of change (Fig. 8.7) reminiscent of the logistic model. Indeed, perturbation is an import-
ant ingredient in detecting natural regulation and logistic growth, because it gives
us evidence to work with, unlike populations kept close to their ecological carrying
capacity. We demonstrate how to estimate the parameters for the Ricker logistic model,
and compare it with other possible population growth models, in Chapter 15.
All environments show some degree of variability in conditions from year to year.
Such stochastic or random variation can have a strong influence on the dynamics of
even tightly regulated species. We can explore this by applying the Ricker logistic
model to some typical empirical data. Figure 8.14 shows records of elk censused
in Northern Yellowstone National Park between 1968 and 1989 (Coughenour and
Singer 1996). We see that there is the barest hint of a sigmoid pattern in these data.
Nonetheless, exponential growth rates rtcalculated over this two-decade period
show a strong density-dependent decline in growth rates when the population is
large (Fig. 8.15).
The scatter around the regression line (termed “residual” variation) in Fig. 8.15
shows that natural regulation explains only part of the demographic response by a
wild population to changes in density. Even when the population is tightly regulated,
as is obviously the case here, there can be considerable variation in growth rates from
year to year that is not explained by density dependence. Some of this variability is
due to stochastic climatic variation that characterizes every natural environment, some
places more than others. In the case of Northern Yellowstone elk, for example, pre-
cipitation in the preceding 2 years is probably responsible for much of the residual
variation shown in Fig. 8.15, judging from its effect on offspring production and
survival rates (Coughenour and Singer 1996). This probably stems from a strong
linkage between precipitation and forage availability to elk.
Variability in population growth rates can also stem from “demographic stochas-
ticity.” This term refers to variation in the numbers of individuals born or dying per
unit time, simply due to chance (Chapter 17). The principle is familiar to anyone
who has played a game of cards or spun a roulette wheel. For a given probability of
survival, say 0.25, we do not necessarily expect exactly a quarter of the populationPOPULATION REGULATION, FLUCTUATION, AND COMPETITION WITHIN SPECIES 123
20151050
1965 1970 1975 1980 1985 1990
YearAbundance of Northern Yellowstone elk (thousands)Fig. 8.14Population
dynamics of Northern
Yellowstone elk between
1968 and 1989. (Data
from Coughenour and
Singer 1996.)