In search of Schrödinger's patch: a functional approach to habitat delineation

The effective delineation of habitat is crucial for understanding drivers of habitat loss and fragmentation, and their effects on biodiversity outcomes at local to global scales. The concept of the habitat patch is central to this process but presents both theoretical and methodological challenges related to the seemingly irreconcilable tendency of habitat to simultaneously exhibit characteristics of both gradation and aggregation. This apparent contradiction, recently described as the continuity-contiguity problem in landscape ecology, presents a problem of classification in which the associated ambivalence is analogous to that surrounding the fate of Schrödinger's Cat.

This is the first of a pair of papers that aim to address the theoretical and methodological challenges associated with the habitat patch concept. This first paper aims to (a) articulate the theoretical and practical limitations of working with the habitat patch concept and (b) set out a framework based on a functional definition of habitat that captures the tendency of resources to exhibit both discrete and continuous spatial characteristics. The second paper (Dennis et al. this issue) presents a demonstration of this framework applied to a real-world landscape, in which the impact of adopting alternative perspectives on habitat delineation on potential functional connectivity is revealed.

We present a new methodological approach that integrates alternative gradient and patch-based models of habitat in landscape ecology. We achieve this integration by leveraging the notion of geographical vagueness and the application of fuzzy set theory to land cover classification. We apply this approach to simulated landscapes that contain information on membership values to different land cover classes and their associated uncertainty. We then demonstrate the functional delineation of habitat from these landscapes based on the use of species-specific parameters, the leveraging of spatial kernels, and type-1 and type-2 fuzzy sets. The possibility of incorporating this approach into subsequent workflows is then described using estimates of between-patch distances and potential functional connectivity as examples.

Our method provides a functional spatial delineation of habitat that reflects both resource-based and patch-based habitat perspectives and can be applied to any gradient or patch-based landscape modelling method. This approach achieves the integration of multiple resource types, habitat complementarity associated with neighbouring cover types, and negative edge effects. We refer to this measure of habitat as Functional Habitat so-called as it reflects the total availability of habitat accounting for the influence of all land cover types and positive and negative neighbourhood effects.

This paper describes a functional approach to habitat delineation and its integration into the computation of fragmentation-related metrics. This methodological framework achieves, for the first time, (1) a multivariate delineation of habitat based on type-1 fuzzy membership and the operationalising of neighbourhood effects and (2) the harnessing of uncertainty in land cover classification (type-2 fuzzy membership) to achieve a distribution of possible outcomes that resolves the continuity-contiguity problem. This new methodology provides a long-awaited functional definition of habitat patches for those seeking to understand the role of habitat fragmentation in biodiversity outcomes.