Speciation, diversification, and coexistence of sessile species that compete for space

Diversity and ecotones in a model ecosystems of sessile species

Sessile species compete for space and accessible light, with directed interactions evident in one species overgrowing another and with multispecies systems characterized by nontransitive relationships. Such patterns are observed in coral reefs or lichens on rock surfaces. Open systems with episodic invasions of such species have been predicted to exhibit a stable high-diversity state when the interaction probability is below a certain critical threshold. Here, we explore this metastable high-diversity state and find that the diversity in the high-diversity state scales with the square root of the system area. When introducing two different environments, we predict a hugely increased diversity along mutual environment border. Further, the presence of spatially segregated environments is predicted to allow for increased robustness of the high-diversity state.

Characterization of phase transitions in a model ecosystem of sessile species

We consider a model ecosystem of sessile species competing for space. In particular, we consider the system introduced by Mathiesen et al. [J. Mathiesen, N. Mitarai, K. Sneppen, and A. Trusina, Phys. Rev. Lett. 107, 188101 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.188101] where species compete according to a fixed interaction network with links determined by a Bernoulli process. In the limit of a small introduction rate of new species, the model exhibits a discontinuous transition from a high-diversity state to a low-diversity state as the interaction probability between species, γ, is increased from zero. Here we explore the effects of finite introduction rates and system size on the phase transition by utilizing efficient parallel computing. We find that the low state appears for γ>γ_{c}. As γ is increased further, the high state approaches the low state, suggesting the possibility that the two states merge at a high γ. We find that the fraction of time spent in the high state becomes longer with higher introduction rates, but the availability of the two states is rather insensitive to the value of the introduction rate. Furthermore, we establish a relation between the introduction rate and the system size, which preserves the probability for the system to remain in the high-diversity state.