Abstract
Trisomy is a genetic abnormality of considerable medical importance. The most familiar example is trisomy 21, which causes Down Syndrome [Cummings, M. R. (1988) Human Heredity: Principles and Issues (West Publishing Company, New York)]. In a classic paper, Axelrod and Hamilton [Axelrod, R. & Hamilton, W. D. (1981) Science 211, 1390-1396] offered a chromosomal drive (CD) hypothesis based on the game iterated prisoner's dilemma (IPD) to explain the evolution of an increased frequency of trisomic pregnancies with maternal age. In this paper we explore this hypothesis and its predictions in detail. On closer examination we find that IPD does not provide an adequate model for the CD hypothesis. Therefore, we develop a more suitable model and explore the conditions necessary for it to explain maternal age-dependent trisomy. Our results demonstrate that a relationship between the decay of a female's reproductive potential and chromosomal drive must exist for the CD hypothesis to work. With appropriate parameter values, a comparison of model predictions with empirical estimates for the age-dependence of trisomy reveals a striking correspondence. We point out a close correspondence between other predictions made by the CD hypothesis and empirical observations, as well.