The mathematical theory of endosymbiosis I

This work presents a new model of the evolutionary process formulated by the Serial Endosymbiosis Theory represented by a succession of stages involving different metabolic and ecological interactions among populations of bacteria considering both the population dynamics and production processes of these populations. In such an approach we make use of systems of differential equations known as Volterra–Hamilton systems as well as some geometric concepts involving KCC Theory and the Projective Geometry of Berwald Spaces and also correct a statement of M. Matsumoto in the literature on this topic. We also recount in some detail previous work comparing production stability of Endosymbiosis Theory with that of Ancestral Commune Theory.