Download Cochran, 1951

Improvement by Means of Selection: Then and Now
Cari Schmitz
Abstract
The statistician William Gremmel Cochran made several contributions to statistics with a
special emphasis on examples in agriculture. One pioneering contribution of his, regarding
the mathematics of initiating a selection program, was presented at the 1951 Berkeley
Symposium on Mathematical Statistics and Probability (Cochran, 1951). This paper covers
mathematical formulas for predicting gain from selection, multiple stage selection, and
selection indices. Cochran considers personnel selection as well as applications to plant and
animal breeding. With over 300 citations of this work on record with Google Scholar (as of
Feb. 2015), of which nearly ten percent were published in the last five years, Cochran’s
contributions continue to prove relevant to modern applications in plant breeding. Two
papers, published in the last two years, citing this historical paper will be presented as
evidence of its lasting impact. The first example reports the construction of a package in the
R environment for calculations in optimizing resource allocation in multiple stage selection
(Mi et al., 2014). With modern computational resources, the authors are able to examine
questions put forth by Cochran on a much larger scale. The second example is a comparison
of possible selection strategies applied to historical data from the CIMMYT international
wheat breeding program. Arief et al. (2015) compare testing strategies using the criteria of
genetic repeatability, probability of acceptance, and potential gain per cycle of selection.
These two papers exemplify that Cochran’s work in optimizing selection remains relevant
for resource allocation in modern breeding programs.
References
Areif, V.N., I.H. DeLacy, J. Crossa, T. Payne, R. Singh, H. Braun, T. Tian, K.E. Basford and M.J.
Dieters. Evaluating testing strategies for plant breeding field trials: Redesigning a
CIMMYT international wheat nursery. Crop Sci. 55:164-177.
Cochran, W.G. 1951. Improvement by means of selection. Proc. Second Berkeley Sym. Math.
Stat. and Prob., pp. 449-470.
Mi, X., H.F. Utz, F. Technow and A.E. Melchinger. 2014. Optimizing resource allocation for
multistage selection in plant breeding with R package selectiongain. Crop Sci.
54:1413-1418.