Theories and models in symbiogenesis: A reply to nature and the introduction of environmental noises

Two modern theories of biological evolution are compared with the aid of stochastic Volterra-Hamilton systems used as a logical method. Previous results used only the deterministic equations, whereas here, these are augmented with environmental noises. The ancestral commune theory model (C. Woese) exhibits stochastic chaos in the sense that the Feynman-Kac potential for the probability density of the forward Cauchy problem contains a curvature R term which is negative. Moreover, its magnitude |R| increases more than quadratically with the number n of proto-cell types in the commune. On the other hand, our model of serial endosymbiosis (L. Margulis) exhibits relative stochastic stability in that the relevant curvature term is positive when the primordial eukaryote is modelled as a single cell with a parasitic proto-mitochondrian with the tools of Volterra-Hamilton Theory. Our results seem consistent with the previously published deterministic model.