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CHAPTER FOUR Niches and Distributions in Practice: Overview Part I of this book set out a conceptual framework for understanding relationships between niches (in environmental space, or E-space) and spatial distributions (in geographic space, or G-space). This theory forms the base for the next sections, which deal with the practice of modeling ecological niches and estimating geographic distributions (part II) and applications of these methods (part III). Although we cover a wide variety of modeling methods and applications in this set of chapters, the same basic approach is used throughout. This process can be outlined as follows (Hirzel et al. 2002): 1. The study area is conceptualized as a raster map with extent G, composed of grid cells at a specific resolution (grain). 2. The dependent variable is the distribution of the species (GO, GP, or GA), as inferred from occurrence records G⫹, sometimes with true absences also being known (presences and absences together referred to as Gdata). 3. A suite of environmental variables is collated to characterize each cell of the study area in environmental terms; known as E. 4. A function μ(Gdata, E) that characterizes the dependent variable in terms of the environmental variables is generated, to indicate the degree to which each cell in G is suitable for the species. In this section of the book (part II), we describe the process of building ecological niche models, mainly in very practical terms, but based on the conceptual foundation presented in part I. The process includes selecting and obtaining appropriate biological occurrence records and environmental data, choosing and applying modeling algorithms, and assessing the accuracy of the predictions quantitatively. In this chapter, we first set out general principles and definitions necessary for understanding the coming chapters, and then describe—in less formal terms—principal steps to be followed in building niche models. 52 CHAPTER 4 GENERAL PRINCIPLES Quite generally, the setup for a prediction problem is as follows. Nature issues a response Y. Two sets of predictor variables, denoted generically by X and Z, exist that represent conditions that cause effects on Y. The distinction between two types of predictor variables is that X is observable and easily estimated and visualized (e.g., temperature), while Z is not (e.g., most biotic interactions). Nature’s response is denoted as Y ⫽ f(X, Z), for some function f. In this book, Y refers to the presence or absence (Y ⫽ 1 or Y ⫽ 0, or Y ⫽ 1, 0 for simplicity) of a species at a given site or in a given environment, giving rise to what is termed a classification problem. X ⊂ E, while Z refers to other, complex variables that are less easily observed and characterized. As noted already, and as is developed more fully in chapter 5, the very notion of what “presence” and “absence” truly mean is critical, and has many interpretations. That is, in the function f, the variables in X can change, and Y may change accordingly. In defining terms, we assume here that this function is given with clear meaning, albeit unknown. The notion of approximating nature through use of a model is to concede that the most that we can do is to attempt to discover Y ⫽ f(X). Note that the dependence on the additional factor Z is disregarded completely: we implicitly assume that any effects caused by Z are minor (see chapter 3). This set of assumptions necessarily introduces a notion of possible randomness, incompleteness , or even outright error, such as variability in Y even for equal values of X, since the unobserved Z variables may still cause variation in responses. Models f ˆ(X) of the true relation f(X) can be obtained by means of algorithms for the purpose of approximating nature’s true f. The term “model” is frequently used as a synonym with the words algorithm, prediction, or method, represented in the last chapter by the expression μ(Gdata, E). Therefore, f(X) is estimated by use of a given algorithm μ(Gdata, E). The different algorithms summarized in chapter 7 have the common goal of producing functions f ˆ(X) that can be used to compute a prediction of Y for a given X. Some methods produce a 0,1 output directly, such that their predictions are of the form Ŷ ⫽ f ˆ(X). Other methods produce a continuous output ĉ(X), with the property that larger values indicate greater likelihood of presence (or, more precisely, larger values represent areas more similar to pixels at which the species has...


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