This chapter is largely focused on the species–area relationship (SAR), although it may not seem so for much of the time. Bear with us; we will get there in the end. Our aim is to provide insights into how the relationship works, and how it is built. This leads us to take a rather reductionist approach, and to break down the SAR into its component parts. We will spend a substantial section of this chapter examining these pieces and their properties. We will then explore the logic by which the parts are reassembled, and will explore how biological and biogeographical properties of a system may affect the SAR. Before attempting this feat, however, we should begin with a brief discussion of the SAR itself, to explain why it is worth making such a fuss over. The SAR is, after all, only a simple graph: a plot of the number of species found in a sample as a function of the area sampled. Ecologists being an argumentative lot, we cannot even all agree on what this plot should look like; Gleason (1922, see also Williams 1964) argued that the absolute number of species should be plotted as a function of the logarithm of area, whereas Arrhenius (1921, see also Preston 1960) suggested that both species and area should be plotted logarithmically. Connor and McCoy (1979) found cases that fit both models, and two others besides (log species by untransformed area, and neither variable transformed). However it’s plotted, the SAR is not even a particularly attractive or elegant graph—at its best (!) it is simply a straight diagonal line within a tight scatter of datapoints on a rectangular plot. Hardly something to set the pulse racing. Yet the SAR is exciting stuff; that simple line encapsulates a great deal of information about the diversity of biological systems across a wide range of scales.
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