Prof. T. Lucas mentor
The Santa Monica mountain range located in Southern California is home to many species of chaparral shrubs. These plants can be divided into three categories according to their response to wildfires: obligate sprouters (OS) are not completely destroyed by fire and resprout, but their seeds are destroyed by fire; facultative sprouters (FS) both resprout and reproduce by seeds that survive the fire; non-sprouters (NS) are completely killed by fire and reproduce by seeds that germinate in response to fire. A mathematical model of this system is of particular importance given the increase in fire frequency in the Santa Monica Mountains that has the potential to render some species locally extinct. From 1925-2001, the average fire frequency for the entire Santa Monica Mountains was 32 years. The average fire frequency from 1985-2011 for our study site in Malibu was just over 6 years. The extinction of some species of chaparral plants is altering the region's landscape and its viability for inhabitants as the paucity of chaparral leads to an increase in rock and mudslides, floods, and an overall atrophy of structural foundations. Our first model is system of difference equations that tracks the population of each type of chaparral species over time. The second model describes the growth of individual plants and their influence on the surrounding space due to seed dispersal, shading of young plants and competition for space.