1. T(auk)ing about Auks: A Temporal and
Quantitative Analysis of Dive Parameters
Cassin’s auklets (Ptychoramphus aleuticus) are diving seabirds
which feed on primarily krill in the Pacific North [1]. Our
objectives were 1) to find if there were correlations between
certain dive parameters and krill levels and 2) to test the
hypothesis that auklets dive deeper during midday (as more
sunlight penetrates the ocean surface, the krill can congregate
at deeper depths).
Introduction
For this project, seven years of data were collected during
the summer months from 2008 to 2015 on the Farallon
Islands, off the San Franciscan coast. We attached sensors
measuring temperature and depth every half second to
individual birds and retrieved raw data after a few days of
tracking. In total, we recorded 98632 dives performed by
118 birds over 62 separate days (Figure 2). We then
parsed the raw data into readable text files using the
programming language Python. It was at this point that we
Methods
Figure 3: Comparison of maximum dive depth and krill levels
30 m underwater. Top) Ln(krill30)by year. Middle) Average
maximum dive depth by year. Bottom) Dive depth vs.
ln(krill30) and the corresponding linear regression analysis.
Results
o Linear Regression: Finds the least-squares line of fit between
two variables
o Tukey HSD: Compares differences between multiple means
(similar to a t-test)
o ANOVA (linear mixed models): For this specific case, ANOVA
takes the least-squared quadratic equation (the full model)
and tests if a reduced model is sufficiently similar and if it can
effectively approximate full model values
• Full model: dive depth ~ (hour+hour 2) * year
• Reduced model: dive depth ~ hour*year + hour 2
Statistical Methods
Frances Hung, Gail Gallaher, the Karnovsky Lab
Conclusion Acknowledgments
I would like to thank Professors Cavalcanti and Karnovsky for their
mentorship, Professor Hardin for her expert advice in statistics, and
HHMI for funding this project. I also am grateful for my very inspiring,
funny, and cool labmates Angel, Ryan, Julie, and Owen.
There were quantitative relationships between the yearly
krill levels and seven parameters: maximum dive depth
(dive pressure), dive length, dive PDI (rest time between
dives), dive efficiency, dive bottom (time spent at >80%
maximum depth), bout diving (% time spent diving in a
cluster of dives), and bout efficiency. All these were
significant with a p-value ~.01 or less.
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It appears that there is a correlation between dive maximum
pressure and the time of day. A Tukey HSD analysis shows
that dives during midday(11-4 PM) are deeper than dives
during other times with a high level of statistical
significance. However, ANOVA illustrates that we cannot
describe the yearly relationship between dive depth and
hours using a generalized equation.
There are statistically significant correlations between certain
dive and bout parameters and krill levels throughout the
years. We didn’t find a specific quantitative relationship
between hours and dive depth, but generally, auklets dive
deeper during midday.
Figure 5: Cumulative boxplots of maximum dive pressure by time of
day and the corresponding Tukey HSD analysis.
Estimate Std. Error t-value Pr(>|t|)
log(krill30) 1.603139 0.233323 6.870901 3.89E-10
(Intercept) 10.256229 0.2698348 38.009288 1.81E-65
Figure 4: A set of bar charts comparing the maximum
dive depth by year. The bars are colored by the total
number of dives by hour for each year.
Temporal Dive Depth
Future Work
We plan to analyze the data for more correlations and
trends. For example, we can compare individual years to
others to see if abnormal trends correspond to low-krill
years (2008, for instance, had little krill and auklets were
forced to change their diet).
We used three statistical methods to analyze the two sets of
data for our objectives: linear regression analysis for parameter-
krill analysis, and Tukey HSD (honest significant difference)
and ANOVA (for linear mixed models) for temporal analysis of
dive depth. For the former of these analyses, we averaged data
at the individual bird level (n=118) while for the latter, we used
data averaged at the individual dive level (n= 98632).
Figure 1: A Cassin’s auklet on the Farallon Islands [2]
References
[1] Manugian S, Elliott ML, Bradley R, Howar J, Karnovsky N, Saenz B, Studwell A, Warzybok P, Nur N, Jahncke J. (2015) Spatial Distribution and Temporal Patterns of Cassin’s Auklet Foraging and Their
Euphausiid Prey in a Variable Ocean Environment. PLoS ONE 10(12): e0144232. doi: 10.1371/journal.pone.0144232
[2] LeValley, Roy. Cassin’s Auklet SE Farallon Island..2008. Web. 19 July 2016.
Year Days Hours Birds Dives
2008 7 101 15 9252
2009 8 126 15 14898
2010 11 171 11 6885
2011 7 101 20 14183
2012 4 63 6 3603
2013 9 140 15 15700
2014 8 130 17 18015
2015 8 124 19 16096
Figure 2: Distribution
of dive data from
2008-2015.
started analyzing and
visualizing the data
with Python, R, and
the graphing interface
Plotly.
Figure 6: Cumulative boxplots of average maximum dive pressure by
hour. Each year’s least-squares polynomial fit to its specific data is
graphed in a different color. The ANOVA table summarizes the
similarity of the full and reduced model: the p-value of the models
being similar is <.0001.
Model df AIC BIC logLik Test L.Ratio p-value
reduced
model
1 19 626521.2 626701.7 -313241.6
full model 2 26 624858.2 625105.2 -312403.1 1 vs 2 1676.959 <.0001
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year
2008
2009
2010
2011
2012
2013
2014
2015
Dive Parameters vs. Krill
Estimate
Std.
Error
z
value
Pr(>|z|)
midday -
morning
== 0
1.93048 0.04797 40.25 <2e-16
night -
morning
== 0
0.88967 0.04612 19.29 <2e-16
night -
midday
== 0
-1.04082 0.04647 -22.40 <2e-16
0
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morning midday night
TOD
MaxPress