Gajanan
Can you provide more details about your question? Is this a covariate you want to include in your detection function model? It might not be the case that the covariate of interest influences detectability; model selection might not choose the model, perhaps
making the issue moot.
The pooling robustness property of distance sampling also indicates that density or abundance estimates are not biased when sources of variation in detectability are not included in the detection function models used for inference. You can read more about the
pooling robustness property in this paper:
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Rexstad, E., Buckland, S., Marshall, L., & Borchers, D. (2023). Pooling robustness in distance sampling: Avoiding bias when there is unmodelled heterogeneity.
Ecology and Evolution, 13, e9684.
https://doi.org/10.1002/ece3.9684