-stage selection

Multi-stage selection is practised in numerous fields of the life sciences and particularly in breeding. A special characteristic of multi-stage selection is that candidates are evaluated in successive stages with increasing intensity and efforts, and only a fraction of the superior candidates is selected and promoted to the next stage. For the optimum design of such selection programs, the selection gain $$\varDelta G(y)$$ΔG(y) plays a central role. It can be calculated by integration of a truncated multivariate normal distribution. While mathematical formulas for calculating $$\varDelta G(y)$$ΔG(y) and $$\psi (y)$$ψ(y), the variance among the selected candidates, were developed a long time ago, solutions and software for numerical calculations were not available. We developed the R package selectiongain for efficient and precise calculation of $$\varDelta G(y)$$ΔG(y) and $$\psi (y)$$ψ(y) for (i) a given matrix $$\varvec{\varSigma }^{*}$$Σ∗ of correlations among the unobservable target character and the selection criteria and (ii) given coordinates $$\mathbf Q $$Q of the truncation point or the selected fractions $$\varvec{\alpha }$$α in each stage. In addition, our software can be used for optimizing multi-stage selection programs under a given total budget and different costs of evaluating the candidates in each stage. Besides a detailed description of the functions of the software, the package is illustrated with two examples.