Exercise 1: What is the spatial pattern of western hemlock dwarf mistletoe at the Wolf Rock reference stand?

For Exercise 1, I wanted to analyze the spatial pattern of western hemlock dwarf mistletoe infections in live western hemlocks on my 2.2 ha reference stand (Wolf Rock). This was without considering any attributes of the western hemlock trees themselves. Simply, what was the spatial pattern of infection?

To answer this I used the “Average Nearest Neighbor” tool in the Spatial Statistics toolbox in ArcMap. This tool calculates a z-score and a p-value from that z distribution. This is a commonly used method in dwarf mistletoe literature for assessing the clustering of infection centers. Also, the equations for this tool assume that points are free to locate wherever in space and that there are no barriers to spread.

ArcMap makes running these analyses very simple so I created a selection of infected trees (red dots), created a new feature, and then ran the tool. The p-value from my test was 0.097 and my Nearest Neighbor Index was 0.970, indicating that the spatial pattern of the infections are somewhat clustered with an alpha of 0.10.

Average Nearest Neighbor is a good test for analyzing whether or not a set of coordinates are clustered. The degree of clustering of may be harder to interpret as a lower p-value may not necessarily mean points are more clustered. Also I was unable to see where my clusters are, and if my intuitions match the analysis (see map). One other important consideration is the study area. Changes in analysis area can drastically change the result of your clustering analysis (i.e. larger study areas may make data look more clustered). Lastly, there was no option for edge correction. This may have skewed some of the clustering results along the edge of my study site and 2.2 ha is pretty small to be subsampled without losing a lot of my data.


After confirming that my infections were clustered, I wanted to see if the pattern I saw in my map, was actually on the ground. I wanted to know, where are infected trees clustered with infected trees and where are uninfected trees clustered with uninfected trees? Again, this was without considering any attributes of the western hemlock trees themselves.

I used the “Optimized Hot Spot Analysis” tool in the Mapping Clusters toolbox to analyze the incidence of infection data (0 = absence, and 1 = presence). The Optimized Hot Spot Analysis tool can automatically aggregate incidence data that are normally not appropriate for hot spot analysis. It also calculates several other metrics for me that made analysis easy. I could take these automatically calculated metrics and alter them in a regular hot spot analysis if needed.

This map displays clustering that matched up closely with my intuitions from Map 1. On the left, the blue values show a cluster of uninfected trees that are closely clustered with other uninfected trees. The larger swath on the right show a cluster of trees that are closely clustered with other infected trees. In the middle a mix of uninfected trees and infected trees are mixed without displaying any significant clustering. Lastly, small clusters in the top left and bottom left of infected trees were identified. These clusters may be edge of larger clusters outside my stand, or lightly infected trees that are starting a new infection center. These results will be extremely valuable in informing my steps for Exercise 2 because I can assess the conditions of both patches and determine differences between the two. I can also determine if distance to the refugia impact the clustering of infection because it appears the infected cluster is closer to the fire refugia.

The hot spot analysis was extremely useful for analyzing and displaying the information I needed about the clustering and was very useful for building off of the Average Nearest Neighbor analysis.

My data set also included a severity rating for dwarf mistletoe infected western hemlocks in my study site. I ran a similar hot spot analysis to above to determine if there were any similarities with how severity played out in the stand compared to solely incidence data. My data ranged from 0 – 5, 0 indicating uninfected trees and 5 indicating most heavily infected. These are classified data, not continuous but still appropriate for the optimized hot spot analysis. Western hemlock dwarf mistletoe forms infection centers, starting from a residual infected western hemlock that survived some disturbance. From there the infection spreads outwards. Another facet of infection centers is that the most heavily infected trees are almost always aggregated in the center of the infection center and infection severity decreases as you move towards the outside of the infection center. This is intuitive when you think about infected trees in terms of the time they’ve been exposed to a dwarf mistletoe seed rain: the trees in the center of the infection center likely have been exposed to infectious seed the longest. These trees can be rated using a severity rating system that essentially determines the proportion of tree crown infected. This is calculated in a way that gives a rating that is easily interpretable, in this case, 0-5.

This third map tells me about how severity is aggregated in the stand. I can see that the wide swath in the middle of the stand, associated with the fire refugia, has the largest aggregation of severely infected trees. This is what I expected in the stand because the trees in the fire refugia survived the fire and provide an infectious seed source for the post-fire regeneration. Also, on the edges of this high severity cluster, are lower severity values indicating the expected pattern of infection centers are playing out. The west side of the stand shows a large clustering of low severity ratings. We can see that the high density of uninfected trees, falls into our cold spot of low or no severity. Interestingly, the hot spot of trees found previously  in the southwest corner, is actually a cluster of low severity trees. This may be a new infection center forming or an exterior edge of another infection center outside the plot.  Lastly, the two pockets of low severity on the east side of the stand are more distinct when considering their severity.

This second application of hot spot analysis tells another story about my data and how dwarf mistletoe is patterned spatially. The non-significant swath in the center of my stand using the incidence data turns out to be a significant clustering of highly infected trees among other new observations.


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2 thoughts on “Exercise 1: What is the spatial pattern of western hemlock dwarf mistletoe at the Wolf Rock reference stand?

  1. jonesju

    Stephen, very effective use of hotspot analysis. As we’ve discussed the next step for Ex 2 is to accumulate the area within mapped fire refugia as a function of distance from 5 points each in the middle of the hot and cold spots (think about how to select these randomly). Also, please check how the fire refugia poylgons were determined. They must be based on individual trees – but there may be diferent ways to represent the fire refugia, including as surviving older trees (points) which would create interesting potential Ex 2 and 3 analyses.

  2. jonesju

    hi Stephen, good analysis. can you please reformat following the instructions for the Exercise? (see Canvas).

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