Conceptual and mathematical relationships among methods for spatial analysis

Abstract

A large number of methods for the analysis of the spatial structure of natural phenomena (for example, the clumping or overdispersion of tree stems, the positions of veins of ore in a rock formation, the arrangement of habitat patches in a landscape, and so on) have been developed in a wide range of scientific fields. This paper reviews many of the methods and describes the relationships among them, both mathematically, using the cross‐product as a unifying principle, and conceptually, based on the form of a moving window or template used in calculation. The relationships among these methods suggest that while no single method can reveal all the important characteristics of spatial data, the results of different analyses are not expected to be completely independent of each other.

Orchidaceae das Serras Negra e do Funil, Rio Preto, Minas Gerais, e similaridade florística entre formações campestres e florestais do Brasil

“…O teste de Mantel é um método para testar hipóteses em que as distâncias (ou similaridades) entre objetos na matriz A são linearmente independentes das distâncias (ou similaridades) entre alguns objetos na outra matriz B (Dale et al 2002). Neste trabalho, foram utilizadas as matrizes de similaridade fl orística e distância geográfi ca entre as áreas com inventários exclusivos de Orchidaceae, ou que incluíam a família.…”

Fission‐Fusion Dynamics

“…Given that there is a great complexity in the environments in which grouping takes place, producing null expectations of grouping patterns should take as a starting point a spatially-explicit description of the environment inhabited by a species. Spatial analysis is a mature field that offers many tools useful to socioecologists for describing how resources (e.g., food, watering holes, sleeping sites) or predation risk vary in space and time (Dale, Dixon, Fortin, Legendre, Myers, and Rosenberg 2002;Fortin, Dale, and van Hoef 2002 Subsequently, deviation from what is predicted from these first principles can be analyzed to understand the relevant factors that, in addition to environmental variation, influence grouping patterns and social relationships. Some of these deviations will not lead too far (e.g., sleeping sites could physically constrain spatial dispersion), while others could be fascinating (e.g., quantitative descriptions of how alternative social strategies, such as infanticide avoidance, might influence grouping).…”

Concepts of Scale and Scaling

“…We believe that the observed scale of a given phenomenon is the result of the interaction between the observer and the inherent scale of the phenomenon. Although the existence of intrinsic scales does not mean that they are always readily observable, a suite of methods, including spectral analysis, fractal analysis, wavelet analysis, scale variance, geostatistics, aidrnultiscale object-specific analysis (e.g., Turner et al 1991, Hay et al 2001Dale et al 2002, Hall et al 2004, have been used in detecting characteristic scales or scale breaks. Effective scale detection requires that the scale of analysis be commensurate with the intrinsic scale of the phenomenon under study (Bloschl and Sivapalan 1995, Wu and Loucks 1995, Dungan et al 2002.…”