This paper develops a mathematical theory for holobiont evolution that parallels the population-genetic theory of classical evolutionary biology. It presents theory for hologenomes having two haploid microbial strains and two diploid host alleles. The theory shows how selection on holobionts causes the joint evolution of microbial and host components of the hologenome. The theory also reveals the distribution of microbiome configurations across hosts as well as stable strategies for microbiome-host coadaptation. This paper first reviews previous research about how to define a theory of holobiont evolution, how to define a "hologenotype", and what the significance is of horizontal vs. vertical microbiome transmission. The paper then presents new research in stages: holobionts with two haploid microbial strains, holobionts with two diploid host alleles, holobionts having both two haploid microbial strains and two diploid host alleles combined, and finally, strategies of coadaptation. The mathematical theory here shows how selection on holobionts causes the joint evolution of the microbial and host components of the hologenome. It also reveals the distribution of microbiome configurations across hosts and stable strategies for microbiome-host coadaptation.
Previous Research
Definition of a Theory of Holobiont EvolutionThe classical population-genetic theory for evolution supplies an equation (or equations) that comprise a dynamical system, that is, equations that map gene or genotype frequencies at time t to the gene or genotype frequencies at time t + 1, or symbolically p t → p t+1 where p denotes a vector of gene or genotype frequencies. Therefore, a theory of holobiont evolution should do the same, that is, the theory should supply equations that map the current state of a population of holobionts at time t to the state at time t + 1, or symbolically, H t → H t+1 where H denotes the state of the holobiont population.