Geoscience Reference
In-Depth Information
,
logit(
ψ=+⋅
)
aaD
76,
i
1
2
i
where
D
i
is the distance band for route
i
scaled such that
D
i
= 1 for the
1000- to 1099-km distance band (i.e., essentially the distance in 1000s of
kilometers from the Long Island release point). The probability of house
finches colonizing route
i
between periods
t
and
t
+ 1 (γ
t,i
) was modeled
with the effect of distance being different in each period, that is, an inter-
action between period and distance effects so that
logit(
γ= +⋅
)
ti
bbD
.
,
t
,1
t
,2
i
The probability of house finches going locally extinct from route
i
between periods
t
and
t
+ 1 (ε
t,i
) was modeled as a function of distance
only, with no period effects, that is, with no annual variation in the
extinction probability of
logit(
ε=+⋅
)
ti
ccD
.
,
1
2
i
The effect of distance on detection probability was also allowed to vary
for each time period (as for colonization), with an additional effect for
the local abundance that was consistent in all time periods. That is, the
probability of detecting house finches at a stop along route
i
in time
period
t
(given house finches present at route
i
) was modeled as
logit(
pddDdLA
)
ti
=+⋅
+⋅
,
t
,1
t
,2
i
3
t i
,
where
LA
t,i
= 1 if house finches were detected at more than 10 stops in a
period previous to
t
and zero otherwise.
The resulting parameter estimates from the analysis of the data are
given in Table 9.1 and suggest that the probability of house finch pres-
ence on a route in 1976 declined with the distance from Long Island
(
ˆ
2
), and that the colonization probability also declined with distance,
although the magnitude of the effects also (generally) declined through
time (i.e.,
ˆ
t
,2
were negative but became closer to zero as the time period
increase). The extinction probability increased with distance ( >
<
ˆ
2
), and
the effect of distance on detection exhibited a similar pattern to coloni-
zation probability over time. House finches were also more detectable
at a stop if they had been detected at more than 10 stops along a route
previously (
ˆ
3
). Plots of the estimated occupancy-related biologi-
cal probabilities are given in Figures 9.1 to 9.3. Note that the estimated
probabilities can be used to calculate other quantities, such as the prob-
ability of presence in each time period (Figure 9.4) or rate of change in
occupancy (Figure 9.5) as a function of distance as alternative ways to
describe the expansion of the house finch across eastern North America
(MacKenzie et al., 2006).
Using the distance from Long Island (the initial source of the eastern
population) as a covariate on all parameters and allowing the nature of
that relationship to change through time was an attempt by MacKenzie
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