Question Asked
I am interested in how the spatial pattern of non-forested areas influences invasibility of forest plots by the exotic annual grass vententata (Ventenata dubia). For exercise 3 I asked the question, how are forest plots with high and low ventenata cover related to the spatial pattern of canopy openness?
Tools and Approaches Used
To explore this question, I performed a Ripley’s cross-K between ventenata forest plots with high and low cover and non-forest areas (Ripley 1976). This analysis is used to interpret spatial relationships between two point patterns. I used ArcGIS and R to answer the question following the steps below:
- I added my sample plots with ventenata cover and coordinates and fire perimeters into ArcGIS.
- To generate non-forest points, I added canopy cover raster data for the study area into ArcGIS with values ranging from 0 to 95% canopy cover.
- I buffered the sampled fire perimeters by 3000m using the “buffer” tool and generate 200 random points, not closer than 100m in each buffer using the “create random points” tool in ArcGIS.
- I extracted the raster values to the random points using the “values to points” tool, and extracted points that had <10% canopy cover into a new layer file for open areas.
- I then extracted my sample plots only from forested areas into a forest_plots layer.
- I exported these plots and the random points into a data frame with spatial data and an indicator for sites with high ventenata (>15% cover), low ventenata (0-15% cover), or random open points with no ventenata recorded (labeled “high”, “low”, and “open” respectively).
- I performed a Ripleys cross K between the high and low ventenata forest plots and non-forest “open” areas and plotted the response in R with the package “spatstat” (Thanks, Stephen C. for sharing R code!). I repeated the analysis individually for three sampled fires (Fox, South Fork, and Canyon Creek) to avoid picking up the inherently clustered spatial pattern of my sample plots and overshadowing the research question. However, I also performed the analysis on the entire sample area to view where issues arise when ignoring a clustered sample design and compare to results from individual fires.
- In order to perform the cross Ripleys K on each sampled fire, I first had to establish rectangular “windows” around each fire and provide the xy coordinates for the vertices using tools in ArcGIS depicted below.
Results & Discussion
Most annual grass species prefer areas of low canopy cover. These open areas can, however, act as source populations for invasion into more resistant forested areas. I hypothesized that ventenata (an annual grass) abundance in forested areas would increase with increased proximity and abundance of open areas near the sampled forest (i.e. sites with high ventenata cover in forested areas would be more spatially “clustered” around non-forest areas than sites with low ventenata cover).
The results of my Ripley’s cross-K show that the spatial relationship between sites with high/ low ventenata cover differs between fires. At the Fox fire (FOX), high and low sites closely follow the projected Poisson distribution when crossed with open areas, suggesting that ventenata abundance in forest sites is not related to nearby open areas. However, in the Corner Creek (CC) and South Fork (SF) fires, heavily invaded forest sites are more clustered around open points and low sites are more dispersed around open points than would be expected by chance. I may not have seen a relationship between open areas and high/ low sites at the fox fire because of the relatively low number of forest sample plots (n = 5 high and 4 low). Another explanation could be that I am missing an interaction between fire and invasion by not accounting for canopy lost in forest plots as a function of fire. Analyzing burned vs. unburned forest plots (with fire as an additional driver of invasion) would have been ideal, but would have dropped the sample size too low to perform analyses.
When I performed the cross-K on the entire study area it shows strong clustering of both high and low plots around open areas. However, this is likely the result of the clustered spatial pattern of my sampling method (targeting specific burned areas), and less representative of the actual spatial relationship between ventenata invasion and canopy cover.
Critique of Method
Overall, I thought the cross-K was a useful method for evaluating the spatial relationship between two variables (ventenata cover and open areas). However, a method that could include interaction terms (burning) would probably have been more appropriate for this study. Additionally, the arrangement of sample plots made it difficult to evaluate overall patterns across the study region. It would have been a more useful analysis had my samples been evenly distributed across the region.
Ripley, B.D., 1976. The second-order analysis of stationary point processes. Journal of applied probability, 13(2), pp.255-266.
Claire, this is an interesting approach. I’m unsure whether it meets the assumptions required for Ripley’s K analysis: all point pattern methods require that the point locations are NOT determined by the researcher. To test the effect of adjacent openings given your clustered plot sample, could you ask whether the proportions of open space surrounding your plots differ between sites which have high ventenata vs. low ventenata? I agree, you do have an issue in that your sampling locations are quite clustered. In your final project, I would be interested to know how you will use what you have learned in these exercises to guide your hypothesis testing and field work in the coming summer.