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CHAPTER THREE Niches and Geographic Distributions In chapter 2, we began developing and exploring a concept of niche that emphasizes multidimensional spaces of scenopoetic variables, typically measured at coarse spatial resolutions and over broad geographic extents. Such a niche concept not only has had a long and fruitful tradition in ecology, but also provides a natural connection to the study of geographic distributions of species and the broader field of biogeography. In this chapter, we develop this idea in greater detail. First, we must consider the concept of the geographic distribution, or range, of a species, and the approaches available by which to measure it. Ranges are usually represented as maps, but maps of what? In a thought experiment, we could make all individuals of a species fluoresce and observe them from space (Brown 1995). We could then define a grid on the surface of the planet, and agree that the set of all cells within which fluorescent dots can be detected during a certain time interval constitutes the distribution of the species. Even such a detailed, pointillist map, however, would be a static simplification of the complex spatial and temporal footprint within which individuals of a species are distributed on Earth (Brown 1995). It is not possible to follow each individual at the spatial resolution of its movements, except, perhaps, for a very few large-bodied and high-profile species (Maurer and Taper 2002). As a consequence, retreat to coarser resolutions becomes necessary, as well as adoption of conventions about which individuals and populations will be regarded as comprising the species’ distribution—e.g., breeding versus migratory populations, or source versus sink populations (Udvardy 1969). The concept of the distribution is then related intrinsically to the resolution (grain) at which the grid is defined (Erickson 1945, Mackey and Lindenmayer 2001, Maurer and Taper 2002, Gaston 2003), although no single grid resolution can be taken as the “right” one (Gaston 2003): quite simply, distributions are scale-dependent. Therefore, we can define the distribution of a species as the set of all grid elements in which, within a given sampling time period, the probability of recording an individual of that species exceeds some given threshold. In some situations, to be more specific, it may 24 CHAPTER 3 be more important to emphasize “reproductive populations,” rather than mere presence of individuals. In sum, the concept of the distribution of a species includes the ideas of presence of individuals, presence of reproductive populations, and probability of detection, all considered at spatial and temporal resolutions and extents that are normally relatively coarse and broad, respectively. In what follows, then, the operational concept of distributional area of a species will be subsets of geographic space in which the presence of individuals or populations of a species can be detected. Some other areas, lacking observable populations or individuals but otherwise suitable, can also be defined. Relationships between areas of distribution and niches therefore depend on how ecological properties of species delineate subregions of the world for each species. RELATIONS BETWEEN ENVIRONMENTAL AND GEOGRAPHIC SPACES Let us go back to the two spaces introduced in chapter 2. One is a “geographic space,” denoted by G, which is composed of cells (⫽ grid cells or pixels) covering a particular region. This space is usually two-dimensional (and possibly three-dimensional in some future applications), and the grid is characterized by a particular extent and a particular resolution (⫽ grain). In most applications discussed later in this book, the grain is typically 1 km2 per cell or more. The corresponding “environmental space” of environmental variables, at a given time, is denoted by E. This space is defined by a suite of environmental attributes , such as climate, solar radiation, topography, and so on, all of which are generally characterized in relatively coarse environmental variables (see chapter 6). These dimensions are the scenopoetic variables of Hutchinson (1978). Hutchinson (1957) called G the “biotope.” The linkage between environmental niches and the corresponding biotopes has been termed “Hutchinson’s Duality ” (Colwell and Rangel 2009). Now, we will explore this set of concepts in more formal terms. Since one can take measures of v scenopoetic variables in each cell g in G (or in symbols, g ∈ G), we can define vectors denoted by e → g ⫽ (e1, e2,... ev)g, one for each cell in G, which describe the environmental characteristics of cell g. The space of all existing values of e → g comprises the environmental space denoted as E. Jackson and Overpeck (2000) called E the...


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