A Discrete Mathematical Model of Newt Population Dynamics in Santa Monica Mountain Streams During a Period of Drought
Presentation Type
Poster
Keywords
Local California Newt Population, Drought, Mathematical Modeling
Department
Biology
Major
Math
Abstract
We introduce a mathematical model of local newt populations to explore the impact of California’s extreme drought upon newt persistence and to inform the need for and effectiveness of restorative measures. Our model captures the observed decline of California newt (Taricha torosa) populations in Santa Monica Mountain streams under drought conditions. We develop a set of nonlinear difference equations to model each life stage of the newt. This allows us to track the population level of each newt life stage by incorporating probabilities for newt maturation and survivorship. In the model, the fecundity of the newt is dependent upon variable precipitation and stream characteristics. We ground our model biologically with local newt population data collected since 1992 from Cold Creek. Our model allows us to forecast newt persistence under long-term drought and other variable rainfall patterns. We make predictions about newt recovery versus extinction following drought that can be used to evaluate the potential success of restorative measures. Based on model simulations we predict how the number of available newt egg-laying sites varies with annual precipitation. Also, we see that even with severe drought, newt populations can rebound if the drought is sufficiently short.
Faculty Mentor
Dr. Courtney Davis, Assistant Professor of Mathematics, Pepperdine University; Dr. Timothy Lucas, Associate Professor of Mathematics, Pepperdine University
Funding Source or Research Program
Academic Year Undergraduate Research Initiative, Summer Undergraduate Research in Biology
Location
Waves Cafeteria
Start Date
1-4-2016 2:00 PM
End Date
1-4-2016 3:00 PM
A Discrete Mathematical Model of Newt Population Dynamics in Santa Monica Mountain Streams During a Period of Drought
Waves Cafeteria
We introduce a mathematical model of local newt populations to explore the impact of California’s extreme drought upon newt persistence and to inform the need for and effectiveness of restorative measures. Our model captures the observed decline of California newt (Taricha torosa) populations in Santa Monica Mountain streams under drought conditions. We develop a set of nonlinear difference equations to model each life stage of the newt. This allows us to track the population level of each newt life stage by incorporating probabilities for newt maturation and survivorship. In the model, the fecundity of the newt is dependent upon variable precipitation and stream characteristics. We ground our model biologically with local newt population data collected since 1992 from Cold Creek. Our model allows us to forecast newt persistence under long-term drought and other variable rainfall patterns. We make predictions about newt recovery versus extinction following drought that can be used to evaluate the potential success of restorative measures. Based on model simulations we predict how the number of available newt egg-laying sites varies with annual precipitation. Also, we see that even with severe drought, newt populations can rebound if the drought is sufficiently short.