Computational Aspects of N-Mixture Models

Dennis, Emily B.; Morgan, Byron J. T.; Ridout, Martin S.

doi:10.1111/biom.12246

Cited by 90 publications

(125 citation statements)

References 29 publications

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“…Model estimates based on simulated data recovered true parameters well. This was not surprising, as previous simulation studies have shown that N ‐mixture models usually perform well for estimating abundance and detection probability for a variety of conditions with varying level of detection probability, few replicate temporal counts, and few sites (Couturier, Cheylan, Bertolero, Astruc, & Besnard, ; Dennis, Morgan, & Ridout, ; Hunt, Weckerly, & Ott, ; Kéry, Royle, & Schmid, ; McCaffery, Nowak, & Lukacs, ; Yamaura, ). The novel application in our simulation was the use of the intersection of two overlapping spatial sites as temporal replication.…”

Section: Discussionmentioning

confidence: 73%

Estimating occupancy and abundance using aerial images with imperfect detection

et al. 2017

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Species distribution and abundance are critical population characteristics for efficient management, conservation, and ecological insight. Point process models are a powerful tool for modelling distribution and abundance, and can incorporate many data types, including count data, presence‐absence data, and presence‐only data. Aerial photographic images are a natural tool for collecting data to fit point process models, but aerial images do not always capture all animals that are present at a site. Methods for estimating detection probability for aerial surveys usually include collecting auxiliary data to estimate the proportion of time animals are available to be detected. We developed an approach for fitting point process models using an N‐mixture model framework to estimate detection probability for aerial occupancy and abundance surveys. Our method uses multiple aerial images taken of animals at the same spatial location to provide temporal replication of sample sites. The intersection of the images provide multiple counts of individuals at different times. We examined this approach using both simulated and real data of sea otters (Enhydra lutris kenyoni) in Glacier Bay National Park, southeastern Alaska. Using our proposed methods, we estimated detection probability of sea otters to be 0.76, the same as visual aerial surveys that have been used in the past. Further, simulations demonstrated that our approach is a promising tool for estimating occupancy, abundance, and detection probability from aerial photographic surveys. Our methods can be readily extended to data collected using unmanned aerial vehicles, as technology and regulations permit. The generality of our methods for other aerial surveys depends on how well surveys can be designed to meet the assumptions of N‐mixture models.

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Section: Discussionmentioning

confidence: 73%

Estimating occupancy and abundance using aerial images with imperfect detection

et al. 2017

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“…Dennis et al. () show that the Binmix model with Poisson mixture can sometimes yield estimates of abundance and detection probability ( p ) that are infinite and zero, respectively. They found this especially for small abundance, detection probability and number of repeat visits.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, stability of the estimates for increasing K can be used as a criterion for parameter identifiability (Dennis et al. , Haines ). Barker et al.…”

Section: Introductionmentioning

confidence: 99%

Identifiability inN‐mixture models: a large‐scale screening test with bird data

Kéry

2018

Ecology

126

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Binomial N-mixture models have proven very useful in ecology, conservation, and monitoring: they allow estimation and modeling of abundance separately from detection probability using simple counts. Recently, doubts about parameter identifiability have been voiced. I conducted a large-scale screening test with 137 bird data sets from 2,037 sites. I found virtually no identifiability problems for Poisson and zero-inflated Poisson (ZIP) binomial N-mixture models, but negative-binomial (NB) models had problems in 25% of all data sets. The corresponding multinomial N-mixture models had no problems. Parameter estimates under Poisson and ZIP binomial and multinomial N-mixture models were extremely similar. Identifiability problems became a little more frequent with smaller sample sizes (267 and 50 sites), but were unaffected by whether the models did or did not include covariates. Hence, binomial N-mixture model parameters with Poisson and ZIP mixtures typically appeared identifiable. In contrast, NB mixtures were often unidentifiable, which is worrying since these were often selected by Akaike's information criterion. Identifiability of binomial N-mixture models should always be checked. If problems are found, simpler models, integrated models that combine different observation models or the use of external information via informative priors or penalized likelihoods, may help.

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“…Several studies have compared estimates between N-mixture and other models that accommodate imperfect detection using field data Hunt et al 2012;Couturier et al 2013). In addition, some simulation studies related to their performance have also been conducted (Ke´ry 2008;McIntyre et al 2012;Yamaura 2013;Dennis et al 2015). However, estimation performance of community N-mixture abundance models has not been examined to date.…”

Section: Introductionmentioning

confidence: 99%

Study of biological communities subject to imperfect detection: bias and precision of communityN‐mixture abundance models in small‐sample situations

Yamaura

Kéry

Royle

2016

Ecological Research

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Community N-mixture abundance models for replicated counts provide a powerful and novel framework for drawing inferences related to species abundance within communities subject to imperfect detection. To assess the performance of these models, and to compare them to related community occupancy models in situations with marginal information, we used simulation to examine the effects of mean abundance ð k: 0.1, 0.5, 1, 5), detection probability ðp: 0.1, 0.2, 0.5), and number of sampling sites (n site : 10, 20, 40) and visits (n visit : 2, 3, 4) on the bias and precision of species-level parameters (mean abundance and covariate effect) and a community-level parameter (species richness). Bias and imprecision of estimates decreased when any of the four variables ð k, p, n site , n visit ) increased. Detection probability p was most important for the estimates of mean abundance, while k was most influential for covariate effect and species richness estimates. For all parameters, increasing n site was more beneficial than increasing n visit . Minimal conditions for obtaining adequate performance of community abundance models were n site ‡ 20, p ‡ 0.2, and k ‡ 0.5. At lower abundance, the performance of community abundance and community occupancy models as species richness estimators were comparable. We then used additive partitioning analysis to reveal that raw species counts can overestimate b diversity both of species richness and the Shannon index, while community abundance models yielded better estimates. Community N-mixture abundance models thus have great potential for use with community ecology or conservation applications provided that replicated counts are available.

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Computational Aspects of N-Mixture Models

Cited by 90 publications

References 29 publications

Estimating occupancy and abundance using aerial images with imperfect detection

Estimating occupancy and abundance using aerial images with imperfect detection

Identifiability inN‐mixture models: a large‐scale screening test with bird data

Study of biological communities subject to imperfect detection: bias and precision of communityN‐mixture abundance models in small‐sample situations

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