Occupancy Models - Introduction to Ecological Sampling - page 125

9.3 Single-Season Models

Single-season models can be used when interest is in how the species is dis-
tributed on the landscape at a single time point. Patterns in the current dis-
tribution could be described and related to covariates or predictor variables
that are available for each sampling unit. Initially, the single-season model
is developed in terms of a two-category occupancy model (e.g., presence-
absence), then an extension to multiple categories is discussed.

9.3.1 Two-Category Model

In a two-category application, the status of the species at each sampling unit
may be one of two possible categories. Typical examples are the presence or
absence of the species from each unit or whether a unit is used or unused by
the species. Other definitions are also possible, for example, high abundance
or not high abundance. Field observations from the surveys correspond to
each of these categories (e.g., detection-nondetection), but while one type of
observation would confirm the status of the species at the unit (e.g., the spe-
cies would have to be present to be detected), there is ambiguity associated
with the other observation (e.g., a nondetection could result both when the
species was present or when it was absent).
The repeat surveys are necessary to reliably disentangle the species occur-
rence from the observation process. An example detection history from a sin-
gle unit would be h i = 101, with the 1 indicating the species was detected in
that survey and a 0 indicating nondetection. Presuming the two categories
of interest are presence-absence, a verbal description of the detection history
would be that “the species was present at the unit, detected in the first sur-
vey, not detected in the second, and then detected in the third.”
Let ψ be the probability of the species being present at a unit and p j be
the probability of detecting the species in the j th survey of the unit given
the species is present. From the verbal description, an expression for the
probability of observing the detection can be developed by substituting the
respective phrases for the associated probability. Here, the resulting expres-
sion is referred to as a probability statement. The probability statement for the
previous detection history at unit i ( h i ) would therefore be

Pr( h = 101) ψ− p pp (1)

3 . i 1 2

If the species was never detected in any of the three surveys (i.e., 000), then
there is ambiguity regarding whether the species was truly present or absent
from the unit. Again, a verbal description of that detection history would be
that “ the species was present but went undetected in all three of the surveys,
or the species was absent . ” While it is not possible to resolve this ambiguity