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On the parsimony of null models of plant–pollinator networks

Posted by PLOSBiology on 07 May 2009 at 22:18 GMT

Author: Diego Vázquez
Position: No occupation was given
Institution: Instituto Argentino de Investigaciones de las Zonas Áridas, Centro Regional de Investigaciones Científicas y Tecnológicas, CONICET, CC 507, (5500) Mendoza, Argentina
Submitted Date: June 08, 2007
Published Date: June 8, 2007
This comment was originally posted as a “Reader Response” on the publication date indicated above. All Reader Responses are now available as comments.

There has been much recent interest in describing the structural patterns of plant–animal mutualistic networks. Most of this work has been descriptive, aimed at documenting existing patterns. Hypotheses about the underlying causes of the observed patterns have been proposed, but few attempts have been made to evaluate those hypotheses. A recent paper by Santamaría and Rodríguez-Gironés [1] (hereafter SRG) is a bold attempt to provide such an evaluation. In particular, these authors propose that the nested pattern usually observed in mutualistic networks [2] may result from rules that dictate the phenotypic matching between interacting species. A nested pattern is one in which each species interacts only with a subset of those species interacting with more connected species [2]. Using models with two kinds of rules (complementarity traits and barrier traits), SRG simulate the process of network assembly, showing that for one of their models (the mixed model, combining two complementarity traits and two barrier traits for plants and another two and two for animals) the simulated networks exhibit a substantial degree of nestedness, similar to that observed in real-world networks. SRG also use two kinds of neutral models, asuming that probabilities of interaction are determined by the relative abundances of species, with abundances coming from a uniform distribution (neutral model) or a lognormal distribution (lognormal neutral model). The latter model generated simulated matrices with nestedness comparable to that observed in real networks, thus providing a fit to the data at least as good as that obtained for the mixed model.

As SRG argue, the principle of parsimony dictates that when two alternative models can explain a certain phenomenon, the simpler one should be accepted. However, SRG reject the lognormal neutral model as more parsimonious than their mixed model. In my opinion, the three justifications provided by SRG for such rejection are questionable. I explain why I think so below.

First, SRG argue that assuming random interactions is not sufficient to reproduce network topology, given that the uniform null model provided a very poor fit to the data and that to fit the model they had to assume a lognormal distribution of abundances. SRG believe that using a lognormal distribution is problematic, apparently because there is no theoretical basis for preferring a lognormal over a uniform distribution of abundances. In my opinion, it is unrealistic to assume that abundances come from a uniform distribution. We know, as SRG mention in their paper, that in most communities studied to date the distribution of abundances is not uniform, but highly right-skewed (many rare species, few abundant species). Furthermore, although this is indeed an empirical result, different types of community assembly models (ranging from neutral to niche-based) predict this pattern (see, e.g., [3-6]), giving a theoretical justification for this choice. Therefore, using a model that assumes that species’ relative abundances come from some right-skewed distribution like the lognormal does seem appropriate. On the other hand, it is possible to evaluate the parsimony of a model by counting the number of parameters it includes [7]. Both the single trait models and the neutral models calculate interaction probabilities by drawing from either a uniform or a lognormal distribution, which requires two parameters (mean and variance) for plants and another two for pollinators. These four-parameter models are arguably simpler and more parsimonious than the mixed model, which requires sixteen parameters (two means and two variances for barrier traits for plants, another two and two for complementarity traits for plants, and the same for pollinators). For this reason, I think SRG’s claim that the lognormal neutral model is not more parsimonious than the mixed model is untenable.

Second, the authors point out that “The neutral model assumes that species abundance determines the frequency of interactions,” and cite two studies providing conflicting evidence for this assumption, only one of which was among the 37 used by SRG for their analysis. An analysis of one out of 37 datasets seems like a weak test of this assumption. Furthermore, if the aforementioned deviations from the assumptions of the model were indeed important enough, the hypothesized link between abundance and network structure whould be weakened, which should be reflected in the results of the model comparison, putting the neutral model in a poor position in comparison to alternative models.

Third, the authors quote a conclusion of a previous paper of mine, namely that “most phenotypic characteristics of interacting species may be irrelevant” [8], and suggest that this statement “is at odds with all reported empirical data, which show that phenotypic traits often prevent the interaction between specific pairs of plants and pollinators.” I was referring to the irrelevance of these traits to the broad-scale network patterns considered in that paper (specifically, degree distribution, i.e., the distribution of interspecific links among species), not to their general irrelevance for species interactions. What I was arguing (and still argue) is that including this sort of constraints based on phenotypic matching between interacting species is not necessary for generating some broad-scale patterns observed in networks, and that a simpler neutral model that does not include these constraints is sufficient to generate the observed patterns.

Although based on the above arguments we cannot conclude that trait complementarity and exploitation barriers play a role in determining the structure of plant–pollinator networks, the issue will be ultimately resolved by data. Future insight will come from studies that measure the contribution of both neutrality and phenotypic matching rules to observed network patterns in real-world networks. In this sense, the study by Stang et al. [9] is a promising start.

I thank Octavio Bruzzone, Natacha Chacoff and Juan Manuel Morales for discussion and comments.

[1] Santamaría L, Rodríguez-Gironés MA (2007) Linkage rules for plant–pollinator networks: trait complementarity or exploitation barriers? PLoS Biology 5:e31.
[2] Bascompte J, Jordano P, Melián CJ, Olesen JM (2003) The nested assembly of plant-animal mutualistic networks. Proceedings of the National Academy of Sciences (USA) 100:9383–9387.
[3] Bell G (2001) Neutral macroecology. Science 293:2413–2418.
[4] Hubbell SP (2001) The unified neutral theory of biodiversity and biogeography. Princeton, NJ: Princeton University Press.
[5] Chave J, Muller-Landau HC, Levin SA (2002) Comparing classical community models: Theoretical consequences for patterns of diversity. American Naturalist 159:1–23.
[6] Wilson WG, Lundberg P, Vázquez DP, Shurin JB, Smith MD, et al. (2003) Biodiversity and species interactions: extending lotka-volterra community theory. Ecology Letters 6:944–952.
[7] Burnham KP, Anderson DR (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Springer.
[8] Vázquez DP (2005) Degree distribution in plant-animal mutualistic networks: forbidden links or random interactions? Oikos 108:421–426.
[9] Stang M, Klinkhamer PGL, van der Meijden E (2007) Asymmetric specialization and extinction risk in plant–flower visitor webs: a matter of morphology or abundance? Oecologia 151:442–453.

Competing interests declared: I declare that I have no competing interests.