Geoscience Reference
In-Depth Information
Vales and Peek (1995) modeled elk (
Cervus elaphus
) and mule deer (
Odocoileus
hemionus
) populations on the Rocky Mountain East Front of Montana,
attempting to anticipate the consequences of wolf predation. So for a given
number of wolves and an estimate of the number of elk eaten per wolf, Vales
and Peek estimated the effect of wolf predation and hunter kill on population
growth rate for the elk and deer. This is akin to a sensitivity analysis for elk
population growth in which the effect of predation mortality is figured, hold-
ing all else constant. But such a modeling approach cannot possibly anticipate
the rich dynamic behaviors known to emerge from predator-prey interactions
simply because the model structure precludes interaction between popula-
tions. Mack and Singer (1993) generated a similarly restricted model using the
software POPII for conducting demographic projections for ungulate popula-
tions. POPII projections are structurally identical to the Leslie matrix projec-
tion approach followed by Vales and Peek (1993).
Compensatory versus additive mortality
Field studies of predation (and hunter harvest) on bobwhite (
Colinus virgini-
anus
), cottontail rabbits (
Sylvilagus floridanus
), muskrats (
Ondatra zibethicus
),
wood pigeons (
Columba palumbus
), and waterfowl have shown that fall and
overwinter mortality can be compensated by a reduction in other sources of
“natural” mortality yielding constant spring breeding densities for prey irre-
spective of predation mortality (Errington 1946, 1967; Murton et al. 1974;
Anderson and Burnham 1976). The principle of compensatory mortality has
led some biologists to question whether wolf recovery in Yellowstone National
Park will actually have any measurable effect on elk population size (Singer et
al. 1997).
On the surface compensatory mortality appears to be at odds with the pre-
dictions of classic predator-prey or harvest models because increased preda-
tion or harvest mortality should always reduce equilibrium population size.
This apparent contradiction is simply a consequence of not modeling the
details of within-year seasonality and the timing of mortality. Compensatory
mortality emerges, of course, as a consequence of density dependence whereby
reduced prey numbers results in heightened survival among the individuals
that escaped predation or harvest. But these seasonal details are all ignored in
the classic predator-prey models in continuous time with no explicit seasonal-
ity. Likewise, if the models are difference equations, the within-year details of
the seasonality usually are not incorporated into the models.
Seasonal models are certainly possible. In continuous time we can make
