Thursday, January 18, 2018

A general expectation for the paradox of coexistence

There are several popular approaches to the goal of finding generalities in ecology. One is essentially top down, searching for generalities across ecological patterns in multiple places and at multiple scales and then attempting to understand the underlying mechanisms (e.g. metabolic scaling theory and allometric approaches). Alternatively, the approach can be bottom up. It may consider multiple models or multiple individual mechanisms and find generalities in the patterns or relationships they predict. 

A great example of generalities from multiple models is in a recent paper published in PNAS (from Sakavara et al. 2018). It relies on, links together, and adds to, our understanding of community assembly and the effects of competition on the distribution of niches in communities. In particular, it adds additional support to the assertion that both combinations of either highly similar or highly divergent species can coexist, across a wide variety of models.

Work published in 2006 by Scheffer and van Nes played an important early role towards a reconciliation of neutral theory and niche-based approaches. They used a Lotka-Volterra model to highlight that communities could assemble with clusters of coexisting, similar species evenly spaced along a niche axis (Figure 1). Neutrality, or at least near-neutrality, could result even when dynamics were determined by niche differences. [Scheffer, van Nes, and Remi Vergnon also provide a nice commentary on the Sakavara et al. paper found here].
Fig. 1: From Scheffer and van Nes, emergent 'lumpiness' in communities.
One possibility is that Scheffer and van Nes's results might be due to the specifics of the L-V model rather than representing a general and biologically realistic expectation. Sakavara et al. address this issue using a mechanistic consumer-resource model in "Lumpy species coexistence arises robustly in fluctuating resource environments". Under this model, originally from Tilman's classic work with algae, coexistence is limited by the number of resources that limit a species' growth. For 2 species, for example, 2 resources must be present that limit species growth, and further the species must experience a tradeoff in their competitive abilities for the 2 resources. Coexistence can occur when each species is limited more by the resource on which it is most competitive (Figure 2). Such a model– in which resources limit coexistence—leads to an expectation that communities will assemble to maximize the dissimilarity of species.
Fig 2. From Sakavara et al. (2017).
Such a result occurs when resources are provided constantly, but in reality the rates of resource supply may well be cyclical or unpredictable. Will community assembly be similar (resulting in patterns of limiting similarity) when resources are variable in their supply? Or will clumps of similar species be able to coexist? Sakavara et al. considered this question using consumer-resource models of competition, where there are two fluctuating limiting resources. They simulated the dynamics of 300 competing species, which were assigned different trait values along a trait gradient. Here the traits were the half-saturation coefficients for the 2 limiting resources: these were related via a tradeoff between the half saturation constants for each resource.

What they found is strikingly similar to the results from Scheffer and van Nes and dissimilar to the the results that emerge when resources are constant. Clumps of coexisting species emerged along the trait axis. When resource fluctuations occurred rapidly, only fairly specialized species survived in these clumps (R* values that were high for either resource 1, or resource 2, rather than intermediate). But when fluctuations were less frequent, clusters of species also survived at intermediate points along the trait axis. However, in all cases the community organized into clumps composed of very similar species that were coexisting (see Figure 3). It appears that this occurs because the fluctuating resources result in the system having non-stationary conditions. That is, similar sets of species can coexist because the system varies between those species' requirements for persistence and growth. 

Fig. 3. "Lumpy species coexistence". The y-axis shows the trait value (here, the R*) of species present under 360 day periodicity of resource supply.  
Using many of the dominant models of competition in ecology, it is clearly possible to explain the coexistence of both similar or dissimilar species. This is true across approaches from the Lotka-Volterra results of Scheffer and van Nes, to Tilman's R* resource competition, to Chessonian coexistence (2000). It provides a unifying expectation upon which further research can build. Perhaps the paradox of the planktons is not really a paradox anymore?

Thursday, January 4, 2018

Some of the best advice on the internet: several years of links

I started off the New Year with a much-needed bookmark reorganization and deletion, which also gave me a chance to re-read some of the links I've held onto (sometimes for years). There's an ever-increasing amount of useful content on the internet, but these have proven some of the most helpful, concrete, and lasting guides for navigating a scientific life.

I thought I'd collate the list here with the hope others might find some of these useful.

How to make it as early career researcher and new faculty: 
Identity and academia:
  • I think most of us took different and often interesting routes to science (for example, I grew up in an evangelical Christian family, took a number of years to finally start my undergrad, and had no particular knowledge of ecology when I started my BSc. I wanted to be a vet, but now I'm an ecologist. Close enough :) ) and so I like to hear the many different routes by which scientists found science (SEAS).
  • Overcoming imposter syndrome - there are many websites devoted to the topic, but this one provides particularly concrete steps to overcoming this common problem. 
  • No one is perfect, and feedback can hurt - why feedback hurts and how to over come that. And no, it isn't enough to say, 'grow a thicker skin' (The Thesis Whisperer).
  • Diversify EEB - a useful list of women and minorities working in EEB, worth keeping in mind when making nominations, selecting reviewers, and making various invitations. 
  • And it's worth remembering that there is a dark side (one slightly bitter take on it). (Fear and Loathing in Academia)
Mentoring and leadership:
Computing/Data management:
Data visualization:
  • There are some really beautiful infographics about science from Eleanor Lutz here (Tabletop Whale).
  • Information is Beautiful - infographics for inspiration
  • Show me Shiny - some great examples of how R Shiny has transformed data visualization and interaction.
  • If you are familiar with Edward Tufte's influential work on data visualization, you can use R to produce similar plots here. (Lukasz Piwek)
Miscellaneous links: