Maximum entropy in ecology

Use of the maximum entropy (MaxEnt) formalism in ecol-ogy smouldered for nearly two decades (Macchiato et al. 1992). Th at changed in 2006 when Bill Shipley, Denis Vile and Eric Garnier published a paper in Science that ignited the eld (Shipley et al. 2006). Shipley and colleagues alleged to have by-passed the need for population dynamics – species abundance could be predicted from information about species’ traits, such as speci c leaf area. Th e Science paper was accompanied by a Perspectives article written by Brian McGill, which as well as providing an intuitive description of MaxEnt, suggested some lack of clarity about the source of its apparently incredible explanatory power (94% of inter-speci c variation in abundances) (McGill 2006). Two Techni-cal Comments soon appeared, one by Stephen Roxburgh and Karel Mokany (Roxburgh and Mokany 2007), the other by Christian Marks and Helene Muller-Landau (Marks and Muller-Landau 2007); these were accompanied by a response from Shipley, Vile and Garnier. Th e argument was about if Shipley’s and colleagues’ remarkable ndings were due to MaxEnt, or were features of the particular datasets and assump-tions used. Discussion has continued, most recently in a back-and-forth between Shipley, Bart Haegeman and Michel Loreau, published in Oikos (Haegeman and Loreau 2008, Haegeman and Loreau 2009, Shipley 2009). As well as concerning the inter-pretation and use of MaxEnt in ecology, these papers contain some simple and intuitive explanations of what is MaxEnt.Following are four commissioned Forum articles that con-sider di erent aspects of MaxEnt in ecology. First, Fangliang He’s article re ects on what has at times been a quite heated debate, and illuminates links with better know models, such as logistic regression (He 2010). Stephen Roxburgh and Karel Mokany follow up their previous work by developing and testing an appropriate statistical test of the relative abundance predictions of MaxEnt (Roxburgh and Mokany 2010). Brian McGill and Je Nekola provide a broad perspective on what are mechanisms in ecology, and suggests where MaxEnt might t in (McGill and Nekola 2010). Th ey provocatively suggest that ecologists might bene t from a more pragmatic and less puritanical approach to mechanism. Brian Shipley concludes with a discussion of a mechanistic basis for the use of MaxEnt in ecology (Shipley 2010). In short, Shipley views his use of MaxEnt as a quantitative expression of the common concept of environmental ltering for individuals with particular traits.As well as predicting abundances of particular spe-cies, MaxEnt has been used to predict the shape of species abundance distributions (Pueyo et al. 2007), geographic distributions (Phillips and Dudik 2008), and even the distribution of trophic links in food webs (Williams 2010). It will be interesting to see what other applica-tions arise, and how MaxEnt settles (or doesn’t) in the heterogeneous landscape that is theory and mechanism in ecology.