Boros István (szerk.): A Magyar Természettudományi Múzeum évkönyve 52. (Budapest 1960)
Thoma, A.: Anthropometric characters and selective survival
a% = total variance, CT'H = variance due to heterogeneity (genetic and peristatic), a\ = variance due to aging, al — variance due to selective survival. Of the three partial variances only the last two are functions of time. The relative intensity of selection is given by the following term : It is for this term that we must make an estimate on the basis of a sample. The component referable to heterogeneity is given by the variance within the age groups. We may omit it here. The variance between the groups, which is shown by the mean square deviation between the mean of the sample and those of the age groups, comprises components A and S if our series of measurements may be considered a random sample drawn from the population. Thus we possess already an adequate estimate for the denominator of the fraction. As this variance was obtained by breaking up the sample into age groups, that is by a generalizing method, we shall call it sf.. We are not able to make a direct estimate of the component related to selection, but we can do so for the variance due to aging. We namely measure our sample on two consecutive occasions, and subsequently divide it into age gropus corresponding to the time elapsed between the two measurements. The mean — recorded between the two measurements — of the mean square deviations of each age group amounts to the o\ estimate, comprising only the aging component. The variance thus obtained by the individual method shall be indicated by s?. The value of &\ does not depend on the form of the regression of the measurement upon time. Conversely, the variance calculated by the generalizing method presupposes a linear regression. We know from practice that this condition is not always fulfilled : as a matter of fact, it frequently happens that in the course of adult age the value of some measurement at firsty rises and then decreases — or inversely. Under such circumstances the value of the variance shall be smaller than with identical age deviations, for a linear regression. In order to eliminate this error, and also for the sake of comparability, we shall calculate s'~ G too after sf, viz. by figuring the deviation of the age group means not from the mean of the entire sample, but from that of the preceding age group. Also this method studies the deviation from the 0 hypothesis of age stability — seeing that if the hypothesis is valid, the age means equal both each other and the sample mean —, but the variance thus obtained is already independent on the form of the regression. Disregarding the contingencies of the sampling, we shall throughout consider the number of cases of the age groups to be infinite, so that from this point of view we abstain from all weighting. Thus, if „k" is the number of differences, both kinds of variances are given by the following formula : By reason of the interpretation previously given, the quotient of the variance found by the individual and by the generalizing method shows the aging component of the total variances. According to our definition, the adjustment of this fraction to 1 serves as parameter for measuring the relative incensity of selestion :
