Figure 1.
Attenuation in detection and its consequences for occupancy when detection depends on abundance.
The first panel shows the distributions of the detection probabilities (with means represented by a circle) for each value of years since planting. The solid blue curve is the fitted logistic detection component when and the dashed blue curve is the fitted constant detection probability when
. The solid green curve is the fitted logistic detection component when
and the dashed green curve is the fitted constant detection probability when
. The solid brown curve is the fitted logistic detection component and the dashed brown curve is the fitted constant detection probability when
(and
either
or
). The pink and orange dashed line represents
(i.e. ignoring non-detection). The second panel shows the corresponding fitted logistic occupancy probabilities in the same pattern and colour combinations. Note that orange dashed curve (slightly below the dashed blue curve) is the fitted logistic detection component when
and the pink dashed curve (which coincides with the dashed green curve) is the fitted logistic detection component when
.
Figure 2.
Fitted single-species, single-season detection and occupancy probabilities for the Brown Thornbill for
separate surveys in the Nanangroe Study. The first and second rows show the fitted detection and occupancy probabilities for the first four surveys (1998–2001) and the third and fourth rows show the fitted detection and occupancy probabilities for the last four surveys (2003–2009). In each panel, the fitted probabilities with the highest log-likelihood are shown as a solid curve and the fitted probabilities corresponding to other solutions of the log-likelihood estimating equations are shown as dashed curves. Fitted models with increasing occupancy are shown in blue and those with decreasing occupancy in green. The fitted detection probabilities when
are shown in brown.
Figure 3.
Fitted single-species, single-season detection and occupancy probabilities for the Yellow-rumped Thornbill for
separate surveys in the Nanangroe Study. The first and second rows show the fitted detection and occupancy probabilities for the first four surveys (1998–2001) and the third and fourth rows show the fitted detection and occupancy probabilities for the last four surveys (2003–2009). In each panel, the fitted probabilities with the highest log-likelihood are shown as a solid curve and the fitted probabilities corresponding to other solutions of the log-likelihood estimating equations are shown as dashed curves. Fitted models with increasing occupancy are shown in blue and those with decreasing occupancy in green. The fitted detection probabilities when
are shown in brown.
Table 1.
Counts of different kinds of fits for detection and occupancy from the simulation fitting occupancy and detection models in an ideal situation.
Figure 4.
Simulation results for fitting occupancy models in an ideal situation.
The first row shows fitted logistic curves for detection and occupancy for the first samples. The samples with positive/negative fitted relationships between occupancy and years since planting the surrounding Radiata pine are shown in blue/green; the true relationship is shown in black. The middle row shows boxplots of the fitted values for detection and occupancy for each year since planting; the true relationship is again shown as a black curve. The final row shows histograms (after trimming
values with standard error greater than
) of the estimates of the slope in the occupancy component of the model and the standard errors of these slopes; the vertical dashed lines are the true value of the slope parameter and the standard deviation of the slope estimates.
Figure 5.
Simulation results for fitting occupancy models to sparse data.
The first row shows fitted logistic curves for detection and occupancy for the first samples. The samples with positive/negative fitted relationships between occupancy and years since planting the surrounding Radiata pine are shown in blue/green; the true relationship is shown in black. The middle row shows boxplots of the fitted values for detection and occupancy for each year since planting; the true relationship is again shown as a black curve. The final row shows histograms (after trimming
values) of the estimates of the slope in the occupancy component of the model and the standard errors of these slopes; the vertical dashed lines are the true value of the slope parameter and the standard deviation of the slope estimates.
Table 2.
Counts of different kinds of fits for detection and occupancy from the simulation fitting occupancy and detection models when the data are sparse.
Table 3.
Counts of different kinds of fits for detection and occupancy from the simulation fitting occupancy and detection models when detection depends on abundance.
Figure 6.
Simulation results for fitting occupancy models when detection depends on abundance.
The first row shows fitted logistic curves for detection and occupancy for the first samples. The samples with positive/negative fitted relationships between occupancy and years since planting the surrounding Radiata pine are shown in blue/green; the true relationship is shown in black. The middle row shows boxplots of the fitted values for detection and occupancy for each year since planting; the true relationship is again shown as a black curve. The final row shows histograms (after trimming
values with standard deviation great than
) of the estimates of the slope in the occupancy component of the model and the standard errors of these slopes; the vertical dashed lines are the true value of the slope parameter and the standard deviation of the slope estimates.
Figure 7.
Simulated sampling distributions of the slope estimates and their standard errors when fitting occupancy models when detection depends on abundance.
Histograms of the estimates of the slope in the occupancy component of the model and the standard errors of these slopes for sites with
visits,
sites with
visits and
sites with
visits. The vertical dashed lines are the true value of the slope parameter and the standard deviation of the slope estimates.
Table 4.
Solutions of the expected estimating equations that maximize the expected log-likelihood under the settings used in the simulations.
Table 5.
The standard deviations of the parameter estimates under the settings used in the simulations.
Figure 8.
Simulation results for fitting logistic occupancy models that ignore the possibility of non-detection.
The first row shows results for an ideal situation, the second for sparse data and the third for when detection depends on abundance so the rows should be compared with Figures 4, 5 and 6 respectively. The first column shows fitted logistic curves for occupancy for the first samples. The samples with positive/negative fitted relationships between occupancy and years since planting the surrounding Radiata pine are shown in blue/green; the true relationship is shown in black. The second column shows boxplots of the fitted values for occupancy for each year since planting; the true relationship is again shown as a black curve.