Ecologists generally represent species distribution as a simple binary matrix where rows correspond to species, and columns correspond to different localities. A cell at the intersection of a given row and column is filled by a 1 if the species corresponding to the row is present at the locality identified by the column, and by a 0 if not. Ecological networks, such as those that map the interactions between plants and pollinators, can be represented (and investigated) in the same way.
Several indexes to qualify and quantify structural patterns in binary matrices have been developed. For example, a typical ecological analysis consists of counting how often two species are (or are not) found together in the same locality. Finding them together quite often suggests that they have an ecological relationship, finding them together only rarely suggests that they are competitors.
The reasoning seems straightforward, but it hides a fundamental problem: how often should two species be found together or separately in order to identify a positive or negative relationship between them?
The binary matrix indicates the exact frequency of species co-occurrence for all possible pairwise combination of localities, but the problem is that this sole number is affected by several potential confounding factors of the species/locality matrix, and so does not provide a conclusive result. These confounding factors should be eliminated in order to verify whether or not the observed value is significant, i.e. substantially different from chance expectation.
For example, the proportion of filled cells in the matrix generates important constraints. Imagine a set of poorly inhabited islands with very few species. In this scenario, we have a very high chance not finding pairs of species together in the same island. In islands abundantly stocked with species we will often find pairs of species together, but this, instead of suggesting the existence of intimate ecological relationships of dependence, may simply indicate that the islands offer enough resources to support high levels of diversity.
To get around this, ecologists commonly generate a large set of randomized (i.e. ‘null’) versions of the matrix under study, which preserve some of the properties of the original matrix. The set of random matrices is then used as a frame of reference to assess whether or not a pattern departs from chance. For example, if the number of random matrices where species co-occur in the same localities less often than observed in the real matrix is less than 5%, we can conclude that competition is an important ecological structuring factor of the communities.
However, there is a fundamental issue that further complicates the procedure: how should the original matrix be randomized in order to generate the null matrices? Or, to put it another way, which features of the original matrix should be preserved in the null matrices, and which that need not?
Since the early 1970s, world-renowned scientists have debated whether or not competition is important in determining species distribution patterns. An important part of this controversy lies in the constraints to be used in generating random matrices, specifically regarding marginal totals. Some ecologists argue for strict constraints, but this can complicate the identification of ecological patterns, because they will often appear to have the same intensity in the original and in the null matrices. Generating null matrices with random marginal totals leads to null matrices that are very different from the original matrix, making it highly likely that any ecological pattern observed in the real matrix will be significantly different from that observed in the randomized set. The alternative choice of an ‘intermediate’ level of constraints has many technical and theoretical problems which, until now, have left ecologists in troubled waters.
This new paper presents a new procedure that can replace at once all previous techniques. By providing a fresh perspective on the issue, the new method could help finally settle the controversies described above. While previous procedures could provide a circumstantial response to ecological questions based on well-defined constraints, the approach of Strona et al. can provide a synthetic view embracing the whole set of hypotheses that could be explored with previously available techniques, plus all the intermediate ones.
“Considering the long history of species-area matrix analysis, we ecologists have often focused on one or another single dot of a Georges Seurat pointillist painting. We hope our method could help us taking some steps back, and get a better look at the big picture” conclude the authors. It is time to bring null model analysis into a new dimension, and this could be a first, fundamental step.
Links:
Bi-dimensional null model analysis of presence-absence binary matrices