Transcript ckwasp-poster4

Florida’s Cicada Killer Wasps Cast Doubt on Current Dogmas
Katie Jones - Grayson Rodriguez - Advisor: Dr. Andrew Long (Mathematics and Statistics)
Meet Sphecius speciosus
Eastern cicada killer wasps (Sphecius
speciosus, Drury) are ground-nesting, mass
provisioning wasps that have a one-year life
cycle. The female wasps are the hunters. They
dig burrows with many chambers, search for
cicadas on trees, paralyze them with their
stingers, and carry them back
to a chamber where their larva
eats the paralyzed cicadas
alive. Through past studies on
cicada killer wasps several dogmas have arisen,
and we argue against two of these dogmas.
Dogma 1 : The first dogma refers to how the
wasps hunt: the theory is that cicada
killer wasps are opportunistic hunters,
whether that pertain to the size, sex, or
species of cicada. This is akin to a wasp
that sets out with no preference and
grabs the first cicada it spots (a random
process). We argue against this dogma and
show how the female wasps are selective
based on prey size.
The data were collected by Dr. Hasting
from two locations in Florida: Newberry and
St. Johns. Smaller wasps
were found at the former and
larger wasps at the latter.
Both locations have the
same abundance and distribution of cicada
species. The cicadas come in
three sizes, which we classify
as small, medium, and large.
Dogma 2 : The second dogma has to do with
sex allocation: females reputedly allocate one
cicada if they choose to create a male
wasp (fertilized eggs), whereas they
allocate two cicadas to the unfertilized
(and hence female) eggs. We characterize this as the "one if by male, two if
by female" strategy, and argue that this
strategy is not always used by the female
wasp. We do not believe the wasps count, but
rather that they allocate meals based on mass.
Non-opportunistic Predation
It is currently believed that cicada killer wasps are opportunistic hunters. We believe
that they are non-opportunistic hunters, and that they are selective based on prey size.
Each point in the
scatterplot above can be
thought of as a “hunting
expedition” where
a female wasp
went out and
captured a cicada.
The horizontal line
shows the model
that we would expect to
see if the wasps were in
fact opportunistic hunters.
In order to get an idea for
a model we used a
process called kernel
smoothing. This is a
method for picking up a
trend in a cloud of messy
data and producing a
smooth map over the data
by doing local averaging.
From this we estimated a
7-parameter model using
two S shaped curves.
Our final model shows that
there is an abrupt shift
from one cicada population
to the next as the wasp
size gets larger. Thus
larger wasps hunt larger
cicadas and choose not to
hunt the smaller cicadas.
This model was obtained
by performing non-linear
regression on the 7parameter model.
Conclusion: Mass Provisioning
We believe that Eastern cicada killer wasps
allocate a certain mass (or volume) to male and
female eggs and that the dogma did get the
female-to-male ratio correct (females get twice
as much). Also, female wasps selectively hunt
for the largest cicadas that they can carry.
If the female wasps are half
the size of the cicadas they
are bringing back, then they
are in the “sweet spot” (the
dogma holds). The “sweet
spots” in our data occur
when the wasps have just
switched to hunting the next cicada population.
Away from the “sweet spots” the wasps are
gathering combinations
of cicadas. For example,
in Newberry, four small
cicadas are needed for
a male and seven for a
female. These numbers
have been observed in
focal studies in the field.
Sex Allocation
It is currently believed that a female wasp lays male eggs in a nest with one cicada and
female eggs in a nest with two cicadas. We believe that it is not that clear cut, but rather
they allocate certain masses -- not certain numbers -- of cicadas.
We modeled the dogma in
the figure above. The
conversion of cicada
mass into wasp mass
is 25%. The mass of a
male wasp is m and a
female is twice so 2m.
This implies that cicadas in
the environment would be
of mass 4m. This is the
most efficient way to
reproduce (given those
mass relationships). This
we call the “sweet spot”.
The cicadas in Newberry
were roughly the same size
of the male wasps. The
figure above shows the
cumulatives of male wasp
mass and captured cicada
mass. Given that 25% of a
cicada becomes a wasp it
is not possible that these
male wasps were
provisioned with just one
cicada. This data
contradicts the dogma.
There are small, medium
and large cicadas that form
three humps in the
distribution of cicada mass.
If the dogma were true we
would see three humps in
the distribution of male
wasp mass. We don’t!
There is only one size male
wasp, not three. This data
further contradicts the
dogma, and leads us to a
mass-provisioning model.
Future Work
We are running numerical simulations based on
models of wasp predation to further illustrate the
breakdown of the dogmas, and to address
additional mysteries. For example, the wasps in
Newberry are significantly smaller than the wasps
in St. Johns, yet the wasps hunt from the same
abundance and distribution of cicada species. Why
is this? Numerical simulations are helping us to
investigate two possibilities: natural fluctuations in
animal size, and human predation (the wasps a
likely to be exterminated by fussy homeowners).
Acknowledgements
Our thanks to Dr. Jon Hastings and Dr. Chuck
Holliday, who provided the field data and many
references. Also, Dr. Michael Dorff, The Center
for Undergraduate Research in Mathematics
(CURM), and the National Science Foundation
(NSF Grant DMS-0636648) for their funding of
this project.