A robust-design formulation of the incidence function model of metapopulation dynamics applied to two species of rails

The incidence function model (IFM) uses area and connectivity to predict metapopulation dynamics. However, false absences and missing data can lead to underestimates of the number of sites contributing to connectivity, resulting in overestimates of dispersal ability and turnovers (extinctions plus colonizations). We extend estimation methods for the IFM by using a hierarchical Bayesian model to account both for false absences due to imperfect detection and for missing data due to sites not surveyed in some years. We compare parameter estimates, measures of metapopulation dynamics, and forecasts using stochastic patch occupancy models (SPOMs) among three IFM models: (1) a Bayesian formulation assuming no false absences and omitting site-year combinations with missing data; (2) a hierarchical Bayesian formulation assuming no false absences but incorporating missing data; and (3) a hierarchical Bayesian formulation allowing for imperfect detection and incorporating missing data. We fit the models to multiyear data sets of occupancy for two bird species that differ in body size and presumed dispersal ability but inhabit the same network of sites: the small Black Rail (Laterallus jamaicensis) and the medium-sized Virginia Rail (Rallus limicola). Incorporating missing data affected colonization parameters and led to lower estimates of dispersal ability for the Black Rail. Detection rates were high for the Black Rail in most years but moderate for the Virginia Rail. Incorporating imperfect detection resulted in higher occupancy and lower turnover rates for both species, with largest effects for the Virginia Rail. Forecasts using SPOMs were sensitive to both missing data and false absences; persistence in models assuming no false absences was more optimistic than from robust models. Our results suggest that incorporating false absences and missing data into the IFM can improve (1) estimates of dispersal ability and the effect of connectivity on colonization, (2) the scaling of extinction risk with patch area, and (3) forecasts of occupancy and turnover rates.