David W. Gilbert, A Population Density Model for the Long-billed Curlew (Numenius americanus) on Humboldt Bay While Affected by an Oil Spill.

Abstract: Oil disperses through different media depending on the forces acting on the oil. During an oil spill there are many factors affecting the movement of the spill. A few of these factors are wind, tide, current, and human cleanup efforts. As a result of an oil spill, there are many harmful affects to wildlife in the area.

The purpose of the thesis is to determine the affects of an oil spill on the Long-billed Curlew (Numenius americanus) population on Humboldt Bay. This thesis uses a simulation model to project the Long-billed Curlew population before and after an oil spill. Potential oil spells in all sections of the bay are considered.

We analyze a four-age class, density dependent, discrete-time model. The time step is one year when there is no oil present, and the population is modeled on a daily time step when oil is present. In order for a population to persist it was found that age classes two and above need to fledge young at a rate of 0.44 when the survival rates for the Long-billed curlew are 40%, 60%, 75%, and 90% for age classes one through four, respectively.

Oil was found to remain on the mudflats for 11 days when 50 hectares of mudflat was initially covered and 52 days when 250 hectares were initially covered. Simulations ere run and the number of curlews that died varied from 0 to 69 when a stable population of approximately 300 curlews existed at Humboldt Bay and an oil spill was introduced. The simulations were run while oil covered 50 to 250 hectares of mudflat, the hours of foraging ranged from 2 to 10 hours per day, and the probability of death per day was 20% and 40% if a curlew foraged in an oiled area.

Teresa Ann Matsumoto, Sampling Threatened and Endangered Species with Non-constant Occurrence and Detectability: A Sensitivity Analysis of Power when Sampling Low-Occurrence Populations with Varying Probability Parameters.

Abstract: Detecting populations of low-abundance species has become increasingly important.  The mathematics involved in a sampling design generally require that probability parameters be fixed numbers; whereas, the reality is that the parameters vary widely within time and space. This is an issue of great concern for biologists and is of particular importance when sampling endangered or threatened species.  The power of a sampling design with varying probability values of the generalized binomial distribution model was investigated using computer simulations.  These empirical estimates of power compare favorably to theoretical estimates which use fixed probabilities, indicating that the sampling design is robust against variability in actual probability parameters in situations with low levels of occurrence where detectability is low.  Thus, theoretically calculated estimates of power using fixed probability values yield a good estimate of the actual power of such a sampling design.
 

Barry K. McKee, Modeling Population Responses of Rainbow Trout to Fishing Pressure in the Henry's fork of the Snake river in Eastern Idaho.

Abstract: Anglers on The Henry's Fork of the Snake River have a unique opportunity to enjoy fishing in one of the greatest fishing spots in the United States. Their fishing experience is catch-and-release only, a restriction that has been in effect on the river since 1988. When anglers catch a rainbow trout (Oncorhynchus mykiss), there is a possibility that the fish will be severely injured when released, thus creating an induced mortality rate due to the fish being caught. This induced mortality is referred to as catch-induced-mortality. Of course, there is also mortality due to natural elements in the environment, such as raptors, parasites, etc. How the natural and catch-induced-mortality rates combine in the trout population for each age class are modeled in the thesis. A discrete, nonlinear, age-structured model is used to describe the dynamics of the rainbow trout population. Computer simulations of the model are used to study the effects of different levels of the birth rates and catch-induced-mortality rates for each age class. The results are compared to current data, where as expected, the population would increase if the fishing activities were to cease. For the model developed here, the increase for the age class 1 to 6 trout would be about 68%. The difference is so great because of the compounding effect of each fish being caught an average of four times per season! The fishing pressure on The Henry's Fork is extraordinary, and is indeed a significant contributor to the mortality of the rainbow trout population even thought the river is restricted to catch-and-release.

Indika Rajapakse, A Geometric Analysis of Forest Pest Dynamics.

Abstract: The Spruce budworm model produced by several scientists at the University of British Columbia (D. Ludwig, D. Jones and C.S. Holling) is a complicated representation of the interaction between the spruce budworm and the forests of Northeastern Canada. The model describes the way in which the budworm population undergoes periodic outbreaks, which lead to severe defoliation and widespread tree mortality. They modeled the budworm-foliage system using a system of coupled differential equations involving three time scales: the fast time scale of the budworm population, the intermediate time scale of the tree energy reserves and the slow time scale of the tree surface area. They analyzed the system by considering only the dynamics of the fast variable, that is assuming the tree surface area and energy reserves remain constant.

Muratori and Rinaldi developed a technique to analyze models such as Ludwig's, using singular perturbation theory. Using their techniques, one can analyze systems, which have more than one differential equation with different time scales. The goal of this research is to apply Muratori and Rinaldi's technique and other standard dynamical system techniques to Ludwig's model to characterize the dynamics of the entire system. Analysis of the model shows a periodic behavior that disappears through a Hopf bifurcationwhen varying the threshold value of the energy reserve.