Mathematical models, problems, and controversies of evolutionary theory

1. The year 1982, the centenary of Charles Darwin's death, witnessed conferences, symposia, and publications in many disciplines devoted to reassessing the theory of evolution by natural selection and all its ramifications. A brief historical review on developments in evolutionary theory emphasizing the role of mathematics is given in 3 of this paper. 2 presents background material on agents of evolutionary processes. 4 contains an annotated listing of several problems and controversies pertaining to evolutionary processes, and a more extended discussion of the neutralist-selectionist controversy. 5 presents background information relating to sex ratio in various plant and animal species. Several classes of mathematical models of much recent interest centering on sex ratio evolution and related dynamical systems are examined in 6-8; the purely mathematically oriented reader can pass directly to these sections. The concluding section presents our views on several philosophic issues in evolutionary theory today, and on the nature of the mathematics relevant to the genetics of the current decade.

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