point-transect hybrids or transects with rounded ends

[qures...@yahoo.com]

I am not sure how to search for this topic, so please point me in the right direction if this issue has already been addressed.

I am interested in applying distance sampling to data from nest searches along transects. Surveyors initially record detections of individuals (white-headed woodpeckers) along the transect, and then followed detected individuals back to their nests. We then recorded spatial coordinates for nest locations, for which frequency declines with distance to the transect. I want to estimate nest density and model nest density as a function of habitat.

When searching for nests, surveyors are not restricted to areas perpendicular to the transect, so some nests were located off the ends of transects. Thus, sampling units are actually something of a hybrid between points and transects (rounded at the ends, rectangular along the body).

I am wondering if anyone has looked into or thought about how to model detection probability in this scenario, and specifically how to get (g[d]) from density (f[d], where r is the distance to the object subject to detection). Given that for line transects f(d) = g(d), and for points f(d) = d*g(d), I imagine that for rounded-end transects the conversion equation is somewhere in between these. For example, we could model f(d) = A*d*g(d), where 0 < A < 1, and A = f(L * ESW), where L is the length of the transect and ESW is effective strip width, which would depend on detection probability. So, for very short transects A ~= 0 and the the situation would approach that of a survey point, for very long transects A ~= 1 and the situation would approach that of a line transect, and with A ~= 0.5 (i.e., the hybrid situation) the conversion factor between f(d) and g(d) would depend on detection probability.

Has anyone attempted to develop this or a comparable approach for rounded-end transects? If not, would you have any suggestions for developing this idea further?

Also, on a tangential note, another issue I have to deal with is that some of my rounded-end transects bend, so I'd appreciate any suggestions for references that describe how to deal with non-linear transects. I have found a couple references so far:

Hiby, L., and M. B. Krishna. 2001. Line transect sampling from a curving path. Biometrics 57:727-731.

Strindberg, S., and S. T. Buckland. 2004. Zigzag survey designs in line transect sampling. Journal of Agricultural, Biological, and Environmental Statistics 9:443.

I'd appreciate any suggestions for more recent references that preferably provide a generalized framework for dealing with curvy or bendy transects.

Thanks in advance!

Quresh