Biomedical subjects

G T Vickers

Publications and source records attributed to G T Vickers.

4 recordsLinked to original sources

PubMed1991

Spatial patterns and travelling waves in population genetics.

We consider a reaction-diffusion equation to model a multi-allelic, single locus problem. The population can migrate in a homogeneous region and the diffusion rates depend upon the genotype. It is shown that if there is an equilibrium point with all alleles present and if this polymorphism is stable for the classical reaction system then it is also stable for the reaction-diffusion equation. Also a simplified model is used to investigate which allele will spread in the two-allele case. Alleles which are associated with large fitness and small dispersion do best.

Alleles↗

PubMed1989

Spatial patterns and ESS's.

The classical idea of an evolutionarily stable strategy (ESS) does not involve any spatial dependence. An evolution equation for analyzing games in a region is suggested and the possibility of spatial patterns is investigated. It is shown that an ESS is so stable that it forbids any spatial dependence but that other equilibria may have patterns associated with them if the dispersion rates are suitably chosen.

Biological Evolution↗

PubMed1988

Patterns of ESS's. I.

A matrix may have several evolutionarily stable strategies (ESS's). It is thus possible for different populations of a species to adopt a different ESS even when the pay-offs for the populations are the same. The occurrence of different strategies does not imply different circumstances. However, there are constraints upon the collection of supports of the ESS's (i.e. pattern) that any matrix can have. The best-known of these is that the support of one ESS cannot be contained in that of another and this gives bounds on the number of different patterns possible for n x n matrices. Other general constraints are presented here. The enumeration of the patterns for 3 x 3 and 4 x 4 matrices is completed and considerable progress made on 5 x 5 matrices where the number of (permutationally distinct, maximal) patterns exceeds 16.

Biological Evolution↗

PubMed1988

Patterns of ESS's. II.

For symmetric matrix conflicts with aij = +/- 1 and aii = 0, an ESS corresponds to a clique in an associated graph. This result is proved and exploited to yield results on the attainable patterns for this class of conflicts and bounds for the number of ESS's which may coexist. Randomly generated matrices in this class are considered, and some results on the size of the support of a typical ESS given.

Biological Evolution↗