SPRING 2005

Lisa Song

 (Honors thesis for both Mathematics and Biology)

Lisa Song became the first student to graduate with Honors in both the Matematics department and the Biology department. She chose to work on a thesis under the guidance of myself and Dr. Alan Griffith, and plant ecologist in the Biology department. One focus of his research is the plant Aeschynomene virginica, an endangered species found only on the mid-Atlantic coast. This plant has an interesting life cycle summarized by the graph below.

transition graph

  • Seed 2 seeds were deposited 2 years ago

  • Seed 3 seeds were deposited 3 years ago

  • Adult 1 plants germinate from seeds deposited the previous year

  • Adult 2 plants germinate from seeds deposited 2 years ago

  • Adult 3 plants germinate from seeds deposited 3 years ago


Adult populations are difficult to predict because of the seeds' ability to lay dormant for one or two years. Thus a stochastic model is ideal for modeling this population. Lisa created first a deterministic population model and conducted a throrough mathematical analysis. She then derived a stochastic model using randomly generated covariance matrices.


  



This graph shows one stochastic simulation of the adult plant population. As seen in the field, the number of adult plants can vary greatly from one year to the next, as years with poor conditions will lead to many seeds remaining dormant.  Stochastic modeling is a great tool for investigating populations with highly unpredictable behavior.

 stochastic simulation