Evolution,games theory and polyhedra

The problem of finding an Evolutionary Stable Strategy (ESS) for an animal species is defined. It is shown how such strategies are a subset of the equilibrium solutions for a particular non-zero sum game. These equilibrium solutions are then shown to arise from the vertices of a particular convex polyhedron. A method of finding these equilibrium solutions through the vertices and then the ESS solutions is given. This is illustrated by a number of numerical examples taken from the literature. Finally an alternative approach based on solving a Linear Complementarity Problem is discussed.     

The donation game with roles played between relatives

We consider a social game with two choices, played between two relatives, where roles are assigned to individuals so that the interaction is asymmetric. Behaviour in each of the two roles is determined by a separate genetic locus. Such asymmetric interactions between relatives, in which individuals occupy different behavioural contexts, may occur in nature, for example between adult parents and juvenile offspring. The social game considered is known to be equivalent to a donation game with non-additive payoffs, and has previously been analysed for the single locus case, both for discrete and continuous strategy traits. We present an inclusive fitness analysis of the discrete trait game with roles and recover equilibrium conditions including fixation of selfish or altruistic behaviour under both behavioural contexts, or fixation of selfish behaviour under one context and altruistic behaviour under the other context. These equilibrium solutions assume that the payoff matrices under each behavioural context are identical. The equilibria possible do depend crucially, however, on the deviation from payoff additivity that occurs when both interacting individuals act altruistically.     

Research note: Identity of the Qingdao algal bloom

In early July 2008, news agencies worldwide reported on a vast algal bloom that was threatening the upcoming Olympic sailing events in Qingdao, China. The identity of the culpable alga, however, remained undiscussed. We have identified the alga that caused the bloom by means of morphological and molecular data, including sequence data of the plastid encoded large subunit ribulose 1,5-bisphosphate carboxylase gene ( rbc L) and the nuclear encoded rDNA internal transcribed spacer (ITS) region. The bloom-forming alga falls within the morphological limits of the green seaweed Ulva prolifera O.F. Müller (' Enteromorpha prolifera (O.F. Müller) J. Agardh') but our phylogenetic analyses show that it forms a clade with representatives of the Ulva linza-procera-prolifera (LPP) complex. The Chinese rbc L sequences are identical to those of specimens collected from Japan, New Zealand, Finland and Portugal, suggesting that the taxon is widely distributed. rDNA ITS sequences showed a close affinity with Japanese isolates of the species complex. The Qingdao bloom is a typical illustration of a green tide, which occurs increasingly along several coasts worldwide.