The feasibility domain of an ecological community can be described by the set of environmental abiotic and biotic conditions under which all co-occurring and interacting species in a given site and time can have positive abundances. Mathematically, the feasibility domain corresponds to the parameter space compatible with positive (feasible) solutions at equilibrium for all the state variables in a system under a given model of population dynamics. Under specific dynamics, the existence of a feasible equilibrium is a necessary condition for species persistence regardless of whether the feasible equilibrium is dynamically stable or not. Thus, the size of the feasibility domain can also be used as an indicator of the tolerance of a community to random environmental variations. This has motivated a rich research agenda to estimate the feasibility domain of ecological communities. However, these methodologies typically assume that species interactions are static, or that input and output energy flows on each trophic level are unconstrained. Yet, this is different to how communities behave in nature. Here, we present a step-by-step quantitative guideline providing illustrative examples, computational code, and mathematical proofs to study systematically the feasibility domain of ecological communities under changes of interspecific interactions and subject to different constraints on the trophic energy flows. This guideline covers multitrophic communities that can be formed by any type of interspecific interactions. Importantly, we show that the relative size of the feasibility domain can significantly change as a function of the biological information taken into consideration. We believe that the availability of these methods can allow us to increase our understanding about the limits at which ecological communities may no longer tolerate further environmental perturbations, and can facilitate a stronger integration of theoretical and empirical research.
Empirical studies have found that the mutualistic interactions forming the structure of plant-pollinator networks are typically more nested than expected by chance alone. Additionally, theoretical studies have shown a positive association between the nested structure of mutualistic networks and community persistence. Yet, it has been shown that some plant-pollinator networks may be more nested than others, raising the interesting question of which factors are responsible for such enhanced nested structure. It has been argued that ordered network structures may increase the persistence of ecological communities under less predictable environments. This suggests that nested structures of plant-pollinator networks could be more advantageous under highly seasonal environments. While several studies have investigated the link between nestedness and various environmental variables, unfortunately, there has been no unified answer to validate these predictions. Here, we move from the problem of describing network structures to the problem of comparing network structures. We develop comparative statistics, and apply them to investigate the association between the nested structure of 59 plant-pollinator networks and the temperature seasonality present in their locations. We demonstrate that higher levels of nestedness are associated with a higher temperature seasonality. We show that the previous lack of agreement came from an extended practice of using standardized measures of nestedness that cannot be compared across different networks. Importantly, our observations complement theory showing that more nested network structures can increase the range of environmental conditions compatible with species coexistence in mutualistic systems, also known as structural stability. This increase in nestedness should be more advantageous and occur more often in locations subject to random environmental perturbations, which could be driven by highly changing or seasonal environments. This synthesis of theory and observations could prove relevant for a better understanding of the ecological processes driving the assembly and persistence of ecological communities.
We present an overlooked but important property of modern coexistence theory (MCT), along with two key new results and their consequences. The overlooked property is that stabilizing mechanisms (increasing species' niche differences) and equalizing mechanisms (reducing species' fitness differences) have two distinct sets of meanings within MCT: one in a two-species context and another in a general multispecies context. We demonstrate that the two-species framework is not a special case of the multispecies one, and therefore these two parallel frameworks must be studied independently. Our first result is that, using the two-species framework and mechanistic consumer-resource models, stabilizing and equalizing mechanisms exhibit complex interdependence, such that changing one will simultaneously change the other. Furthermore, the nature and direction of this simultaneous change sensitively depend on model parameters. The second result states that while MCT is often seen as bridging niche and neutral modes of coexistence by building a niche-neutrality continuum, the interdependence between stabilizing and equalizing mechanisms acts to break this continuum under almost any biologically relevant circumstance. We conclude that the complex entanglement of stabilizing and equalizing terms makes their impact on coexistence difficult to understand, but by seeing them as aggregated effects (rather than underlying causes) of coexistence, we may increase our understanding of ecological dynamics.
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