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. 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 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. Florida’s Cicada Killer Wasps Cast Doubt on Current 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. 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 charact- erize 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. 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. 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. 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 7- parameter model. Katie Jones - Grayson Rodriguez - Advisor: Dr. Andrew Long (Mathematics and Statistics) 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. 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. 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. species. The cicadas come in three sizes, which we classify as small, medium, and large. 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”. 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 ) for their funding of this project.