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.

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.