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

Summary

The dynamics of populations of self-replicating, hierarchically structured individuals, exposedto accidents which destroy their sub-units, is analyzed mathematically, specifically with regardto the roles of redundancy and sexual repair. The following points emerge from this analysis:0

• 1. A population of individuals with redundant sub-structure has no intrinsic steady-statepoint; it tends to either zero or infinity depending on a critical accident rate α _c .

• 2. Increased redundancy renders populations less accident prone initially, but populationdecline is steeper if a is greater than a fixed value α _d .

• 3. Periodic, sexual repair at system-specific intervals prevents continuous decline and stabilizesthe population insofar as it will now oscillate between two fixed population levels.

• 4. The stabilizing sexual interval increases with increased complexity provided this is accom-panied 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 functionof the statistical make-up of the population as a whole at that particular period. Populationsliving at α > α _c either engage in sexual repair at the appropriate time or they die out.

• 7. The mathematical properties of the model illustrate mechanisms which possibly played arole in the evolution of a mortal soma in relation to sexual reproduction.