yields a statistically significant result (that is, yields a Pvalue less than 0.05), this
may be of trivial biological significance. Hence, slavish adherence to statistical
significance alone can distract one from the real issues at hand. It is often much more
important to decide which factor has the strongest effect on the pattern or variable
of interest.
Recognizing these limitations, ecologists have developed an alternative branch
of statistics that allows them to evaluate a series of alternative models of the same
phenomena (Hilborn and Mangel 1997; Burnham and Anderson 1998; Anderson
et al. 2000; Johnson and Omland 2004). The philosophical spirit of this approach,
called model evaluation, is not so much to discriminate significant from insignificant
factors, but rather to decide which of many competing explanations is most consis-
tent with the facts at hand, so that one can make an informed judgment about the
best course of management action.While model fitting can be readily applied to experimental data (e.g. Hobbs et al.
2003), it is applied most frequently to evaluation of observational data that are
routinely gathered by many wildlife agencies, such as mark–recapture studies
( Jorgenson et al. 1997), spatial distribution data (Fryxell et al. 2004), or annual
censuses of abundance (Hebblewhite et al. 2002; Taper and Gogan 2002). Early in
the exercise of model fitting one should ensure that no major changes have occurred
over time in the way that data have been gathered, or if they have, that some method
exists directly to compare data gathered at different points in time. Discrepancies
in the way data are gathered are more frequent than one would like. Biologists are
constantly tempted to modify observational techniques, either to improve the ease
of observation or to improve the repeatability of observations. Such changes in method-
ology can be a good idea, but they can make it difficult to compare data from
different eras. Methodological changes are often neglected when someone (e.g. a
consultant) decides to analyze the cumulative historical data. For this reason, any
analysis team ought to include at least one person familiar with the original data;
even better if that person has gathered the data themselves.
As an example of a long-term data set we shall consider the census data on migra-
tory wildebeest in Serengeti National Park illustrated in Fig. 8.7. Population estimates
in this system date back to the early 1960s, when the Serengeti Research Institute
was first established. It was recognized early that aerial counting was perhaps the
best way to monitor the broad expanses of savanna grasslands and broadleaf wood-
lands that comprise Serengeti National Park. Counting methods were established early,
with little deviation over the years despite different observers and technological changes
in aircraft and navigation equipment. Serengeti wildlife ecologists used a stratified
aerial count design, with photographs taken at known altitude used to count indi-
viduals in the center of wildebeest aggregations and visual counts made in areas with
lower numbers of animals.
Results of these censuses over the past 40 years show a rapid increase in wilde-
beest abundance over the first 20 years, with subsequent leveling off and erratic
fluctuation around roughly 1,250,000 individuals. There are numerous ways one could
mathematically depict this general pattern, however, and they all have different
management implications with respect to long-term viability of the wildebeest
population. Which model is most consistent with the data? We’ll use a formal model
evaluation, based on information criteria, to find out.254 Chapter 15