Tag Archives: Disease ecology

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