The mathematical theory of endosymbiosis, II: Models of the Fungal Fusion hypothesis

A dynamical model of evolution of vascular plants via the Fungal Fusion hypothesis is presented. As in previous work on carbon flux in forest stands, solutions of the Volterra–Hamilton equations representing production of biomass satisfy Huxley’s Allometric Law and are stable curves, but the explicit form of the production cost functional presented here, is simpler. Evolution of the dynamics takes place in stages, via random perturbation of cost produced by genetic drift at the molecular level, natural selection and time-sequencing changes in development. The relationship to the lichen symbiocosm is discussed. Our model presents a new feature, namely, in the final evolutionary stages, physiological production variables are expressed as nonlinear transformations of products of development in earlier epochs. Finally, we point out that, neither the parabolic cone nor the right circular cone method of measurement of carbon production is needed for the mostly young forest stand data gathered by Fonseca in the Mata Atlântica. The cylindrical approximation is sufficient for the most part. Old growth forests, however, will require the more mathematically elaborate techniques.