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In-degree cumulative distributions

The last post on this topic reported that alpha vertebrate diversity differs among reef communities in the Cayman Islands, Cuba and Jamaica, with the Caymans having the greatest species richness. I also showed that if we consider the reef communities to be random draws from the gamma-level (regional) species pool, we cannot reconstruct food webs with the observed Jamaican connectance. What’s causing this? At least a partial answer is the bias in the degrees of trophic specialization in the communities. Jamaica has greater than expected connectance because it has a relatively greater proportion of generalist species, i.e. those with high in-degrees (incoming links). Interestingly, if we compare the in-degree distributions of the communities, we find no significant differences (Kolmogorov-Smirnov tests). This first figure illustrates the cumulative frequency functions of each community. While the K-S test says no difference, however, we note that there are asymmetries in the distributions, and it could well be worth decomposing these distributions into pre- and post-modal portions. They are right-skewed and relatively long-tailed.

Another way to compare the interaction or link distributions is to look at the properties of those species, present in the regional pool, that are missing from each community. The box plots at left plot the in-link distributions of “missing” vertebrates from each community. There is a clear trend, suggesting again that Jamaica is relatively poor in trophic specialists, while the Caymans are relatively rich, with Cuba in between. K-S tests fails to confirm any significance here, but sample sizes are pretty small, and there is likely a problem with test power.

A final interesting observation. Given that there are species common to two or more of the communities, we can compare the in-degree distributions of those species only. A series of paired t-tests confirm that species in Jamaica have significantly more incoming interactions than conspecifics in the Caymans and Cuba (Pr(T>t)=0.0004 and 0.0001 respectively). Can this be reconciled with the above observations? This result is telling us that if a species exists in Jamaica and elsewhere, it will have more prey resources in Jamaica! Given that we are recording only vertebrate differences among the communities, then it means that they have more vertebrate prey resources. I find this to be very odd, and I’m going to have to wrap my brain around it a bit to explain it. Might be time to decompose those distributions.

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