**Questions**

First, to gain a better understanding of the relative heterogeneity in slope angle among sites, I reexamined the cumulative spatial buffers of benthic bathymetry, and calculated non-overlapping ‘donuts’ of expanding space around each site, Mirroring tutorial 2, I then recalculated slope angle minimum, maximum, mean, and standard deviation.

Next, I expanded off multivariate analyses (NMDS) previously completed for my project. Given the observed differences among in spatial patterning of the sample units in my ordination (consistently clustered or clusters spread apart my abrupt and large movement through species-space, i.e., abrupt and lasting community change), my objective was to calculate to quantify metrics of ‘transect change through species-space over time.’

**Hypotheses**

My hypotheses for this tutorial (and the final project in general) are that low-relief sites, or sites with low substrate heterogeneity are associated with dramatic community change over time. Likewise, I hypothesize that high-relief sites, or sites with high substrate heterogeneity exhibit a single stable community structure through time.

**Data Used**

The bathymetry data used is same as described in Tutorial 2, being side scan sonar derived (2m grain), with an extent approximately 1km offshore all around SNI.

To calculate transect movement in species-space, I used a community matrix comprised of 13 macroalgal and invertebrate species. Abundances were recorded for all species, and given the preponderance of purple urchins (1000s vs. 10s of other species), I log(x+1) transformed all species. To reduce the dimensionality of my community matrix down to the key axes, I used non-metric multidimensional scaling (NMDS) with the Bray-Curtis distance metric, a proportional area metric that tolerates messy and 0 filled community data relatively well. The ordination converged on a two-dimensional solution with stress (departure from montonicity) = 0.16.

**Approach **

Calculating donut buffers was relatively straightforward, and employed the ‘Erase’ tool in ArcGIS. Otherwise, the methods of creating buffers, and extracting raster buffers containing the desired statistics mirrored exercise two.

To quantify transect movement through species space, I used the adehabitatLT package in R. This package requires evenly spaced time intervals, so minor fudging was required to trick the analysis into calculating paths for the transects (these data are biannually collected, though the exact day is most definitely not consistent, given inclement field conditions and the vagaries of the sea). One complete, I extracted step lengths and net-squared displacement values, both of which were subsequently viewed as (1) distributions and as (1) a response variable plotted through time. Distances plotted against time provided insight into total community change between any two time points, while net-squared displacement plotted against time provided more insight into ‘lasting’ changes in community shift (as displacement values are relative to the starting value).

Net-squared displacement is usually viewed against expected displacement, a null hypothesis generated from randomizing step length and turning angles. Comparison of net-squared vs expected displacement provides a metric for whether your animal, or transect, is moving more or less than expected given ‘random movement.’ I choose not to focus on expected displacement, given that I don’t quite see how the null hypothesis is as relevant for movement through species space (i.e., what would a null hypothesis be for community change. . . no change, random change? Neither are fully satisfactory). Instead, I opted to view the relative differences in displacement among sites.

Finally, despite spatial scaling issues (discussed in results) for comparing these transect track metrics against substrate heterogeneity, I plotted the mean and standard deviation for step distances against the mean and standard deviation of slope angle at increasing spatial scales. This is spatially mismatched as the step distances are recorded at the smallest scale only (the transects), while the slope angle mean and standard deviation values are for the spatially increasing scales of donut buffers.

**Results**

I was a little surprised to find that calculating non-overlapping donut layers did not actually differ all that much from the cumulative donut values. I suspect that redoing this and incrementally calculating every 1m addition in buffer space around the site would give more nuanced behavior, but it is unclear to me whether this would significantly change the overall pattern. (I believe it will be worthwhile to redo this as described, but in R, with code to automate).

Transect movement distances: frequency histogram (distribution) and distances against time. I expected more bimodality from some of the sites for the distances, but I didn’t account for the fact that even the sites which exhibited dramatic community change (large distances) are still relatively consistent most of the time (many short distances interspersed with a few large distances). Distances against time provided a ‘pure’ representation of community change between any two points in time. However, as these distances do not account for lasting change, they can provide a misleading representation of ‘lasting’ vs immediately reversed community change (hence the need for net displacement).

Net-squared displacement: distributions and net-squared displacement through time. The distribution of net-squared displacement provides a good visual representation of my understanding of the time series and the ecology of the system. These distributions are at this time mostly visual, and the differences among distributions are qualitative, but I can see how formally fitting a CDF may be useful in the future. Net-squared displacement through time actually provides the best visual representation of community change that I’ve generation thus far. As the displacement values account for the starting position, lasting shifts in community structure are represented, as is high community consistency.

The relationship between the mean and standard deviation of distances traveled in species space (transect movement) and the mean and standard deviation of slope angle was negative. I did not formally fit a regression or a curve, but the relationship is visually clear, and I believe a visually approximation of the relationship suffices for the purposes of this project. It is worth noting that large step distances (dramatic community change) occur at homogenous low-relief sites (low slope), while small step distances (little change in community structure) occur at heterogenous high-relief sites (high slope angle), with higher variation in slope angle. Thus, while only a cursory comparison, this analysis supports an early hypotheses that heterogenous substrate is associated with community consistency through time.

**Critique of Method, My Learning, and Statistics **

** **All aspects of these analyses were useful, and I find myself more limited by the spatial constraints of the data, and the subsequent limitations on testing direct relationships between statistics of community structure and substrate heterogeneity at increasing scales. This all of course is a product of the data, and doesn’t reflect on the usefulness of the methods.

I still want to find a better way of account for substrate heterogeneity. I think creating 1m donut buffers of increasing scale is a potential option, and one that would benefit from R automation. Additionally, mean and standard deviation may be too high level of a summary. I want to see the distribution of slope angles (frequency histograms).

The adehabitatLT package in R was straightforward to use, though I did have to fudge the ‘time steps’ of my data to create the desired tracks, and my application of the package was very rudimentary (i.e., calculate tracks and extract step distances and net-squared displacement).

Altogether, this class has been extremely useful as a crash-course into ArcGIS, and additionally has provided glimpses of future directions (e.g., use spatial analyses in R, and one day potentially use ESRI bridge to link ArcGIS and R). As discussed in class, my software usage was either (1) R studio, where I was already quite comfortable, or (2) ArcGIS, where each step performed in the course of the class provided useful experience to me.

Regarding statistics, it was very useful for me to go through the motions to calculate correlation and cross-correlation. I was generally familiar with these analyses from GEOG 556, but actually using them was quite illustrative. Perhaps most useful was being able to see how spatial and temporal problems are tackled, both with my own work, and through seeing how other people tackle problems. I was able to get R package recommendations from the tutorials, along with ideas for analyses and overall analytical approaches.