BACKGROUND

For those who have not seen my previous posts, my research involves building a model to simulate the spread of black stain root disease (a disease affecting Douglas-fir trees) in different landscape management scenarios. Each of my landscapes are made up of stands assigned one of three forest management classes. These classes determine the age structure, density, thinning, and harvest of the stands, factors that influence probability of infection.

 QUESTION

Are spatial patterns of infection probabilities for black stain root disease related to spatial patterns of forest management practices via the connectivity structure of the network of stands in my landscape?

TOOLS AND APPROACH

 I decided to look at how landscape connectivity influenced the spatial relationship between forest management practices and infection probabilities. This approach builds off of a network approach based in graph theory (where each component of the landscape is a “node” with “edges” connecting them) and incorporates concepts from landscape ecology regarding distance-dependent ecological processes and the importance of patch characteristics (e.g., area, habitat quality) in the contribution of patches to the connectivity of the landscape. I used ArcMap, R, and a free software called Conefor (Saura and Torné 2009) to perform my analysis.

 DESCRIPTION OF STEPS I FOLLOWED TO COMPLETE THE ANALYSIS

 1. Create a mosaic of the landscape

The landscape in my disease spread model is a torus (left and right sides connected, top and bottom are connected). The raster outputs from my model with stand ID numbers and management classes do not account for this and are represented as a square. Thus, in order to fully consider the connectivity of each stand in the landscape, I needed to tile the landscape in a 3 x 3 grid so that each stand at the edge of the stand map would have the correct spatial position relative to its neighbors beyond the original raster boundary. I did this in R by making copies of the stand ID raster and adjusting their extent. In ArcMap, I then assigned the management classes to each of those stands, converting to polygon, using the “Identity” tool with the polygon for management class, and then using the “Join Field” tool so that every stand with the same unique ID number would have the relevant management class assigned. If I had not done this step, then the position of stands at the edge of the raster in the network would have been misrepresented.

2. Calculate infection probability statistics for each stand

I then needed to relate each stand to the probability of infection of trees in that stand (generated by my model simulation and converted to point data in a previous exercise). In ArcMap, I used the “Spatial Join” tool to calculate statistics for infection probabilities in that stand, because each stand contains many trees. Statistics included the point count, median, mean, standard deviation, minimum, maximum, range, and sum.

3. Calculate the connectivity of each stand in the network of similarly managed stands in the landscape

3a. For this step, I used the free software Conefor, which calculates a variety of connectivity indices at the individual patch and overall landscape level. First, I used the Conefor extension for ArcMap to generate the input files for the Conefor analysis. The extension generates a “nodes” file for each feature and a “connection” file, which contains the distances between features a binary description of whether or not a link (“edge”) exists between two features. One can set the maximum distance for two features to be linked or generate a probability of connection based on an exponential decay function (built-in feature of Conefor, which is an incredible application). For my analysis, I performed connectivity analyses that only considered features to be linked if (i) they had the same management class and (ii) there were no more than 10 meters of distance between the stand boundaries. Ten meters is about the upper limit for the maximum likely root contact distance between two Douglas-fir trees.

3b. For each management class, I ran the Conefor analysis to calculate multiple metrics. I focused primarily on:

• Number of links in the network
• Network components – Each component is a set of connected patches (stands) that is internally connected but has no connection to any other set of patches.
• Integral Index of Connectivity (IIC) – Essentially, this index gives each patch (stand) a value in terms of its importance for connectivity in the network based on its habitat attributes (e.g., area, habitat quality) and its topological position within the network. For this index, higher values indicate higher importance for connectivity. This is broken into three non-redundant components that sum to the total IIC:
  • IIC intra – connectivity within a patch
  • IIC flux – area-weighted dispersal flux
  • IIC connector – importance of a patch for connecting other patches in the network) (Saura and Rubino 2010)

4. Analyze the relationship between connectivity metrics and infection probabilities

I reduced the mosaic to include only feature for each stand, eliminating those at the periphery and keeping those in the core. I confirmed that the values were similar for all of the copies of each stand near the center of the mosaic. I then mapped and plotted different combinations of connectivity and infection probability metrics to analyze the relationship for each management class (Fig. 1, Fig. 2).

Fig. 1. Map of IIC connectivity index and mean infection probability for the extensively managed stands.

RESULTS

I generally found no relationship between infection probability and the various metrics of connectivity. As connectivity increased, infection probabilities did not change for any of the metrics I examined (Fig. 2). I would like to analyze this for a series of landscape simulations in the future to see whether patterns emerge. I could also refine the distance used to generate links between patches to reflect the dispersal distance for the insects that vector the disease.

Fig. 2. Plots of infection probability statistics and connectivity metrics for each of the stands in the landscape. Each point represents one stands in the randomly distributed landscape, with extensively managed stands in red, intensively managed stands in blue, and old-growth stands in green.

CRITIQUE OF THE METHOD – What was useful, what was not?

I had originally planned to use the popular landscape ecology application Fragstats (or the R equivalent “landscapemetrics” package), but I ran into issues. As far as I could tell (though I may be incorrect), these options only use raster data and consider one value at a time. What I needed was for the analysis to consider groups of pixels by both their stand ID and their management class, because stands with the same management class are still managed independently. However, landscapemetrics would consider adjacent stands with the same management class to be all one patch. This meant that I could only calculate metrics for the entire landscape or the entire management class, which did not allow me to look at how each patch’s position relative to similarly or differently managed patches related to its probability of infection. In contrast, Conefor is a great application that allows for calculation of a large number of connectivity metrics at both the patch and landscape level.

References

Saura, S. & J. Torné. 2009. Conefor Sensinode 2.2: a software package for quantifying the importance of habitat patches for landscape connectivity. Environmental Modelling & Software 24: 135-139.

Saura, S. & L. Rubio. 2010. A common currency for the different ways in which patches and links can contribute to habitat availability and connectivity in the landscape. Ecography 33: 523-537.