Estimating the ecological drivers of insect abundance when detection is imperfect.

Biodiversity conservation hinges on a clear understanding of the ecological drivers of species abundance. In studies of insect abundance, researchers often estimate the effects of hypothesized drivers by applying generalized linear models and generalized linear mixed models (GLMs/GLMMs) to count data. However, a significant issue with conventional GLMs/GLMMs is that they cannot account for a failure to detect some individuals that are present ('imperfect detection'), which can bias model estimates. To account for this, some researchers adopt hierarchical modelling approaches, including multinomial N-mixture (multimix) models for mark-recapture data and binomial N-mixture (binmix) models for repeated count data. Currently, we lack side-by-side comparisons to determine the ecological and study design conditions that require the use of these more cumbersome approaches to achieve accurate estimates. We collected abundance data on wild bees in a study designed to compare unrestored to restored urban parks, which had more flowers and taller vegetation. We applied all three modelling approaches to these data, using either mark-recapture data (multimix approach) or ignoring whether individuals were marked and treating the data as traditional counts (binmix and GLMM approaches). Our models indicated that capture rates for individual bees were below ~5%. The multimix mark-recapture model found that bees were ~1.6-fold more likely to be detected in restored habitats. A GLMM, which did not account for detection bias, overestimated the effects of restoration on bee abundance. Using simulation, we found that multimix mark-recapture models had the highest accuracy and precision for estimating an abundance driver, including when individuals have the potential to move in/out of sampling areas; however, we also found that increasing baseline detection rates minimized the impacts of detection bias on GLMM estimates. Our results emphasize that environmental factors can influence our ability to detect insects in field studies, and that these factors may be confounded with the experimental design. We recommend that studies planning to apply GLMs/GLMMs to count data prioritize methods that maximize detection over other aspects of study design such as the number of sites. Together, our results provide needed guidance on how to design and implement studies that accurately quantify the ecological drivers of insect abundance.