Microbial diversity and ecological complexity emerging from environmental variation and horizontal gene transfer in a simple mathematical model.

Microbiomes are generally characterized by high diversity of coexisting microbial species and strains that remains stable within a broad range of conditions. However, under fixed conditions, microbial ecology conforms with the exclusion principle under which two populations competing for the same resource within the same niche cannot coexist because the less fit population inevitably goes extinct. To explore the conditions for stabilization of microbial diversity, we developed a simple mathematical model consisting of two competing populations that could exchange a single gene allele via horizontal gene transfer (HGT). We found that, although in a fixed environment, with unbiased HGT, the system obeyed the exclusion principle, in an oscillating environment, within large regions of the phase space bounded by the rates of reproduction and HGT, the two populations coexist. Moreover, depending on the parameter combination, all three major types of symbiosis obtained, namely, pure competition, host-parasite relationship and mutualism. In each of these regimes, certain parameter combinations provided for synergy, that is, a greater total abundance of both populations compared to the abundance of the winning population in the fixed environments. These findings show that basic phenomena that are universal in microbial communities, environmental variation and HGT, provide for stabilization of microbial diversity and ecological complexity.

Coevolution of reproducers and replicators at the origin of life and the conditions for the origin of genomes.

There are two fundamentally distinct but inextricably linked types of biological evolutionary units, reproducers and replicators. Reproducers are cells and organelles that reproduce via various forms of division and maintain the physical continuity of compartments and their content. Replicators are genetic elements (GE), including genomes of cellular organisms and various autonomous elements, that both cooperate with reproducers and rely on the latter for replication. All known cells and organisms comprise a union between replicators and reproducers. We explore a model in which cells emerged via symbiosis between primordial "metabolic" reproducers (protocells) which evolved, on short time scales, via a primitive form of selection and random drift, and mutualist replicators. Mathematical modeling identifies the conditions, under which GE-carrying protocells can outcompete GE-less ones, taking into account that, from the earliest stages of evolution, replicators split into mutualists and parasites. Analysis of the model shows that, for the GE-containing protocells to win the competition and to be fixed in evolution, it is essential that the birth-death process of the GE is coordinated with the rate of protocell division. At the early stages of evolution, random, high-variance cell division is advantageous compared with symmetrical division because the former provides for the emergence of protocells containing only mutualists, preventing takeover by parasites. These findings illuminate the likely order of key events on the evolutionary route from protocells to cells that involved the origin of genomes, symmetrical cell division, and antiparasite defense systems.

Polymorphism in rapidly changing cyclic environment.

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric payoffs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic (fine-grained) environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a nonlinear fitness that is induced by environmental changes. The nonlinear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is exemplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment.