Analysing Patterns in Population Dynamics using Repeated Population Surveys with Three Types of Detection Data

ABSTRACT We generalize the distance sampling protocol to accommodate three types of detection data in population surveys (population counts): distance to the observer, multiple observers, and time-to-detection. We also account for the effect of a partially-observed individual covariate, with the aim to account for the non-independence of individuals in groups and the effect of group size on detection probability. Finally, we separate the probability of availability to detection and the probability of detection when available. We compute the statistical power of our new model using simulations and illustrate some of the biases in the simpler alternative analytical procedures that oue new formulation allows to avoid. We discuss issues of weak identifiability (an issue shared with other state-space models) and the bias-precision tradeoff in population survey analyses. We recommend maintaining both simple analyses of population survey data and more complex analyses of the detection process, maybe in a dashboard of indicators. Discrepancies between results from simple and complex analyses can help identify sources of biases and loss of precision.