Effect of Non- normality on Response to Selection

Abstract

Very rarely, realized selection responses agree with those expected. One of the causes could be the assumption of normality of criterion of selection when in effect it follows a non-normal distribution. That quite a few quantitative traits may depart from the normal form has been borne out by empirical studies made by various investigators. It is the purpose of this thesis to investigate the effect of non-normality on response to selection when the criterion of selection is assumed to be normally distributed. For fixed values of accuracy of selection and genetic standard deviation this problem, however, amounts to studying the relative magnitude of intensity of selection, corresponding to a given proportion of individuals saved on the assumption of normality vis-à-vis actual distribution. From the empirical studies. It is seen that pearsonian types I and III provided adequate representation to many types of data in the field of animal husbandry and poultry. In a few cases exponential and lognormal distributions also fitted well. Accordingly, the expressions of selection intensity have been derived for Pearson’s Type I distribution including its derivative namely beta distribution, Type III along with its derived distributions namely gamma, chi-square and exponential and for lognormal distribution as applicable to both large and small populations. Using these expressions the value of intensities of selection for different proportions of population retained were tabulated for different sample sizes. It has been observed that beta and gamma distributions for parametric values characterizing common situations can be approximated to normal distribution for moderately heavy and low cullings without any serious error. However, the use of normal approximation for exponential and lognormal distributions is not warranted as the discrepancy in response to selection for almost all values of p, the proportion of individuals saved, is too serious to ignore.