Accounting for observation biases associated with counts of young when estimating fecundity: case study on the arboreal-nesting red kite (Milvus milvus)

Abstract

AO_SCPLOWBSTRACTC_SCPLOWCounting the number of young in a brood from a distance is common practice, for example in tree-nesting birds. These counts can, however, suffer from over and undercounting, which can lead to biased estimates of fecundity (average number of nestlings per brood). Statistical model development to account for observation bias has focused on false negatives (undercounts), yet it has been shown that these models are sensitive to the presence of false positives (overcounts) when they are not accounted for. Here, we develop a model that estimates fecundity while accounting for both false positives and false negatives in brood counts. Its parameters can be estimated using a calibration approach that combines uncertain counts with certain ones, which can be obtained by accessing the brood, for example during ringing. The model uses multinomial distributions to estimate the probabilities of observing y young conditional on the true state of a brood z (i.e., true number of young) from paired uncertain and certain counts. These classification probabilities are then used to estimate the true state of broods for which only uncertain counts are available. We use a simulation study to investigate bias and precision of the model and parameterize the simulation with empirical data from 26 red kite nests visited with ground and nest-based counts during 2021 and 2022 in central Europe. In these data, bias in counts was at most 1 in either direction, more common in larger broods, and undercounting was more common than overcounting. This led to an overall 5% negative bias in fecundity in uncertain counts. The model produced essentially unbiased estimates (relative bias < 2%) of fecundity across a range of sample sizes. This held true whether or not fecundity was the same for nests with paired counts and those with uncertain-only counts. But the model could not estimate parameters when true states were missing from the paired data, which happened frequently in small sample sizes (n = 10 or 25). Further, we projected populations 50 years into the future using fecundity estimates corrected for observation biases from the multinomial model, and based on "raw" uncertain observations. We found that ignoring observation bias led to strong negative bias in projected population size for growing populations, but only minor negative bias in declining populations. Accounting for apparently minor biases associated with ground counts is important for ensuring accurate estimates of abundance and population dynamics especially for increasing populations. This could be particularly important for informing conservation decisions in projects aimed at recovering depleted populations.