Line transect detection function fitting

In this practical, we plot a histogram of line transect data and estimate a detection function. The data were collected during a line transect survey of duck nests in Monte Vista National Wildlife Refuge, Colorado, USA (Anderson & Pospahala, 1970). Twenty lines of 128.75 km were specified and a distance out to 2.4m was searched and the perpendicular distances of detected nests were recorded and summarised (Table 1).

Table 1. Frequency of duck nests detected in perpendicular distance bands (metres)

Distance.band	Frequency
0.0-0.3	74
0.3-0.6	73
0.6-0.9	79
0.9-1.2	66
1.2-1.5	78
1.5-1.8	58
1.8-2.1	52
2.1-2.4	54

Objectives

The aim of this exercise is to plot a histogram of the perpendicular distances to the detected duck nests and estimate (by eye) a detection function and hence estimate density of duck nests, i.e. the number of nests per square metre or per square kilometre (be careful of units).

Answer these questions in sequence

These steps will produce an estimate of duck nest density.

1. With the graph paper PDF found at this link, print the PDF and plot a histogram of the data in Table 1 and fit a detection function by eye.
2. Estimate the areas under the rectangle and the fitted detection function curve and hence estimate the proportion of nests that are detected in the covered region, i.e. the region within 2.4m of the transect centre line.

\[ Area_{rectangle} = \] \[ Area_{curve} = \]

\[ \hat{P}_a = \frac{Area_{curve}}{Area_{rectangle}} = \]

3. Obtain an estimate of the number of nests in the covered region (Note \(n=534\)):

\[ \hat{N}_a = \frac{n}{\hat{P}_a} = \]

4. Estimate density (Note \(L = 20 \times 128.75 = 2575\) km):

\[\hat{D} = \frac{\hat{N}_a}{a} = \frac{\hat{N}_a}{2wL} = \]

References

Anderson, D. R., & Pospahala, R. S. (1970). Correction of bias in belt transect studies of immotile objects. The Journal of Wildlife Management, 34(1), 141–146. https://doi.org/10.2307/3799501