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Vector Representation of Biologic Fields of Force¹

Synopsis: A vector method was developed to describe planes of force due to the interaction of a set of genotypes and the environment. Vector analysis was used to estimate the effect of a disease and of night temperature on sets of genotypes. The effect of mildew on barley was described in terms of an angle from a given axis which represented the severity of the epiphytotic, and in terms of the degree of determination by the forces in the so-called mildew plane.

² Professor of Farm Crops and Associate Professor of Botany and Plant Pathology. The authors are grateful to several reviewers and especially to C. M. Harrison and H. M. Brown for their critical help in the preparation of this manuscript. Permission to use the data supplied by the various State cooperators and compiled by G. A. Wiebe is gratefully acknowledged. Part of the costs of this research was paid by a research grant by the Michigan Brewers' Association. This assistance is gratefully acknowledged.

Received for publication April 14, 1958.