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  1. The Evolution of Sexual Reproduction as a Repair Mechanism Part II. Mathematical Treatment of the Wheel Model and its Significance for Real Systems.R. M. Williams & I. Walker - 1978 - Acta Biotheoretica 27 (3-4):159-184.
    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 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 . Increased redundancy renders populations less accident prone initially, but populationdecline is steeper if a is greater than a fixed (...)
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  • The Evolution of Sexual Reproduction as a Repair Mechanism. Part I. A Model for Self-Repair and its Biological Implications.I. Walker - 1978 - Acta Biotheoretica 27 (3-4):133-158.
    The theory is presented that the sexual process is a repair mechanism which maintains redundancy within the sub-structure of hierarchical, self-reproducing organisms. In order to keep the problems within mathematically tractable limits , a simple model is introduced: a wheel with 6 spokes, 3 of them vital and 3 redundant, symbolizes the individual . Random accidents destroy spokes; the wheels replicate at regular cycles and engage periodically in pairing and repair phases during which missing spokes are copy-reproduced along the intact (...)
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  • Compartmentalization and Niche Differentiation: Causal Patterns of Competition and Coexistence.I. Walker - 1987 - Acta Biotheoretica 36 (4):215-239.
    The current major models of coexistence of species on the same resources are briefly summarized. It is then shown that analysis of supposedly competitive systems in terms of the physical four dimensions of phase-space is sufficient to understand the causes for coexistence and for competitive exclusion. Thus, the multiple dimensions of niche theory are reduced to factors which define the magnitudes of the phase-spatial system, in particular the boundaries of population spaces and of periods of activity. Excluding possible cooperative interaction (...)
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