Either approach should be fine. In your approach, the detection function is exactly that – the probability of detection of a nest from the line, as a function of distance from the line. In their approach, the detection function doesn’t have that interpretation. And the only reason that their approach works is the ‘pooling robustness’ property of distance sampling, which is described and investigated in
Rexstad, E., Buckland, S., Marshall, L. and Borchers, D. 2023. Pooling robustness in distance sampling: avoiding bias when there is unmodelled heterogeneity. Ecology and Evolution 13, e9684.
It would be interesting to do a comparative study, to see how the 2 approaches compare wrt precision achieved for the same level of resources.
Steve Buckland
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