THE EVOLUTION OF CONTINUOUS VARIATION. III. JOINT TRANSMISSION OF GENOTYPE, PHENOTYPE AND ENVIRONMENT

Abstract

ABSTRACT Evolutionary models of continuous traits are developed. The models are based on the ideas that: (1) the phenotype is the result of the interaction between genotype and environment; (2) the phenotype is the object of natural selection; (3) not only the genotype but also environmental variables and even phenotypes can be directly transmitted. The phenotype of an offspring at birth is a linear combination of its genotypic value, the phenotypic values of its parents, and their environmental values, all measured on the phenotypic scale. The genetic effects are additive polygenic, and a mutation contribution to the within family variance is admitted.—The values of the offspring phenotype and environment before selection are each linear combinations of these values at birth, the coefficients defining what we call "development." Selection is mostly stabilizing of the Gaussian type, but directional selection is introduced using a Gaussian fitness function with a large variance and a mean far from the current population.—Assortative mating for both phenotype and environment are considered. The analysis in all cases is made by iteration of the means, variances and covariances of the trivariate random variable (genotype, phenotype, environment) whose changes over time completely specify the evolution. In most cases numerical methods are used. The problems of estimating the relative roles of each of the variates in the parents in determining the variates in the offspring are discussed. The major results concern the relative magnitudes of the variances and correlations of the three variates, genotype, phenotype and environment, in a variety of selective, developmental and assorting situations with complex transmission in which G-(genetic), F-(phenotypic), E-(environment) inheritance mechanisms operate jointly. The transmission rules and development patterns (i.e., interactions between phenotype and environment during development) are of major importance in determining qualitative features of the equilibrium distribution.