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can be used for the detection probabilities in addition to the unit-specific
covariates.
Finally, it should be noted that both continuous and categorical covariates
may be used. Continuous covariates could potentially take on any positive
or negative value; categorical covariates can only have a number of spe-
cific values and will often need to be converted to a series of indicator or
dummy variables. However, if the categories have been ranked in order and
assigned meaningful numeric values, then the covariates can be considered
as ordinal categorical covariates and are essentially treated as continuous
covariates.
EXAMPLE 9.2 Spread of the House Finch across Eastern North America
To illustrate the usefulness of multiple-season models and the incorpo-
ration of covariates, a data set from the North American Breeding Bird
Survey (BBS) for the house finch (
Carpodacus mexicanus
) is used. This
data set was previously discussed by MacKenzie et al. (2006), and greater
detail of the data set can be found in Section 7.3 of that topic.
The house finch is native to western North America but not midconti-
nental and eastern North America. A small population was released in
Long Island, New York, in 1942 and began expanding their range west-
ward. The BBS conducts surveys along secondary roads during the peak
of the breeding season, with observers traveling an approximately 39.2-
km route of 50 equally spaced stops. At each stop, a 3-minute point count
is conducted, and observers note which species they detected within a
400-m radius. Here, the BBS route is considered as the sampling unit and
the 50 replicate stops as the repeat surveys to detect house finches if they
are present along the route.
BBS data from 1976 to 2001, at 5-yearly intervals, were analyzed with
a two-category (i.e., presence-absence) multiseason model with depen-
dent changes to model the expansion of house finch range across east-
ern North America. The parameters in the model are the probabilities of
occupancy in 1976, local colonization between periods
t
and
t
+ 1, local
extinction between periods
t
and
t
+ 1, and the detection of house finches
in a survey if they were present at a route in period
t
(MacKenzie et al
.
,
2003, 2006). Data were extracted for 694 BBS routes that were surveyed
in at least one of the 6 years of interest. Distance bands of 100 km from
Long Island were defined (e.g., 0-99 km, 100-199 km, etc.) and consid-
ered as a potential covariate for all parameters in the model. MacKenzie
et al. (2006) also defined a covariate to enable the probability of detecting
house finches at a stop along a route to be different if house finches had
been detected at greater than 10 stops along that route in a previous year.
The logic of such a covariate was to attempt to account for any effect of
local abundance on the detection of house finches (at the species level).
MacKenzie et al. (2006) considered a number of different models for
the data, but for simplicity only the results from a single model are con-
sidered here. The initial probability of house finches being present at
route
i
in 1976 ψ
76,
i
was modeled as
