Occupancy Models - Introduction to Ecological Sampling - page 128

A second example for which there is ambiguity is the outcome 110. Then,
the detection of the species at least once precludes the possibility of the spe-
cies being absent from the unit, but not detecting evidence of reproduction
does not preclude the possibility of reproduction actually occurring there.
The probability statement for this would be

( )

[2] [1,2] [1,2] [0,2] [1] [1,1] [1,1] [0,1]

Pr h = 110 = φ ppp ppp + φ .

i 1 2 3 1 2 3

Here, the two options relate to whether reproduction is occurring at the unit
or not. That is, the species may have been present with reproduction, the spe-
cies was detected but no evidence of reproduction was observed in the first
and second surveys, and the species was not detected in the third survey, or ,
the species was present but there was no reproduction at the unit and the
species was detected in the first and second survey but not in the third sur-
vey. Note that in the second option it is presumed that there is no reproduc-
tion occurring at the unit; therefore, there is no chance of observing it. Hence,
the second superscript on the detection probabilities is a 1 (species is present
without reproduction).
As before, once the probability statement for all sampled units has been
determined, the statements can be combined and used to provide maximum
likelihood estimates or used within a Bayesian framework to obtain poste-
rior distributions for the parameters.

9.4 Multiseason Models

When changes in the distribution and occurrence of the species are of inter-
est, then multiseason occupancy models can be used. These can be developed
such that the current occupancy state of a sampling unit is independent of its
state in the previous time point or by allowing a dependency to exist between
the occupancy status of the unit in the two time periods. In this section, the
independent modeling approach is briefly outlined before moving on to the
dependent case, which is likely to be more realistic in many situations. The
modeling is described in terms of a multicategory situation, of which the two-
category situation (e.g., presence-absence) is just a special case.

9.4.1 Independent Changes

Just because the following modeling approach assumes that the current sta-
tus of a unit is independent of its state in the previous time period does
not mean the model cannot be used when there really is dependence. In
terms of modeling the overall patterns of occurrence each time period, using