Ecological Archives C006-046-A1

Matthew J. Clement, Joy M. O'Keefe, and Brianne Walters. 2015. A method for estimating abundance of mobile populations using telemetry and counts of unmarked animals. Ecosphere 6:184. http://dx.doi.org/10.1890/es15-00180.1

Appendix A. Details of social attraction modeling.

This appendix explains how we modeled social attraction. The process is largely arbitrary, but the results generally conform to typical aggregation patterns in bat species. Each location r was assigned a score S_r, according to S_r = b + a×log(n_r+1), where b is an arbitrary base score, a is the level of attraction, n_r is the number of animals at that location, and log is the natural logarithm. One animal was randomly selected and assigned to a random location following a multinomial distribution, with the probability at each location = S_r/ΣS_r. Location scores were updated (because n_r has changed at one location) and a second animal was randomly selected and assigned. This process repeated until all animals were assigned a location. Each survey period, we assigned all animals to locations again.

For example, if the base score was b = 20, then the initial score for each location was S_r = 20 + a×log(0+1) = 20. If there were r = 20 locations, then the probability of being assigned to each location was S_r/ΣS_r = 0.05. After assigning the first animal to a location, and assuming a = 800, then the updated scores remained S_r = 20 at 19 locations, while equaling S_r = 20 + 800×log(1+1) = 575 at the location with one animal. At the location with one animal, the probability of assigning the second animal would be 575/955 = 0.60, while at each of the other 19 locations (with no animals), the probability would be 20/955 = 0.02. If more animals join a location, the score would continue to increase, but at a diminishing rate, due to the logarithm. We found this approach worked well, but other formulas could be substituted, such as S_r = b + a× n_r or S_r = b + exp(a× n_r). We set b = 20 and a equal to 400, 800, or 1600 in the low, medium, and high social attraction scenarios.

To model two separate social units, we modified the score formula above so that S_r = b + a1×log(n_r1+1) + a2×log(n_r2</i>+1). In this case, n_r1 is the number of animals at location r from the same social unit as the animal that is about to be assigned, and a1 is the relatively high attraction to that social unit; n_r2 is the number of animals at location r that do not share a social unit with the animal that is about to be assigned, and a2 is the relatively low (or negative) attraction to those animals. In our simulation of two social units, we set a1 = 800 and a2 = -21, and we compared this to one social unit with a = 450.