A binomial N‐mixture model for estimating arrival and departure timing

• Published in: Methods in ecology and evolution Vol. 10; no. 7; pp. 1062 - 1071
• Main Authors: Mizel, Jeremy D., Schmidt, Joshua H., Phillips, Laura M., Mcintyre, Carol L., Sutherland, Chris
• Format: Journal Article
• Language: English
• Published: London John Wiley & Sons, Inc 01-07-2019
• Subjects: Abundance; Availability; closure assumption; Computer simulation; Dependence; detection probability; Fitness; Formulations; Inference; Life cycle assessment; Life cycles; long‐term monitoring; National parks; phenological mismatch; phenology; Population studies; Populations; Probabilistic models; Seasonal distribution; Seasonal variations; unmarked populations
• ISSN: 2041-210X; 2041-210X
• DOI: 10.1111/2041-210X.13192

The timing of life cycle events has strong fitness consequences, suggesting that monitoring of arrival and departure timing may help understand spatial and population dynamics. Several existing models with inference to arrival and departure in unmarked populations are applicable to detection/non‐detection data which is a reduced information summary of the underlying population and phenological dynamics. These models also do not directly address the dependence of seasonal variation in availability (e.g. song rate) on arrival timing, often treating the seasonal distribution of availability as fixed across years despite allowing variation in arrival. Model development in an abundance framework has largely occurred in the context of stopover populations, rather than populations that exhibit some period of closure between arrival and departure phases.
We developed an N‐mixture model that accommodates the dependence of seasonal availability on arrival timing, providing inference about abundance and both arrival and departure timing based on repeated count data. The model is applicable to populations in which there exists some period of closure between the arrival and departure phases. We developed two general formulations of the model, both of which include a model for the arrival process, but differ in the model for seasonal availability. The first formulation is applicable to cases in which seasonal availability is a function of cue production. The other is applicable to situations where seasonal availability is a function of departure of individuals or their transition to a state in which they remain unavailable for detection.
We demonstrated through simulation that both versions provide unbiased and precise estimates of phenology and abundance and illustrated the cue production formulation using data collected in Denali National Park, Alaska for three passerine species.
We expect that our inference framework will be broadly applicable in studies of unmarked populations where joint assessment of population, spatial and phenological dynamics is of interest.