GEOG 566






         Advanced spatial statistics and GIScience

April 24, 2018

Among-site differences in giant kelp (Macrocystis pyrifera) temporal autocorrelation

Filed under: 2018,Exercise/Tutorial 1 2018 @ 5:15 pm

Questions

As a preliminary analysis to explore pattern before incorporating other variables, I investigated how giant kelp (Macrocystis pyrifera) autocorrelation varied through time. By way of refresh, these abundance data are from seven subtidal sites, with each site comprised of five 10x2m2 transects. All 35 transects were sampled biannually (every 6 months) since 1980. Based on personal observations, I suspect that the physical substrate underlying these sites to be highly variable, both within- and among-sites (as is the associated subtidal community structure), such that averaging these transects up to the site level would gloss over pattern that might otherwise provide insight into spatiotemporal dynamics. Specifically, for this exercise I asked:

  • Are patterns of M. pyrifera temporal autocorrelation similar within-sites (among-transects)?
  • Are patterns of M. pyrifera temporal autocorrelation similar among-sites?

Approach

I used the base autocorrelation function in R studio (acf) and ggplot2 to visualize these data, and excel to create a spreadsheet tallying instances outside of the confidence interval.

Steps

  • Existing code was used to structure my data into data frames for the relevant sites and transects (dplyr)
  • Use the base R acf function to calculate lagged temporal autocorrelation coefficients for each of the 35 transects.
  • Create new data frame of correlation coefficients, and use those data to group and visualize with ggplot2 the five transects comprising each site.
  • Use correlation coefficient data to create spreadsheet tallying the instances of positive autocorrelation before the ‘first drop’ below the noise confidence interval, and tally subsequent peaks or dips above or below the confidence interval.
  • Examine within- and among-site patterns

Results

While I did not use a statistical test to evaluate my spreadsheet values, a visual examination provides insight into the differences both within and among sites. To address my first question (within-site, or among-transect variation), I do see differences in the temporal scale of correlation, though it is unclear how significant or meaningful these differences are.

The patterns among-site are more apparent, with certain sites exhibiting either no instances of positive autocorrelation, or a single point before dropping into the confidence interval (e.g., West Dutch, East Dutch). This indicates rapid shifts in M. pyrifera abundance at the 6 month interval. These same two sites also exhibited the longest lagged temporal scale of positive correlation (e.g., at the 15, 16, and 18 lagged scale, or 8-9 years).

Other sites exhibited longer periods of positive autocorrelation before the ‘first drop’ (i.e., West End Urchin, West End Kelp, and NavFac), with one site—Sandy Cove—almost uniformly exhibiting positive autocorrelation out to 7 (3.5 years). However, results from this site must be cautioned by the dramatic shifts in M. pyrifera over time, and thus non-stationarity is almost guaranteed. That being said, Sandy Cove also exhibited long periods of negative autocorrelation, often into the ‘uninterpretable range’ (i.e., past approximately 1/3rd of the total temporal scale).

Critique of the method

I did find it useful to calculate and view the temporal autocorrelation coefficients for M. pyrifera. These results support my ‘sense’ of the system that there is substantial variation among-sites (despite all these sites being within 10km of one another). While differences were found within-site, it is unclear how significant or substantive the within-site variation is. While autocorrelation obviously cannot shed light on causal factors, mechanisms, or even associations (without other variables included) underlying these patterns of correlation coefficients, I do believe they provide grounds to proceed with an investigation into the associations between physical substrate complexity and M. pyrifera density through time.

Day_acf Day ED_acf ED WD_acf WD WEK_acf WEK WEU_acf WEU SC_acf SC NF_acf NF

Table 1: temporal lag of steps before dropping into the confidence interval, and any subsequent departures from the confidence interval. The orange box are sites exposed to high storm surge, and the blue box are sites relatively sheltered from large wave events. The column on the far right uses color to qualitativley depict the relative degree of physical substrate complexity at each site, with red sites exhibiting large pinnacle structures (i.e., high-relief), and green sites almost uniformly flat (i.e., low-relief).

Fig. 1: 2m bathymetry for Sandy Cove, Dutch Harbor, and Dayona (L-R), with red depicting vertical slope, and green depicting flat (i.e., no slope)

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