Unsolved Problems in Evolutionary Theory

Abstract

The theory of evolution is a field of research in which many mathematical investigations have been made and in which many unsolved problems remain. Whatever one's opinions are about the ultimate causes of evolutionary progress (a still debatable problem), it is now clear that an overwhelming part in determining the direction of evolution is played by selection and mutation, and furthermore, that the only empirically testable theory of evolution that has at the present time any plausibility is that evolution is the result of these two factors. So long as the population size is effectively finite, use of the theory of random processes is essential. In this way we can study such problems as the rate at which a population becomes homozygous at some locus when there is no mutation(a phenomenon called "Drift" by Sewall Wright and which he holds, I think incorrectly, to be of importance in evolution), the stationary distributions of gene frequencies when there is mutation, and the probability of survival of new mutants. Although these problems must remain of great interest to students of stochastic processes, I believe that the study of the deterministic processes which effectively describe what happens when the population size is large are more important from the evolutionary point of view. This is due to the fact that the theory of stochastic genetic processes shows that the influence of the random element is of the same order as the reciprocal of the population size. Our aim, therefore, in this paper is to consider the theory of evolution in populations large enough for stochastic variations to be ignored. Since we arethen concerned with average numbers or proportions of individuals of a specifictype, the subject can still be rightly regarded as a part of statistical analysis.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1967
Accession Number
AD1027620

Entities

People

  • P. A. Moran

Organizations

  • Australian National University

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Blood Groups
  • Demographic Cohorts
  • Differential Equations
  • Diseases And Disorders
  • Equations
  • Frequency
  • Genes
  • Genetic Variation
  • Genetics
  • Genotypes
  • Mathematical Analysis
  • Medical Genetics
  • Mutations
  • Probability
  • Statistical Analysis
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Educational Psychology
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.

Technology Areas

  • Biotechnology