Comment on "From Plant Traits to Plant Communities: A Statistical Mechanistic Approach to Biodiversity"

Abstract

Shipley et al. (Reports, 3 November 2006, p. 812) predicted plant community composition and relative abundances with a high level of accuracy by maximizing Shannon's index of information entropy (species diversity), subject to constraints on plant trait averages. We show that the entropy maximization assumption is relatively unimportant and that the high accuracy is due largely to a statistical effect. S hipley et al.(1) combined a trait-based framework and the assumption of maximum entropy to predict relative abundances of plant species at sites varying in successional age. Specifically, they chose relative abundances such that Shannon's index of information entropy (i.e., Shannon's diversity index) was maximized, subject to the constraint of reproducing the average values of traits at different sites. Both their use of traits and their maximization of entropy are interesting. The maximum entropy assumption is particularly novel and intriguing as this assumption essentially maximizes biodiversity, which could be interpreted in terms of minimizing harm due to specialized natural enemies (2) and/or maximizing niche differentiation with respect to unmeasured traits, thereby gaining hypothesized benefits of high diversity such as resilience against environmental fluctuations (3, 4).A key question raised by the results in Shipley et al.(1) is the relative importance of the entropy assumption versus the trait constraints in achieving good predictions of abundances. We tested the importance of the maximum entropy criterion by repeating the analysis under the opposite assumption; specifically, we chose relative abundances to minimize entropy (5), while maintaining the same trait constraints as in (1). Predictions of relative abundances of species in individual plots were almost as good when entropy was minimized (r 2 = 0.86) as when it was maximized (r 2 = 0.94), which suggests that this assumption is relatively unimportant (6). In contrast, when we tested the importance of the trait constraints by repeating the analysis using only four traits instead of eight traits as constraints, the accuracy of the predictions dropped substantially (Table 1). Thus, although the maximum entropy assumption consistently improves predictions, the constraints on trait averages are clearly much more important.The primacy of the trait-based assumption for obtaining good predictions of abundances leads to the further question of the degree to which this assumption is successful because of strong convergence in traits at a given successional stage or merely because the predictions are being made for the same sites from which the trait averages were calculated. To assess this question, we used cross-validation analysis. Specifically, we fit the trait patterns across successional ages based on data from all but one site and then predicted abundances at the remaining site using the same constrained entropy maximization approach as before. The key difference between the crossvalidation and the original analysis is that under cross-validation, t...

A structured and dynamic framework to advance traits‐based theory and prediction in ecology

“…We do not consider statistical mechanics models such as that of Shipley et al. (2006) because they lack a clear mechanistic linkage of traits and environment (performance filter) (Marks & Muller‐Landau 2007; Roxburgh & Mokany 2007; Shipley et al. 2007).…”

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