Effects of random and non-random errors on phenotypic selection in autotetraploids

Abstract

A theoretical investigation was made to ascertain the effects of random and non-random deviations, called errors, of phenotypic from genotypic values on population means and on the response to phenotypic recurrent selection. The study was motivated as a selection experiment for disease resistance where there was either variability in the inoculation or environment (the random errors) or where the inoculation was above or below the the optimum rate where genetic differences in resistance are maximized (the non-random errors). The study was limited to the genetics at a diallelic locus (alleles B and b) in an autotetraploid population in random mating equilibrium. The response to selection was measured as the covariance of selection and compared to the exact covariance which was the covariance of selection without errors in phenotype. The random errors were modeled by assuming that a given percentage (α) of the population was uniformly distributed among the five possible genotype classes independent of their true genotypes. This model was analyzed numerically for a theoretical population with the frequency of the B allele (p) ranging from 0.0 to 1.0 and assumed errors ofα=0.1 and 0.5 for the following six types of genic action of the B allele: additive, monoplex dominance, partial monoplex dominance, duplex dominance, partial duplex dominance, and recessive. The effect of random error was to consistently reduce the response to selection by a percentage independent of the type of genic action at the locus. The effect on the population mean was an upward bias when p was low and a downward bias when p approached unity. In the non-random error model below optimum inoculations altered the phenotypes by systematically includingα percentage of susceptible genotypes into one or more other genotype classes with more genetic resistance (a positive shift). With above optimum inoculations, some resistant genotypes are classed with the non-resistant genotypes (a negative shift). The effects on the covariance of selection were found by numerical analysis for the same types of genic action andα's as investigated for random error. With a negative shift and a low p, the covariance of selection was always reduced, but for an increasing p the covariance approached and exceeded the exact covariance for all types of genic action except additive. With a positive shift and a low p, response to selection was greatly improved for three types of genic action: duplex dominance, partial duplex dominance, and recessive. The effect of a non-random error on population means was to greatly bias the means upwards for a low p and positive shift, but with increasing p the bias decreased. A relatively slight decrease in the mean occurred with a negative shift. This study indicated check varieties commonly used to monitor selection pressures in screening programs are very responsive to positive non-random shifts, but are relatively unresponsive to negative shifts. The interaction of selection pressure, types of genic action, and genotypes in the class shift models was suggested as a partial explanation for the lack of response to increasing selection pressures observed in some breeding programs.