A criterion for the evolution of life historical pattern is derived based on the density dependent selection mechanisms. The time development of the population is analyzed mathematically by separating the time scale into two stages, relatively rapid change of population size with fixed gene frequency and slow evolutional change of the gene frequency. The result proposes that the weighted sum of the evolutional change of population sizes at all life historical stages is always positive, where the weight is given by a characteristic parameter of density dependence of survival rate or fertility at each stage. As an example, the direction of evolutional change between two types of life historical pattern, large reproduction and high mortality pattern and small reproduction and low mortality pattern, is discussed. The criterion is extended also to the time continuous model and its is shown that as a special case the condition for invasibility of a mutant gene presented by Christiansen & Fenchel (1977) can be derived. From the result, it can be generally said that the life historical stage with the strongest density regulation plays the most important role in determining the evolutional direction.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modelling and Simulation
- Immunology and Microbiology(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics