We discuss a model of population dynamics under selection pressure from a c
hanging environment. The population, subject to mutations, is composed of d
iploidal organisms reproducing quasi-sexually (two parents, recombination b
ut no sexes) and with overlapping generations. Two cases are considered in
one we do not influence the dynamics of the population, while in the other
we perform eugenics, i.e. we eliminate all individuals which have phenotype
s not conforming to the optimal one at the place where the change has been
made. We show that eugenics reduces greatly genetic diversity of the popula
tion, increases the percentage of homozygotes and therefore leads to a popu
lation badly prepared to cope with the next changes of the environment. The
present paper is an extension of our previous work (Ref. [9]).