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The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population
Author(s) -
Manly B. F. J.
Publication year - 1981
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710230307
Subject(s) - selection (genetic algorithm) , multivariate statistics , population , statistics , mathematics , distribution (mathematics) , dispersion (optics) , multivariate normal distribution , function (biology) , multivariate analysis , estimation , demography , biology , computer science , evolutionary biology , mathematical analysis , artificial intelligence , sociology , physics , management , optics , economics
The situation is considered where the multivariate distribution of certain variables X 1 , X 2 , …, X p is changing with time in a population because natural selection related to the X 's is taking place. It is assumed that random samples taken from the population at times t 1 , t 2 , …, t s are available and it is desirable to estimate the fitness function w t ( x 1 , x 2 ,…, x p ) which shows how the number of individuals with X i = x i , i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating w t . The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.