Noël Bonneuil | Search PubMed

PubMed2003

Making ecosystem models viable.

Viability conditions permit to characterize all processes compatible with given constraints, notably of available food, so that there exists at least one possibility for the system to perpetuate itself forever. The concept of contingent cone to a set of constraints permits to identify two classes of corrections to apply to equations of natural growth. Usual basic models convey those corrections only in certain regions of the parameter space. A general model-building stemming from the constraints is presented. Experimental populations from historical case studies highlight the mathematical concept of viability corrections.

Animals↗

PubMed2002

Minimal number of generations out of polymorphism in the one-locus two-allele model with unpredictable fertilities.

Fertilities varying in time in an unpredictable manner raise the question of the maintenance of polymorphism, and the subsequent question of the minimal total number of generations spent by the system in impoverished polymorphism. In the one-locus two-allele model, level surfaces of this minimal time out of a given set K of constraints defining polymorphism are delineated. The surface of null minimal time is also the largest set of genotype frequencies from which there exists at least one route remaining in K forever. The influence of the range of admissible fertilities clarifies the trade-off between homozygotes and heterozygotes. Notably, ranges of fertility forbidding a system leaving K to ever return to it are determined. Generally, keeping a chance to regain polymorphism demands a sufficiently relatively high fertility for matings involving heterozygotes.

Alleles↗