*Ecological Archives* C006-046-A1

Matthew J. Clement, Joy M. O'Keefe, 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}/Σ*S*_{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}/Σ*S*_{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.

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*To model Markovian movement, we adjusted location scores so that *S*_{r} = *b* + *Ir*×*h* + *a*×log(*n*_{r}+1), where *I*_{r} is an indicator variable that equals 1 if the bat to be assigned was at location *r* the previous time period and 0 otherwise, and *h* is the strength of attraction to the previously occupied location. In our simulation of Markovian movement, we set *a* = 3200 and *h* = 26,500 and compared this to *a* = 360 and *h* = 0.

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