Appendix B. Psuedo-absences generation.
The ability of an observer to detect dolphins is a function of the dolphin’s distance from the trackline and the sighting conditions. Beaufort Sea State (BSS) scale was used as a measure of sighting conditions in Florida Bay. BSS is an integer scale used to describe the sea conditions (wind speed and wave height) which affect the sightability of dolphins. For this study in Florida Bay, survey conditions ranged from a BSS 0 (flat calm) to BSS 4 (constant white caps). As conditions deteriorated from a BSS 0 to a BSS 4, the ability to detect a dolphin decreases and an observer is less likely to spot a dolphin further from the trackline. Using the program DISTANCE 5.0 (Thomas et al. 2005) probability of detection functions were created using sightings data from 2004 and 2005 relative to BSS and perpendicular distance from trackline. The analysis was run using Multiple Covariates Distance Sampling with BSS as the only covariate. The data set consisted of 99 sightings, 2228.6 km of trackline, and 543 samples. The optimal model, based on the lowest Akaike information criterion (AIC), was a hazard-rate model with a cosine expansion function, 5% truncation, and manually set intervals of 50 m. The resulting detection functions for BSS 0-4 were then used to generate pseudo-absences.
For each zone/year combination, 10× the number of sightings in each BSS class were created as pseudo-absences. The choice to generate 10× as many absences as presences was arbitrary, but due to the rarity of true sightings relative to the large amount of survey effort, the contrast between presence and absence locations was increased by generating more pseudo-absences according to stringent dispersal patterns. Moreover, through multiple trials it was determined that the ability of both the binomial Mantel Tests and GAMs to differentiate habitat characteristics between presence and absence points dramatically increased with a larger sample size while maintaining robustness despite an unbalanced sample (more absences than presences).
Each trackline was buffered out to 450 m because this was the maximum perpendicular sighting distance according to DISTANCE (five sightings were made at perpendicular distances between 450820 m, but these were considered outliers by the program). Each 450 m buffered polygon was segmented into consecutive 50 m distance from trackline intervals and then classified by BSS (0, 1, 2, 3, or 4). Using these polygons, the area of survey effort, on each survey day, in each BSS was calculated. Additionally, to prevent absence points from occupying the same habitat as actual sightings, a 450 m buffer was created around each sighting, within which no pseudo-absence point could be created.
Each probability of detection function relative to BSS and distance from trackline was used to calculate the percent area under the curve at each distance interval of 50 m. The percentage for each distance class was multiplied by 10× the number of sightings in the same BSS/zone/year class. This number of absences was then distributed between survey days proportional to the amount of area surveyed within each distance bin.
Finally, Hawth’s Tools in ArcGIS (Beyer 2004) was used to randomly distribute the correctly apportioned pseudo-absence points within each BSS class and distance from trackline bin for every survey day. In summation, 10× the number of sightings in each BSS/zone/year group were generated according to the probability of detection functions and randomly distributed in proportion to the amount of survey effort within each distance class bin.
Beyer, H. L. 2004. Hawth's Analysis Tools for ArcGIS.
Thomas, L., J. L. Laake, S. Strindberg, F. F. C. Marques, S. T. Buckland, D. L. Borchers, D. R. Anderson, K. P. Burnham, S. L. Hedley, J. H. Pollard, J. R. B. Bishop, and T. A. Marques. 2005. Distance. Research Unit for Wildlife Population Assessment, University of St. Andrews, UK.