Spatial Autocorrelation (Moran’s I): This tool measures spatial autocorrelation using feature locations and feature values simultaneously.   The spatial autocorrelation tool utilizes a multidimensional and multi-directional factors.  The Moran’s I index will be a value between -1 and 1. Positive spatial autocorrelation will show values that are clustered. Negative autocorrelation is dispersed. Random is close to zero. The tool generates a Z-score and p-value which helps evaluate the significance of the Moran’s index.

Figure 1: Calculations used for the Moran’s I tool. (ESRI image)

The output of the Moran’s I tool can be found in the results section of ArcGIS.  Upon opening the HTML report for the Moran’s I results you will see a graph showing how the tool calculated the data and whether or not the data is dispersed, random, or clustered.  This report will also include the Moran’s Index value, z-score, p-value.  It will also provide a scale for the significance of the p-value and critical value for the z-score.

Figure 2: Sample output for the Moran’s I tool. (ESRI image)

Data and Analysis

Before conducting this test, I sampled the SST and the CHL-a values at each of the feature locations (sea turtle locations) using the Extract Multi Values to Points tool. This tool “Extracts cell values at locations specified in a point feature class from one or more rasters, and records the values to the attribute table of the point feature class.”

Figure 3: Sea turtle locations in the Gulf of Mexico, derived from http://seamap.env.duke.edu/

Figure 4: Chlorophyll-a(mg/m^3) data for January 2005 within the Gulf of Mexico, derived from NOAA.

Figure 5: Sea Surface Temperautre (Celsius) data for January 2005 within the Gulf of Mexico, derived from NOAA.

I tested the spatial autocorrelation of chlorophyll-a and sea surface temperature at each feature location.  The conceptualization of spatial relationships method used was the inverse distance and the Euclidean distance measure was used for the distance method.  I selected a 500km distance (smaller distances were too small for the study site).

Results:

Sea Surface Temperature: The results of the spatial autocorrelation tool suggest that the pattern of sea surface temperature at each feature location is clustered. The Moran’s Index was 0.402514, the z-score was 2.608211, and the p-value was 0.009102.  Since the critical value (z-score) was greater than 2.58 there is less than 1-percent likelihood that the clustered pattern is a result of random chance.

Figure 6: Sea surface temperature results for Moran’s I tool.

Chlorophyll-a :  The results of the spatial Autocorrelation tool suggest that the pattern of chlorophyll at each feature location is clustered.  The Moran’s Index was 0.346961, the z-score was 2.216243, and the p-value was 0.026675.  The critical value (z-score) was less than 2.58 but greater than 1.96 thus suggesting that there is less than 5-percent likelihood that the clustered pattern is a result of random chance.

Figure 7: Results of the spatial autocorrelation Moran’s I for chlorophyll-a at the leatherback sea turtle locations.

What does this mean:

As suggested in the hotspot analysis there is clustering of the data.  The spatial autocorrelation tool indicates that clustering is occurring with regard to the sea surface temperature and chlorophyll values at their respective locations with regard to sea turtles.   Conducting an ordinary least squared analysis may lead to more information about which factors contribute more to the clustered pattern.

Introduction:  Leatherback sea turtles are endangered world wide.  Their habitat is often impeded due to the oil and gas industry in the Gulf of Mexico.  In 2010, the Deepwater Horizon Oil Spill affected much of the biota when 200million gallons of oil spilled into the Gulf.  Leatherback sea turtles are the most endangered sea turtle. My research  question is focused on the extent to which these turtles utilize the Gulf of Mexico.  Leatherback sea turtles feed almost exclusively on jellyfish. I will be assessing their range by looking at the correlation between leatherback sea turtle point data, sea surface temperature and chlorophyll as proxies for where jellyfish may occur.

„Research Question: What is the correlation between the location of leatherback sea turtles, sea surface temperature, and chlorophyll?

Approach: I used the hotpsot analysis tool in order to explore the sea turtle point data.  the hotspot analysis tool identify where statistically significant hotspots or clusters of sea turtles are located within the Gulf of Mexico.

Sea turtle data:

Results:  The results of the hotspot analysis (shown below) suggest that the turtle locations are significantly clustered off the coast of Louisiana and Texas between approximately 2,000m to 3,000m depth of water.  However, the results of this analysis appear to be quite deceptive.  Upon taking measurements of turtles in the hotspot cluster it appears as though they may be more dispersed.  Further analysis is needed in order to determine further patterns of sea turtle locations.

Introduction

In my last post, I discussed the importance of quantifying social contacts to predict microbe transmission between individuals in our study herd of African Buffalo. This post deals with the other half of the equation: environmental transmission. My overarching hypothesis is that spatial and social behaviors are important for transmission of host-associated microbes. The goal of this pilot project is to establish a method for quantifying habitat overlap between individuals in the herd so that I can (eventually) compare habitat overlap with microbe community similarity and infection risk.

Methods/Results

Workflow:

I used the following outline to determine pairwise habitat overlap between a “test” pair of buffalo:

1. Project GPS points in ArcMap
2. Clip GPS points to the enclosure boundary layer
3. Use GMe to generate kernel density estimates and 95% isopleths
4. Back in Arc, used the identity tool to calculate area of overlap between the two individuals
5. Computed percent overlap using Excel

Geospatial Modelling Environment (GME):

GME is a free geostatistical software that combines the computational power of R with the functionality of ESRI ArcGIS to drive geospatial analyses. A few of the functions that are especially useful for analyzing animal movement are: kernel density, minimum convex polygons, movement parameters (step length, turn angle, etc), converting locations to paths and paths to points, and generating simulated random walks. For this analysis, I used GME to generate kdes and estimate home ranges using 95% isopleths.

Kernel density estimates and isopleth lines

Kernel densities can be conceptualized as 3-dimensional surfaces that are based on density of points. Isopleth lines can be drawn in GME based on a raster dataset (such as a kernel density) and can be set to contain a specified volume of surface area. For this analysis, I was interested in calculating 95% isopleths based on the kernel densities of GPS points. In real life, this means the area that an animal spends the majority of its time in.

Using the identity tool to compute overlap

After generating home range estimates for two individuals, I uploaded the resulting shapefiles to ArcMap and used the Identity tool to overlap the home ranges.  To use the identity tool, you input one identity feature and one or more input features. Arc then computes a geometric intersection between input features and identity features and merges their attributes in the output.

The map above shows 95% isopleths from animal 1 (yellow), animal 13, (purple), and the area of overlap computed using the intersect tool (red line). I exported the output table to excel, where I calculated percent overlap between animals.

Conclusion

Overall, this method seems like it will be great for estimating habitat overlap. A few things that I’m concerned about are:

(a) Habitat use may be so similar for all animals that overlap cannot be related to differences in microbe transmission.

(b) Habitat use may correlate very strongly with contacts, in which case it will be difficult to control for the effects of contacts on microbe transmission.

(c) Percent overlap can be different for each individual in a pair. In my example, #13 overlapped #1 by ~80%, while #1 overlapped #13 by 90%.

I just want to be aware of these potential issues and start thinking about how to deal with them as they arise. Any suggestions would be appreciated, as always!

Introduction 

My research goal is to determine the effects of social and spatial behavior on disease transmission and nasal microbiome similarity. The overarching hypothesis of this project is that composition of microbial communities depends on host spatial and social behavior because microbe dispersal is limited by host movement. My research group studies a herd of African Buffalo in Kruger National Park that is GPS collared and lives in a 900 hectare predator-free enclosure. In conjunction with the GPS collars, each animal has a contact collar that records contact length and ID of any animal that comes within ~1.5 meters. However, for this class I focused on the GPS collars in the effort to test whether they are sufficient for inferring contact networks.

The purpose of this step in my research was to establish a method for creating distance matrices between animals at different time points using only GPS data. I wanted to determine whether this is a viable option for inferring contact networks and could be used in lieu of the contact collars. If this method is effective, my plan was to iterate through multiple time points to determine average distances between animals over time.

Results from this pilot study showed that the method is feasible, however, GPS collars would be less effective for inferring a contact network than the contact collars because temporal resolution is sacrificed.

Data Manipulation in R

The raw data from the buffalo GPS collars is in the form of individual text files, one text file per individual per time point. Step one was to generate a csv file that included all individuals at one time point. This was done in R using the following code:

##Load necessary packages

library(reshape2)
library(ggplot2)

##Set working directory and set up loop to import data

setwd(“C:\\Users\\couchc\\Documents\\GPS_captures_1215\\GPS_capture_12_15”)
SAVE_PATH <- getwd()
BASE_PATH <- getwd()

CSV.list<-list.files(BASE_PATH,pattern=glob2rx(“*.csv”))

all.csv<-read.csv(CSV.list[1], header = TRUE)

names(all.csv)

buffalo<-data.frame(ID=all.csv$title,X=all.csv$LATITUDE,Y=all.csv$LONGITUDE, Day=all.csv$MM.DD.YY, Hour=all.csv$HH.MM.SS, s.Date=all.csv$s.date, s.Hour=all.csv$s.hour)
## Now we want to melt them and cast them based on some data within the frame.

melted.all.csv<-melt(buffalo,id=c(“ID”))
names(melted.all.csv)

casted.all.csv<-dcast(melted.all.csv, LATITUDE+LONGITUDE~id)
# Where our previous data was organized with ID as a column,
# now ID is a row, and we can see what value an ID took at a given location.

length(buffalo[,1])
ggplot(buffalo[buffalo$ID==buffalo$ID[1],], aes(x=X, y=Y, value = ID))+
geom_raster()

Distance Matrix

Because the GPS collars are not synchronized, the 30-minute time intervals can be offset quite a bit, and there are quite a few missing time intervals. To try and correct this problem, I rounded times to the nearest 30 minutes in excel. I then imported the new excel file back into R to generate a “test” distance matrix for a single time point using the following code:

-Show code and output once I’m able to run it on a lab computer (My computer doesn’t have the processing power to do it in a reasonable time).

Conclusion

This method showed some interesting results: inter-individual distances can be calculated in R using GPS collar data, and if the process were iterated over multiple time points, average pairwise distances could be computed between each individual. A mantel test could be used to determine correlation between . The problem with rounding time points to the nearest 30 minutes is that it doesn’t guarantee that the buffalo are actually ever coming within the distance that is given by the matrix. Since some of the collars are offset by up to 15 minutes, the animals could be in the recorded locations at different times, and never actually come into contact with each other. The benefit of using GPS collars to infer social behavior is that it gives us actual distances between individuals, which adds an element of spatial resolution not provided by the contact collars. Contact collars only read when another animal is within a specific distance, but no measure of actual distance is recorded. However, since we are looking for the best way to predict contact transmission of microbes for this pilot project,  we are not interested in contact distances past a certain threshold. Although the distance matrix could prove useful for other behavior studies, it provides less relevant information than the contact collars. This could be a useful method if we wanted actual distances between organisms. However, to simplify we would like to set a threshold distance for microbe transmission, which is easily done with the contact collars. However, we would need much higher temporal resolution in our GPS data to be able to build distance matrices that are precise enough to infer contact networks, and this process is more easily done using contact collars.

Overall, this pilot project was useful because it demonstrated some of the potential benefits and drawbacks of using GPS intervals to infer contact networks. Although I do not plan to use the method described in this post for my dissertation research, it may be beneficial in future studies of animal behavior or herd structure. The exercise was very useful for improving my confidence in R — with lots of help from my classmates of course!

Relationships that vary in space and time: A challenge for simple linear regression

Regression is a fundamental analytical tool for any researcher interested in relating cause and effect. A basic assumption of regression is that of stationarity, the principal that the relationship between a predictor variable and its response is constant across its sample space; that a relationship is true in all regions where it is being applied. This assumption is a particularly poor assumption in spatially based analyses, where we know that interactions may exist between known and often unknown factors in how response variable relates to a given explanatory variable. While this is a  challenge to simple linear regression, it is also what generally makes spatial problems interesting: the fact that relationships are not constant across space and time.

Spatially weighted regression challenges the assumption of stationary in that where simple linear regression develops a single relationship to describes a phenomena, spatially weighted regression allows the relationship to vary spatially. Unhinging the relationship between a explanatory variable and its response spatially creates a set of local coefficient for each instance where an explanatory variable is offered. This is done through the use of a  weighting function. Wherein simple linear regression, each data point assumes equal weight with regards to the final relationship, a weighting function applies greater import to values closer to where a regression point would be calculated.

Fig 1: A spatial weighting function weights data points closer to a  regression point. In this way bandwidths can vary across a feature space, such that two local regression values may be constructed of a different number of data points.

Fig 2: Spatially weighted regression allows the relationship between a response and explanatory to vary across a study region.

NDVI and weed density: A case study in spatially weighted regression

Normalized difference vegetation index (NDVI) has been used in remote sensing  as a proxy for phenology in many remote sensing and cropping systems studies. NDVI is calculated as the ratio of red to near-infrared light, and is generally related to the amount of green photo-synthetically active tissue. In principal, weeds and crops should be distinguishable based on how their NDVI response varies in time.

Question: Can NDVI be used to predict weed density? Does the relationship between NDVI and weed density vary spatially? 

Fig 3: A general hypothesis for how weeds and crop may in their NDVI response. Weeds may mature earlier or later than a crop, but this relationship may also vary spatially.

Here, spatially weighted regression is offered as a method for distinguishing relationships between weed density and NDVI. Allowing the relationship between NDVI and weed density to vary spatially may allow one classify areas of the field based on the nature of these relationships.

Fig 4: NDVI over the course of the growing season at a 17 acre field located NE of Pendleton, OR, Summer 2015. Note that the field does not increase or decrease in NDVI evenly, but rather peak NDVI passes as a wave across the field. [ Note: GIF does not appear animated in preview. Click on the GIF directly if animation is not working ]

An important first step in deciding if a data set is suitable for spatially weighted regression is to look at the residuals of the linear relationship you are choosing to model. Here we examine the following function for predicting weed density:

This function uses 3 samples of NDVI over the course of the growing season, centered around the time of peak NDVI. The purpose of using these 3 times was to try and emphasize time periods where weeds and crop would vary in their relative response in NDVI.

Fig 5: Weed densities were calculated based on linear transects made prior to harvest. Weed hot spots were calculated using the Getis-Ord Gi* statistic in ArcMap. Weed hot spots from a prior analysis were used as input for predicting weed density in this exercise.

Fig 6: Predicted weed density for a multiple regression model based on 3 measurements of NDVI surrounding peak NDVI.  Multiple R2:  0.044, P-value < 0.001

Fig 7: Residuals from a multiple regression model based on 3 measurements of NDVI surrounding peak NDVI.  Both high and low residuals cluster spatially, indicating that the relationship between NDVI and weed density may vary spatially and may be a good candidate for geographically weighted regression.

Fig 8: Predicted weed density from a spatially weighted regression. Quasi-global R2: 0.92.

By using a spatially weighted regression, we’re able to account for 92 percent of the variance that occurs in the distribution of weeds in this field. Unlike in a standard regression, the result of this process is a collection of local regression formula. In this sense, the result is not a result that can be easily extrapolated to predict weeds distributions in future data sets. However, these coefficients do offer us the opportunity to look for some spatial patterns that may yield additional information as to what the nature of these local spatial relationships might be

Fig 10:  Map classified by coefficient slope.

Introduction:

Hotspot analysis is a method of statistical analysis for spatially distributed data whereby both the magnitude of a point and its relationship to the points around it are taken into consideration to identify statistically significant extreme values in a data set. While a single spatial data point may represent an extreme value, in the context of weeds management what often matters is being able to identify aggregates of values which taken as a whole represent an extreme condition. Where one large weed may have some impact, many medium and smaller weeds are likely to have a disproportionate impact. This has implications for weed management and weed science, specifically of the variety of techniques available to users for mapping the spatial distribution of invasive weeds, most rely on expert knowledge to decide what constitutes a “weedy” versus a “non-weedy” condition. This consideration is made independently of the geographic context of a value, usually by visually evaluation of the distribution of measured values, and deciding some cutoff, real or perceived, in the distribution of values. These cutoffs are often subjective, and are typically yield poor results when applied to independently generated data sets. Hotspot  analysis offers us a road forward where statistically significant extreme regions can be identified, and various mapping techniques compared by how well they predict these extreme regions.

My goal for this project was to see if hotspot analysis provided a better technique for mapping weeds populations in wheat fields at the time of harvest. Previously, we visually evaluated the histograms, and using some knowledge of how the weeds were distributed to determine cutoffs for “weedy” and “non-weedy” values. Here I wanted to see if I could generate more accurate maps of weed density relative to a reference data set.

Sources of data:

Fig. 1: Sampling for weed density was done at the time of harvest using a spectrometer in the grain stream of a combine, and with a visual evaluator watching for green weeds during harvest.
In Summer 2015 we harvested a field winter wheat NE of Pendleton, OR using combine outfitted with a spectrometer in the grain. A ratio of red to near infrared reflectance was taken, along with visual observations made by an observer from inside the cab of the combine. Prior to harvest, we walked the field on gridded transects, recording observations of all weeds at the species level. These data were all re-gridded to a common 7m X 7m grid using bilinear interpolation, and brought into ArcGIS for analysis.

Classification:

In ArcGIS, hotspot analysis was conducted using Hotspot analysis tool. The Getis-Ord Gi* statistic identifies statistically significant hot and cold spots in whatever spatially referenced value you use as an feature class for classification. For the purposes of this exercise, positive Getis-Ord Gi* statistics were considered to be “weedy”, while not-significant and negative scores were considered to be “non-weedy”. Cutoffs based on a visual evaluation of histogram, and knowledge of what should represent a weedy condition used to distinguish between “weedy” and “non-weedy” values  and their associated maps classified accordingly.

Fig 2: Ground reference data set classified using Hotspot analysis and histogram classification. All green values were considered positive for weeds.

Fig 3: Spectral assessment of weeds distribution classified using Hotspot analysis and histogram classification. All green values were considered positive for weeds.

Fig 4: Visual assessment of weeds distribution classified using Hotspot analysis and histogram classification.  All green values were considered positive for weeds.

Comparing techniques
Classified maps were then compared for accuracy using a confusion matrix approach. Accuracy here is defined as the rate of true positives and true negatives, divided by the total number of samples. Classified maps were also compared for their precision and sensitivity, where precision is the rate of true positives of the condition positives, and precision is the rate of true positives over the predicted positives. Precision addresses the question of if I predict it positive, how often am I correct? Sensitivity addresses the question, when the reference data predicts it positive, how often was my prediction correct?

Fig 5: Error assessment comparing spectral assessment of weediness to ground reference data using the histogram classification.

Fig 6: Results of the error assessments for all mapping techniques compared with their ground reference data.

Results:

These results show that hotspot analysis was a superior method for image classification when compared with a visual evaluation of the distribution.  This is probably a result of the fact that hotspot analysis takes into consideration the neighborhood of values a measurement resides in. Hotspot analysis increased the accuracy for both the spectral and the on-combine visual assessments. There were mixed results regarding its impacts on sensitivity and precision however. Hotspot classification increased the precision of the visual assessment, but did so at a cost to sensitivity. Conversely, the hotspot technique increased the sensitivity of the spectral assessment, but did so at a cost to its precision. It may be that precision comes at a cost to sensitivity using this method for comparing classifications. In general however, the most substantial gains were in accuracy, which is the most important factor for this mapping effort.