1. ABSTRACT Population dynamics can be examined using a variety of models. I wanted to explore the relationship between Douglas squirrels (Tamiasciurus douglasii) and Northern goshawk (Accipiter gentilis) and the effects that Douglas fir (Pseudotsuga menziesii) cone production and another predator, Great-horned owl (Bubo virginianus) had on that relationship. I used logistic growth models and Lotka-Voltarra predator-prey models to illustrate these relationships. I found that cone production has little effect on squirrel logistic growth but that the predator-prey relationship between squirrels and goshawks exhibit displaced population cycles as predicted by the Lotka-Voltarra model. I also found that Great-horned owls rapidly go extinct when introduced without an additional Lotka- Volterra competition model. The Predator-Prey relationship between Douglas squirrel and Northern goshawk in an old-growth Douglas fir forest Kevin P. Cahill Bio 260: Dr. Ron Coleman Department of Biological Science California State University, Sacramento Dr. Coleman Kevin and Bubo virginanus INTRODUCTION Old-growth Douglas fir forests support a wide range of animal species from reptiles and amphibians to insects, mammals and birds, many of which are linked to the annual production of seeds. Of particular importance is the relationship between Douglas squirrels and the production of Douglas-fir cones, a main source of food for the squirrels. Understanding this relationship is valuable because Douglas squirrel is a favored prey source for Northern goshawk, a species of special concern in California and the subject of two petitions in the 1990’s for federal protection under the Endangered Species Act. Understanding this primary source-prey-predator relationship may help shed light on goshawk population dynamics and assist in the adaptive management of the species. OBJECTIVES The objective of this study was to explore the relationship between three layers of an old-growth Douglas fir ecosystem: Douglas fir cones, Douglas squirrels, and Northern goshawk. A secondary objective, was to see how the addition of Great- horned owl (Bubo virginianus) would affect this relationship. METHODS I used two logistic growth equations, one with a random number generator to represent squirrel intrinsic growth, and the other with a randomly generated reducing “cone factor” to create logistic growth curves for squirrel populations that were affected by Douglas-fir cone production. I then incorporated a Northern goshawk population with the Lotka- Volterra predator-prey equations to examine the dynamics between these three elements of this system. Finally I introduced a Great-horned owl predator-prey equation to see the effects of an additional predator. RESULTS I was able to see the populations react as the models predict. Squirrel populations fluctuated in response to cone production and the squirrel and goshawk populations exhibited displaced cycles with goshawk numbers peaking as squirrel numbers crashed and squirrel populations recovering as goshawks declined. When introduced, great-horned owl populations rapidly declined to extinction and the goshawk/squirrel curves fluctuated with greater amplitude. Tamiasciurus douglasii Accipiter gentilis Pseudotsuga meziesii LOGISTIC GROWTH EQUATIONS Nt +1 = Nt+rNt(1-Nt) Nt +1 = Nt+rNt(1-Nt/C) K K Nt+1 = the population at the next time step Nt = the current population r = the intrinsic rate of growth (determined by random number generator) K = the carrying capacity of the environment C = Cone factor (determined by random number generator) LOTKA-VOLTERRA PREY EQUATIONS Nt +1 = Nt+rNt(1-Nt) – (rV-α1VP1) Nt +1 = Nt+rNt(1-Nt) – (rV-α1VP1) – (rV-α2VP2) K K V = squirrel (victim) population α1 = goshawk attack rate α1 = great-horned owl attack rate P1 = goshawk (predator) population P2 = great-horned owl population βαVP-qP β = predator conversion efficiency α = predator attack rate V = squirrel population q = natural death rate of predator P = goshawk population LOTKA-VOLTERRA PREDATOR EQUATION Figure 1. Squirrel logistic growth with two different cone factors; the r effect and the cone effect. Figure 2. The relationship between fir cones, squirrels, and goshawks. Graph shows displaced population cycles. Figure 3. The interaction of fir cone production, squirrels, goshawk, and owls. The graph shows owl decline and displaced squirrel and goshawk population cycles. DISCUSSION With refinement these models could be a useful tool for managing threatened, declining or secretive species such as goshawk with habitats that make surveying difficult and expensive. Identifying keystone species such as Douglas fir and Douglas squirrels and using them to build models in conjunction with available life history data for the species in question may help identify management goals that can sustain and protect populations long enough to design and conduct long term surveys that sound management decisions can then be made with.