Author Archives: Adam Bouche

About Adam Bouche

Just a human.

Final project: Washing out the (black) stain and ringing out the details

BACKGROUND

In order to explain my project, especially my hypotheses, some background information about this disease is necessary. Black stain root disease of Douglas-fir is caused by the fungus Leptographium wageneri. It infects the roots of its Douglas-fir host, growing in the xylem and cutting the tree off from water. It spreads between adjacent trees via growth through root contacts and grafts and long-distance via insects (vectors) that feed and breed in roots and stumps and carry fungal spores to new hosts.

Forest management practices influence the spread of disease because of the influence on (i) the distance between trees (determined by natural or planted tree densities); (ii) adjacency of susceptible species (as in single-species Douglas-fir plantations); (iii) road, thinning and harvest disturbance, which create suitable habitat for insect vectors (stumps, dead trees) and stress remaining live trees, attracting insect vectors; and (iv) forest age distributions, because rotation lengths determine the age structure in managed forest landscapes and younger trees (<30-40 years old) are thought to be more susceptible to infection and mortality by the disease.

RESEARCH QUESTION

How do (B) spatial patterns of forest management practices relate to (A) spatial patterns of black stain root disease (BSRD) infection probabilities at the stand and landscape scale via (C) the spatial configuration and connectivity of susceptible stands to infection?

In order to address my research questions, I built a spatial model to simulate BSRD spread in forest landscapes using the agent-based modeling software NetLogo (Wilensky 1999). I used Exercises 1-3 to focus on the spatial patterns of forest management classes. Landscapes were equivalent in terms of the proportion of each management class and number of stands, varying only in spatial pattern of management classes. In the exercises, I evaluated the relationship between management and disease by simulating disease spread in landscapes with two distinct spatial patterns of management:

  • Clustered landscape: The landscape was evenly divided into three blocks, one for each management class. Each block was evenly divided into stands.
  • Random landscape: The landscape was evenly divided into stands, and forest management classes were randomly assigned to each stand.

MY DATA

I analyzed outputs of my spatial model. The raster files contain the states of cells in forest landscapes at a given time step during one model run. States tracked include management class, stand ID number, presence/absence of trees, tree age, probability of infection, and infection status (infected/not infected). Management class and stand ID did not change during the model run. I analyzed tree states from the last step of the model run and did not analyze change over time.

Extent: ~20 hectares (much smaller than my full models runs will be)

Spatial resolution: ~1.524 x 1.524 m cells (maximum 1 tree per cell)

Three contrasting and realistic forest management classes for the Pacific Northwest were present in the landscapes analyzed:

  • Intensive – Active management: 15-foot spacing, no thinning, harvest at 37 years.
  • Extensive – Active management: 10-foot spacing, one pre-commercial and two commercial thinnings, harvest at 80 years.
  • Set-aside/old-growth (OG) – No active management: Forest with Douglas-fir in Pacific Northwest old-growth densities and age distributions and uneven spacing with no thinning or harvest.

HYPOTHESES: PREDICTIONS OF PATTERNS AND PROCESSES I LOOKED FOR

Because forest management practices influence the spread of disease as described in the “Background” section above, I hypothesized that the spatial patterns of forest management practices would influence the spatial pattern of disease. Having changed my experimental design and learned about spatial statistics and analysis methods throughout the course, I hypothesize that…

  • The “clustered” landscape will have (i) higher absolute values of infection probabilities, (ii) higher spatial autocorrelation in infection probabilities, and (iii) larger infection centers (“hotspots” of infection probabilities) than the “random” landscape because clustering of similarly managed forest stands creates continuous, connected areas of forest managed in a manner that creates suitable vector and pathogen habitat and facilitates the spread of disease (higher planting densities, lower age, frequent thinning and harvest disturbance in the intensive and extensive management). I therefore predict that:
    • Intensive and extensive stands will have the highest infection probabilities with large infection centers (“hotspots”) that extend beyond stand boundaries.
      • Spatial autocorrelation will therefore be higher and exhibit a lower rate of decrease with increasing distance because there will be larger clusters of high and low infection probabilities when stands with similar management are clustered.
    • Set-aside (old-growth, OG) stands will have the lowest infection probabilities, with small infection centers that may or may not extend beyond stand boundaries.
      • Where old-growth stands are in contact with intensive or extensive stands, neighborhood effects (and edge effects) will increase infection probabilities in those OG stands.
    • In contrast, the “random” landscape will have (i) lower absolute values of infection probabilities, (ii) less spatial autocorrelation in infection probabilities, and (iii) smaller infection centers than the “clustered” landscape. This is because the random landscape will have less continuity and connectivity between similarly managed forest stands; stands with management that facilitates disease spread will be less connected and stands with management that does not facilitate the spread of disease will also be less connected. I would predict that:
      • Intensive and extensive stands will still have the highest infection probabilities, but that the spread of infection will be limited at the boundaries with low-susceptibility old-growth stands.
        • Because of the boundaries created by the spatial arrangement of low-susceptibility old-growth stands, clusters of similar infection probabilities will be smaller and values of spatial autocorrelation will be lower and decrease more rapidly with increasing lag distance. At the same time, old-growth stands may have higher infection probabilities in the random landscape than in the clustered landscape because they would be more likely to be in contact with high-susceptibility intensive and extensive stands.
      • I also hypothesize that each stand’s neighborhood and spatial position relative to stands of similar or different management will influence that stand’s infection probabilities because of the difference in spread rates between management classes and the level of connectivity to high- and low-susceptibility stands based on the spatial distribution of management classes.
        • Stands with a large proportion of high-susceptibility neighboring stands (e.g., extensive or intensive management) will have higher infection probabilities than similarly managed stands with a small proportion of high-susceptibility neighboring stands.
        • High infection probabilities will be concentrated in intensive and extensive stands that have high levels of connectivity within their management class networks because high connectivity will allow for the rapid spread of the disease to those stands. In other words, the more connected you are to high-susceptibility stands, the higher your probability of infection.

APPROACHES: ANALYSIS APPROACHES I USED

Ex. 1: Correlogram, Global Moran’s I statistic

In order to test whether similar infection probability values were spatially clustered, I used the raster package in R (Hijmans 2019) to calculate the global Moran’s I statistic at multiple lag distances for both of the landscape patterns. I then plotted global Moran’s I vs. distance to create a correlogram and compared my results between landscapes.

Ex. 2: Hotspot analyses (ArcMap), Neighborhood analyses (ArcMap)

First, I performed a non-spatial analysis comparing infection probabilities between (i) landscape patterns (ii) management classes, and (iii) management classes in each of the landscapes. Then, I used the Hotspot Analysis (Getis-Ord Gi*) tool in ArcMap to identify statistically significant hot- and cold-spots of high and low infection probabilities, respectively. I selected points within hot and cold spots and used the Multiple Ring Buffer tool in ArcMap to create distance rings, which I intersected with the management classes to perform a neighborhood analysis. This neighborhood analysis revealed how the proportion of each management class changed with increasing distance from hotspots in order to test whether the management “neighborhood” of trees influenced their probability of infection.

Ex. 3: Network and landscape connectivity analyses (Conefor)

I divided my landscape into three separate stand networks based on their management class. Then, I used the free landscape connectivity software Conefor (Saura and Torné 2009) to analyze the connectivity of each stand based on its position within and role in connecting the network using the Integrative Index of Connectivity (Saura and Rubio 2010). I then assessed the relationship between the connectivity of each stand and infection probabilities of trees within that stand using various summary statistics (e.g., mean, median) to test whether connectivity was related to infection probability.

RESULTS: WHAT DID I PRODUCE?

As my model had not been parameterized by the beginning of this term, I analyzed “dummy” data, where infection spread probabilities were calculated as a decreasing linear function of distance from infected trees. However, the results I produced still provided insights as to the general functioning of the model and factors that will likely influence my results in the full, parameterized model.

I produced both maps and numerical/statistical relationships that describe the patterns of “A” (infection probabilities), the relationship between “A” and “B” (forest management classes), and how/whether “A” and “B” are related via “C” (landscape connectivity and stand networks).

In Exercise 1, I found evidence to support my hypothesis of spatial autocorrelation at small scales in both landscapes and higher autocorrelation and slower decay with distance in the clustered landscape than the random landscape. This was expected because the design of the model calculated probability of infection for each tree as a function of distance from infected trees.

In Exercises 2 and 3, I found little to no evidence to support the hypothesis that either connectivity or neighboring stand management had significant influence on infection probabilities. Because the model that produced the “dummy” data limited infection to ~35 meters from infected trees and harvest and thinning attraction had not been integrated into infection calculations, this result was not surprising. In my full model where spread via insect vectors could span >1,000 m, I expect to see a larger influence of connectivity and neighborhood on infection probabilities.

A critical component of model testing is exploring the “parameter space”, including a range of possible values for each parameter. This is especially for agent-based models where there are complex interactions between many individuals that result in larger-scale patterns that may be emergent and not fully predictable by the simple sum of the parts. In my model, the disease parameters of interest are the factors influencing probability of infection (Fig. 1). In order to understand how the model reacts to changes in those parameters, I will perform a sensitivity analysis, systematically adjusting parameter values one-by-one and comparing the results of each series of model runs under each set of parameter values.

Fig.1. Two of the model parameters that will be systematically adjusted during sensitivity analysis. Tree susceptibility to infection as a function of age (left) and probability of root contact as a function of distance (right) will both likely influence model behavior and the relative levels of infection probability between the three management classes.

This is especially relevant given that in Exercises 1 through 3, I found that the extensively managed plantations had the highest values of infection probability and most of the infection hotspots, likely due to the fact that this management class has the highest [initial] density of trees. For the complete model, I am hypothesizing that the intensive plantations will have the highest infection probabilities because of high frequency of insect-attracting harvest and short rotations that maintain the trees in an age class highly susceptible to infection. In the full model, the extensive plantations will have higher initial density than the intensive plantations but will undergo multiple thinnings, decreasing tree density but attracting vectors, and will be harvested at age 80, thus allowing trees to grow into a less susceptible age class. In this final model, thinning, harvest length, and vector attraction will factor in to the calculation of infection probabilities. My analysis made it clear that even a 1.5 meter difference in spacing resulted in a statistically significant difference for disease transmission, with much higher disease spread in the denser forest. Because the model is highly sensitive to tree spacing, likely because the parameters of my model that relate to distance drop off in sigmoidal or exponential decay patterns, I would hypothesize that changes in the values of parameters that influence the spatial spread of disease (i.e., insect dispersal distance, probability of root contact with distance) and the magnitude of vector attraction after harvest and thinning will determine whether the “extensive” or “intensive” forest management class will ultimately the highest levels of infection probabilities. In addition, the rate of decay of root contact and insect dispersal probabilities will determine whether management and infection within stands influence infection in neighboring stands and the distance and strength of those neighborhood effects. I would like to test this my performing such analyses on the outputs from my sensitivity analyses.

SIGNIFICANCE: WHAT DID I LEARN FROM MY RESULTS? HOW ARE THESE RESULTS IMPORTANT TO SCIENCE? TO RESOURCE MANAGERS?

Ultimately, the significance of this research is to understand the potential threat of black stain root disease in the Pacific Northwest and inform management practices by identifying evidence-based, landscape-scale management strategies that could mitigate BSRD disease issues. While the results of Exercises 1-3 were interesting, they were produced using a model that had not been fully parameterized and thus are not representative of the likely actual model outcomes. Therefore, I was not able to test my hypotheses. That said, this course allowed me to design and develop an analysis to test my hypotheses. The exercises I completed have also provided a deeper understanding of how my model works. Through this process, I have begun to generate additional testable hypotheses regarding model sensitivity to parameters and the relative spread rates of infection in each of the forest management classes. Another key takeaway is the importance of producing many runs with the same landscape configuration and parameter settings to account for stochastic processes in the model. By only analyzing one run for each scenario, there is a chance that the results are not representative of the average behavior of the system or the full range of behaviors possible for those scenarios. For example, with the random landscape configuration, one generated landscape can be highly connected and the next highly fragmented with respect to intensive plantations, and only a series of runs under the same conditions would provide reliable results for interpretation.

WHAT I LEARNED ABOUT… SOFTWARE

(a, b) Arc-Info, Modelbuilder and/or GIS programming in Python

This was my first opportunity to perform statistical analysis in ArcGIS, and I used multiple new tools, including hotspot analysis, multiple ring buffers, and using extensions. Though I did not use Python or Modelbuilder, I realized that doing so will be critical for automating my analyses given the large number of model runs I will be analyzing. While I learned how to program in Python using arcpy in GEOG 562, I used this course to choose the appropriate tools and analyses for my questions and hypotheses rather than automating procedures I may not use again. I would now like to implement my procedures for neighborhood analysis in Python in order to automate and increase the efficiency of my workflow.

(c) Spatial analysis in R

During this course, I learned most about spatial data manipulation in R, since I had limited experience using R with spatial data beforehand. I used R for spatial statistics, data cleaning and management, and conversion between vector and raster data. I also learned about the limitations of R (and my personal limitations) in terms of the challenge of learning how to use packages and their functions when documentation is variable in quality and a wide variety of user-generated packages are available with little reference as to their quality and reliability. For example, for Exercise 2, I had trouble finding an up-to-date and high-quality package for hotspot analysis in R, with raster data or otherwise. However, this method was straightforward in ArcMap once the data were converted from raster to points. For Exercise 1, the only Moran’s I calculation that I was able to perform with my raster data was the “moran” function in the raster package, which does not provide z- or p-values to evaluate the statistical significance of the calculated Moran’s I and requires you to generate your own weights matrices, which is a pain. Using the spdep or ncf packages for this analysis was incredibly slow (though I am not sure why), and the learning curve for spatstat was too steep for me to overcome by the Exercise 1 deadline (but I hope to return to this package in the future).

Reading, manipulating, and converting data: With some trial and error and research into the packages available for working with spatial data in R (especially raster, sp/spdep, and sf), I learned how to quickly and easily convert data between raster and shapefile formats, which was very useful in automating the cleaning and preparation for multiple datasets and creating the inputs for the analyses I want to perform.

(d) Landscape connectivity analyses: I learned that there are a wide variety of metrics available through Fragstats (and landscapemetrics and landscapetools packages in R), however, I was not able to perform my desired stand-scale analysis of connectivity because I could not determine whether it is possible to analyze contiguous stands with the same management class as separate patches (Fragstats considered all contiguous cells in the raster with the same class to be part of the same patch). Instead, I used Conefor, which has an ArcMap extension that allows you to generate a node and connection file from a polygon shapefile, to calculate relatively few but robust and ecologically meaningful connectivity metrics for the stands in my landscape.

WHAT I LEARNED ABOUT… SPATIAL STATISTICS

Correlograms and Moran’s I: For this statistical method, I learned the importance of choosing meaningful lag distances based on the data being analyzed and the process being examined. For example, my correlogram consists of a lot of “noise” with many peaks and troughs due to the empty cells between trees, but I also captured data at the relevant distances. Failure to choose appropriate lag distances means that some autocorrelation could be missed, but analyses of large raster images at a high resolution of lag distances results in very slow processing. In addition, I wanted to compare local vs. global Moran’s I to determine whether infections were sequestered to certain portions of the landscape or spread throughout the entire landscape, but the function for local Moran’s I returned values far outside the -1 to 1 range of the global Moran’s I. As a result, I did not understand how to interpret or compare these values. In addition, global Moran’s I did not tell me where spatial autocorrelation was happening, but the fact that there was spatial autocorrelation led me to perform a…

Hotspot analysis (Getis-Ord Gi*): It became clear that deep conceptual understanding of hypothesized spatial relationships and processes in the data and a clear hypothesis are critical for hotspot analysis. I performed multiple analyses with difference distance weighting to compare the results, and there was a large variation in both the number of points included in hot and cold spots and the landscape area covered by those spots between the different weighting and distance methods. I ended up choosing the inverse squared distance weighting based on my understanding of root transmission and vector dispersal probabilities and because this weighting method was the most conservative (produced the smallest hotspots). The confidence level chosen also resulted in large variation in the size of hotspots. After confirming that there was spatial autocorrelation in infection probabilities, using this method helped me to understand where in the landscape these patterns were occurring and thus how they related to management practices.

Neighborhood analysis: I did not find this method provided much insight in my case, not because of the method itself but because of my data (it just confirmed the landscape pattern that I had designed, clustered vs. random) and my approach (one hotspot and one coldspot point non-randomly selected in each landscape. I also found this method to be tedious in ArcMap, though I would like to automate it, and I later learned about the zonal statistics tool, which can help make this analysis more efficient. In general, it is not clear what statistics I could have used to confirm whether results were significantly different between landscapes, but perhaps this is an issue caused by my own ignorance.

Network/landscape connectivity analyses: I learned that there are a wide variety of tools, programs, and metrics available for these types of analyses. I found the Integrative Index of Connectivity (implemented in Conefor) particularly interesting because of the way it categorizes habitat patches based on multiple attributes in addition to their spatial and topological positions in the landscape. The documentation for this metric is thorough, its ecological significance has been supported in peer-reviewed publications (Saura and Rubio 2010), and it is relatively easy to interpret. In contrast, I found the number of metrics available in Fragstats to be overwhelming especially during the data exploration phase.

REFERENCES

Robert J. Hijmans (2019). raster: Geographic Data Analysis and Modeling. R package version 2.8-19. https://CRAN.R-project.org/package=raster

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.

Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Ex. 3: Does black stain spread through landscape networks?

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)
  1. 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.

Ex 2: A stain on the neighborhood… How does management relate to infection for black stain root disease?

Sorry for the bad puns in the title… Could not help myself.

QUESTION

How do spatial patterns of black stain root disease infection probabilities relate to spatial patterns of forest management classes? How do these spatial relationships differ between landscapes where similar management classes are clustered and landscapes where management classes are randomly distributed?

TOOLS AND APPROACH

I used neighborhood analysis to analyze the spatial relationship between hot and cold spots of infection probabilities and the three forest management classes simulated in my model (extensively managed plantations, intensively managed plantations, and passively managed old-growth stands).

I used a combination of ArcMap (to perform the majority of the procedure) and R (mostly for spatial data wrangling and analyzing and plotting results).

DESCRIPTION OF STEPS YOU FOLLOWED TO COMPLETE THE ANALYSIS

1. Compare the distribution of infection probabilities between landscapes and management classes

I performed this step in R to determine whether there was evidence of significant differences in the infection probabilities (a) between the clustered and the random landscapes and (b) between management classes both within and among landscapes.

2. Hotspot analysis

Converted my raster data of infection probabilities to point data (in R, using the “raster” package) and perform a hotspot analysis (hotspot tool in ArcMap) (Fig. 1). For the hotspot analysis, I used inverse squared distance weighting to conservatively include trees within hotspots.

I also created polygon shapefiles for areas identified as hotspots to the 99% confidence level in each of the landscapes and calculated the area of these hotspots for each landscape, management class, and landscape X management class.

Figure 1. Hotspot analysis overlaid on forest management classes for the “clustered” landscape. The same analysis was performed on the “random” landscape.

3. Select point for neighbor analysis

For this step, I chose one point in a hot spot and one point in a cold spot for each of the two landscapes to perform the neighborhood analysis. In the future, I would write a script to repeat this procedure with a random sample of a large number of points, but for this exercise, I just used one point for each.

For the hotspots, I only used points identified in hotspots at the 99% confidence level. For the cold spots, I used a point from the 99% confidence level for the clustered landscape, but my only options for the random landscape were points identified at the 90% confidence level. I visually selected the points for analysis (non-random), but I would not do so for my full analysis.

4. Create concentric ring buffers for the neighborhood analysis

I used the Multiple Ring Buffer tool in ArcMap to generate hollow ring buffers at a series of distances around each hotspot and cold spot point selected for analysis (Fig. 2). I then intersected these buffers with the management class shapefile and calculated the proportion of each buffer ring composed of each management class (by area). I plotted these proportions as a function of distance to complete the neighborhood analysis.

Figure 2. Concentric ring buffers used for the neighborhood analysis, with outer ring distances labeled. Example shown for the “random” landscape for both hot and cold spots.

RESULTS

Non-spatial analysis

Before performing the neighborhood analysis, I wanted to know whether there was any difference in the infection probabilities between the two landscapes and the three management classes. Visual assessment of the box plots (Fig. 3) led me to believe that there were significant differences between the means of the infection probabilities between the landscapes and management classes, which was supported by the results of student t-tests (p << 0.01). There were also significant differences in the infection probabilities between management classes both within and among the two landscapes. Since the outputs I am analyzing are “dummy data” because my model is not fully complete, this does not surprise me and I did not perform further, more rigorous statistical analysis. The higher infection probabilities simply reflect the density of trees in each of these management classes. Extensive management had the highest infection probabilities (highest initial planting density, evenly spaced), followed by old-growth (lower density but clustered trees) and finally intensive management.

Figure 3. Comparisons of infection probability distribution between (a) landscapes, (b) management classes, (c) management classes by landscape; (d) the proportion of each management class covered by an infection hot spot in each of the two landscapes (by area).

Neighborhood analysis

For the clustered landscape, the management class in which the point was located made up the largest proportion of the first several distances analyzed (cold spot: old-growth, hot spot: extensive). This makes sense given that the management classes were spatially clustered in this landscape. At a certain threshold, the proportion of this management class started to decrease, as the other two management classes increased in proportion at a similar rate. For the random landscape, the decrease in the starting management class proportion was relatively rapid with distance, and all three management classes converged at their landscape proportion by 150 meters, with some fluctuation (in both landscapes, each of the three management classes makes up about 1/3 of the total landscape).

Figure 4. Neighborhood analysis showing the proportion of each (hollow) ring buffer accounted for by each management class for hot and cold spot points in each of the two landscapes.

Critique of the method – what was useful, what was not?

Most of the drawbacks of this analysis were due to my process and the nature of my data. Because I only used one hotspot and one cold spot point for each of the two landscapes, it is difficult to say much from this analysis. If I were to automate the analysis and run it on a series of random points drawn from the hot and cold spots, I would get a lot more insight as to the patterns of neighborhood effects if any exist. In addition, the “dummy data” used for analysis come from model runs that only have local disease transmission (between neighbors at a radius of several meters). However, the full model will also incorporate long-distance dispersal by insect vectors (on the scale of kilometers), which will likely be much more interesting and less predictable when neighborhood analysis is performed.

Issues with the method itself is that it is quite time intensive – an issue that could be cleared up with a script written in Python or R to automate this process given a set of input files. If there is a way to do this already built into either of these platforms (or Arc/QGIS), I was not able to find it. Also, there is a lack of clear quantitative interpretation for these plots to separate statistically significant variability in the proportion of each management class at each distance from non-significant variability. A means of doing so would enrich the analysis.

Ex 1: Mapping the stain: Using spatial autocorrelation to look at clustering of infection probabilities for black stain root disease

My questions:

I am using a simulation model to analyze spatial patterns of black stain root disease of Douglas-fir at the individual tree, stand, and landscape scales. For exercise 1, I focused on the spatial pattern of probability of infection, asking:

  • What is the spatial pattern of probability of infection for black stain root disease in the forest landscape?
  • How does this spatial pattern differ between landscapes where stands are clustered by management class and landscapes where management classes are randomly distributed?

    Fig 1. Left: Raster of the clustered landscape, where stands are spatially grouped by each of the three forest management classes. Each management class has a different tree density, making the different classes clearly visible as three wedges in the landscape. Right: Raster of the landscape where management classes are randomly assigned to stands with no predetermined spatial clustering. The color of each cell represents the value for infection probability of that cell. White cells in both landscapes are non-tree areas with NA values.

Tool or approach that you used: Spatial autocorrelation analysis, Moran’s I, correlogram (R)

My model calculates probability of infection for each tree based on a variety of tree characteristics, including proximity to infected trees, so I expected to see spatial autocorrelation (when a variable is related to itself in space) with the clustering of high and low values of probability of infection. Because some management practices (i.e., high planting density, clear-cut harvest, thinning, shorter rotation length) have been shown to promote the spread of infection, there is reason to hypothesize that more intensive management strategies – and their spatial patterns in the landscape – may affect the spread of black stain at multiple scales.

I am interested in hotspot analysis to later analyze how the spatial pattern of infection hotspots map against different forest management approaches and forest ownerships. However, as a first step, I needed to show that there is some clustering in infection probabilities (spatial autocorrelation) in my data. I used the “Moran” function in the “raster” package (Hijmans 2019) in R to calculate the global Moran’s I statistic. The Moran’s I statistic ranges from -1 (perfect dispersion, e.g., a checkerboard) to +1 (perfect clustering), with a value of 0 indicating perfect randomness.

Moran’s I = -1

Moran’s I = 0

Moran’s I = 1

 

 

 

 

 

 

 

 

I calculated this statistic at multiple lag distances, h, to generate a graph of the values of the Moran’s I statistic across various values of h. You can think of the lag distance of the size of the window of neighbors being considered for each cell in a raster grid. The graph produced by plotting the calculated value of Moran’s I across various lag values is called a “correlogram.”

What did I actually do? A brief description of steps I followed to complete the analysis

1. Imported my raster files, corrected the spatial scale, and re-projected the rasters to fall somewhere over western Oregon.

I am playing with hypothetical landscapes (with the characteristics of real-world landscapes), so the spatial scale (extent, resolution) is relevant but the geographic placement is somewhat arbitrary. I looked at two landscapes: one where management classes are clustered (“clustered” landscape), and one where management classes are randomly distributed (“random”). For each landscape, I used two rasters: probability of infection (continuous values from 0 to 1) and non-tree/tree (binary, 0s and 1s).

2. Masked non-tree cells

Since not all cells in my raster grid contain trees, I set all non-tree cells to NA for my analysis in order to avoid comparing the probability of infection between trees and non-trees. I used the tree rasters to create a mask.
c.tree[ c.tree < 1 ] <- NA # Set all non-tree cells in the tree raster to NA
c.pi.tree <- mask(c.pi, c.tree) # Combine the prob inf with tree, leaving all others NA
# Repeat with randomly distributed management landscape
r.tree[ r.tree < 1 ] <- NA # Set all non-tree cells in the tree raster to NA
r.pi.tree <- mask(r.pi, r.tree) # Combine the prob inf with tree, leaving all others NA

Fig 2. Filled and hollow weights matrices.

3. Calculated Global Moran’s I for multiple values of lag distance.

For each lag distance, I created a weights matrix so the Moran function in the raster package would know how to weight each neighbor pixel at a given distance. Then, I let it run, calculating Moran’s I for each lag to create the data points for a correlogram.

I produced two correlograms: one where all cells within a given distance (lag) were given a weight of 1 and another “hollow” weights matrix when only cells at a given distance were given a weight of 1 (see example below).

4. Plotted the global Moran’s I for each landscape and compare.

 

 

 

 

 

 

What did I find? Brief description of results I obtained.

The correlograms show that similar values become less clustered at greater distances, approaching a random distribution by about 50 cell distances. In other words, cells are more similar to the cells around them than they are to more-distant cells. The many peaks and troughs in the correlogram are present because there are gaps between trees because of their regular spacing in plantation management.

In general, the highest values of Moran’s I were similar between the landscape with clustered management landscape and the landscape with randomly distributed management classes. However, the rate of decrease in the value of Moran’s I with increasing lag distance was higher for the random landscape than the clustered landscape. In other words, similar infection probabilities had larger clusters when forest management classes were clustered. For the clustered landscape, there was actually spatial autocorrelation at lag distances of 100 to 150, likely because of the clusters of higher infection probability in the “old growth” management cluster.

Correlogram for the clustered and random landscape showing Moran’s I as a function of lag distance. “Filled” weights matrix.

Correlogram for the clustered and random landscape showing Moran’s I as a function of lag distance. “Hollow” weights matrix.

 

 

 

 

 

 

 

 

 

 

 

 

 

Critique of the method – what was useful, what was not?

My biggest issue initially was finding a package to perform a hotspot analysis on raster data in R. I found some packages with detailed tutorials (e.g., hotspotr), but some had not been updated recently enough to work in the latest version of R. I could have done this analysis in ArcMap, but I am trying to use open-source software and free applications and improve my programming abilities in R.

The Moran function I eventually used in the raster package worked quickly and effectively, but it does not provide statistics (e.g., p-values) to interpret the significance of the Moran’s I values produced. I also had to make the correlogram by hand with the raster package. Other packages do include additional statistics but are either more complex to use or designed for point data. There are also built-in correlogram functions in packages like spdep or ncf, but they were very slow, potentially taking hours on a 300 x 300 cell raster. That said, it may just be my inexperience that made a clear path difficult to find.

References

Glen, S. 2016. Moran’s I: Definition, Examples. https://www.statisticshowto.datasciencecentral.com/morans-i/.

Robert J. Hijmans (2019). raster: Geographic Data Analysis and Modeling. R package version 2.8-19. https://CRAN.R-project.org/package=raster

 

A stain on the record? Have forest management practices set up PNW landscapes for a black-stain-filled future?

Describe the research question that you are exploring.

I am looking at how forest management practices influence the spread of black stain root disease (BSRD), a fungal root disease that affects Douglas-fir in the Pacific Northwest. While older trees become infected, BSRD primarily causes mortality in younger trees (< 30-35 years old). Management practices (e.g., thinning, harvest) attract insects that carry the disease and are associated with increased BSRD incidence. As forest management practices in the Pacific Northwest change to favor shorter-rotations of Douglas-fir monocultures, the distribution of Douglas-fir age classes is shifting towards younger stands and the frequency of harvest disturbance is increasing across the landscape. Though limited, our present understanding of this disease system indicates that these management trends, as well as the resulting disturbance regime and forest landscape age structure, may be creating favorable conditions for BSRD spread.

In this course, I would like to use spatial analyses to answer the question of whether forest management and the conditions that it creates act as a driver of the spread of black stain root disease. Specifically:

  • How do spatial patterns of forest management practices and the forest stand and landscape conditions that they create relate to spatial patterns of BSRD infection probabilities at the stand and landscape scale?
  • How do spatial patterns of forest management practices relate to landscape connectivity with respect to BSRD by affecting the area of susceptible forest and creating dispersal corridors and/or barriers throughout the landscape?

Example landscape with stands of three different forest management regimes (shades of green) and trees infected by black stain root disease (red). Forgive the 90s-esque graphics… NetLogo, the program I am using to develop and run my model, is powerful but old-school.

Describe the dataset you will be analyzing, including the spatial and temporal resolution and extent.

I will be analyzing the raster outputs of a spatial model that I built in the agent-based modeling program NetLogo (Wilensky 1999). The rasters contain the states of forested landscapes (managed as individual stands) at a given time during the model run. Variables include tree age, presence/absence of trees, management regime, probability of infection, infection status (infected/not infected), and cause of infection (root transmission, vector transmission).

The forested landscapes I am looking at are about 3,000 to 4,000 ha, with each pixel representing a ~1.5 m x 1.5 m area that can occupied by one tree. I run each model for a 300-year time series with 1-year intervals, though raster outputs may be produced at 10-year intervals.

Hypotheses: predict the kinds of patterns you expect to see in your data, and the processes that produce or respond to these patterns.

I hypothesize that landscapes with higher proportions of intensively managed, short-rotation stands will have higher probabilities of BSRD infection at the stand and landscape scales. In landscapes with high proportion of short-rotation stands, there will be large areas of suitable habitat for the pathogen and its vectors, frequent harvest that attracts disease vectors, and greater levels of connectivity for the spread of disease. In landscapes with a large proportion of older forests managed for conservation, I hypothesize that these forests will act as barriers to the spread of BSRD. High connectivity could be evidenced by greater landscape-scale dispersion of infections, whereas low connectivity would lead to a high degree of clustering of infections in the landscape.

I also hypothesize that intensively managed, short-rotation stands will have the highest probabilities of infection, followed by intensively managed, medium-rotation stands, and finally old-growth stands. However, I hypothesize that each stand’s probability of infection will depend not only on its own management but also on the management of neighboring stands and the broader landscape. At some threshold proportion of intensive management in the landscape, I hypothesize that there will be a shift in the scale of the drivers of infection, such that landscape-scale management patterns overtake stand-scale management as a predictor of infection probability.

Approaches: Describe the kinds of analyses you ideally would like to undertake and learn about this term, using your data.

I would like to learn about landscape connectivity analyses and spatial statistics such as clustering/dispersion as well as spatiotemporal analyses to analyze the relationships between discrete disturbance events and disease spread. I would like to learn how to separate the effects of connectivity from the effect of the area of suitable pathogen habitat. I am most interested in using R or Python to analyze my data, and I would like to move away from ESRI programs because of my interest in open-source and free tools for science and the prohibitive cost of ESRI software licenses for independent researchers and organizations with limited financial means.

Expected outcome – What do you want to produce – Maps? Statistical relationships?

My primary interest is to evaluate statistical relationships between spatial patterns of management and disease measures, but I would also like to produce maps to demonstrate model inputs and outputs (i.e., figures for my thesis).

Significance – How is your spatial problem important to science? To resource managers?

From a scientific perspective, this research aims to contribute to the body of research examining relationships between spatial patterns and ecological processes and complex behaviors in ecological systems. This research will examine how the diversity of the landscape age structure and disturbance regimes affect the susceptibility of the landscape to disease, contributing to literature relating diversity and stability in ecological systems. In addition, “neighborhood” and “spillover” effects will be tested by analyzing stand-scale infection probability with respect to the infection probability of neighboring stands and more broadly in the landscape. Analysis of threshold responses to changes in stand- and landscape-scale management patterns and shifts in the scale of disease drivers will contribute to understanding of cross-scale system interactions and emergent properties in the field of complex systems science.

From an applied perspective, the goal of this research is to inform management practices and understand the potential threat of black stain root disease in the Pacific Northwest. This will be achieved by improving understanding of the drivers of BSRD spread at multuiple scales and highlighting priority areas for future research. This project is a first step towards identifying evidence-based, landscape-scale management strategies that could be taken to mitigate BSRD disease issues. In addition, the structure of this model provides a platform for looking at multi-scale interactions between forest management and spatial spread processes. Its use is not restricted to a specific region and could be adapted for other current and emerging disease issues.

Your level of preparation – How much experience do you have with: (a) Arc-Info, (b) Modelbuilder and/or GIS programming in Python, (c) R, (d) image processing, (e) other relevant software

Over the past 5 years, I have worked on and off with all the programs/platforms listed. For some, I have been formally trained, but for others, I have been largely self-taught. However, lack of continuous use has eroded my skills to some degree.

a. I have frequently used ArcInfo for making maps, visualizing data, and processing and analyzing spatial data. However, I do not have a lot of experience with spatial statistics in ArcInfo.

b. Modelbuilder/Python: Last spring, I took GEOG 562 and learned to program in Python, developing a script that used arcpy to prepare and manipulate spatial data for my final project. I felt comfortable programming in Python at that time, but I have not used Python much since the course.

c. I have frequently used R to clean and prepare data, perform simple statistical analyses (ANOVA, linear regression), and create plots. I have taken several workshops on using R for spatial analysis, but I have used rarely used the R packages I learned about outside of those workshops.

d. I have used ENVI to correct, patch, and combine satellite images, and I have performed supervised classifications to create land cover maps. I have worked primarily with LANDSAT images. I have also used CLASlite (an image processing software designed for classifying tropical forest cover).

e. Covered in part d.

References

Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Adam Bouché