Abstract:

With increasing data availability in the big data era, many traditional statistical analyses based on the mean or median are insufficient or inappropriate to elucidate the complex patterns of variation. This is particularly the case when multiple factors are involved and the bivariate scatter occurs as scatter clouds. In such circumstances, constraint line (or envelope) method could be an alternative and effective tool to extract the data boundaries, thus improves our understanding of the complex relationships between limiting factor and response factor. Here, we synthesize the major findings and achievements in the field of applying the constraint line method in ecology. Specifically, we first describe the history and development of the constraint line method. We then discuss the techniques to establish the constraint lines with examples, and discuss the applications and implications of the constraint lines in species distribution, population performance, and optimization problem. We suggest simultaneously application of both constraint lines and regression techniques to the same datasets to achieve a comprehensive understanding of ecological process and underlying mechanisms. Such combined methods should be used with special attention to the role of spatial heterogeneity and scale dependency. We also discuss in detail the potential applicability of the constraint line method in studying the linkages between ecosystem services, and land system design.

Key words: scatter cloud, informative boundary, constraint envelope, limiting response, species distribution, population performance, optimization