Linked paper: Evaluating time-removal models for estimating availability of boreal birds during point count surveys: Sample size requirements and model complexity by P. Sólymos, S.M. Matsuoka, S.G. Cumming, D. Stralberg, P. Fontaine, F.K.A. Schmiegelow, S.J. Song, and E.M. Bayne, The Condor: Ornithological Applications 120:3, August 2018.
Point count survey duration rarely changes within projects but varies greatly among projects. As more and more large-scale studies are compiling and analyzing point count data from disparate sources, standardization becomes critical, because count duration greatly affects observations. The Boreal Avian Modelling (BAM, www.borealbirds.ca) project aims to further continental scale avian conservation through the integration and analysis of point count data collected across northern North America. In order to estimate population density and population size for landbird species, data integration became a real issue for us.
Two of the main sources of variation in the observed counts have nothing to do with ecological variables of interest, such as land cover and climate, but rather are considered nuisance variables. These are point count radius and point count duration. Recognizing that most studies do not follow survey protocol recommendations aimed to facilitate data integration (see e.g. Matsuoka et al. 2014), we opted to use model-based techniques to place our variable data on a common footing.
We first tackled standardizing for varying point count radii through distance sampling (Matsuoka et al. 2012) and eventually combined this with a removal model-based correction for varying point count duration. We named the method QPAD, referring to terms of our statistical notation: probability of detection (q), probability of availability (p), area surveyed (A) and population density (D) (Solymos et al. 2013). In the present paper we assessed different ways of controlling for point count duration. As the title indicates, we performed a cost-benefit analysis to make recommendations about when to use different types of the removal model.
We evaluated a conventional removal model and a finite mixture removal model, with and without covariates, for 152 bird species. We found that the probabilities of predicted availability under conventional and finite mixture models were very similar with respect to the range of probability values and the shape of the response curves to predictor variables. However, finite mixture models were better supported for the large majority of species. We also found overwhelming support for time-varying models irrespective of the parametrization.
So what is a finite mixture model? In our case, it splits the population of birds present at a location into frequent and infrequent singers. In previous parametrizations, researchers assumed that the singing rate of the infrequent group varies with date and time, whereas frequent singers remain frequent singers independent of time of year or time of day. We compared this to an alternate parametrization that assumes that individuals change behaviour over time and switch from frequent to infrequent singing behaviour—so it is the proportion of the two groups that varies. We found that the latter assumption was favoured.
Finite mixture models provide some really nice insight into how singing behaviour changes over time and, due to having more parameters, they provide a better fit and thus minimize bias in population size estimates. But all this improvement comes with a price: Sample size requirements (or more precisely, the number of detections required) are really high. To have all the benefits with reduced variance, one needs about 1000 non-zero observations to fit finite mixture models—20 times more than needed to reliably fit conventional removal models. This is much higher than previously suggested minimum sample sizes.
All of our findings indicate that lengthening the count duration from 3 minutes to 5-10 minutes is an important consideration when designing field surveys to increase the accuracy and precision of population estimates. Well-informed survey design, combined with various forms of removal sampling, is useful in accounting for availability bias in point counts, thereby improving population estimates and allowing for better integration of disparate studies at larger spatial scales. To this end, we provide our removal model estimates as part of the QPAD R package and the R functions required to fit all the above outlined removal models as part of the detect R package. We at the BAM project and our collaborators are already utilizing the removal model estimates to correct for availability bias in our continental and regional projects to inform better management and conservation of bird populations. Read more about these projects in our annual report.