GEOG 566

         Advanced spatial statistics and GIScience

May 23, 2017

Tutorial 2: Investigate Spatial Autocorrelation (Mantel Test)

Filed under: 2017,Tutorial 2 2017 @ 1:30 pm

For this Tutorial I revisited a principle that I learned about in the Spatio-Temporal Statistics (Variation) statistics course that I took with Dr. Jones last fall. Autocorrelation is an important component to address within ecological work, as well as geographic work. Plots that are closer to each other may have a greater probability of capturing the same species during fieldwork and it is important to know if my data are influenced by distance and spatial relationships. Examining auto-correlation within my data may also reveal information about spatial patterns related to patch size, or gradients at my field site (Salmon River Estuary).

Research Question:

My research question fits the framework “how is yi related to xi + h? I am investigating spatial autocorrelation for my field survey plots and species assemblages represented by those plots. I want to know if I can predict or expect the presence of a plant species in one plot, based on its proximity (distance) to another plot. The presence of spatial autocorrelation in my plots would imply some sort of dependency or relatedness between plots, i.e. the closer two plots are located to each other, the more likely they are to overlap in terms of species present. Spatial autocorrelation can provide context for interpreting scale of patterns and causal variables related to spatial vegetation patterns (likely elevation, salinity, land use history).

My Approach (Tools for Analysis):

PC-Ord was very helpful in structuring my data for the Mantel test. I was able to run the test several times with different combinations of data to detect patterns of auto-correlation. Again, I formatted my data in Excel and used the Excel sheets to produce matrices for the Mantel text. Each matrix pair had species data, and UTM coordinate data.

Steps to Complete Analysis:

I organized my data in excel, started a new project in PC-Ord, assigned species and location matrices, and ran a Mantel test (Group > Mantel test). I used Sorensen (ranked) distance measures for my percent cover data, and Euclidean distance for my coordinate data. I set the test to complete 999 randomized runs for a Monte Carlo comparison to test significance. I also used my species data to conduct an Indicator Analysis, to identify species that are more common, faithful, or exclusive to particular marsh that I surveyed. I directed PC-Ord to conduct an ISA, and grouped by data by tidal marsh surveyed. The ISA produced a number for each species surveyed that indicated the percentage of plots that species was found in, and whether or not it was significant for that species. From the indicator analysis, I found that certain upland marsh species are indicative of remnant sites, certain species are indicative of salty conditions, and other species are indicative of restored sites.


examples of matrix inputs from Excel to PC-Ord. The data were structured as matricies with sample units (plots) x species cover, or sample units x UTM coordinates.

Results and Outcomes:

I conducted a Mantel test on all of my data and found that none of my plots were spatially autocorrelated (Mantel’s r statistic Transect: r = 0.037797, p = 0.182182; MW plot: r = 0.027994, p = 0.164164, accept null hypothesis of no relationship). This is a little surprising, but may be indicative of noise within my dataset, and variation of species at this scale. It is possible that autocorrelation is not detectable at this scale, or perhaps I need a larger dataset with less proportional noise to sort out the autocorrelation signal. I was however able to detect spatial autocorrelation at the 1,000 square meter scale for the Modified Whittaker plots (r = 0.638224, p = 0.00010), suggesting that there may be more fine scale patichness, variation, or nestedness among plant species at each of the SRE tidal marshes. Salt may also be a confounding factor that drives spatial diversity of vegetation, in addition to dike removal, as salt is a limiting factor for some salt marsh plants; not all species are equally tolerant of it.

For my ISA test, I found that (1) Triglochin maritima, Sarcocornia perennis, and Distichlis spicata were significant indicators of salty, restored conditions, (2) Dechampsia caespitosa, Juncus arcticus var. littoralis, Potentilla pacifica, Glaux maritima, and Hordeum brachyantherum were significant indicators of upland, high elevation conditions, and (3) Carex lyngbyei was a significant indicator of restored conditions. I broke my dataset up and conducted a mantel test for each of the groups, using only plots that recorded the presence of at least one species in each of the groups. I did not find any significant autocorrelation either with any of the strong indicator species (that were all found in a high proportion of plots surveyed). I am curious if my plots were located closer to each other, and/or I had surveyed more plots over a larger area, spatial autocorrelation patterns would begin to emerge.

an example of PC-Ord output for a Mantel test. The R statistic implies the amount of correlation between species cover and distance, the p value implies the significance of the correlation/similarity in comparison to chance (computed by Monte Carlo randomizations).

I also produced a map in Arc, to visulalize the patterns of diversity I saw in my data. I coded each of my plot locations (for Transects and Modified Whittaker plots) by the dominant plant strategy type: Carex lyngbyei dominant (A plot that had at least 50% or more cover of Carex lyngbyei ), salt dominant (at least 50% or more cover of one or more salt tolerant species), or mid-high marsh dominant (at least 50% 0r more cover of a mid-high marsh species that is not Carex lyngbyei). I think the map helps to visualize spatial patterns of diversity well, on a broader scale, by grouping plots into different assemblies or types/guilds based on their content.

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

This method was manageable to set up and execute, however I feel that it was difficult to negotiate useful outcomes with my data. It is highly plausible that my data do not capture these patterns, however, it was somewhat difficult for PC-Ord to work with my data on this problem. I have many zeroes in my dataset, as not all species are represented in every single plot (I have a grid of plot number X species, with cells filled in for percent cover ranging from 0 – 100). I was not able to complete mantel tests with certain assemblage combinations, as PC-Ord could not compute a randomization outcome with the number of zeroes present (random shuffling of the dataset produced too many identical outputs because I have too many zeros). Ultimately, I think I would approach this problem again with a larger dataset over a greater extent of my study site.


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