Models for Estimating Abundance from Repeated Counts of an Open Metapopulation

Abstract

Using only spatially and temporally replicated point counts, Royle (2004b, Biometrics 60, 108-115) developed an N-mixture model to estimate the abundance of an animal population when individual animal detection probability is unknown. One assumption inherent in this model is that the animal populations at each sampled location are closed with respect to migration, births, and deaths throughout the study. In the past this has been verified solely by biological arguments related to the study design as no statistical verification was available. In this article, we propose a generalization of the N-mixture model that can be used to formally test the closure assumption. Additionally, when applied to an open metapopulation, the generalized model provides estimates of population dynamics parameters and yields abundance estimates that account for imperfect detection probability and do not require the closure assumption. A simulation study shows these abundance estimates are less biased than the abundance estimate obtained from the original N-mixture model. The proposed model is then applied to two data sets of avian point counts. The first example demonstrates the closure test on a single-season study of Mallards (Anas platyrhynchos), and the second uses the proposed model to estimate the population dynamics parameters and yearly abundance of American robins (Turdus migratorius) from a multi-year study.

Site Occupancy and Density of Marsh Birds in Coastal and Freshwater Habitats of Florida

“…pcountOpen fits the open population model of Dail and Madsen (2011) to repeated count data. This is a genearlized form of the Royle (2004a) N-mixture model that includes parameters for recruitment and apparent survival.…”

“…Fit the models of Dail and Madsen (2011) and Hostetler and Chandler (in press), which are generalized forms of the Usage pcountOpen(lambdaformula, gammaformula, omegaformula, pformula, data, mixture = c("P", "NB", "ZIP"), K, dynamics=c("constant", "autoreg", "notrend", "trend", "ricker", "gompertz"), fix=c("none", "gamma", "omega"), starts, method = "BFGS", se = TRUE, immigration = FALSE, iotaformula =~1, ...)…”

Herpetological monitoring and assessment on the Trinity River, Trinity County, California—Final report

“…To estimate trends in abundance in basking western pond turtles, we used the function "pcountOpen" from the package "unmarked" in R. This function is based on the models of Royle (2004) and Dail and Madsen (2011), and fits an N-mixture model that accounts for the number of animals counted during a field survey is less than the number of animals present and that the difference is variable and unobserved (Royle, 2004;Dail and Madsen, 2011). N-mixture models require repeated count data to assess the probability of detection, and are based in the assumption of a closed population within a season, relaxing that assumption to an open population between seasons.…”

Too risky to settle: avian community structure changes in response to perceived predation risk on adults and offspring

“…To separate effects of detection probability from population abundance, formulations of N-mixture models must make assumptions regarding population closure; that is, the extent to which the surveyed population size remains unchanged ('closed') across repeated surveys [37]. To avoid unsupported assumptions about population closure, we contrasted three model categories with decreasing strictness of population closure and increasing model complexity: (i) 'Closed' models (assuming closure across all surveys) [38]; (ii) 'Robust Design' models (assuming closure within but not between clusters of survey periods, aka, 'primary periods'; sensu [39]) [38] and (iii) 'Open' models (assuming no closure across all surveys) [40].…”

“…We used two criteria to evaluate the fit of successfully converged models. First, because N-mixture models tend to overestimate abundance and underestimate detection probability when closure is inappropriately assumed [40], we accepted only models that produced estimates that largely aligned with our biological knowledge of the species (e.g. known territory sizes of species).…”