Geoscience Reference
In-Depth Information
R
0
N
t
}}
1 + (
R
0
- 1)
N
t
+1
=
c
1
N
k
2
t
}
}
Each of these models results in a different relationship between per capita
recruitment and population size. Furthermore, these simple models can be
applied to various segments of the life cycle, such as fecundity rates, neonatal
survival, and adult survival, to achieve more realistic biological models. But
the use of different models means that density dependence is implemented dif-
ferently at a particular population level and population viability is affected. For
example, Mills et al. (1996) reported widely differing estimates of population
viability of grizzly bear (
Ursus arctos horribilis
) depending on which of four
computer programs were used to compute the estimate. Probably part of the
discrepancy is in how density dependence was implemented in each of the pro-
grams, but different functions probably were used and these relationships
probably were applied to differing segments of the life cycle. Unfortunately,
distinguishing between these various models of density dependence with data
is not practical because of the stochasticity (noise) in observed population lev-
els, as Pascual et al. (1997) demonstrated by fitting a collection of models to
Serengeti wildebeest (
Connochaetes taurinus
) data.
Fowler (1981, 1994) argues that both theory and empirical information
support the conclusion that most density-dependent change occurs at high
population levels (close to the carrying capacity) for species with life history
strategies typical of large mammals, such as deer (
q
> 1). The reverse is true for
species with life history strategies typical of insects and some fishes, with
q
< 1).
Note that explicit estimates of carrying capacity (
K
) and its variance are not
needed to incorporate density dependence into a population model, although
such an approach is possible. If the functional relationships between birth and
death rates and population density are available, the carrying capacity is deter-
mined by these relationships. Furthermore, if these relationships incorporate
temporal and spatial variation, then the resulting model will have temporal
and spatial variation in its carrying capacity, and thus stochastic density
dependence.
Another example of how density dependence can operate in small popula-
tions is provided by the Allee effect (Allee 1931): The per capita birth rate
declines at low densities (figure 9.8) because, for example, of the increased dif-
ficulty of finding a mate (Yodzis 1989). This is known as Allee-type behavior
(of the per capita birth rate), and its effect on the per capita population growth
rate,
R
(
t
), is called an Allee effect. In theory, a low-density equilibrium would
