Estimating negative binomial parameters from occurrence data with detection times

What can occupancy models gain from time-to-detection data?

The time taken to detect a species during site occupancy surveys contains information about the observation process. Accounting for the observation process leads to better inference about site occupancy. We explore the gain in efficiency that can be obtained from time-to-detection data and show that this model type has a significant benefit for estimating the parameters related to detection intensity. However, for estimating occupancy probability parameters, the efficiency improvement is generally very minor. To explore whether time-to-detection data could add valuable information when detection intensities vary between sites and surveys, we developed a mixed exponential time-to-detection occupancy model. This new model can simultaneously estimate the detection intensity and aggregation parameters when the number of detectable individuals at the site follows a negative binomial distribution. We found that this model provided a much better description of the occupancy patterns than conventional detection/non-detection methods among 63 bird species data from the Karoo region of South Africa. Ignoring the heterogeneity of detection intensity in the time-to-detection model generally yielded a negative bias in the estimated occupancy probability. Using simulations, we briefly explore study design trade offs between numbers of sites and surveys for different occupancy modelling strategies.

An Overview of Modern Applications of Negative Binomial Modelling in Ecology and Biodiversity

Negative binomial modelling is one of the most commonly used statistical tools for analysing count data in ecology and biodiversity research. This is not surprising given the prevalence of overdispersion (i.e., evidence that the variance is greater than the mean) in many biological and ecological studies. Indeed, overdispersion is often indicative of some form of biological aggregation process (e.g., when species or communities cluster in groups). If overdispersion is ignored, the precision of model parameters can be severely overestimated and can result in misleading statistical inference. In this article, we offer some insight as to why the negative binomial distribution is becoming, and arguably should become, the default starting distribution (as opposed to assuming Poisson counts) for analysing count data in ecology and biodiversity research. We begin with an overview of traditional uses of negative binomial modelling, before examining several modern applications and opportunities in modern ecology/biodiversity where negative binomial modelling is playing a critical role, from generalisations based on exploiting its Poisson-gamma mixture formulation in species distribution models and occurrence data analysis, to estimating animal abundance in negative binomial N-mixture models, and biodiversity measures via rank abundance distributions. Comparisons to other common models for handling overdispersion on real data are provided. We also address the important issue of software, and conclude with a discussion of future directions for analysing ecological and biological data with negative binomial models. In summary, we hope this overview will stimulate the use of negative binomial modelling as a starting point for the analysis of count data in ecology and biodiversity studies.