Producing least‐cost paths

Within selected MCRs for each species, we ranked each 2.96‐km cell (i.e., native resolution of eBird Status and Trends products) by seasonal relative abundance and selected as the breeding and nonbreeding cores (i.e., high‐abundance clusters) the minimum number of cells that represented 30% of the total sum of cells (sensu Schuster et al., 2019; Lin et al., 2020) within each MCR (Figure ​(Figure2a).2a). Relative abundance models for the breeding and nonbreeding seasons for each of the focal species were expert‐reviewed and met performance standards of eBird Status and Trends products (Fink, Auer, Johnston, Ruiz‐Gutierrez, et al., 2020). We used these breeding and nonbreeding cores for initiation of LCPs (i.e., source of origin points) for postbreeding and prebreeding migration, respectively, because we were primarily interested in identifying major migratory pathways among population clusters. We designed this approach to incorporate two important attributes of identifying natural population structures in the absence of genetic data: abundance and spatial proximity (Rushing et al., 2016).

We randomly selected 50 grid cells within each breeding MCR core to serve as postbreeding migration origin points for species‐specific LCPs. Next, we randomly paired each origin point with a destination point in a randomly selected grid cell (n = 50) within nonbreeding MCR cores using the relative proportions estimated from the migratory connectivity analysis described earlier (Figure ​(Figure2b).2b). We then computed a probabilistic (i.e., randomized) LCP (Adriaensen et al., 2003; Storfer et al., 2007; Wang et al., 2009) between each breeding–nonbreeding core pixel pair that minimized the total cumulative cost, where the cost of moving between paired pixels was determined by the intervening distance weighted by a conductance surface representing average (i.e., arithmetic mean across weeks; see Appendix S1: Table S2) postbreeding occurrence probabilities obtained from eBird (Figure ​(Figure2c).2c). Thus, higher occurrence values during migration coincided with higher conductance. We chose to use occurrence probabilities as the conductance surface, rather than relative abundances, because abundance values for several focal species were highly right‐skewed (e.g., high‐abundance aggregations of migrating tree swallows), which resulted in LCPs directed toward regions of unusually high abundance, masking the known movements of smaller, regional populations.

To create biologically reasonable LCPs, we modified conductance surfaces by adding minimum conductance values where eBird occurrence probabilities were zero or had missing values. These conductance values varied across species to reflect relevant migratory behaviors (e.g., likelihood of long‐distance overwater movements). See Appendix S1 for more details on assigning values to each of the 12 focal species and the potential for customization in future analyses. Partial randomization of the deterministic LCPs was incorporated via a constrained random walk using the passage() function from the gdistance package in R (Van Etten, 2017). The passage function simulates movements from a starting location to an ending location, with movements between intervening cells governed by a random process superimposed on a cost surface. Random movements are derived from a probability distribution constrained by a parameter that controls the degree of randomization (Saerens et al., 2009). During model development, we evaluated a wide variety of values and algorithms for choosing the degree of randomization and ultimately opted to use half the minimum conductance value, which resulted in individual probabilistic LCPs that had a longitudinal range of ~100 km (see Appendix S1 for more details on the partial randomization process).

Each set of paired grid cells yielded one raster layer (rescaled to a 26.6‐km resolution due to computational demands; see Appendix S1) with values between zero and one that described the probability of passage (i.e., LCP index) through a given grid cell during postbreeding migration. We repeated this process for the 50 sets of paired grid cells for each breeding MCR and then repeated the entire procedure in reverse (i.e., nonbreeding season origin points paired with breeding season destination points) using average prebreeding eBird occurrence probabilities as the conductance surface to produce LCP indices during prebreeding migration. Finally, we averaged (i) across the 50 probabilistic LCP surfaces for each season‐specific MCR and (ii) across all nonbreeding or breeding MCRs to illustrate probable pathways during pre‐ and postbreeding migrations, respectively, for each species (Figure ​(Figure2d).2d). For example, for a species with 10 breeding MCRs, 10 × 50 = 500 total LCPs were averaged to produce a postbreeding migration surface.