On the robustness of N‐mixture models

Link, William A.; Schofield, Matthew; Barker, Richard J.; Sauer, John R.

doi:10.1002/ecy.2362

Cited by 129 publications

(148 citation statements)

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“…The trade‐off between data collection and the complexity of analytical modelling often decides how ecologists approach a question, and ever more complex modelling is not the solution to all questions (Field, Gjerdrum, & Elphick, ). We agree with the valid concerns on the use of N‐mixture models, and we simply argue that the unique characteristics of a stopover population and intensive daily surveys may provide the “adequate” (Link et al., ) or “better quality” (Barker et al., ) data that this modelling approach requires. When the population lacks uniquely identifiable individuals and mark–resight methods are impractical, generalized N‐mixture models can estimate daily abundances of unmarked migratory populations at a staging site, using environmental effects and temporal trends to predict detection probability and immigration rate, on an important condition that there are adequate data.…”

Section: Discussionsupporting

confidence: 77%

“…() nicely summarized the fast‐developing suite of N‐mixture models extended to handle the overdispersion or spatial correlation of counts, open population assumptions and a varying degree of survey frequency, and compared those to established methods such as GLMs and distance sampling. At the same time, recent studies raised significant caution of over‐fitting N‐mixture models in regard of the model's key assumptions (Barker, Schofield, Link, & Sauer, ; Dennis, Morgan, & Ridout, ; Duarte, Adams, & Peterson, ; Kéry, ; Link, Schofield, Barker, & Sauer, ). We are addressing each of these assumptions below.…”

Section: Discussionmentioning

confidence: 99%

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Estimating transient populations of unmarked individuals at a migratory stopover site using generalized N‐mixture models

Kwon

Houghton

Settlage

et al. 2018

Journal of Applied Ecology

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Migration counts are popular indices used to monitor population trends over time. Advanced analytical methods for estimating abundance of unmarked, open populations now incorporate population growth models and simultaneously test for covariate effects on abundance and detection probability. However, estimating population abundance at a staging site is complicated by daily immigration and emigration of unmarked individuals. We applied a set of generalized N‐mixture models to simulated count data to test their applicability for transient populations. Using simulated datasets, parameters were unbiased when the apparent survival rate varied within a season or was mis‐specified in a model, but not when the immigration or detection probability was mis‐specified. With knowledge from the simulated data, we applied these models to daily counts of staging migratory shorebirds and estimated daily abundances accounting for variation in the detection and immigration rates. Daily counts of ruddy turnstones (Arenaria interpres) staging at Westhampton Island, New York, were collected during northward migration (1997–1999). We tested the effects of weather and tides on detection probability, and we modelled within‐season variation in immigration rates as a function of time. Covariates affecting the detection probability differed among years, but tide height consistently was correlated with detection probability. Accounting for detection and immigration rates, the predicted maximum single‐day populations of ruddy turnstones were 172%, 165% and 129% of the observed counts for each year. Synthesis and applications. Management and conservation plans for migratory species require abundance estimates that are near the true population size though they are difficult to obtain. Our study is the first empirical application of the generalized N‐mixture model that incorporates temporal trends in immigration and estimates daily abundance of a staging unmarked migratory population. Despite its inherent limitation, we suggest that the generalized N‐mixture model can estimate the abundance of transient populations with low individual heterogeneity when counts are intensively surveyed. Correct estimation of population sizes and the environmental factors affecting them can aid the conservation prioritization of species and staging sites. Moreover, the use of generalized N‐mixture models can improve our understanding of the environmental factors that shape migratory movements.

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Section: Discussionsupporting

confidence: 77%

Section: Discussionmentioning

confidence: 99%

Estimating transient populations of unmarked individuals at a migratory stopover site using generalized N‐mixture models

Kwon

Houghton

Settlage

et al. 2018

Journal of Applied Ecology

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“…No model received unequivocal support, so we model‐averaged the predicted abundance values for each site across the top three models (Tables and ). Due to the potential limitations of this modelling approach given the use of unmarked animals and its sensitivity to statistical assumptions (Barker, Schofield, Link, & Sauer, ; Link, Schofield, Barker, & Sauer, ; but see Kéry, ), these predicted values were interpreted as relative abundances, rather than absolute abundances. Detection probabilities for each survey method were also estimated using model‐averaging.…”

Section: Methodsmentioning

confidence: 99%

Dermal denticle assemblages in coral reef sediments correlate with conventional shark surveys

et al. 2020

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It is challenging to assess long‐term trends in mobile, long‐lived and relatively rare species such as sharks. Despite ongoing declines in many coastal shark populations, conventional surveys might be too fleeting and too recent to describe population trends over decades to millennia. Placing recent shark declines into historical context should improve management efforts as well as our understanding of past ecosystem dynamics. A new palaeoecological approach for surveying shark abundance on coral reefs is to quantify dermal denticle assemblages preserved in sediments. This approach assumes that denticle accumulation rates correlate with shark abundances. Here, we test this assumption by comparing the denticle record in surface sediments to three conventional shark survey methods at Palmyra Atoll, Line Islands, central Pacific Ocean, where shark density is high and spatially heterogeneous. We generally found a significant positive correlation between denticle accumulation rates and shark abundances derived from underwater visual census, baited remote underwater video and hook and line surveys. Denticle accumulation rates reflected shark abundances, suggesting that denticle assemblages can preserve a signal of time‐averaged shark abundance in low‐energy coral reef environments. We offer suggestions for applying this tool to measure shark abundance over long time‐scales in other contexts.

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“…In the last decade, the application of N ‐mixture models (Royle ), which use repeated count data without the need of individual capture and identification, seem to give great advantages for estimating population size with reduced field effort. N ‐mixture models received a great interest in the last few years and their reliability has been evaluated by simulation studies, casting doubts on the usefulness of these models because of parameter identifiability problems, in particular in the presence of assumption violations and unmodeled heterogeneity in the abundance or the detection parameter (Barker et al , Link et al ). However, Kéry () showed how binomial N ‐mixture model estimates are in agreement with those obtained with a hierarchical variant of a capture‐recapture model.…”

mentioning

confidence: 99%

Time‐for‐space substitution in N‐mixture modeling and population monitoring

2019

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Population size is a fundamental state variable in ecology, and the analysis of temporal variation in abundance (i.e., detection of trends) is a prime objective in wildlife monitoring. However, population abundance cannot be directly observed because part of the population remains undetected and methods that account for imperfect detection are often not used. Capture‐mark‐recapture approaches give reliable estimates of abundance but are time‐ and effort‐consuming. In the last decade, the application of hierarchical, or N‐mixture, models that use repeated counts of unmarked animals seem to give great advantages in the estimation of population size. Hierarchical models require repeated surveys at multiple sites, but sometimes only data obtained for a single site in successive years are available. We applied the time‐for‐space substitution implemented within the N‐mixture modeling framework to estimate population size and evaluate the dynamics of the endangered European leaf‐toed gecko (Euleptes europaea) surveyed >20 years. We compared these results with capture‐mark‐recapture estimates obtained from the same population and over the same time period. Estimates and trends were comparable and both methods indicated similar population declines; moreover, N‐mixture modeling indicated temperature affected detection. Therefore, the application of the time‐for‐space substitution in hierarchical modeling seems valuable and may be useful in species monitoring and conservation. © 2019 The Wildlife Society.

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On the robustness of N‐mixture models

Cited by 129 publications

References 10 publications

Estimating transient populations of unmarked individuals at a migratory stopover site using generalized N‐mixture models

Estimating transient populations of unmarked individuals at a migratory stopover site using generalized N‐mixture models

Dermal denticle assemblages in coral reef sediments correlate with conventional shark surveys

Time‐for‐space substitution in N‐mixture modeling and population monitoring

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