| Recent technological advances facilitating the acquisition of spatial observational data and an increasing awareness of issues of spatial pattern and scale have fostered the development and use of statistical methods for multi-scale analysis. These methods can be interesting tools to improve our understanding of natural systems, but their use must be guided by a good comprehension of the statistics and their assumptions. This thesis is an effort to develop a coherent framework for multi-scale analysis and to identify theoretical, statistical and practical issues and solutions. After defining terminology and concepts, several methods are compared using a common dataset in Chapter 2. The geostatistical method of regionalized multivariate analysis is identified as possessing several advantages, but shortcomings are identified, discussed and addressed in two manuscripts. In the first one (Chapter 3), a mathematical formalism is presented to characterize the spatial uncertainty of cokriged regionalized components and an approach is proposed for the conditional Gaussian co-simulation of regionalized components. In the second manuscript (Chapter 4), the theory underlying coregionalization analysis is discussed and its robustness and limits are assessed through a theoretical and mathematical framework. The assumptions underlying the method and the high levels of uncertainty associated with its use highlight problems with the interpretation of results, and issues with the application of probabilistic models in a spatial context (Chapter 5). Coregionalization analysis with a drift (CRAD), presented in detail in two co-authored publications, is proposed as a sensible alternative for multi-scale analysis. In Chapter 6, CRAD is used in an application to discuss the role of scale in site-specific agricultural management and study the relationships between spatial structure and temporal heterogeneity in soil variables. In Chapter 7, the use of CRAD is extended to the multi-scale causal modelling of relationships between physical factors, tree species distribution and soil variables in a forest ecosystem. These applications show the great potential of multi-scale analysis to facilitate ecological understanding, but highlight the need for further development of ecological theories to generate precise expectations about process-pattern linkages within and across scales. |
