Friday, November 25, 2016

Can coexistence theories coexist?

These days, the term ‘niche’ manages to cover both incredibly vague and incredibly specific ideas. All the many ways of thinking about an organism’s niche fill the literature, with various degrees of inter-connection and non-independence. The two dominant descriptions in modern ecology (last 30 years or so) are from ‘contemporary niche theory’ and ‘modern coexistence theory’. Contemporary niche theory is developed from consumer-resource theory, where organisms' interactions occur via usage of shared resources. (Though it has expanded to incorporate predators, mutualists, etc), Analytical tools such as ZNGIs and R* values can be used to predict the likelihood of coexistence (e.g. Tilman 1981, Chase & Leibold 2003). Modern coexistence theory is rooted in Peter Chesson’s 2000 ARES review (and earlier work), and describes coexistence in terms of fitness and niche components that allow positive population growth.

On the surface these two theories share many conceptual similarities, particularly the focus on measuring niche overlap for coexistence. [Chesson’s original work explicitly connects the R* values from Tilman’s work to species’ fitnesses in his framework as well]. But as a new article in Ecological Monographs points out, the two theories are separated in the literature and in practice. The divergence started with their theoretical foundations: niche theory relied on consumer-resource models and explicit, mechanistic understanding of organisms’ resource usage, while coexistence theory was presented in terms of Lotka-Volterra competition models and so phenomenological (e.g. the mechanisms determining competition coefficients values are not directly measured). The authors note, “This trade-off between mechanistic precision (e.g. which resources are regulating coexistence?) and phenomenological accuracy (e.g. can they coexist?) has been inherited by the two frameworks….”

There are strengths and weaknesses to both approaches, and both have been used in important ecological studies. So it's surprising that they are rarely mentioned in the same breathe. Letten et al. answer an important question: when directly compared, can we translate the concepts and terms from contemporary niche theory into modern coexistence theory and vice versa?

Background - when is coexistence expected? 
Contemporary niche theory (CNT) (for the simplest case of two limiting resources): for each species, you must know the consumption or impact they have on each resource; the ratio at which the two resources are supplied, and the ZNGIs (zero net growth isoclines, which delimit the resource conditions a species can grow in). Coexistence occurs when the species are better competitors for different resources, when each species has a greater impact on their more limiting resource, and when the supply ratio of the two resources doesn’t favour one species over the other. (simple!)

For modern coexistence theory (MCT), stable coexistence occurs when the combination of fitness differences and niche differences between species allow both species to maintain positive per capita growth rates. As niche overlap decreases, increasingly small fitness differences are necessary for coexistence.

Fig 1, from Letten et al. The criteria for coexistence under modern coexistence theory (a) and contemporary niche theory (b).  In (a), f1 and f2 reflect species' fitnesses. In (b) "coexistence of two species competing for two substitutable resources depends on three criteria: intersecting ZNGIs (solid red and blue lines connecting the x- and y-axes); each species having a greater impact on the resource from which it most benefits (impact vectors denoted by the red and blue arrows); and a resource supply ratio that is intermediate to the inverse of the impact vectors (dashed red and blue lines)."

So how do these two descriptions of coexistence relate to each other? Letten et al. demonstrate that:
1) Changing the supply rates of resources (for CNT) impacts the fitness ratio (equalizing term in MCT). This is a nice illustration of how the environment affects the fitness ratios of species in MCT.

2) Increasing overlap of the impact niche between two species under CNT is consistent with increasing overlap of modern coexistence theory's niche too. When two species have similar impacts on their resources, there should be very high niche overlap (weak stabilizing term) under MCT too.

3) When two species' ZNGI area converge (i.e. the conditions necessary for positive growth rates), it affects both the stabilizing and equalizing terms in MCT. However, this has little meaningful effect on coexistence (since niche overlap increases, but fitness differences decrease as well).

This is a helpful advance because Letten et al. make these two frameworks speak the same (mathematical) language. Further, this connects a phenomological framework with a (more) mechanistic one. The stabilizing-equalizing concept framework (MCT) has been incredibly useful as a way of understanding why we see coexistence, but it is not meant to predict coexistence in new environments/with new combinations of species. On the other hand, contemporary niche theory can be predictive, but is unwieldy and information intensive. One way forward may be this: reconciling the similarities in how both frameworks think about coexistence.

Letten, Andrew D., Ke, Po-Ju, Fukami, Tadashi. 2016. Linking modern coexistence theory and contemporary niche theory. Ecological Monographs: 557-7015.
(This is a monograph for a reason, so I am just covering the major points Letten et al provide in the paper. It's definitely worth a careful read as well!).

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