Species overlap - Githubissues

As of 12/4 I'm leaning strongly towards focusing on the overlap in the body size distributions of species within communities, rather than trying to divine the "multimodality"/"gappyness"/"lumpiness" of the overall ISD.

As I understand it at the moment, both Holling and ESS predict a polarized distribution of species-species bsd overlap. That is, species are either very similar (high overlap) or very different (little to no overlap), with few species in between. This is potentially easier to measure than the ISD, and has more room for variation that might distinguish (or meaningfully fail to distinguish) between various sims/communities/etc. Also, it more directly gets at the behavior predicted by the theories. The ISD is emergent and there are multiple routes to a single ISD, which obscure the underlying species' similarities.

Let's call a species level body size distribution SBSD. This is the distribution of body sizes of all the individuals of a species.

I've imported the SBSD overlap metric from Read et al 2018:

For all pairs of species in a community, construct the KDEs across the entire body size range and standardize so each KDE integrates to 1.
Integrate the minimum of the two KDEs at each evaluation point.

In principle this varies from 0 to 1 for each pair of species.

Read et al weighted overlap values by the harmonic mean of the two species abundances and used the median overlap for each community. We don't want that kind of a holistic/center-ed metric - we want to know how polarized it is, or how little density is in the middle. Defining the "middle" is a little fuzzy.

I do think it's constructive to weight according to species abundances. Low abundance species might be present but losing. They also have less reliable and pointier KDEs than they presumably would if we were constructing the KDE over more individuals.

Sensitivities

I expect the distribution of overlap vectors to be contingent on S, N, and the body size range. You can't get as many nonoverlapping species if you have high N and a short body size range as if you had either fewer individuals or a wider range. Ditto scaling of standard deviation with mean body size.

Read et al found their median metric not sensitive to choice of density method, bw, etc. This is a slightly different application, so it would be good to check on those wrt using it here.

Defining the middle

Early playing around with this metric shows that even when a human would say "those SBSDs are on top of each other", the overlap might be more like .9 or .8. This is because, for these small numbers of individuals, you're just never going to get exactly the same set of values even if you draw from the exact same distribution twice. So the "middle" is not really in the center. At the moment I'd say something like .1 - .6 as "intermediate".

I am not sure if the "middle" is going to vary based on the state variables. I think I might try establishing "high" overlap by dropping S species with the right number of individuals all in the same place on the body size axis and calculating all the overlaps, many times.

So far the low end seems less squishy, but TBD.

A couple caveats

I forsee using this metric to summarize many sims constructed using some ground-rules state variables, especially the body size range, S, and N. This makes this analysis appropriate for asking whether empirical SBSDs are more polarized than sim ones subject to some noncontroversial constraints, but explicitly makes it not appropriate for asking about things like limiting similarity or strength of competition. My logic here is that competition, etc would presumably affect N. This analysis is good for looking at these distributions in a statistical space, but taking the state variables as givens is questionable in a competition space.

diazrenata / isds

Species overlap #10