1. Quantifying Diving Data from Christmas Shearwaters (CHSH) Ilana Nimz: Mars 6300
Dataset: Time-depth-recorder (TDR) raw data 1. Date 2. Time of dive (H:M:S, recorded every second underwater) 3. Pressure (dBar, every second underwater)
Collected from 8 CHSH over 33 tag-days

2. Objective: Quantify Diving of Christmas Shearwaters (CHSH)
Hypothesis: CHSH are diving exclusively during daylight hours (civil twilight a.m. to civil twilight p.m.) Prediction: CHSH dive more frequently in the late afternoon and evening, prior to civil twilight Approach: Summarize dive profiles from TDR raw data Standardize time across 3 months of tagging (Jun-Aug) by dividing 24hrs into 4 time blocks 1) Twilight hrs, 2) Middle of Day, 3) Twilight -3.5 hrs, 4) Night Start by exploring correlations between depth measurements and dive frequency via ordination

3. Dataset Description Main_CHSHsummary.wk1 (main matrix)
125 samples & 5 variables Samples: Bird-Tag Day-Time Block (Twilight, Morning, Daytime, Evening) Variables: Dives per Hour: # dives/time-block hrs Maximum Depth: meters Average Maximum Depth: meters Median Maximum Depth: meters %CV Max Depth: meters
Second_CHSHgroups.wk1 (Second matrix)
Samples:
Bird-Tag Day- Time Block
Grouping Variables:
Time: Morning 1, Daytime 2, Evening 3, Twilight 4
Bird: Bird # (1-8)

4. Dataset Processing
Outliers: “No… outliers given cutoff of 2.0 SD from the grand mean”
Empty samples: 500 cells in main matrix; % empty =   32
Samples discarded: All night samples were empty- 26 discarded Some morning samples empty- 12 discarded
Data transformations / relativizations: -Attempted to normalize w/ log transform- skew and kurtosis reduced but not normal range for all variables, so Non-parametric route! - Using Median to describe non-parametric data: removed average depth column -Give variables the same weight General Relativization (will relativize during ordination)
Describe your sample size: Sample total= 85: 19 Morning, 33 Mid-day, 33 Evening

5. Dataset Exploration Identifying correlations:
Dives/hr and Depth metrics
Weaker correlation with dives/hr and Depth: Max, Med, CV Tau= 0.605, , 0.604
Max depth & Median depth Strongest Positive Correlation Tau=
0.36
Weakest correlation between Med max and CV
Tau =
*Data not normal, so used Kendall Tau correlation

6. Dataset Analysis Settings used in the analysis Distance: Rel Sorensen
NMS_DiveMaxAvgMedCV_RelSor_999                                                  
Ordination of plots    in metrics  space.         85 plots           4 metrics 
         The following options were selected:
ANALYSIS OPTIONS
         1. REL.SOREN. = Distance measure
         2.          6 = Number of axes (max. = 6)
         3.        250 = Maximum number of iterations
         4.     RANDOM = Starting coordinates (random or from file)
         5.          1 = Reduction in dimensionality at each cycle
         6. NO PENALTY = Tie handling (Strategy 1 does not penalize
                         ties with unequal ordination distance,
                         while strategy 2 does penalize.)
         7.       0.20 = Step length (rate of movement toward minimum stress)
         8.   USE TIME = Random number seeds (use time vs. user-supplied)
         9.         50 = Number of runs with real data
        10.        999 = Number of runs with randomized data
        11.         NO = Autopilot
        12.   = Stability criterion, standard deviations in stress
                         over last 200 iterations.
OUTPUT OPTIONS
        14.        YES = Write distance matrix?
        15.         NO = Write starting coordinates?
        16.         NO = List stress, etc. for each iteration?
        17.        YES = Plot stress vs. iteration?
        18.        YES = Plot distance vs. dissimilarity?
        19.        YES = Write final configuration?
        20.  UNROTATED = Write varimax-rotated, principal axes, or unrotated scores for graph?
        21.        YES = Write run log?
        22.        YES = Write weighted-average scores for metrics ?
      1500 = Seed for random number generator.
Settings used in the analysis
Distance: Rel Sorensen
Randomizations: 999

7. Results Interpretation
1 significant axis = final stress for 1-dimensional solution *Excellent! (lower stress with fewer “species”) Minimum stress real data > Minimum randomized stress p-value =  (23+1 / 999+1)
STRESS IN RELATION TO DIMENSIONALITY (Number of Axes)
Stress in real data Stress in randomized data
50 run(s) Monte Carlo test, 999 runs
Axes Minimum Mean Maximum Minimum Mean Maximum p
p = proportion of randomized runs with stress < or = observed stress
i.e., p = (1 + no. permutations <= observed)/(1 + no. permutations)
Conclusion: a 1-dimensional solution is recommended.

8. Results Interpretation
Scree Plot
Stress very low at 1st axis- real data
High variability of
Randomized stress
In 1st axis
Overlap: 23 times, randomized > real

9. Results Interpretation
Coefficient of Determination (% of Variance):
Coefficients of determination for the correlations between ordination
distances and distances in the original n-dimensional space:
            R Squared
Axis   Increment   Cumulative
 1       .998        .998
Extremely high amount of variance (99.8%) explained with 1 axis
Report Orthogonality: N/A- only 1 axis

10. Results Interpretation
Strongest correlation indicates Med Max is explaining axis- negative correlation with axis
correl_DiveMaxMedCV
Pearson and Kendall Correlations with Ordination Axes   N= 85
Axis:               1                               r    r-sq   tau   
dives pe    .351   .123   .019
max dep     .082   .007  -.390
median m     .161  -.525
%CV         .768   .590   .328
Most significant correlation with axis: Median Depth
Max & Median Max had strong negative influence
CV weak positive influence on axis 1 Not much influence from dive frequency

11. Discussion – Method
What do these results mean for the hypotheses / predictions you proposed ?
-Accept hypothesis: CHSH dive exclusively during the day
Need further analysis to test predictions, but NMS was good exploration of patterns prior to testing temporal frequency and depth with a grouping test
-Max depth and Median Max depth strongest influences
-Frequency of dives not as strong as depth measures in axis

12. Discussion – Next Steps
What do you propose to do for your re-analysis?
MRPP- test the prediction to identify when during daylight hours CHSH are diving more frequently
What would be the next steps for this study?
Look at time under water and time between dives
Compare to other shearwater species