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.     

Relationship between elver recruitment and changes in the sex ratio of silver eels Anguilla anguilla L. migrating from Lough Neagh, Northern Ireland

Between 1932–1947 and from 1960 onwards, elvers have been trapped near the mouth of the River Bann, Northern Ireland, and released into Lough Neagh. Each period of elver transport has been followed by a marked increase in the proportion of male silver eels migrating from the lough. Catches of silver eels were sampled on several nights each year from 1965–1974, and the lengths of a total of 20358 eels measured showed a progressive increase in the percentage of male eels from 9.3-86.0 % during this period. Various reasons for this change were examined. The different ages at which male and female eels migrate to the sea was not important. There was no evidence to support the hypothesis that male elvers normally remain in estuarine conditions, and their transport to the lough was therefore unnatural. An increasing fishing effort for yellow eels, such as occurred following the introduction of trawling in 1960, would favour males since small eels were returned to the lough. It was not thought, however, that this was a major cause of the change in sex ratio. Instead, elver transport appeared to be directly implicated, possibly by the overstocking of Lough Neagh, and the phenotypic determination of progressively more male eels, but the evidence for this suggestion was inconclusive.     

On a criterion for survival of species in models governed by difference equations

The difficulty of deciding on the survival of species in models governed by difference equations is pointed out. We show that a recently proposed criterion may overestimate the range of parameter values for which survival is assured.