and investigate opposing constraints. Using the bioenergetics
approach, the shark can reproduce only if there is remaining energy
after the metabolic demands of producing a head and pushing it
through water have been paid. These variations within the population
result in differential reproductive success, which is the driving force in
The Hammerhead Shark
Hammerhead sharks are charismatic megafauna characterized by
their laterally widened rostrum, called the cephalofoil. The cephalofoil is dense with ampullae of Lorenzini, which allow the shark to
detect the electromagnetic fields of its prey. Mello (2009) hypothesized that the widened cephalofoil aids in prey detection by allowing the shark to scan a larger electromagnetic field. Additionally,
the elongation of the rostrum provides wide eye spacing, producing
acute binocular vision for visual detection of prey (McComb et al.,
2009). Furthermore, the wide spacing of nostrils on the rostrum
allows the shark to determine the direction of scent trails (Kajiura
et al., 2005).
I chose to model the winghead (Eusphyra blochii) because it is the
most basal of the hammerhead species (Lim et al., 2010) and has the
highest rostrum-to-body ratio, ranging from 0.4 to 0.5. In contrast,
that of the great hammerhead (Sphyrna mokarran) ranges from
0.20 to 0.25. Hammerhead evolution has incrementally reduced
cephalofoil width in the more derived species (Lim et al., 2010).
By investigating the upper limits of cephalofoil widths and associated costs, students will understand the opposing evolutionary constraints that give natural selection direction, and they can see why
“bigger is not always better.” Wingheads eat a variety of fishes and
cephalopods. Once sexual maturity is achieved at ~1.0 m in length,
an average female winghead gives live birth to 6–25 pups/year.
Suggested Teaching Narrative
Instructors are recommended to give the students background context before using the bioenergetics model. Particular attention
should be paid to the equations that calculate the energy budget.
I distribute a “pre-lab” exercise of these concepts and equations that
students must complete before using the computer model. The following narrative is the basis of the one I assign and may serve as a
If the widened rostrum aids in prey detection, is a wider rostrum
better? A wider rostrum should allow the shark to survey larger
volumes of water per unit time than narrower rostrums. So, why
is the rostrum-to-body ratio limited to 0.4–0.5 for wingheads?
Phenotypic performance is limited because every form is a bal-
ance of strengths and weaknesses. Water is 775 times denser than
air; therefore, moving through it requires considerably more energy
than moving through air. Since wingheads are constantly swim-
ming in search of prey, the energy gained from digesting prey must
exceed the energy spent pursuing and capturing the prey. Every
object that moves through a fluid, such as air or water, is met
with resistance, called drag. The drag equation for all objects is
FD = ½ρμ2CDA (Equation 1), where FD is drag force measured in
Newtons (N), ρ is the mass density of the fluid (kg/m3), μ is the
flow velocity (m/s), CD is the drag coefficient, and A is the area of
the object (m2).
The combined surface areas of the cephalofoil and body
directly contribute to the total drag the shark experiences while
swimming. The widened rostrum protrudes laterally off the head
of the shark, adding to the drag the shark encounters when swimming. Subsequently, a trade-off exists between gains from the rostrum during prey detection and the drag generated during prey
pursuit. Therefore, there is a compromise of not being too small
and limiting foraging success but not being too large and risking
massive expenditures; this concept is known as opposing constraints.
Bioenergetics is the study of energy movement and transformation
through biological systems. This concept is modeled for fish in the
equation C = R + W + G (Equation 2), where C is consumption,
R is respiration, W is waste, and G is growth. A typical carnivorous
fish, such as a winghead, has a baseline bioenergetics budget of
1 unit consumed = 0.44 units of respiration + 0.27 units of waste
+ 0.29 units of growth (Kitchell et al., 1977).
As soon as food enters the digestive tract, a flat percentage is
lost as waste. Respiration sustains the organism, which includes
basal metabolism, movement, prey capture, and the action of
digesting the meal. Basal metabolism is fixed, based on shark size,
but the others are variable, depending on swimming speed and
number of prey consumed. After the costs of waste and respiration
have been calculated, remaining energy can be invested in growth.
Reproduction comes out of the growth budget because gonads
have to develop and the developing young require energy. If the
organism cannot balance metabolic demands, it cannot reproduce
and may die.
The energy trade-off of energy gained from prey and metabolic
expenses will determine the amount of energy available for reproduction. Sharks with higher drag have less energy left over for reproduction, so they will have lower differential reproduction. Sharks
with decreased prey detection will also have less energy for reproduction. Natural selection will favor the shark body plans that maximize the energy gained to energy lost because, all other things being
equal, those individuals within the population should have the
greatest reproductive success.
Using the Bioenergetics Model
The model (Figure 1) is a Microsoft Excel file that has been tested on
several versions of Excel for both Windows and Macintosh. It is not
compatible with mobile apps and other spreadsheet applications.
It is provided “as is” and is free to download and distribute from
https://goo.gl/jnPUJ9 (through Weebly.com). I will also share the
model when contacted by email. The model has three spreadsheet
tabs: Bioenergetics Model, Model Assumptions, and an optional
Graph Builder. The first two tabs are locked to prevent user alterations to the equations and source code, but I will distribute an
unlocked version upon direct request.