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a model that assumes independence still provides appropriate results. What
it fails to do, however, is to provide insight into the underlying processes of
change as it essentially assumes that any changes in occupancy are random
(MacKenzie et al
.
, 2006).
By assuming independence, a multiseason model can be constructed by
fitting a series of single-season models to each season of data. Changes in the
overall patterns of occurrence (such as trends over time) can be incorporated
by creating a functional link between the parameters for each season. For
example, when interest is in the presence or absence of the species, the prob-
ability of occupancy in each year
t
could be modeled as
(
ψ=β+β⋅
t
logit
,
t
0
1
where β
1
is the trend in occupancy measured on the logit scale (as discussed
further in the section on incorporating covariates).
Although it is advisable to survey the same units each time period, when
this has not happened, then the data collected in each season might be rela-
tively independent (e.g., if the units to be surveyed are randomly selected
each season). It is therefore unlikely that there will be data from consecu-
tive time periods on the same unit. Hence, in this situation, this modeling
is likely to be more successful than the next approach, which specifically
models the underlying changes at the sampling unit scale.
9.4.2 Dependent Changes
MacKenzie et al. (2003) extended the two-category, single-season model of
MacKenzie et al
.
(2002) to the situation in which data are collected at system-
atic points in time at the same sampling units, hence providing data of a lon-
gitudinal nature. As for the single-season model, at each time point repeat
surveys are conducted to provide information about detection probability.
The model accounts for changes in the occupancy status of units between
seasons through the processes of local colonization and extinction. Although
different terms could be used for them, basically they enable the probability
of the species being present at a unit to be different depending on whether
the species was present at the unit in the previous season. Barbraud et al.
(2003) described a similar approach developed from mark-recapture models.
For multiple categories, MacKenzie et al. (2009) extended the single-season
models of Royle and Link (2005) and Nichols et al. (2007) to the multiple-
season situation, again assuming that the data are of a longitudinal nature.
Probability statements can again be developed by adding together various
options to account for any ambiguity in the true state of a unit caused by the
imperfection of the observations. This is most efficiently achieved by using
matrix multiplication with appropriately defined vectors and matrices, and
