Tag Archives: fire refugia

Final Project: Western Hemlock Dwarf Mistletoe Spatial Patterns and Drivers

Western Hemlock Dwarf Mistletoe

Western hemlock dwarf mistletoe is a hemi-parasite of primarily western hemlock trees. It absorbs water, nutrients, and carbohydrates from its host. Infected branches produce small structures called aerial shoots that have minor photosynthetic capabilities, but are primarily for pollination and seed production and require a certain amount of light to emerge from an infection site. Seeds are explosively discharged from aerial shoots when fully mature. Once landing on a susceptible host branch they being germination and mechanical penetration of the host branch.

Research Question

I wanted to explore the spatial patterns of dwarf mistletoe infections after a mixed severity fire and the roles post-fire, forest structure and fire refugia play.

How does the spatial pattern of post-fire stand structure and species composition affect spatial patterns of dwarf mistletoe distribution throughout the stand through physical barriers to susceptible hosts and seed dispersal?

Description of Dataset

I have a 2.2 ha rectangular study area (Wolf Rock), just northwest of the HJ Andrews Exp. Forest that was stem mapped in 1992. Each tree has an X and Y coordinates, as well as the tree species, height, diameter, and a variety of other tree inventory related data. I only have ages for a few western hemlocks, but many more for Douglas-fir. Only one western hemlock core was identified as being over 100 years old, at 170 years. I have a polygon layer for the fire refugia that are documented on the study area. For the western hemlocks I have a presence/absence of western hemlock dwarf mistletoe as well as a severity measure. However, I am unsure of the scale and ethod of rating, so I will not be using it. The infection presence and absence are from a single measurement season.

Hypotheses and Predictions

Western hemlock dwarf mistletoe spreads easily through moderate canopy densities, where distances between trees are close to the average dispersal distance of 2-4 meters. Disturbances that create patchy gaps increase likelihood of spread because of increased light reaching infected branches and increase the rate of infection abundance because of the lack of physical barriers such as high densities of branches and foliage.

Disturbances can also remove the disease from a forested stand by killing or knocking down infected western hemlocks. Post-disturbance regeneration can enable or inhibit the parasite’s reintroduction to the stand. Non-susceptible hosts such as Douglas-fir or western redcedar regenerate readily alongside western hemlock and will intercept seeds. Some gaps are only conducive to western hemlock regeneration which will be readily infected by any surviving infected western hemlocks post-disturbance.

The Wolf Rock stand experienced two fires that created a mosaic of ~110 year old regeneration and >110 year old remnant trees in fire refugia. Remnant, infected western hemlocks survived the most recent fire in those fire refugia. From this stand structure, I have several hypotheses and predictions:

  1. Remnant, infected western hemlocks form the center of new infection centers post disturbance so infections in the regenerating susceptible hosts, will be clustered around these remnant trees.
  2. Non-susceptible hosts regulate the rate of infection spread through physical barriers to dispersal, so infection cluster size will have an inverse relationship with non-host density.
  3. Western hemlock infection spreads from a central remnant tree, so uninfected western hemlocks will have a dispersed spatial pattern from the remnant western hemlock, regardless of non-host density.
  4. Post-fire regeneration with higher western hemlock composition will have more susceptible hosts and less physical barriers to spread so infection cluster size will have a positive relationship with western hemlock composition.

Analysis Approaches

For Exercise 1,  I wanted to know about the spatial pattern of western hemlock trees infected with western hemlock dwarf mistletoe. I used a hotspot analysis to determine where clusters of infected and uninfected trees were in my 2.2 ha study area. I discovered a hot spot and a cold spot, indicating two clusters, one of high values (infected) and one of low values (uninfected).

For Exercise 2, I wanted to know how the spatial pattern of these clustered infected and uninfected trees were related to the spatial pattern of fire refugia outlined in my study site. I used Geographically Weighted Regression to determine the significance of this relationship, however I did not find a significant relationship between a western hemlock, its intensity of clustering and infection status, and it’s distance to its nearest fire refugia polygon edge.

For Exercise 3, I wanted to know how the spatial patterns of remnant western hemlocks related to the spatial patterns of regeneration western hemlocks, uninfected western hemlocks, and non-western hemlock tree species. I used the Kcross and Jcross functions in spatstat in R and prepared the data in ArcMap to analyze spatial relationships between trees. I found clustering between regenerating western hemlocks and non-hosts to remnant western hemlocks but the uninfected western hemlock’s spatial pattern was independent of the remnant western hemlocks.

Results

I produced several maps that showed the spatial patterns in my study site which were helpful for understanding and investigating further relationships. I produced several charts from my exercise 3 analysis that were useful for visual representations of the relationships between trees. In Exercise 3 I also produced a map from raster addition that gave me the best visualization of where western hemlock and non-host trees were in the stand. Exercise 2 produced a map and statistical relationship but was not significant in explaining a hemlock’s infection and density status.

Significance

The biggest finding was that the fire refugia polygons are not significant for my analysis, the remnant infected hemlocks are more important explanatory variables in spatial patterns of infected trees. This supported hypothesis 1. Because refugia can be effectively defined using the “for what, from what” framework, western hemlock dwarf mistletoe refugia from fire could be delineated differently in the field focusing only on the remnant western hemlocks.

Data was not available to determine the rates of infection spread over time because I only had one season of measurements. I also could not evaluate the size of clusters because I did not have GPS points of infection center extent so I could not assess hypothesis 2 and 4 directly. However using Ripley’s K and the cross-variant I could see how the clusters changed over distance. I learned that infected, regenerating trees are going to be found closer to the remnant infected trees and that non-host trees may be blocking the spread of mistletoe into an uninfected patch because they were found clustered around remnant trees as well. This provides support for Hypothesis 1, 2, and 3.

Silvicultural prescriptions with the goal to preserve old growth forest structure, but that want to limit the amount of dwarf mistletoe in a forest can appropriately remove old infected hemlocks to preserve infection spread and extent. These prescriptions will also be able to predict future dwarf mistletoe spread. Forest operations that simulate disturbances that leave remnant hemlocks such as harvests, can incorporate spread predictions to limit regeneration being infected.

Learning From The Process

I learned a lot about the spatial analyst tools in ArcMap and how to produce easily interpretable maps and graphs. I also learned how to use several function in spatstat. I learned a lot about interpreting R outputs and spatial. Spatial autocorrelation can tell you a lot about what your data are doing but I thought it was most useful to be able to see on a map or chart what is specifically happening.

Comparing the Spatial Patterns of Remnant Infected Hemlocks, Regeneration Infected Hemlocks, and Non-Hosts of Western Hemlock Dwarf Mistletoe

Overview

For Exercise 1, I wanted to know about the spatial pattern of western hemlock trees infected with western hemlock dwarf mistletoe. I used a hotspot analysis to determine where clusters of infected and uninfected trees were in my 2.2 ha study area (Map 1). I discovered a hot spot and a cold spot, indicating two clusters, one of high values (infected) and one of low values (uninfected).

For Exercise 2, I wanted to know how the spatial pattern of these clustered infected and uninfected trees were related to the spatial pattern of fire refugia outlined in my study site. I used Geographically weighted Regression to determine the significance of this relationship, however I did not find a significant relationship between a western hemlock, its intensity of clustering and infection status, and it’s distance to its nearest fire refugia polygon.

This result led to the realization that the polygons as they were drawn on the map were not as relevant as the actual “functional refugia”. I hypothesized that, after the 1892 fire, the only way for western hemlock dwarf mistletoe to spread back into the stand would be from the trees that survived that fire, or “remnant” trees. These would then infect the “regeneration” tree that came after the 1892 fire. The functional refugia I am interested in are defined by the location of the remnant western hemlocks. I also hypothesized that the spatial pattern of non-susceptible host tree (trees that were not western hemlocks) would play a role in the distribution of the mistletoe.

Question Asked

How are the spatial patterns of remnant western hemlocks related to the spatial patterns of regeneration western hemlocks, uninfected western hemlocks, and non-western hemlock tree species, and how are these relationships related to the spread of western hemlock dwarf mistletoe in the stand?

The Kcross and Jcross Functions

The cross-type functions (also referred to as multi-type functions) are tools capable of comparing the spatial patterns of two different type events (type i and j) in a similar spatial window, of some point process, X. It does this by assigning labels to the events differentiating the type and summarizing the number or distance, of and between events, at differing spatial scales, or radius circles (r).

The statistic Kij (r) , summarizes the number of type j events, around a type i event at a distance of r, or a point process X. Deviations of the observed Kij(r) curve from the the Poisson curve, or if type j events are truly randomly distributed, indicates dependence of type j events on type i events. Similar results can be obtained from the regular Ripley’s K: deviations above the curve indicate clustering and deviations below indicate dispersal.

(Incredibly helpful and interactive explanation link: https://blog.jlevente.com/understanding-the-cross-k-function/)

The statistic Jij(r) = (1 – Gij(r))/(1-Fj(r)) summarizes the shortest distance between a type i and j event and compares it to the empty space function of type j event. This is another test for inferring independence or dependence of type j events to type i. Deviations of the Jij(r) curve the value of 1, indicate levels of dependence of the events to each-other. Specific deviations from 1 can be hard to interpret without an understanding of the Fj(r) function so imagining it stationary in the ratio makes it easier. As Gij(r) increases, the numerator shrinks, creating a smaller Jij(r) statistic. Deviations below 1 indicate that type i and j events are dependent and that as r increases, the shortest distance between points of type i and j increases. As Gij(r) decreases, the numerator grows, creating a larger Jij(r) statistic. Deviations above 1 indicate that type i and j events are dependent and that as r increases, the shortest distance between points of type i and j decreases.

Methods Overview

In R, the package “spatstat” provides a suite of spatial statistic functions including the cross-type functions. In order to use these you need to create a “point pattern process” object. These objects incorporate X and Y coordinates, and a frame of reference, or a “window,” and give spatial context top a list of values. Then marks are applied to these points that create the necessary multi-type point pattern process object. These marks serve to distinguish the type i and type j events described earlier in your analysis. Then running the “Kcross()” or “Jcross()” functions with the specified type events produces a graph that you can interpret, very similar to producing the normal Ripley’s K plot.

  • I took my X – Y coordinates of all trees on the stand and added a column called “Status” to serve as my mark for the point pattern analysis.
    1. The four statuses were “Remnant,” “Regen,” “Uninfected,” and “NonHost” to identify my populations of interest.
      1. I had access to tree cores, so I identified trees that were older than 170 yrs old and these trees’ diameters served as my cutoff for the “Remnant” diameter class.
      2. All trees DBH > 39.8 cm.
    2. Doing this in ArcMap removed steps I would have to have taken when I migrated the dataset to R.
    3. I removed all the dead trees because I wasn’t concerned with them for my analysis.
  • I exported this attribute table to a csv and loaded it into R Studio.
  • I created the boundary window of my study site using the “owin()” function, and the corner points from my study site polygon.
  • The function “ppp()” creates the point pattern object and I assigned the marks to the data set using the “Status” column I created in ArcMap
    1. It’s important your marks are factors otherwise it is not converted into a multi-type point pattern object.
  • The last step is running the “Kcross()” and “Jcross” to compare the “Remnant” population to the “Regen,” “Uninfected,” and “NonHost” populations.
    1. This produced 6 plots, 3 of each type of cross-type analysis.
    2. Compare these easily using the “par()” function, for example:

par(mfrow = c(1,3))

plot(Ex3.Kcross1)

plot(Ex3.Kcross2)

plot(Ex3.Kcross3)

This produces the three plots in a single row and three columns.

Results

Because I am assuming the remnant, infected western hemlock trees are one of the main factors for the spread of western hemlock dwarf mistletoe and that they are the center of  new infection centers on the study site, I did all my analysis centered on the remnant trees (points with status = “Remnant” treated as event type i).

1)   i = Remnant, j = Regen

The first analysis between remnant and regeneration trees demonstrate that there is dependence on the two events to each other. At fairly small distances, or values of r, infected western hemlocks that have regenerated after the 1892 fire cluster around infected remnant western hemlocks that survived the 1892 fire. This stands to reason because we assume that infected trees will be near other infected trees, and that infection centers start usually with a “mother tree.” In this case the remnant trees serve as the start of the new infection centers. The Jcross output also shows me that the two types of trees are clustered using the frequency of the shortest distances. After ~8 meters the two tree types exhibit definite clustering. In terms of the function, the Gij(r) in the numerator of the Jij(r) function is approaching 1, or the highest frequency of very short distances.

2)   i = Remnant, j = Uninfected

The Kcross plot from the second set of analyses between remnant and uninfected trees demonstrates that there is independence between the two events up to ~15 meters. After that, the trees exhibit slight clustering effects. The lack of dispersal tendencies is strange for these two types of trees because we expect uninfected trees to be furthest away from the center of infection centers. The presence of clustering may be indicative of the small spatial scale of my study site. It may also be that the size of the infection centers are only about 15 meters (if we assume that remnant trees are the center). The Jcross plot shows something similar: at small distances the types of trees seem independent and then around 8 meters they exhibit clustering.

3)   i = Remnant, j = NonHost

The Kcross from the last set of analyses between the remnant trees and the non-hosts demonstrates a similar pattern exhibited by the regeneration trees. After about 4 meters, the trees tend to be clustered. This is an interesting find because if the non-hosts cluster to remnant trees but uninfected trees are independent, then the non-hosts may be playing a role in this. The Jcross plot shows the same: the two types of trees exhibit clustering.

4)   Comparing Kcross Functions with eval.fv()

A useful way to compare patterns of Kcross functions is using the eval.fv function. The titles of each plot tell which Kcross was subtracted from which; note the difference in scales. The first plot shows that the regenerating trees’ spatial pattern as related to remnant trees is very different from the uninfected trees’ pattern. The regenerating trees’ spatial pattern is much more similar to the non-hosts’ spatial pattern at short distances, until about 15 meters. Then the patterns differ with the regenerating trees exhibiting more of a clustering tendency. However the scale is much smaller than the other two graphs. Lastly, the third plot shows the difference between the non-host trees’ spatial pattern and the uninfected trees’ spatial pattern. There appears to be a stepwise relationship where, at very near and very far distances the non-host trees are much more clustered, but at moderate distances the differences may be less dramatic.

Critique of Cross-Type Functions

The amount of easily interpretable literature on the spatstat package as a whole is sparse, although a wealth of very technical information exists. The function was easy to use and execute though and so was the process of creating the point pattern object. These two functions can clearly show how the spatial patterns of the two types of events change with scale. It would be helpful if there was a way to compare three or more types of events. The last drawback is that there is a lack of specific information for each point on your map or study site. This pattern that is generalizable to a whole set of points may not be as useful when trying to put together a story, such as the story of a stand’s development through time.

Additional Raster Analysis

The last critique of the cross-type functions led me to attempt a visualization of these patterns on my stand. Very briefly, I determined densities of the infected, uninfected, and the non-host trees using the Kernel Density function in ArcMap. Then I classified these densities using natural breaks and coded these for raster addition. After adding all three density rasters together, I coded each unique density classification combination to tell me how the densities of the populations appeared in the study site.

It appears that there are distinct patches of high density separated by areas of low density. On the eastern side of my study site, it appears that the high density areas of infected trees cluster with the remnant infected trees. An interesting interaction is occurring between the high density patches of uninfected trees and infected trees in the western portion of my study site. The mechanism for the seemingly clear divide may be the non-TSHE trees.

Epidemiology of Western Hemlock Dwarf Mistletoe Post – Mixed Severity Fire

Description of the Research Question

My study site is located in the HJ Andrews Experimental Forest, where the two most recent mixed severity fires burned leaving a sizable fire refugia in the middle of the stand. Western hemlock dwarf mistletoe (WHDM) survived the fire in this refugia. WHDM spreads via explosively discharged seed and rarely by animals. This means that for the pathogen to spread, the seed must reach susceptible hosts. WHDM is a obligatory parasite of western hemlock. The regeneration post fire may pose a barrier to the pathogens spread because of the structure and composition. Lastly, the structure of the fire refugia may determine the rate of spread. This is because the structure largely determines where infections exist in the vertical profile of the canopy.

My research question is: How is the spatial pattern of WHDM spread extent and intensification from fire refugia related to the spatial pattern of the structure and composition of the fire refugia and the surrounding regeneration via barriers to viable seed reaching susceptible hosts?

I have three objectives related to the spatial organization or the regenerating forest surrounding the fire refugia and one related to the fire refugia itself. My objectives are to determine how fire refugia affects dwarf mistletoe’s spread and intensification through:

  1. The stand density of regenerating trees and of surviving trees, post fire.
  2. The stand age and structure of regenerating trees and surviving trees in fire refugia.
  3. The tree species composition of the regenerating trees adjacent to fire refugia.

AND…

  1. Whether intensification dynamics of WHDM inside a fire refugia resemble those of WHDM in other infection centers.

Dataset Description

Spatial locations of the extent of spread and intensity (also referred to as severity) of WHDM infection include presence/absence of infection in susceptible hosts and will have a severity rating for each infected tree. The presence/absence data will be two measurements, one from 1992 and one from 2019. The intensity rating will be from 2019 only.

Spatial locations/descriptions of the structure and composition of the fire refugia and regeneration surrounding refugia include X,Y of each tree, a variety of forest inventory attributes such as diameters, heights, and species for each tree, and delineation of the fire refugia boundaries. This data has been measured several times: 1992, 1997, 2013, and 2019. The GPS coordinates were recorded with handheld GPs units most likely under canopy cover so resolution may vary.

These data sets are bounded by a 2.2 ha rectangle that confines the study area.

Hypotheses

The spatial pattern of western hemlock dwarf mistletoe in the study site will be several discrete clusters. This arrangement forms because WHDM spreads from an initial infection point outward. The initial infection serves as an approximate center point and the cluster, or infection center, grows outward from there. Separations between clusters are maintained by forest structure and composition or disturbances. New clusters form from remnant trees surviving disturbances, or random dispersal of seed long distances by animals. In this case, the fire refugia protect the remnant trees from disturbance and these trees are the new focal points for infection centers

The spatial pattern of the forest structure and composition will drive the direction and rate of spread of WHDM because variances in these two attributes will cause varying amounts of barriers to WHDM seed dispersal. Because seeds are shot from an infected tree, that seed needs to reach a new uninfected branch. This means physical barriers to spread can affect seed dispersal and non susceptible species will stop spread.

Approaches

I would like to utilize spatial analyses that allow me to understand how the clustering of WHDM is related to the boundaries of the fire refugia. Also, how the infection centers have changed over time utilizing forest structure and composition metrics of the regeneration surrounding the refugia. Lastly, something that can incorporate a severity rating on a scale instead of simply presence/absence data and describe the distribution of severely infected trees vs lightly infected trees and how that relates to the fire refugia boundary and forest metrics of the regeneration surrounding the refugia.

Expected Outcome

I would like to produce statistical relationships that can determine the significance of forest density, species composition, age, and structure on the ability of WHDM to spread. Also, I would like to produce statistical relationships that can describe whether or not a fire refugia alters the way WHDM spreads and intensifies when compared to commonly observed models. Maps as visuals for describing the change over time would be a useful end product as well.

Significance

Understanding the spread patterns of WHDM is important for resource managers seeking to increase biodiversity and produce forest products. Focus has shifted to creating silvivultural prescriptions that emulate natural disturbances that are still economically viable and that maintain ecosystem functions. Disturbance events can control WHDM but also create opportunities to increase its spread and intensification so managers need to have an understanding of how a particular forest structure will affect WHDM. Also, if we want to maintain biodiversity, understanding how WHDM infection centers created by fire develop is important. Fire frequency and severity may be increasing in the future and the loss of mixed severity fire would mean a significant loss of WHDM. Land managers seeking to emulate burns can use this information to plan burns that preserve patches of WHDM if desired and understand how the pathogen will progress 25 years later. This is not usually the case for forest pathogens.

Level of Preparation

I have worked in ArcMap quite a bit, but I haven’t much experience with the wide range of functionality of ArcInfo. I used ModelBuilder somewhat to keep my queries and basic analyses organized. No experience programming in Python. I have taken two stats classes before this using R and feel I have a working knowledge and have no problem learning new tools in it. However, I have very little work with image processing such as working with rasters and some small exposure to LiDAR processing.