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Cyclic dominance is frequently believed to be a mechanism that maintains diversity of competing species. But this delicate balance could also be fragile if some of the members is weakened because an extinction of a species will involve the annihilation of its predator hence leaving only a single species alive. To check this expectation we here introduce a fourth species which chases exclusively a single member of the basic model composed by three cyclically dominant species. Interestingly, the coexistence is not necessarily broken and we have detected three consecutive phase transitions as we vary only the invasion strength of the fourth pestilent species. The resulting phases are analyzed by different techniques including the study of the Hamming distance density profiles. Some of our observations strengthen previous findings about cyclically dominant system, but they also offer new revelations and counter-intuitive phenomenon, like supporting pestilent species may result in its extinction, hence enriching our understanding about these very simple but still surprisingly complex systems.
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species colonization and local extinction in a given g
Cooperative interactions pervade the dynamics of a broad rage of many-body systems, such as ecological communities, the organization of social structures, and economic webs. In this work, we investigate the dynamics of a simple population model that
The competitive exclusion principle asserts that coexisting species must occupy distinct ecological niches (i.e. the number of surviving species can not exceed the number of resources). An open question is to understand if and how different resource
Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resou
Empirical observations in marine ecosystems have suggested a balance of biological and advection time scales as a possible explanation of species coexistence. To characterise this scenario, we measure the time to fixation in neutrally evolving popula