Geoscience Reference
In-Depth Information
mated using life table analysis, and
W
is the number of wolves in the park. The
condition of the population at the time that the demographic data were esti-
mated will be crucial to determining
l
, so the vital rates estimated during
1988-1990 will establish how many wolves the population of blackbuck can
sustain.
Although attempting to model the differential habitat requirements for
blackbuck and wolves in an area is a novel approach, the interaction between
predator and prey is not sufficiently known to offer an ecological basis for set-
ting the desired ratio of predators to prey. Nor do we have sufficient data on
the predator-prey interaction to know that establishing certain amounts of
preferred habitats for each species would yield the target numbers of each
species when they are allowed to interact dynamically. An implicit assumption
with Jhala's (in press) model is that both the predator and the prey have equi-
librium dynamics set by the amount of habitat.
The Jhala (in press) paper illustrates the dangers of using Keith's (1983)
model, which assumes no functional response. This application of Keith's
model assumes that wolf predation is the only source of mortality, it is not
compensatory, and wolf numbers can increase to a level at which the entire
prey production is removed by the predator. I believe that these assumptions
are usually violated.
Habitat capability models are usually focused on just one species (e.g.,
habitat suitability indices). Methods for extrapolating distribution and abun-
dance have improved with the use of geographic information systems (Mlade-
noff et al. 1997) and resource selection functions (Manly et al. 1993).
TRUE PREDATOR-PREY MODELS
Lotka-Volterra models
The structure of modern predator-prey models in ecology was outlined by
Italian mathematician Vito Volterra (1926), who held the Chair of Mathe-
matical Physics in Rome (Kingsland 1985). Volterra's interest in predator-prey
interactions was piqued by Umberto D'Ancona, a marine biologist who was
engaged to marry Volterra's daughter, Luisa. D'Ancona suggested to Volterra
that there might be a mathematical explanation for the fact that several species
of predaceous fish increased markedly during World War I, when fishing by
humans almost ceased. Volterra suggested the use of two simultaneous differ-
ential equations to model the dynamics for interacting populations of preda-
tor and prey. The model had potential for cyclic fluctuations in predator and
