My mathematical training is in probability theory and stochastic processes. I now apply this to problems in stochastic modeling of biological phenomena.
Probability and stochastic processes can have a great advantage over other methods in dealing with problems concerning moderate size populations, for example, a moderate number of enzymes of a certain type in a cell or a moderate number of individuals in an ecosystem.
This approach was used in modeling historical processes in bacterial cultures. This work was a collaborative effort with Neil Mendelson in the Molecular and Cellular Biology Department and with Kevin Anderson, a recent Ph. D. recipient in the Flinn/IGERT program. Kevin is now a postdoctoral member at the Institute for Mathematics and it Applications for their program Mathematics in Biology.
Fluctuation theorems for a structured populations undergoing demographic noise are best for modeling moderate sized ecosystems. I am now working with Wade Leitner, a Flinn postdoctoral student, on incorporating fluctuations due to environmental changes.
Gloria DeGrandi-Hoffman of the Carl Hayden Bee Research Center, USDA-ARS and I work on models of honey bees and used this to explain the Africanization of the honey bee population. Look for this story early in 1999 as a part of an episode of the The Desert Speaks on PBS.
We are now looking into question concerning swarm dynamics and into environmental modeling of pollination by honey bees and other non-apis bees.
We also work together as a part of the Native American Summer Institute. Students in the Institute use mathematical models as a way to learn biological principles. The University of Arizona and the Carl Hayden Bee Research Center work collaboratively with the Pacqua Yaqui Tribe and the Wa:k O'odham Community. This summer, we established the Wa:k Apiary, the only apiary on tribal land run by tribal people. The Summer Institute is the subject of a documentary film - A Tale for All Nations produced by Stephanie Lucas.
Postdoctoral fellow Kate McGivney is a member of the teaching staff for the Institute.
Recent publications
Watkins, Joseph C. (1997) Mechanical models of cell movement - locomotion, translocation and migration. Advances in Applied Probability 34 827-846.
Degrandi-Hoffman, Gloria, Joseph C. Watkins, Anita M. Collins, Gerald M. Loper, Joseph H. Martin, Maria C. Arias, and Walter S. Sheppard (1998) Queen Development Time as a Factor in the Africanization of Honey Bee Population. Annals of the Entomological Society of America 91 52-58.
Lucas, Stephanie, director, Joe Watkins, producer, J.T. Waldrop, editor (1998) A Tale for All Nations. (documentary film) Arizona Board of Regents.