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CHAPTER SEVEN Modeling Ecological Niches In the preceding two chapters, we discussed the biological occurrence (chapter 5) and environmental (chapter 6) data necessary for developing ecological niche models. In this chapter, we focus on how to use these data to create models that characterize species’ ecological niches in E-space (which can then be applied to and visualized in regions of G). The task is to characterize every cell within a region in terms of quantitative values related to probability of occurrence (or group membership), as a function of the environmental conditions presented in that cell. In the terminology presented in chapter 4, we aim to create a model, f ˆ: a function constructed by means of data analysis, μ(Gdata, E), for the purpose of approximating the true relationship (i.e., the niche) in the form of the function f linking the environment and species occurrences (at least in GO and hopefully also in GI). An important consideration here is the use for which one is developing the model (Peterson 2006c). That is to say, a very basic initial consideration is whether the model is intended for the purpose of prediction or explanation (Araújo and Guisan 2006). In the specific case of niche models, a predictionoriented model might use methods and data that produce optimal predictions in geography, yet provide little in the way of interpretable environmental information regarding the specific qualities of the niche being modeled. An explanation -oriented model, on the other hand, might emphasize characterizing the niche in useful and understandable terms, even though it may not necessarily produce the best predictions across geography. However, some models may fulfill both realms well. These choices are quite fundamental, and should be borne in mind in reading the sections that follow. We first describe general principles regarding how modeling algorithms μ(Gdata, E) approach the task of finding some model f ˆ (several possible probabilities , suitability functions, and so on exist that may be of interest) about the true, but unknown, function. We then describe some commonly used algorithms . We do not aim to give detailed descriptions of individual algorithms, but rather to provide an overview of the different types of approaches that are used (e.g., climatic envelopes, general linear models, machine learning algorithms), 98 CHAPTER 7 and then to classify algorithms according to their requirements in terms of occurrence data. We proceed to describe important considerations about model calibration and definition of thresholds for converting continuous or ordinal suitability values into binary predictions of presence versus absence. Finally, we discuss differences among alternative modeling methods and the difficulties associated with selecting a general “best” approach. WHAT IS BEING ESTIMATED? An important consideration that should perhaps precede all others in this chapter is what is the “meaning” of the function f that is being estimated by the algorithms. Ideally, the model would produce a response variable that would relate directly to some quantity of biological interest, but what variable? Many publications presenting modeling algorithms have indicated that they estimate “probability of occurrence, given the environment” (e.g., Keating and Cherry 2004), which generally requires the existence of true absence data and an unbiased sampling scheme; others estimate degree of resemblance to the environment in the sample points (~ suitability; Hirzel et al. 2002, Farber and Kadmon 2003), or simply membership (or not) in a well-defined set (Busby 1991, Carpenter et al. 1993). Still others (e.g., Maxent) estimate very different quantities that can be transformed to yield probabilities of presence under certain assumptions related to the BAM diagram (Phillips and Dudík 2008). In fact, it has been argued that, strictly speaking, probabilities of occurrence cannot be estimated without rigorous comparisons of presence and absence data (Ward et al. 2009), and that most niche modeling applications using presenceonly data can at best estimate indices of relative suitability (Ferrier et al. 2002). The issue of what different algorithms do is central to all phases of niche modeling , and particularly to model evaluation. To clarify this important point, we will use arguments based on the BAM-related probability tree, developed in chapter 5. Equation 5.6 relates probability of presence to probabilities of different conditions being fulfilled; this equation, by application of Bayes’s rule, gives: P(Y  1) P(Y  1|X  g)  PM(g)P A(g)PB(g)  ———— P(X  g|Y  1). (7.1) b(g) In words, equation 7.1 relates probabilities related to the circles in the BAM diagram (a mechanistic or process-based approach) to...


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