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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 populations in chaotic flows. Contrary to intuition the variation of time scales does not interpolate straightforwardly between the no-flow and well-mixed limits; instead we find that fixation is the slowest at intermediate Damkohler numbers, indicating long-lasting coexistence of species. Our analysis shows that this slowdown is due to spatial organisation on an increasingly modularised network. We also find that diffusion can either slow down or speed up fixation, depending on the relative time scales of flow and evolution.
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The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model describing the competition of two species and incorporating all the above ingredients. We find that the presence of habitat preference --- generating spatial niches --- strongly stabilizes the coexistence of the two species. Eliminating habitat preference --- neutral dynamics --- the model generates patterns, such as distribution of population sizes, practically identical to those obtained in the presence of habitat preference, provided an higher immigration rate is considered. Notwithstanding the similarity in the population distribution, we show that invasibility properties depend on habitat preference in a non-trivial way. In particular, the neutral model results results more invasible or less invasible depending on whether the comparison is made at equal immigration rate or at equal distribution of population size, respectively. We discuss the relevance of these results for the interpretation of invasibility experiments and the species occupancy of preferred habitats.
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 geographic region, are empirically estimated from local observations of species presence/absence. A connected sampling problem is presented, generalized and solved analytically. Species persistence is shown to provide a direct connection with key spatial macroecological patterns like species-area and endemics-area relationships. Our empirical analysis pertains to two different ecosystems and taxa: a herbaceous plant community and a estuarine fish database. Despite the substantial differences in ecological interactions and spatial scales, we confirm earlier evidence on the general properties of the scaling of persistence times, including the predicted effects of the structure of the spatial interaction network. The framework tested here allows to investigate directly nature and extent of spatial effects in the context of ecosystem dynamics. The notable coherence between spatial and temporal macroecological patterns, theoretically derived and empirically verified, is suggested to underlie general features of the dynamic evolution of ecosystems.
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 is driven by cooperative and symmetric interactions between two species. We develop a mean-field and a stochastic description for this cooperative two-species reaction scheme. For an isolated population, we determine the probability to reach a state of fixation, where only one species survives, as a function of the initial concentrations of the two species. We also determine the time to reach the fixation state. When each species can migrate into the population and replace a randomly selected individual, the population reaches a steady state. We show that this steady-state distribution undergoes a unimodal to trimodal transition as the migration rate is decreased beyond a critical value. In this low-migration regime, the steady state is not truly steady, but instead fluctuates strongly between near-fixation states of the two species. The characteristic time scale of these fluctuations diverges as $lambda^{-1}$.
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 dynamics affect this bound. Here, we analyze a generalized consumer resource model with externally supplied resources and show that -- in contrast to self-renewing resources -- species can occupy only half of all available environmental niches. This motivates us to construct a new schema for classifying ecosystems based on species packing properties.
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.
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