Geoscience Reference
In-Depth Information
natural populations were indeed chaotic. Early studies (Hassell et al. 1976)
concluded that most populations were not chaotic. These studies were based
on attempts to fit natural populations to simple models and then to see
whether the values of model parameters representing, for example, density
dependence, time delays, or reproductive rate were such that chaotic behavior
would be expected. The problem was that the conclusion depended on the
particular model used, which was always a simplistic abstraction of the
inevitably complicated dynamics of real populations. Subsequent investigators
offered techniques that were more general and did not assume particular pop-
ulation models (Schaffer and Kot 1985; Turchin and Taylor 1992). Applica-
tions of these techniques have indicated that some but not all population sys-
tems are chaotic. A more detailed discussion of these techniques can be found
in chapter 8. Here I focus on techniques to demonstrate density dependence
and the causes of change in density.
Detection of Density Dependence
j
ANALYSIS OF TIME SERIES OF DENSITY
For data that consist of a time series, that is, a sequence of periodic estimates
of density from a population, a variety of tests have been proposed to detect
the existence of density-dependent processes. If we define R as change in pop-
ulation density on a log scale,
R = log N t +1 / N t = X t +1 - X t
(6.1)
where N t is density and X t is log density at time t , then if density-dependent
processes are at work, population change should be correlated with density.
R =
a
+
b
log N t +
e t
(6.2)
a
b
where
are coefficients representing density-independent and density-
dependent processes, respectively, and
and
e t is any source of random fluctuation.
The processes involved may affect fecundity, mortality, or both. If there is no
density dependence,
b
b
= 0 it means there is no general upward or
downward trend in density over time, in the absence of density dependence.
Alternatively, equation 6.2 can be written as
= 0. If
Search WWH ::




Custom Search