GEOG 566

         Advanced spatial statistics and GIScience

May 23, 2017

Tutorial 2: Using kernel density probability surfaces to assess species interactions

Filed under: Tutorial 2 2017 @ 4:48 pm

Overview: question clarification and approach

Continuing my exploration of changes in cougar predation patterns in time periods with and without wolves, I wanted to expand my evaluation of spatial repulsion and/or shifts to examine how cougar kill site distributions related to wolf activity. I identified several elements in my data sets, besides the presence of wolves, which could produce a shift in kill density or distribution including: 1) catch-per-unit effort discrepancies (i.e. larger sample sizes of cougars (and kill sites) in one data set), or 2) time effects from seasonal distribution shifts (i.e. prey migration patterns). I accounted for catch-per-unit effort issues in tutorial 1, but need to account for seasonal variation in prey distribution as part of my analysis of wolf influence on cougar kill distribution. Density features continued to be a good tool to explore my presence only data (kill events). Studies of sympatric wolves and cougar have shown differences in the attributes of sites where each carnivore makes kills (slope, elevation, physiographic features), but I was interested in how cougar might be positioning themselves (e.g. where they are hunting and making kills) on the landscape relative to centers of wolf activity. Therefore, the next step in understanding my spatial problem was to determine if there were differences in when and where cougar were killing prey by asking:

Does wolf activity account for the distribution differences between pre- and post-wolf cougar kill sites?

For the purposes of this analysis the data would be “location, implicit” with the variable of interest (cougar kill sites) having a covariate (proximity or distance to wolf activity) measurable at each sampled location and the causal mechanism inferred from co-variation. Central areas of wolf activity could be identified from wolf kill density, estimated on a seasonal basis, and related to the distribution of cougar kill sites. A probability surface could be created from wolf kill density and used to calculate the proportion of pre- and post-wolf cougar kill sites within probability features as a proxy for the distribution of wolf activity. This relationship could then be compared as a joint proportion or as an expected/observed relationship across time periods. Alternatively, the isopleth polygon feature could be used to calculate a “distance-to-edge” feature relating each cougar kill to potentially increasing levels of wolf contact. This relationship could be evaluated between time periods and across seasons through ANOVA or regression.

My approach to this question was to relate the proportion of both pre- and post-wolf cougar kill sites (points) to wolf activity using the probability contours (polygon feature) of wolf kill site distribution (density raster) as a proxy for activity. I used several tools in ArcGIS, GME, and R to carry out this analysis. Geospatial Modeling Environment (GME) is a standalone application that makes use of ArcGIS shape files and R software to carry out spatial and quantitative analyses. It was created to take advantage of R computing and replaces the ‘Animal Movement’ plugin many movement ecologists made use of in previous versions of ArcGIS. GME allows a lot of flexibility in tasks related to dealing with large data sets and common analyses performed on animal location data (KDE, MCP, movement paths). Because it can operate as a GUI or command driven operator using R, it is user friendly and allows for iterative processes, quick manipulations of data, and combinations of these process not easily duplicated in Arc.



Prior to evaluating influences from wolf activity, it was necessary to address potential effects from seasonal shifts in prey distribution or density related to ungulate migration patterns. Therefore, the first step for this analysis was to subset kill data into winter (1 Nov – 30 Apr) and summer (1 May – 31 Oct) seasons. I used the ‘select by attribute’ feature in ArcGIS to subset each kill data set (wolf, cougar (pre-wolf), and cougar (post-wolf)) into season-specific shapefiles.


Figure 1. ArcGIS ‘select by attribute’ call from attribute table to subset data into season.

Similar to the procedure for tutorial 1, I used GME to create density and isopleth probability contours for wolf kill sites and the ‘countpntsinpolys’ command to add columns with the number of cougar kills (pre/post) to each seasonal wolf kill isopleth polygon. Finally, I used ArcMap to visualize the data and make a figure showcasing the process.


Figure 2. GME ‘kde’ call in the command builder GUI.



Visual examination of season-specific cougar kills relative to wolf kill activity centers added further evidence toward a spatial shift in the distribution of cougar kills between time periods with and without wolves (Figure 3). The magnitude of the repulsive effect appeared stronger in winter than summer, evident in the uniformly decreased proportions of cougar kills per probability contour of wolf activity, and increased proportion of kills outside any wolf activity between time periods with and without wolves (Table 1). The relationship appeared opposite in summer, with higher proportions of cougar kills observed in the post-wolf period than expected in all but core (25% probability surface) and outside (no wolf activity) areas (Table 2).


Figure 3. Visual comparison of seasonal wolf activity based on kill site density probability contours and the distribution of cougar kill sites across time periods with and without wolves.

Table 1. Winter wolf kill site probability contour attribute table. Isopleths represent the 25th, 50th, 75th, 95th, and 99th quartiles. ‘Out’ refers to areas outside the probability contour surface. Number of kills (No. Kills) is the number of cougar kill sites, and % Kills is the cumulative proportion of all cougar kills within each quartile class.


Table 2. Summer wolf kill site probability contour attribute table. Isopleths represent the 25th, 50th, 75th, 95th, and 99th quartiles. ‘Out’ refers to areas outside the probability contour surface. Number of kills (No. Kills) is the number of cougar kill sites, and % Kills is the cumulative proportion of all cougar kills within each quartile class.


Method Critique

Accounting for seasonal shifts in kill density improved visual interpretation of spatial patterns and reduced a factor that might mask influences of wolf activity. However, the observed shift in winter could still be due to shifts in prey populations as a behaviorally mediated prey response to wolves (i.e. the shift is related to prey responding to wolves, and cougar indirectly shifting distribution to follow prey). The shift could also be related to differences in prey species-specific distributions, as cougar prey predominantly on deer, but show seasonal selection of neonate elk calves in the summer, and wolves prey predominately on elk (i.e. the abundance of newborn calves in the summer creates spatial tolerance between wolves and cougar). The comparison of pre- to post-wolf cougar kill sites relative to the probability of wolf kills may be misleading, since the relationship is based on pre-wolf cougar kill data overlapping a density feature that didn’t exist (i.e. no wolves on the landscape at the time those kills were made). However, the comparison does provide some insight as the pre-wolf cougar kill distribution still represents a ‘prior’ distribution of cougar kills, and overlapping wolf activity demonstrates the proportion of kills we could expect if there were no competition (spatial avoidance/repulsion) between the two species. Using the probability contours as a ‘prior’ distribution of kill sites offered a more robust and meaningful measure to quantify the shift in cougar kill distribution. The method was useful and provide evidence toward the presence of a season-specific shift in where cougars are killing prey (i.e. the answer to my ‘question asked’ is yes, in winter), but the regression analysis discussed above may provide additional support.


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