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
ABSTRACT
Dr. Coleman
Population dynamics can be examined using a variety of
models. I wanted to explore the relationship between Douglas
Kevin and Bubo virginanus
squirrels (Tamiasciurus douglasii) and Northern goshawk
INTRODUCTION
(Accipiter gentilis) and the effects that Douglas fir
(Pseudotsuga menziesii) cone production and another
Old-growth Douglas fir forests support a wide range of animal
predator, Great-horned owl (Bubo virginianus) had on that
species from reptiles and amphibians to insects, mammals and
birds, many of which are linked to the annual production of
relationship. I used logistic growth models and Lotka-Voltarra
seeds. Of particular importance is the relationship between
predator-prey models to illustrate these relationships. I found
Douglas squirrels and the production of Douglas-fir cones, a main
source of food for the squirrels. Understanding this relationship is that cone production has little effect on squirrel logistic growth
but that the predator-prey relationship between squirrels and
valuable because Douglas squirrel is a favored prey source for
Northern goshawk, a species of special concern in California and
goshawks exhibit displaced population cycles as predicted by
the subject of two petitions in the 1990’s for federal protection
the Lotka-Voltarra model. I also found that Great-horned owls
under the Endangered Species Act. Understanding this primary
rapidly go extinct when introduced without an additional Lotkasource-prey-predator relationship may help shed light on
Volterra competition model.
goshawk population dynamics and assist in the adaptive
Tamiasciurus douglasii
management of the species.
Pseudotsuga meziesii
RESULTS
OBJECTIVES
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
The objective of this study was to explore the relationship
between three layers of an old-growth Douglas fir ecosystem: cycles with goshawk numbers peaking as squirrel numbers crashed and squirrel populations
Douglas fir cones, Douglas squirrels, and Northern goshawk. A recovering as goshawks declined. When introduced, great-horned owl populations rapidly
declined to extinction and the goshawk/squirrel curves fluctuated with greater amplitude.
secondary objective, was to see how the addition of GreatPine-Squirrel-Goshawk
Cone effect and r- effect: Squirrel N vs time
horned owl (Bubo virginianus) would affect this relationship.
10000.00
3500
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 LotkaVolterra 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.
1000.00
2500
SQU/Cone effect
1500
r-effect
Nt +1 = Nt+rNt(1-Nt)
K
Nt +1 = Nt+rNt(1-Nt/C)
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)
VSquirrels
10.00
1000
1.00
500
0
0.10
0
20
40
60
80
100
120
Goshawk
0
20
40
60
80
100
140
0.01
Time
Figure 1. Squirrel logistic growth with two different cone factors; the r effect and the
cone effect.
Time
Figure 2. The relationship between fir cones, squirrels, and goshawks. Graph shows
displaced population cycles.
Fir-Squirrel-Goshawk-GHO
10000
1000
100
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.
squirrel
10
Goshawk
GHOW
1
0.1 0
LOGISTIC GROWTH EQUATIONS
Cone effect(squirrel
r)
100.00
N
2000
N
METHODS
Squirrel N
3000
Accipiter gentilis
20
40
60
80
100
120
140
Cones
0.01
0.001
Time
LOTKA-VOLTERRA PREDATOR EQUATION
Figure 3. The interaction of fir cone production, squirrels, goshawk, and owls. The graph shows owl
decline and displaced squirrel and goshawk population cycles.
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