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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.
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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.
Niche and neutral theory are two prevailing, yet much debated, ideas in ecology proposed to explain the patterns of biodiversity. Whereas niche theory emphasizes selective differences between species and interspecific interactions in shaping the community, neutral theory supposes functional equivalence between species and points to stochasticity as the primary driver of ecological dynamics. In this work, we draw a bridge between these two opposing theories. Starting from a Lotka-Volterra (LV) model with demographic noise and random symmetric interactions, we analytically derive the stationary population statistics and species abundance distribution (SAD). Using these results, we demonstrate that the model can exhibit three classes of SADs commonly found in niche and neutral theories and found conditions that allow an ecosystem to transition between these various regimes. Thus, we reconcile how neutral-like statistics may arise from a diverse community with niche differentiation.
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