Selectiongain: an R package for optimizing multi-stage selection. (English) Zbl 1342.65050

Summary: 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 \(\varDelta G(y)\) plays a central role. It can be calculated by integration of a truncated multivariate normal distribution. While mathematical formulas for calculating \(\varDelta G(y)\) and \(\psi (y)\), 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 \(\varDelta G(y)\) and \(\psi (y)\) for (i) a given matrix \(\boldsymbol{\Sigma}^*\) of correlations among the unobservable target character and the selection criteria and (ii) given coordinates \(\mathbf Q\) of the truncation point or the selected fractions \(\boldsymbol{\alpha}\) 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.


62-08 Computational methods for problems pertaining to statistics
62-04 Software, source code, etc. for problems pertaining to statistics
62L10 Sequential statistical analysis
62F07 Statistical ranking and selection procedures
Full Text: DOI


[1] Brent R (1973) Algorithms for minimization without derivatives. Prentice-Hall, Englewood Cliffs, New Jersey · Zbl 0245.65032
[2] Cochran WG (1951) Improvement by means of selection. In: Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, pp 449-470
[3] Falconer DS, Mackay TFC (1996) Introduction to quantitative genetics, 4th edn. Longman Publishing Group, London
[4] Genz, A; Bretz, F, Numerical computation of multivariate \(t\)-probabilities with application to power calculation of multiple contrasts, J Stat Comput Simul, 63, 361-378, (1999) · Zbl 0934.62020
[5] Genz A, Bretz F, Miwa T, Mi X, Leisch F, Scheipl F, Hothorn T (2011) mvtnorm: multivariate normal and t distributions. R package version 0.9-9995
[6] Kim J (1997) Iterated grid search algorithm on unimodal criteria. PhD thesis, Virginia Polytechnic Institute and State University
[7] Longin, CFH; Utz, HF; Reif, JC; Wegenast, T; Schipprack, W; Melchinger, AE, Hybrid maize breeding with doubled haploids: III. efficiency of early testing prior to doubled haploid production in two-stage selection for testcross performance, Theor Appl Genet, 115, 519-527, (2007)
[8] Lynch M, Walsh B (1997) Genetics and analysis of quantitative traits. Sinauer Associates Inc, Sunderland
[9] Mi, X; Miwa, T; Hothorn, T, Mvtnorm: new numerical algorithm for multivariate normal probabilities, R J, 1, 37-39, (2009)
[10] Mi, X; Wegenast, T; Utz, HF; Dhillon, BS; Melchinger, AE, Best linear unbiased prediction and optimum allocation of test resources in maize breeding with doubled haploids, Theor Appl Genet, 123, 1-10, (2011)
[11] Miwa, T; Hayter, AJ; Kuriki, S, The evaluation of general non-centred orthant probabilities, J R Stat Soc B, 65, 223-234, (2003) · Zbl 1063.62082
[12] Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1993) Numerical recipes in FORTRAN; the art of scientific computing, 2nd edn. Cambridge University Press, New York · Zbl 0778.65002
[13] R Core Team (2013) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org · Zbl 0934.62020
[14] Ron L, Bruce H (2009) Calculus, 9th edn. Brooks/Cole Publishing, Los Angeles
[15] Shi, J; Zhou, S, Quality control and improvement for multistage systems : a survey, IIE Trans, 41, 744-753, (2009)
[16] Tallis, GM, The moment generating function of the truncated multi-normal distribution, J R Stat Soc B, 23, 223-229, (1961) · Zbl 0107.14206
[17] Villet, S; Pichoud, C; Villeneuve, JP; Trepo, C; Zoulim, F, Selection of a multiple drug-resistant hepatitis b virus strain in a liver-transplanted patient, Gastroenterology, 131, 1253-1261, (2006)
[18] Wegenast, T; Utz, HF; Longin, CFH; Maurer, HP; Dhillon, BS; Melchinger, AE, Hybrid maize breeding with doubled haploids: V. selection strategies for testcross performance with variable sizes of crosses and \(s_1\) families, Theor Appl Genet, 121, 1391-1393, (2010)
[19] West-Eberhard, MJ, Sexual selection, social competition, and speciation, Q Rev Biol, 58, 155-183, (1983)
[20] Xu, S; Martin, TG; Muir, WM, Multistage selection for maximum economic return with an application to beef cattle breeding, J Anim Sci, 73, 699-710, (1995)
[21] Yan, W; Clack, CD, Evolving robust gp solutions for hedge fund stock selection in emerging markets, Soft Comput, 15, 37-50, (2011)
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