Using isolation-by-distance to jointly estimate effective population density and dispersal distance: a practical evaluation using bumble bees

Effective population density and intergenerational dispersal distance are key aspects of population biology, but obtaining empirical estimates of these parameters can be difficult. This is especially true for my study taxa, wild bees. In this paper, I apply and evaluate an existing but underutilized method to estimate the effective density and dispersal distance of bumble bees (Bombus, Apidae). Specifically, using 10 datasets of bumble bees in North America, I use the relationship between genetic isolation-by-distance and Wright’s neighborhood size to define a density-dispersal isocline—that is, a curve describing pairs of density and dispersal values consistent with observed rates of isolation-by-distance. These parameters are inversely related; as one increases, the other decreases. I then use outside estimates of bumblebee dispersal distances to make more specific estimates of effective colony density. Compared to some prior estimates of census density (100s to 1000s colonies/km2), my estimated effective colony densities were very low (1–41 effective colonies/km2). I also hypothesize, however, that these estimates are affected by the spatial extent of sampling, due to scale-dependent patterns in the distribution of individuals. To test this hypothesis, I subsampled each dataset to simulate varying study extent, and repeated my analysis. Within populations, effective densities tended to decrease when measured across larger spatial extents. Altogether, I demonstrate a useful and under-appreciated tool for studying population biology, especially of small, mobile animals like bees, but also show that researchers must interpret their results carefully within the context of their study design.

Methods
The data on *Bombus impatiens *workers from New Jersey, USA, were collected by me in the summers of 2020 and 2021. I extracted DNA using a bead-based extraction and amplified 11 microsatellite loci. These PCR products were analyzed using fragment analysis by the Rutgers Medical School Genomics Center. I assigned genotypes by first manually defining allele bins, then having software automatically assign allele IDs, and then manually checking allele IDs. Approximately 100 specimens were re-analyzed to assess error rates, which were all < 1%. Using these genotypes, I used the program Colony to determine siblishingship among workers. This dataset includes the full table of all genotypes and another that is filtered to only one worker from each colony. The family assignment output file from Colony is also included. There is also a table that includes geographic location and date of collection for each specimen.

The other nine datasets were collected and processed by other authors. The original works in which these data were published are cited in the Related Works section. In short, these data include microsatellite or SNP genotypes for individual Bombus workers. These have been previously filtered to only include one worker per colony (i.e., no siblings).