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Ecological Networks: Population Dispersal and Supersaturation in Metacommunities

By Lina Sorg

Understanding the abundance and distribution of species, as well as their coexistence with neighboring groups, is central to the field of ecology. Community ecology is a subset of ecology pertaining specifically to the study of the dynamics that influence biodiversity, community structure, and patterns of abundance, species interaction, and dispersal — the coupling of habitats and communities within each network. And a metacommunity is a set of intermingling local communities linked by the dispersion of multiple potentially-interacting species. This concept is a valuable means of analyzing linkages between various ecological spatial scales. As a result, one can think of metacommunities as a community of communities, or a network of networks. Complex networks offer a common framework through which researchers can study many interacting phenomena within large, collaborative systems. 

Within metacommunities, distinct subcommunities inhabit spatially separated patches of habitat.  Metacommunity models, then, depict ecological systems that comprise numerous patches in which distinct populations interact, either as competitors or in a predator-prey relationship (like a food web). Migration corridors—paths followed by animals migrating between seasonal habitats—connect these patches, sustain populations via dispersion, and contribute to food webs and competitive population dynamics. In a minisymposium at the 2017 SIAM Conference on Applications of Dynamical Systems, being held in Snowbird, Utah, Anshul Choudhary (University of Oldenberg) presented a population model investigating the effects of population dispersal on supersaturation within a metacommunity. 

The paradox of the plankton defies the competitive exclusion principle, as many species are able to coexist despite the low number of limited resources. This is an example of supersaturation. Image courtesy of Wikimedia Commons.
Choudhary introduced the theory of competition to better explain supersaturation. The theory states that the number of coexisting species in a habitat patch cannot exceed the number of limiting resources. Furthermore, the competitive exclusion principle—also known as Gause’s law—indicates that two species competing for exactly the same resources cannot stably coexist. However, there are exceptions. The paradox of the plankton, for example, breaks the competitive exclusion principle. “In nature, a large number of phytoplankton species coexist in lakes and oceans despite the low number of limited resources,” Choudhary said. This state of coexistence, in which the number of species is greater than the amount of available resources, is supersaturation. Through supersaturation, long-term species invasion becomes possible.

In most ecological models, a single limiting resource determines the competition among species. In reality, however, nearly all species require more than a single resource to survive. Choudhary thus introduced the multiple limitation hypothesis, which states that several resources simultaneously limit populations. “Usually more than one resources is limiting the growth of an organism,” Choudhary said. This phenomenon is called co-limitation. 

Choudhary presented a model that investigated to what extent population dispersal can sustain supersaturation within a metacommunity, despite the fact that not all habitat patches offer resource conditions in which more species than limiting resources can survive. “The coexistence of more species than resources is occurring through a transcritical bifurcation,” Choudhary said, which represents an extension of classical competition theory. His model searches for the optimal dispersal structure that allows for the persistence of supersaturation in metacommunities under the aforementioned conditions. “How does dispersal topology influence supersaturation at the metacommunity level?” Choudhary asked.

To investigate the impact of dispersal rate variation, Choudhary employed a three-patch metapopulation model of dispersal-induced supersaturation. Patch one and two represent supersaturation, while patch three represents a lack thereof. All three patches are oscillating, and eventually align for synchronization. After evolving the system, one can observe the fraction of habitat patches in a supersaturated state.

Ultimately, Choudhary proves that two critical ingredients are necessary to obtain supersaturation in a metacommunity: spatial heterogeneity and phase differences between each species. Non-equilibrium dynamics are key as well. In the future, he hopes to test his model with scale-free topologies, and quantify the phase order parameter to capture spatial heterogeneity.  The breakdown of certain links in dispersal topology could result in the collapse of global supersaturation.

Lina Sorg is the associate editor of SIAM News
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