Exploring Connectivity across Spatial Scales Using Functional Principal Component Analysis

The interplay between organism dispersal and habitat patch connectivity is crucial for the distribution and dynamics of populations and communities. However, the appropriate spatial scales of connectivity analysis vary among species, populations and individuals, depending on their capacity and propensity to move. This scale dependence poses problems when studying assemblages including species with different appropriate scales or when the scale for a species varies or is difficult to determine. To address these problems, we develop an approach summarizing among-patch variation in structural connectivity across a continuum of scales. We do this by first treating a connectivity metric (e.g. habitat area around a patch) as a continuous function of a scale-defining variable (e.g. distance) for a number of patches. We then extract and summarize information present in the shapes of the resulting collection of “patch connectivity functions”, using methods for functional data analysis (functional principal component analysis, fPCA). We apply the approach to a data set of 36 islands and show that it is possible to effectively summarize the among-patch variation in structural patch connectivity across spatial scales using only a small number of functional principal components. We also show how our functional data analysis approach to connectivity metrics can be useful (i) as an information tool for decisions regarding the design of protected area networks and (ii) in designing spatially explicit ecological studies including multiple species (e.g. metacommunity studies). We explore relationships with widely used methods in landscape ecology and show how continuous function representations can reveal information hidden in single value applications of metrics. The usefulness of the approach for analyses of functional connectivity is discussed. We conclude that the approach provides a powerful methodology to represent variation in connectivity across spatial scales that will serve