1. Coral Species distribution and Benthic Cover type He’eia HI
By: Ashley Fossett

2. How are coral species correlated with different benthic cover types?
Montipora capitata
Porites compressa
Reef building corals
Pocillopora damicornis
Leptastrea purpurea
Resilient / Successional corals
Ho: There is no pattern between coral species and benthic cover type
Ha: There is a significant pattern between coral species and benthic cover type

3. Dataset Description Main Matrix 60 samples and 4 species
Samples were taken along a varying gradient of coral cover
4 species identified:
%MC Montipora capitata
%PC Porites compressa
%PD Pocillopora damicornis
%LP Leptastrea purpurea
Second Matrix
60 samples and 4 Benthic cover types
4 types of Benthic cover:
TCC Total Coral Cover
Hsub Hard Substrate
Rubble Dead Coral/ Rock Piece
Sand/Silt Bare ground

4. Data Processing Outlier Analysis : Same for 1st and 2nd matrix
Main Matrix: Species
Row Summary:
Average Skewness: 1.624
240 cells in main matrix
Percent of cells empty =
Matrix total = E+02
Matrix mean = E+00
2nd Matrix data: Benthic Cover
Row Summary:
Average Skewness:1.152
240 cells in main matrix
Percent of cells empty =
Matrix total = E+04
Matrix mean = E+02
Outlier Analysis : Same for 1st and 2nd matrix
 No samples were recognized as outliers given cutoff of 2.0 standard deviations from the grand mean.

5. Screening #2 – Data Summary
I do not have outliers in my data but I do have a lot of zeros.
I am tying to assume a normal distribution of my species therefore I performed a general relativization and an arcsine transformation.
I used an arcsine transformation because I am dealing with percent cover data that range from 0-1 with 1 being 100% of the coral in a survey.
Main Matrix: Species
Row Summary:
Average Skewness: 1.624
240 cells in main matrix
Percent of cells empty =
Matrix total = E+02
Matrix mean = E+00
Main Matrix: Species
Row Summary:
Average Skewness: 1.234
240 cells in main matrix
Percent of cells empty =
Matrix total = E+01
Matrix mean = E-01

6. Scatterplot Patterns
Due to the fact that coral compete for space and the data are comparing percent coral cover, by design PC and MC are negatively correlated.
If there is more PC this takes up space for MC
However, based on these species making up total coral cover it turns out that MC is negatively correlated with TCC while PC is positively correlated with TCC
Whereas the opposite is true for sand/silt substrate

7. Results of PCA

8. Results Interpretation
correlation matrix (Main)
Pearson and Kendall Correlations with Ordination Axes N= 60
Axis:
r r-sq tau r r-sq tau r r-sq tau
% MC
% PC
% PD
% LP
correlation matrix (second)
Axis:
r r-sq tau r r-sq tau r r-sq tau
TCC
HSub
Rubble
Sand
Look at the r values ( axis 1 is strongly correlated with %MC (neg.) and %PC(pos.)), while (axis 2 is strongly correlated with PD and LP “neg. correlated”)
For the second matrix, (axis 1 is strongly correlated with TCC (pos.) and sand (neg.), while (axis 2 is strongly correlated with rubble (neg.))

9. Results Interpretation
It looks like my data is only correlated with Axis 1.
Coefficients of determination for the correlations between ordination
distances and distances in the original n-dimensional space:
R Squared
Axis Increment Cumulative
Increment and cumulative R-squared were adjusted for any lack
of orthogonality of axes.
Axis pair r Orthogonality,% = 100(1-r^2)
1 vs
1 vs
2 vs
Number of entities = 60
Number of entity pairs used in correlation = 1770
Distance measure for ORIGINAL distance: Euclidean (Pythagorean)

10. Discussion
These results indicate a positive relationship between my species distribution and benthic cover type
Specifically a difference between the two major reef building coral species
This multivariate approach described an underlying hypotheses that Montipora capitata are better at dealing with higher levels of sedimentation and a more turbid habitat compared to Porites compressa.

11. Next Steps
I would like to further this investigation and establish a Weighted Average between species and run the analysis again.
With this knowledge that MC is more associated with a sandy substrate I hope to identify more patterns between the more resilient coral species.
Pocillopora damicornis
Leptastrea purpurea
Resilient / Successional corals