BS

Computer Science

#### College

Physical and Mathematical Sciences

2018-11-16

#### Publication Date

2019-03-13

Sean Warnick

Steven Peck

Zachary Aanderurd

#### Keywords

Yellowstone, Predictive modeling, population dynamics, ecological modeling

#### Abstract

Many of the world’s ecosystems are facing species elimination (2). Whether this elimination is intentional or accidental, the consequences need to be understood in order to make better resource management decisions. Computational models can be helpful in making these management decisions. Yellowstone National Park gives ecologists a unique opportunity to study species elimination and reintroduction.

In the 1920s, wolves were extirpated from the Greater Yellowstone Area. The absence of wolves allowed the elk population to increase unbounded by a natural predator. Over the years, Yellowstone management took various measures to control the elk population. In the 1970s, the National Park Service moved to a natural management policy. Under this management policy, wolves were reintroduced to Yellowstone National Park.

In this thesis, I studied the classic Lotka-Volterra equations to model the pop- ulation dynamics in Yellowstone National Park. I specifically studied the wolf and elk population dynamics. The Lotka-Volterra equations are characterized by a lag in response between the prey and predator populations. The peak in prey population is followed by the peak in predator population. By looking at the raw data of the elk and wolf populations, I observed that the population trends followed the patterns of the classic Lotka-Volterra equations. Since it seems the raw data could be modelled by the Lotka-Volterra equations, I expected to use these equations to create good models for the population dynamics of the elk and wolves.

In my work, I attempted to create a computational model that could predict the population dynamics between the wolf and elk populations in Yellowstone. I used least-squares regression and least absolute deviation to create Lotka-Volterra models that achieved this goal. Using these methods, I found parameters to the model that were good fits to the data. In addition to being a good fit to the data, the parameters estimated through least-squares regression created stable simulations of the Lotka- Volterra equations. Unfortunately, all stable simulations went to an equilibrium where one or both populations went extinct. Future work will be to analyze the stability conditions and basin of attraction of the differential equations to find parameters that create a stable simulation in which both the elk and wolf populations are non-zero.

COinS