A Mathematical Theory of Holobiont Evolution
Roughgarden 2020

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.

Holobiont life cycle for holobiont whose microbiome consists of one or two microbial strains (green and/or brown circle) and whose nucleus consists of one allele (green or brown cog). In each generation the microbiomes for the juvenile hosts are assembled through binomial sampling from the microbial source pool. The host nuclear alleles are transmitted vertically from parent to juvenile with random union of gametes. At the holobiont selection stage, the diagram’s columns indicate the strains being contributed to the microbial source pool and the diagram’s rows indicate alleles being contributed to the host source pool. The microbial source pool is dilute—hologenotypes are assembled via binomial sampling of microbial strains. Generation time of microbes is short relative to host—microbiome comes to community equilibrium within each host generation. The figure illustrates how the transmission of host nuclear genes and the microbiome operate in parallel. The release of microbes to the microbe pool and the release of gametes to the gamete pool both enable genetic recombination in their respective components of the hologenome. Similarly, the statistical process of microbe colonization is the counterpart of the mating system for determining the pattern of inheritance for their respective components of the hologenome.

Trajectories of the combined dynamics of microbe frequency and allele frequency under holobiont selection leading to a combined polymorphism representing coadaptation between the microbiome and host. Trajectories all begin at various spots near the axes and converge through time to the green dot in the interior. The equilibrium frequencies are marked with the vertical and horizontal lines in green.

https://www.biorxiv.org/content/10.1101/2020.04.10.036350v1
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