In the most recent issue of Nature (Aug 22) there was a brief communication about a past article by James et al. (2012) entitled “Disentangling nestedness from models of ecological complexity.” The communication came from Saavedra and Stouffer who offered a criticism of the James et al paper based on their choice of randomization techniques. Included with the communication is a reply by James et al.
For those who don’t know, nestedness here is referring to the statistical pattern of ecological networks (of mutualisms in this case) where more specialist species utilize a subset of resources used by more generalist species. There are a number of ways to measure nestedness, given a binary interaction matrix. In the bipartite package in R I believe there are 5 or 6 measures that a user can implement (two nestedness temperatures, two versions of NODF, and I think one or two others that I cannot think of right now). There has been a lot of uncertainty surrounding nestedness in mutualistic networks in the literature over the past few years. Some suggest that nestedness increases stability, while others argue the opposite. Additionally, there are questions over how best to measure nestedness, not only with respect to which metric to use, but how to know whether the measure you have used is significant or not. By far the most agreed upon statistical method is the comparison to a null model, but of course the question then becomes which null model. When it comes to network level metrics there are a number of possible null models which vary in both implementation and degree of conservative-ness (meaning it takes more to be significant with a conservative null model). Some examples are comparison to a purely random network, and link swapping techniques.
First I should set the stage and summarize the findings of the James et al. paper. They used 59 empirically described plant-pollinator networks as their data set. James et al. then parameterized dynamic models incorporating mutualisms, intra, and inter specific competition, and intrinsic growth. They measure persistence as the proportion of species surviving at equilibrium. They attempt as well to isolate the dynamic impact of mutualism by “shutting off” mutualistic interactions, and running their model with the plant and pollinators as two separate groups (with only competition and intrinsic growth). Their results compare the change in persistence between runs of the model with vs without mutualisms, and against runs of random networks. They show first that mutualism decreases persistence of the community, but more importantly they show that there is no correlation between the degree of nestedness in a community and the change in persistence. Ostensibly if nestedness increased persistence we would expect that more nested networks should have a lower decline in persistence than non-nested networks.
Disentangling “disentangling nestedness”
Saavedra and Stouffer (hereafter SS), in their communication assert that the lack of correlation between nestedness and persistence in comparing against random network is an artifact of the methods used by James et al. SS suggest that the random networks used by James and colleagues altered the number of interactions for each species, the degree distribution, leading to more homogenous random networks. When they repeat the analysis controlling for the degree distribution either statistically or through null model choice, they demonstrate a positive correlation between the degree of nestedness and the persistence of the community.
Tangling “disentangling ‘disentangling nestedness'”
James et al. offered a reply to SS’s communication, reasserting their claim that nestedness does not have an impact on persistence. They redid their analysis, this time using the swap algorithm as a null model for randomization (preserving degree distribution, suggested by SS). Then they plot the change in nestedness from real to random networks against the change in persistence from real to random networks. The result is basically a cloud of points without any clear correlation. Presumably we would expect, given the findings of SS, that a negative change in nestedness should lead to a negative change in persistence, and vice versa.
So, the question of the day then must be: who got it right, and who is wrong? These are clearly contradictory findings, although it is difficult to compare the results directly because the authors of the original paper and SS chose to illustrate and report their results differently. I wonder if small variations in methods, e.g., choice of parameters or number of randomizations, play any role (although I doubt it considering the apparent differences). I also am curious why SS chose only to address part of the findings of James et al. and not both the randomization methods, and the comparison with competition only models. James et al. used both methods to test their hypothesis. Certainly if one method is flawed it takes away some of the weight behind the findings of the other method, but the result is still the result. Maybe it will take a detailed analysis of both of their methods to truly disentangle the apparent contradictions being debated here. I will admit I have not looked too deeply into their methods to discuss it now however.
Long story short, I really don’t know which result is best. What do you think?