Paired Home Range Size, Overlap, Joint-Space Use, and Similarity Indexes Justin Clapp ZOO 5890 Objective - quantify changes in home range

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Godfrey Boyd
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1 Paired Home Range Size, Overlap, Joint-Space Use, and Similarity Indexes Justin Clapp ZOO 5890 Objective - quantify changes in home range distributions using paired GPS location data in R The Brownian Bridge Movement Model (BBMM) is a home range estimator that takes into account animal motion variance, GPS error, and the time and distance between successive locations to provide a cell based output that estimates relative probability of occurrence across a landscape. This cell based output is known as a Utilization Distribution (UD), which provides the spatial extent of the animal home range as well as a measure of the intensity of occurrence within the extent of the home range. The associated R code begins by importing animal location files and creating a TimeLag column (the time elapsed between successive locations in minutes). Starting with a SQL or Access database or a table that includes all animal locations, the provided code runs a nested loop where the first loop pulls out data for i th bighorn, and runs a nested loop which calculates the time difference between successive locations for that bighorn. It then sets the first location TimeLag equal to the second to ensure all rows of data include a TimeLag value (necessary for BBMM function). It then saves this data in a new column in the animal location database before moving to the next animal. These data are necessary to run the BBMM function. We aim to overlap paired BBMM utilization distributions perfectly to conduct cell by cell calculations to obtain desired outputs. Therefore, we need to set the extent and cell size of the BBMM output based on UTMs that encompass each pair of animal locations (incorporating an adequate buffer). This is done for each pair of UDs. The BBMM is based on a Gaussian distribution, where the probability calculations never actually reach zero (infinite probabilities exist). However, the BBMM function runs probabilities to machine precision (e-15) and determines all other probabilities as zero. Because of the extensive amount of time needed to run a BBMM (based of # of locations and desired cell size), it is not recommended to run the BBMM function in a loop. Therefore, much of the BBMM code provided is soft coded. For each BBMM, we will manually manipulate the desired extent (identical for each pair), as well as the timeframe for each comparison before running the model. For example, if animals migrate seasonally and one UD is based on location data acquired from November - May, we may want to restrict the paired UD if it incorporates location data collected for an entire year. It really depends on the goal of the researcher to determine if comparisons will be made by season, by year, or least common timeframes. These alterations are done manually by subsetting desired rows before being input to the BBMM function. After the BBMM has completed, the code saves the BBMM object output as well as the animal locations to a desired folder. Next, the code loads in the saved BBMM object and locations to the workspace, and forces the data into a raster layer, a matrix, and a data frame of the probability values that correspond with differing home range contours of the UD ( rasterlevel data frame) using the locations and BBMM object via the bbmm.contour function. Each pair of BBMM objects is loaded in separately, with each manually coded in the workspace as either pre or post. These outputs can then be analyzed in a variety of ways, including viewing raster plots as 2D or 3D

Post-Fire Pre-Fire surfaces or scatterplots, viewing different contour levels of UDs, overlaying UDs, exporting rasters or contour shapefiles into ArcMap, exporting matrices into ArcScene for 3D

2 Post-Fire Pre-Fire surfaces or scatterplots, viewing different contour levels of UDs, overlaying UDs, exporting rasters or contour shapefiles into ArcMap, exporting matrices into ArcScene for 3D viewing, etc. (e.g. Figure 1, Figure 2, Figure 3). A B Figure 1. Program R plots of BBMM 2-dimensional utilization distribution rasters (A) and associated contour lines (B) before and after fire-mediated habitat alterations for bighorn ewe #9 in the Seminoe Mountains, WY.

3 Figure 2. Dynamic 3D scatterplot in Program R of BBMM relative probability overlap (prefire = blue, postfire = red) from bighorn ewe #9 in the Seminoe Mountains, WY. Figure 3. Bighorn ewe #9 BBMM UD surface overlays imported from R and plotted in ArcScene. (A) Overlay of surfaces before and after fires. Note that due to the relative probability of occurrence, the post-fire distribution expanded (red) at the expense of a decrease in use in core areas (blue and red overlap). (B) UD surface showing the difference in probability of occurrence after fires. Increases in use after fires are shown in green, where decreases in use depicted in pink.

Overlaying UDs can provide great visual representations for comparing 3-dimentional surfaces, but it becomes increasingly difficult to summarize these data in an analysis.

4 Overlaying UDs can provide great visual representations for comparing 3-dimentional surfaces, but it becomes increasingly difficult to summarize these data in an analysis. Because the variation in probability of use, home range size, and home range overlap depends largely on the contour of the UD that is being examined, we aim to summarize the data based on multiple contour levels of the home ranges. The final portion of the code calculates multiple indexes and relative measurements for each pair of UDs and writes them to a.csv table. The pre and post UDs saved in the workspace are run in the loop. The loop begins by conducting raster calculations to determine comparative statistics (Table 1) at the j th contour of the UDs. Table 1. Statistics calculated for home range comparisons in the R code. Statistic Explanation 2D or 3D RelSize Relative change in home range size (1 indicates no change) 2D PreOvl Proportion of preud overlapped by postud 2D PostOvl Proportion of postud that is overlapped by preud 2D VI Volume of intersection (index of minimum joint-space use) 3D BA Bhattacharyya's Affinity (product based UD similarity index) 3D HD Hellinger's Distance (index of distance between distributions) 3D UDOI Utilization Distribution Overlap Index (product based index of degree of joint space use) 3D * Further information on these statistics are extensively discussed by Fieberg and Kochanny (2005). After calculating these statistics at the starting contour level (e.g. 95% home range), the loop reclassifies both pre and post UDs at the next chosen level (e.g. 90% contour; j th + 1 ). This is done by using the rastlevel data frame j value for the desired contour level in a conditional statement, where if the values of the UD cell are below the contour j value, they are set to equal zero. If they are above the contour value they remain unchanged. However, the remaining cells with probability values need to sum to one to remain a relative UD. Therefore, these cells are reclassified by dividing each cell value by the sum of the cell values in the UD. Within this loop it is easy to reclassify the UD at any contour level and plot the UD for visual inspection (e.g. Figure 4), or calculate any of the desired statistics individually. Figure 4. Program R BBMM UD raster plots of bighorn ewe #9 at a 99% contour level and reclassified to a 25% contour level.

5 Mean BA Similarity Index After both pre and post rasters are reclassified to the next contour level, the loop recalculates the statistics. When the loop function is complete, we name the animal or pair ID and save to a.csv file. Then we are ready to run the loop with the next pair of UDs, and update the.csv file. The resulting data allows plots to be made that show how these indexes change across differing contours of the home ranges. Because we used paired distributions for multiple animals, we may then determine trends in these statistics that can be quantified with means, standard errors, and confidence intervals. For example, we find the mean similarity in utilization distributions show a linear decrease at increasing home range contours (Figure 5) mean 95% CI % 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 99% Home Range Contour Figure 5. Mean Bhattacharyya's Affinity (similarity index) across increasing home range contours (core range). It should be noted that there may be a much easier way to conduct similar comparisons, especially if you are not comparing paired distributions, but independent distributions. The adehabitat package in R has a function called kerneloverlap that will calculate these statistics based on a kernel density UD at any contour you desire. It also allows multiple animals to be included and will provide a matrix for all the included animals for the desired statistic. Because people wanted these statistics based on BBMM (or other) UDs, a function was added to this package called kerneloverlaphr, which allows UDs to be used as input. However, this requires a different BBMM function to be used, and this package is finicky about the object class it will accept. If multiple animal or population UDs are to be compared, I would recommend using the adehabitat functions. However, my goal was to compare paired UDs at many different contours, and this code has the advantage of recalculating multiple statistics at multiple contours. I am using this code to compare distributions temporally for the same animal before and after habitat

6 alterations, but it may have other uses, such as comparing day and night distributions for the same animal. It may also be important to note that cell size can influence the results of these statistics. The tradeoff comes when calculating BBMMs at high resolution (e.g. 1m x 1m) could take days to run, and commonly crash the program or max out RAM for the computer. However, at course resolutions (e.g. 100m x 100m) the accuracy of the statistics, particularly at highly concentrated contour levels (e.g. small area 5% core home ranges), may not yield the desired accuracy. Overall, this code calculates the statistics at differing scales, but does not change the resolution of the cell size as home range contour restrictions occur.

7 LITERATURE CITED Fieberg, J., C. O. Kochanny Quantifying home-range overlap: the importance of the utilization distribution. Journal of Wildlife Management 69:

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