PMID: 107687Jan 1, 1978

The evolution of sexual reproduction as a repair mechanism. Part II. Mathematical treatment of the wheel model and its significance for real systems

Acta Biotheoretica
R M Williams, I Walker

Abstract

The dynamics of populations of self-replicating, hierarchically structured individuals, exposed to accidents which destroy their sub-units, is analyzed mathematically, specifically with regard to the roles of redundancy and sexual repair. The following points emerge from this analysis: 1. A population of individuals with redundant sub-structure has no intrinsic steady-state point; it tends to either zero or infinity depending on a critical accident rate alpha c. 2. Increased redundancy renders populations less accident prone initially, but population decline is steeper if alpha is greater than a fixed value alpha d. 3. Periodic, sexual repair at system-specific intervals prevents continuous decline and stabilizes the population insofar as it will now oscillate between two fixed population levels. 4. The stabilizing sexual interval increases with increased complexity provided this is accompanied by appropriate levels of redundancy. 5. The model closely simulates the dynamics of heterosis effects. 6. Repair fitness is a population fitness: the chance of an individual being repaired is a function of the statistical make-up of the population as a whole at the particular period. Populations living at alpha greater than alpha c eithe...Continue Reading

Citations

Jun 1, 1990·Acta Biotheoretica·A Steiner, I Walker
Aug 15, 1983·Experientia·I Walker

Related Concepts

Metazoa
Base Excision Repair
Biological Evolution
Mathematics
Neomalthusianism
Reproduction
Reproduction, Asexual

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