Study of biological communities subject to imperfect detection: bias and precision of community <i>N</i>‐mixture abundance models in small‐sample situations

Yamaura, Yuichi; Kéry, Marc; Royle, J. Andrew

doi:10.1007/s11284-016-1340-4

Cited by 47 publications

(91 citation statements)

References 74 publications

(95 reference statements)

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“…From here on, we refer to Yamaura et al. ()'s approach as the Normal N‐mixture model. Finally, in the example using real data (Section ) we estimated the density of 26 species of neotropical dry forest birds using a previously unpublished dataset.…”

Section: Methodsmentioning

confidence: 99%

“…Besides these two model differences, Yamaura et al. () used a Bayesian approach to fit their hierarchical model, whereas we used the MLE method. Much discussion exists regarding the merits of each inferential approach for hierarchical models in Ecology (see for instance Cressie et al., ; Lele & Dennis, ).…”

Section: Methodsmentioning

confidence: 99%

“…Here we limit ourselves to comparing the results from Yamaura et al. ()'s estimation approach, which is widely used as the benchmark of a known method in the literature, to our approach. Table presents a comparison of the statistical models' structures.…”

Section: Methodsmentioning

confidence: 99%

“…If the objective is to estimate the abundance of S species, the overall likelihood is simply written as the product of all the individual species' likelihoods, i.e.,

L false(\underset{̲}{λ}, \underset{̲}{P} false) = \prod_{s = 1}^{S} \prod_{i = 1}^{r} \sum_{n_{s i} = max false({\underset{̲}{y}}_{s i} false)}^{\infty} \prod_{j = 1}^{t} (\begin{matrix} n_{s i} \\ y_{s i j} \end{matrix}) p_{s}^{y_{s i j}} {(1 - p_{s})}^{n_{s i} - y_{s i j}} \frac{e^{- {normalλ}_{s}} {normalλ}_{s}^{n_{s i}}}{n_{s i}!},

where

{\underset{̲}{y}}_{s i}

is a vector of length r with the observed counts for species s in the i th point count, and both

\underset{̲}{normalλ} = false{λ_{1}, \dots, λ_{S} false}

and

\underset{̲}{p} = false{p_{1}, \dots, p_{S} false}

are vectors of length S . To avoid the proliferation of parameters one could assume that all the p s , s = 1, …, S come from a single probability model that describes the community‐wide distribution of detection probabilities (Barnagaud et al., ; Ruiz‐Gutiérrez et al., ; Sauer & Link, ; Yamaura et al., ). In this case, each species' detection probability can be modelled with a beta distribution.…”

Section: The Modelmentioning

confidence: 99%

See 3 more Smart Citations

An efficient extension of N‐mixture models for multi‐species abundance estimation

et al. 2017

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In this study we propose an extension of the N-mixture family of models that targets an improvement of the statistical properties of rare species abundance estimators when sample sizes are low, yet typical for tropical studies. The proposed method harnesses information from other species in an ecological community to correct each species' estimator. We provide guidance to determine the sample size required to estimate accurately the abundance of rare tropical species when attempting to estimate the abundance of single species.We evaluate the proposed methods using an assumption of 50 m radius plots and perform simulations comprising a broad range of sample sizes, true abundances and detectability values and a complex data generating process. The extension of the N-mixture model is achieved by assuming that the detection probabilities are drawn at random from a beta distribution in a multi-species fashion. This hierarchical model avoids having to specify a single detection probability parameter per species in the targeted community. Parameter estimation is done via Maximum Likelihood.We compared our multi-species approach with previously proposed multi-species N-mixture models, which we show are biased when the true densities of species in the community are less than seven individuals per 100 hectares. The beta N-mixture model proposed here outperforms the traditional Multi-species N-mixture model by allowing the estimation of organisms at lower densities and controlling the bias in the estimation.We illustrate how our methodology can be used to suggest sample sizes required to estimate the abundance of organisms, when these are either rare, common or abundant. When the interest is full communities, we show how the multi-species approaches, and in particular our beta model and estimation methodology, can be used as a practical solution to estimate organism densities from rapid inventory datasets. The statistical inferences done with our model via Maximum Likelihood can also be used to group species in a community according to their detectabilities.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…If the objective is to estimate the abundance of S species, the overall likelihood is simply written as the product of all the individual species' likelihoods, i.e.,

L false(\underset{̲}{λ}, \underset{̲}{P} false) = \prod_{s = 1}^{S} \prod_{i = 1}^{r} \sum_{n_{s i} = max false({\underset{̲}{y}}_{s i} false)}^{\infty} \prod_{j = 1}^{t} (\begin{matrix} n_{s i} \\ y_{s i j} \end{matrix}) p_{s}^{y_{s i j}} {(1 - p_{s})}^{n_{s i} - y_{s i j}} \frac{e^{- {normalλ}_{s}} {normalλ}_{s}^{n_{s i}}}{n_{s i}!},

where

{\underset{̲}{y}}_{s i}

is a vector of length r with the observed counts for species s in the i th point count, and both

\underset{̲}{normalλ} = false{λ_{1}, \dots, λ_{S} false}

and

\underset{̲}{p} = false{p_{1}, \dots, p_{S} false}

Section: The Modelmentioning

confidence: 99%

See 2 more Smart Citations

An efficient extension of N‐mixture models for multi‐species abundance estimation

et al. 2017

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“…Likelihood maximisation for this problem becomes more complex due to the fact that the latent abundance random variables are included in the likelihood in a nonlinear fashion and hence Roth et al (2016) opted for assuming prior distributions for the parameters and sample the posterior distribution using MCMC algorithms in a Bayesian framework. This has also been the case when fitting multispecies models for count or occupancy data (see, for example, Yamaura et al, 2012;Dorazio and Connor, 2014;Riffell et al, 2015;Broms et al, 2016;Ovaskainen et al, 2016a, b;Yamaura et al, 2016). The objective, however, when fitting the so-called multispecies occupancy or abundance models is to estimate species diversity, richness and other types of metrics from a community perspective and is hence different from our approach.…”

Section: Parametermentioning

confidence: 97%

Statistical modelling of data from insect studies

Moral¹

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Using species traits to predict detectability of animals on aerial surveys

Schlossberg

Chase

Griffin

2017

Ecological Applications

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Abstract. In animal surveys, detectability can vary widely across species. We hypothesized that detectability of animals should be a function of species traits such as mass, color, and mean herd size. We also hypothesized that models of detectability based on species traits can be used to predict detectability for new species not in the original data set, leading to substantial benefits for ecology and conservation. We tested these hypotheses with double-observer aerial surveys of 10 mammal species in northern Botswana. We combined all 10 species and modeled their detectability with species traits (mass, mean herd size, color) as predictors while controlling for observer effects, vegetation, and herd size. We found support for effects of mass and an interaction between herd size and mean herd size on detectability. This model accurately predicted the ratio of herds detected by two observers vs. one observer for 8 of 10 species. To test whether a model based on species traits could be applied to a new species, we serially deleted each species from the data set, fit a trait-based model to the remaining nine species, and used this model to predict detectability for the deleted species. The model was able to reproduce the species-trait model for seven species and accurately predicted the ratio of detections by one or two observers for a different set of seven species; the model was successful by both measures for five species. To our knowledge, this represents the first time that a mechanistic model for detectability of animals has been used to predict detectability for new species. Prediction failed for species with extreme values of traits, suggesting that predicting detectability is not possible near or beyond the boundaries of one's data set. The approach taken in this paper can potentially be used with a variety of taxa and may provide new opportunities to apply detectability corrections where they have not been possible before.

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

Cited by 47 publications

References 74 publications

An efficient extension of N‐mixture models for multi‐species abundance estimation

An efficient extension of N‐mixture models for multi‐species abundance estimation

Statistical modelling of data from insect studies

Using species traits to predict detectability of animals on aerial surveys

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