Pierre Dutilleul: Spatio-temporal Heterogeneity: Concepts and Analyses
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Pierre Dutilleul: Spatio-temporal Heterogeneity: Concepts and Analyses Peter M. Atkinson
Received: 23 February 2014 / Accepted: 3 March 2014 / Published online: 21 March 2014 © International Association for Mathematical Geosciences 2014
As the title suggests, this book describes spatio-temporal heterogeneity while, although less obvious from the title, the focus of this interest is strongly in ecological systems. In particular, the book focuses on how to conceptualize heterogeneity for particular purposes, and how to interpret heterogeneity in an ecological context. Importantly, the book includes attention to the effects of scale (of measurement) on heterogeneity. Moreover, the book sets out to introduce the reader to potential pitfalls in analyses of heterogeneity and suggests how to avoid them. According to the author, the book sets out to bridge the gap between statisticians and non-statisticians, writing from the point-of-view of a self-declared non-statistician. The book distinguishes between functional heterogeneity and measured heterogeneity in ecology, and helpfully sets out very early on what it does not do (functional heterogeneity). The focus then is on distinguishing between three main types of measured heterogeneity: heterogeneity of the mean, variance and autocorrelation. These concepts will be familiar to readers of Mathematical Geosciences and need no introduction. This decomposition, and indeed the goal and perceived value of such a decomposition, is core to the whole book. To create an overarching framework with which to structure the book the author creates a “cube” with three cube-dimensions. The author, thus, extends the above cube-dimension of three types of heterogeneity to two further cube-dimensions. The first additional cube-dimension is the choice of the space, time or space–time domain within which the study is undertaken. Here, space can be zero, one, two or three dimensions, while time is a separate and additional dimension. Each study must be conducted in a given space with up to four dimensions, so this conceptualization seems straightforward enough.
P. M. Atkinson (B) University of Southampton, Southampton, UK e-mail: [email protected]
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The third dimension of the cube is created by distinguishing between two different types of spatio-temporal process: first, the point process and second, the random field (RF). Again, both point processes and RFs will be familiar to most readers of Mathematical Geosciences. For others, point patterns are distributions of points in space, time or space–time that are conceptualized as arising as realizations of a stochastic point process. An example of such a point realization could be the distribution of trees in a woodland. The conceptualization extends to marked point patterns where some points are attributed with a given value or “mark” (e.g., some trees are sycamore). Both are covered in the book. RFs on the other hand are continuous spatial processes that lead to realizations in the form of observ
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