Weddell Seal Morphometrics: An Example of a Mathematical Expedition in Polar Science
VCTM Conference
March 14, 2014
Lynn Foshee Reed ([email protected])
Einstein Educator Fellow (NSF – Polar Programs)
Adapted from a field problem suggested by Dr. Jennifer Burns and Michelle Shero, University of Alaska –
Anchorage.
Background
Weddell seals are prominent Antarctic marine predators and are
associated with fast ice -- sea ice that is “fastened” to the
shore or ocean bottom and extends out into the sea. Fast
ice does not move with currents or wind.
The world’s southernmost mammals, Weddell seals are the
subject of one of the longest running research studies of a longlived mammal. “A breeding population of Weddell seals …
has been intensively studied in Erebus Bay at the southern
Figure 1: Weddell Seal and Pup
extent of the Ross Sea since 1968. The long-term database,
Image courtesy of Michelle Shero, University of Alaska Anchorage
which includes data for more than 20,586 marked
individuals, contains detailed population information that
provides an excellent opportunity to study linkages
between environmental conditions and demographic processes in the Antarctic.”
Weddellsealscience.com/project.html
“Morphometrics refers to the quantitative analysis of form, a concept that encompasses size and
shape.” (Wikipedia) Lengths, widths, masses, areas, and ratios are all examples of measurements of size
that are analyzed with traditional morphometrics.
In the 2012-13 Antarctic season, Michelle Shero, a graduate student of Dr. Jennifer Burns of the
University of Alaska Anchorage, set about calculating the amount of subcutaneous fat of seals from
measurements taken in the field as part of her research. The traditional method uses a truncated
circular cone model in which eight (8) measurements are taken of each seal.
Figure 2: Seal Measurement Locations
Image courtesy of Dr. Jennifer Burns, University of Alaska Anchorage
V
blubber
Blubber
depth
Ms. Shero notes, “We’d noticed that while animals are
hauled out and lying flat against the ice, they
appeared more ellipsoid in cross-section. An ellipse
has a major and minor [axis length], and if animals
were ellipsoid-shaped, then that could lead to a
decrease in overall animal volume as well as blubber
volume.” Therefore, she revised the model by using
elliptical cones. To do this, a field technique for
measuring the degree of “ovalness” was needed. A
“slump-ometer” was created out of PVC pipe and a
measuring tape, and it provided an inexpensive yet
accurate method to measure the major and minor
axes length of the ellipse that is assumed to be a more
accurate cross-sectional shape. “While the original,
circular truncated cones method assumes that the
height and width of the animal are the same, at most
sites widths were almost twice that of measured
heights.”
=V
outer cone
–V
inner cone
Figure 3: Weddell Seal and Slump-ometer
Photo courtesy Michelle Shero, University of Alaska Anchorage
Pho
Image courtesy of Michelle Shero, University of Alaska
Anchorage
In addition to the height and width measurements, the
researchers used an ultrasound to measure blubber
depth. The illustration below shows the blubber layer
for a typical cross-section. “Once blubber depths are
subtracted, the inner core is even more ellipsoid.”
Figure 4: Weddell Seal cross section
Image courtesy of Dr. Jennifer Burns, UAA
Assignment:
Use the data provided below to calculate the Total Estimated Volume of Blubber and Estimated
Mass (Total, Core, and Blubber) of Seal WS 12-22.
Dorsal
Lateral
Curved
Height
Width
Blubber
Blubber
WS 12-22
Girths (cm) Length (cm)
(mm)
(mm)
Depth (cm) Depth (cm)
Ears
75
256
200
330
Neck
137
229
270
570
5.25
6.72
Axillary
202
192
420
730
5.10
7.15
Sternum
212
161
440
810
5.57
5.71
Middle
206
123
410
850
5.82
4.82
Umbilicus
181
86
340
680
5.68
5.28
Pelvis
127
44
300
450
4.67
4.42
Ankle
76
21
120
350
Optional Investigations:
Calculate Surface Area and Buoyancy for Seal WS12-22.
Use the girth to calculate volume and mass information using the truncated circular cone method.
What is the error from the measured mass?
References:
Weddell Seal Science, http://weddellsealscience.com
PolarTREC Connect Webinar with Dr. Jennifer Burns
http://www.polartrec.com/resources/event/jennifer-burns-and-the-life-science-of-weddell-seals
Videos:
Antarctica’s Weddell Seals, http://weddellsealscience.com/weddell.html or
http://www.youtube.com/watch?feature=player_embedded&v=mYAbdoh3hgg
About Weddell Seals – an Introduction to the southernmost Mammal on Earth (Weddell Seal Ecology in
Antarctica), http://weddellsealscience.com/intro.html or
http://www.youtube.com/watch?v=FZhy4jw9W2c&feature=player_embedded
http://www.teachersdomain.org/resource/ipy09.sci.life.eco.seals/