Competition and Cooperation in MicroorganismsDavid R. Nelson, Harvard University, DMR 1005289

INTELLECTUAL MERIT•Recent theoretical investigations have explored connections between nonequilibrium statistical mechanics, population genetics and range expansions in microorganisms.[1]

•With range expansions in mind, we have studied how mutualistic competitions between microbes play out within a one-dimensional stepping stone model.[2]

•Even when mutualism confers a selective advantage, it persists only in populations with high density and frequent migrations. When these parameters are reduced, we find that mutualism is generically lost via a directed percolation process, with a phase diagram strongly influenced by an exceptional DP2 phase transition.

•In figure at right, weak mutualism in (a) cannot prevent genetic demixing. However, strains in (b) mix and cooperate indefinitely.

Two yeast strains (S. cerevisiae) with mutualism – the blue variant overproduces the amino acid tryptophan but cannot make leucine. The yellow variant overproduces leucine but cannot make tryptophan.

[1] K. Korolev, M. Avlund, O. Hallatschek and D. R. Nelson, Rev. Mod. 82, 1691–1718 (2010) [2] K. Korolev and D. R. Nelson, Physical Review Letters 107, 088103 (2011)

Time evolution of randomly mixed red and green mutualistic organisms in one dimension with (a) weak and (b) strong mutualism, simulated within a one-dimensional stepping-stone model.

Competition and Cooperation in MicroorganismsDavid R. Nelson, Harvard University, DMR 1005289

BROADER IMPACT

Cooperation is at the heart of many complex systems. On an organism level, gut bacteria help their hosts digest cellulose. On an ecosystem level, plants often rely on fungi to receive important nutrients. Even human societies are products of cooperation between individuals.

Despite the apparent advantage and pervasiveness of mutualism, its existence is often difficult to explain: Cooperation can succumb to cheating and, as shown in Ref. [1] above, to number fluctuations.

Our study of competition and cooperation in stepping-stone models of population genetics preserves the dynamics of well-mixed populations locally, but includes migrations as well as number fluctuations. The later are controlled by the population density. We find that mutualism persists in a much smaller region of parameter space compared to well-mixed populations and that it is more susceptible to spatial demixing when the benefits to the interacting species are unequal. The critical strength of mutualism required to sustain cooperation increases with migration rate and population density.

Phase diagram for evolutionary competitions in one dimension. Here, 1 and 2 describe the strength of the mutualistic interactions.

Mutualism developing from initially segregated green and red organisms The system rapidly forms a mixed phase, which squeezes out the red and green domains.