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 (...) value α d . Periodic, sexual repair at system-specific intervals prevents continuous decline and stabilizesthe population insofar as it will now oscillate between two fixed population levels. The stabilizing sexual interval increases with increased complexity provided this is accom-panied by appropriate levels of redundancy. The model closely simulates the dynamics of heterosis effects. 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. The mathematical properties of the model illustrate mechanisms which possibly played arole in the evolution of a mortal soma in relation to sexual reproduction. (shrink)

Exact definitions in physical and biological terms of the coefficients in Volterra's (1926, 1931) original competition equations are indispensable for the understanding of the system. In agreement with Volterra's own, but not quite sufficient specifications, it is tried in this paper to give more precise definitions of the parameters used by Volterra. This leads to some consequences; i.a. that there does not exist a principle of competitive exclusion. In order to allow for competitive exclusion — or for stabilization — the (...) Volterra equations need additional biophysical specifications and mathematical modifications. Some such modifications are proposed, for instance for aggressive interference as a function of population numbers. (shrink)

A basic model of hierarchical structure, expressed by simple, linear differential equations, shows that the pattern of population growth is essentially determined by conditions of redundancy in the sub-structure of individuals. There does not exist any possible combination between growth rate and accident rate that could balance population numbers and/or the level of redundancy within the population; all possible combinations either lead to extinction or to positive population growth with a decline of the fraction of individuals with redundant substructure. Declining (...) populations, however, can be held fluctuating between certain limits by periodic phases of sub-unit repair. These results are particularly pertinent to the population dynamics of diploid (polyploid) organisms. (shrink)

The inanimate world, including Man's wheeled vehicles, follow the classical mechanical laws: trajectories of objects in phase-space are predictable on the basis of the vectors of forces acting on the objects. Animal locomotion does not involve wheels, but relies on antagonistic contractile fibre systems, and defies prediction of trajectories. These features are tied up with the faculty of immediate steering in response to momentaneous physiological and environmental stimuli. Thus, animal motor systems have two relatively independent inputs: the sensory/information system, which (...) is the cause for specific trajectories, and the erfolg system which permits for the execution of the thus instructed motion. The problem of relative energetic magnitudes between the two systems — in that the causative system involves small, yet the executive system large energies — is specially considered in relation to locomotion by antagonistically functioning mechanical elements. (shrink)

Analysis of the biophysical conditions for a correct application of the Volterra Competition Equations with resource-independent coefficients reveals the following:The traditional, mathematical formalism with the two equations representing two straight lines at the condition of zero growth applies.

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 (...) between consumers, it appears that coexistence of species on thesame kind of limiting resource is possible only in cases of compartmentalization either in space, or in time, of resource consumption, i.e. if each consumer species disposes of a separate resource supply. Three criteria were found to be decisive for successful compartmentalization (i.e. for coexistence): 1. the vector of the resource flow; 2. relative mobility between consumers and resource units; 3. dependence or independence of resource flow on previous consumption. The traditional terminology of niche theory and of competition theory in general proved to be inadequate for analytical treatment of problems of coexistence. (shrink)

A specific mapping mechanism is defined as the basic unit of “Biological Memory”. This mechanism must account for the characteristic frequency patterns in the organic world, where future probability is a function of past experience. The conditions for the function of biological memory are analysed. It is found that asymmetry, and irreversibility as a consequence of complexity, are the basic principles of memory function. The essential asymmetries in genetic memory are pointed out, and the problem of bilateral symmetry in a (...) basically asymmetrical organization is briefly outlined.Complexity is defined in terms of symmetry. The thermodynamic arrow of time and the biological arrow of time are discussed in relation to elementarity and complexity with their specific types of repeatabilities: non-accumulative in the first case and accumulative as a result of “copy-reproduction” by memory in the second case. The application of terminology from Information Theory and Thermodynamics to Memory Mechanics is critically considered.The immediate and inevitable consequences of memory function are shown to be irreversible expansion and irreversible, unpredictable diversification, leading to growing complexity and size on all but the sub-molecular levels of biological structure. (shrink)