Evolutionary Classification of Toxin Mediated Interactions
published: Nov. 28, 2007, recorded: October 2007, views: 3293
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The rock scissors paper game gives atemplate for the structural dynamics of toxin induced oscillations withinbacteria. The first player is the sensitive which is toxified by thesecond, the producer, bearing the metabolic costs for resistance and toxinproduction. The producer is in turn again out-competed by the Resistant, who has no metabolic costs for toxin production. At least the Sensitivewins again, because he has no expenses for resistance. This leads to acoexistive/cyclic dynamics in the population-density of these threespecies. We derive here a scenario for the evolutionary dynamics of three speciesinvolved in this RSP - game. Starting from basic biologicalprinciples we determine evolutionary stable states or pathways in the traitspace of bacteria. For the bacteriocin producing bacteria sample mechanisms aredemonstrated. We derive functional relations between the parameters ofour model necessary for evolutionary dynamics. The process usesadaptive dynamics and we analyze the stability type of the obtained singular point. We investigate this behaviorwith respect to the toxicity of the producer and the yield/intrinsic growthspeed relation of each species. The result can be generalizedto all kinds of toxin or disease interactions of three species. As targetdynamics we get Zeeman class 33, which is permanent and guarantees stablecoexistence of three species by population dynamics and also with respect toadaptive evolution. This implies that all toxin mediated interactions tend toa stable coexistive fixed point given reasonable biological relations betweenthe parameters.
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