Quantifying the strength of migratory connectivity

Technological advancements have spurred rapid growth in the study of migratory connectivity, the linkage of individuals and populations between seasons of the annual cycle. The strength of migratory connectivity is a measure of the co-occurrence of populations throughout the annual cycle and can be represented by a correlation of the distances between individuals during one season and another (Mantel correlation, r(M)). However, measurement of seasonal distributions most often involves incomplete sampling and use of technologies that vary in accuracy and precision. For these reasons, we expanded r(M) to measure the strength of migratory connectivity (MC) with population-specific transition probabilities that can be derived from many data types and uneven sampling. We explore the sensitivity of MC to possible real-world variation in input parameters: transition probabilities, abundance among regions, spatial arrangement of regions, and sample sizes. We compare MC to r(M), present a series of resampling approaches for propagating uncertainty in input values into estimation of MC and r(M), and validate the method with bird tracking data. Migratory connectivity was negative when populations are further apart between seasons, positive when populations remain together between seasons, and zero when populations have no patterns in distribution between seasons. MC is most sensitive to transition probabilities and spatial arrangement of regions and performs better than r(M) when sampling effort is not proportional to true abundance, and when the strength of migratory connectivity varies across the range of the species. Our estimators for MC and r(M) performed well across several data types. We hope that these methods and the MigConnectivity r package will facilitate quantitative comparisons of migratory connectivity across studies, data types, and taxa to better understand the causes and consequences of the seasonal distributions of populations. Several study design recommendations emerge from our simulations: (1) incorporate abundance among regions when sampling is not proportional; (2)measure transition probabilities across as much of the range as logistically possible; (3) define study regions with either biological information about population delineation, or use discrete study locations as centroids of regions; and (4) estimate and report uncertainty from appropriate sources of sampling and process errors.