Sensitivity of binomial N‐mixture models to overdispersion: The importance of assessing model fit

Binomial-discrete Erlang-truncated exponential mixture and its application in cancer disease

Among diseases, cancer exhibits the fastest global spread, presenting a substantial challenge for patients, their families, and the communities they belong to. This paper is devoted to modeling such a disease as a special case. A newly proposed distribution called the binomial-discrete Erlang-truncated exponential (BDETE) is introduced. The BDETE is a mixture of binomial distribution with the number of trials (parameter [Formula: see text]) taken after a discrete Erlang-truncated exponential distribution. A comprehensive mathematical treatment of the proposed distribution and expressions of its density, cumulative distribution function, survival function, failure rate function, Quantile function, moment generating function, Shannon entropy, order statistics, and stress-strength reliability, are provided. The distribution's parameters are estimated using the maximum likelihood method. Two real-world lifetime count data sets from the cancer disease, both of which are right-skewed and over-dispersed, are fitted using the proposed BDETE distribution to evaluate its efficacy and viability. We expect the findings to become standard works in probability theory and its related fields.

Disentangling Exploitative and Interference Competition on Forest Dwelling Salamanders

Exploitative competition and interference competition differ in the way access to resources is modulated by a competitor. Exploitative competition implies resource depletion and usually produces spatial segregation, while interference competition is independent from resource availability and can result in temporal niche partitioning. Our aim is to infer the presence of spatial or temporal niche partitioning on a two-species system of terrestrial salamanders in Northern Italy: Speleomantes strinatii and Salamandrina perspicillata. We conducted 3 repeated surveys on 26 plots in spring 2018, on a sampling site where both species are present. We modelled count data with N-mixture models accounting for directional interactions on both abundance and detection process. In this way we were able to disentangle the effect of competitive interaction on the spatial scale, i.e., local abundance, and from the temporal scale, i.e., surface activity. We found strong evidence supporting the presence of temporal niche partitioning, consistent with interference competition. At the same time, no evidence of spatial segregation has been observed.

Camera Trap Methods and Drone Thermal Surveillance Provide Reliable, Comparable Density Estimates of Large, Free-Ranging Ungulates

Camera traps and drone surveys both leverage advancing technologies to study dynamic wildlife populations with little disturbance. Both techniques entail strengths and weaknesses, and common camera trap methods can be confounded by unrealistic assumptions and prerequisite conditions. We compared three methods to estimate the population density of white-tailed deer (Odocoileus virgnianus) in a section of Pilot Mountain State Park, NC, USA: (1) camera trapping using mark-resight ratios or (2) N-mixture modeling and (3) aerial thermal videography from a drone platform. All three methods yielded similar density estimates, suggesting that they converged on an accurate estimate. We also included environmental covariates in the N-mixture modeling to explore spatial habitat use, and we fit models for each season to understand temporal changes in population density. Deer occurred in greater densities on warmer, south-facing slopes in the autumn and winter and on cooler north-facing slopes and in areas with flatter terrain in the summer. Seasonal density estimates over two years suggested an annual cycle of higher densities in autumn and winter than in summer, indicating that the region may function as a refuge during the hunting season.

Comparing N-mixture models and GLMMs for relative abundance estimation in a citizen science dataset

To analyze species count data when detection is imperfect, ecologists need models to estimate relative abundance in the presence of unknown sources of heterogeneity. Two candidate models are generalized linear mixed models (GLMMs) and hierarchical N-mixture models. GLMMs are computationally robust but do not explicitly separate detection from abundance patterns. N-mixture models separately estimate detection and abundance via a latent state but are sensitive to violations in assumptions and subject to practical estimation issues. When one can assume that detection is not systematically confounded with ecological patterns of interest, these two models can be viewed as sharing a heuristic framework for relative abundance estimation. Model selection can then determine which predicts observed counts best, for example by AIC. We compared four N-mixture model variants and two GLMM variants for predicting bird counts in local subsets of a citizen science dataset, eBird, based on model selection and goodness-of-fit measures. We found that both GLMMs and N-mixture models—especially N-mixtures with beta-binomial detection submodels—were supported in a moderate number of datasets, suggesting that both tools are useful and that relative fit is context-dependent. We provide faster software implementations of N-mixture likelihood calculations and a reparameterization to interpret unstable estimates for N-mixture models.

An Overview of Modern Applications of Negative Binomial Modelling in Ecology and Biodiversity

Negative binomial modelling is one of the most commonly used statistical tools for analysing count data in ecology and biodiversity research. This is not surprising given the prevalence of overdispersion (i.e., evidence that the variance is greater than the mean) in many biological and ecological studies. Indeed, overdispersion is often indicative of some form of biological aggregation process (e.g., when species or communities cluster in groups). If overdispersion is ignored, the precision of model parameters can be severely overestimated and can result in misleading statistical inference. In this article, we offer some insight as to why the negative binomial distribution is becoming, and arguably should become, the default starting distribution (as opposed to assuming Poisson counts) for analysing count data in ecology and biodiversity research. We begin with an overview of traditional uses of negative binomial modelling, before examining several modern applications and opportunities in modern ecology/biodiversity where negative binomial modelling is playing a critical role, from generalisations based on exploiting its Poisson-gamma mixture formulation in species distribution models and occurrence data analysis, to estimating animal abundance in negative binomial N-mixture models, and biodiversity measures via rank abundance distributions. Comparisons to other common models for handling overdispersion on real data are provided. We also address the important issue of software, and conclude with a discussion of future directions for analysing ecological and biological data with negative binomial models. In summary, we hope this overview will stimulate the use of negative binomial modelling as a starting point for the analysis of count data in ecology and biodiversity studies.

N-mixture models provide informative crocodile (Crocodylus moreletii) abundance estimates in dynamic environments

Estimates of animal abundance provide essential information for population ecological studies. However, the recording of individuals in the field can be challenging, and accurate estimates require analytical techniques which account for imperfect detection. Here, we quantify local abundances and overall population size of Morelet's crocodiles (Crocodylus moreletii) in the region of Calakmul (Campeche, Mexico), comparing traditional approaches for crocodylians (Minimum Population Size-MPS; King's Visible Fraction Method-VFM) with binomial N-mixture models based on Poisson, zero-inflated Poisson (ZIP) and negative binomial (NB) distributions. A total of 191 nocturnal spotlight surveys were conducted across 40 representative locations (hydrologically highly dynamic aquatic sites locally known as aguadas) over a period of 3 years (2017-2019). Local abundance estimates revealed a median of 1 both through MPS (min-max: 0-89; first and third quartiles, Q₁-Q₃: 0-7) and VFM (0-112; Q₁-Q₃: 0-9) non-hatchling C. moreletii for each aguada, respectively. The ZIP based N-mixture approach shown overall superior confidence over Poisson and NB, and revealed a median of 6 ± 3 individuals (min = 0; max = 120 ± 18; Q₁ = 0; Q₃ = 18 ± 4) jointly with higher detectabilities in drying aguadas with low and intermediate vegetation cover. Extrapolating these inferences across all waterbodies in the study area yielded an estimated ~10,000 (7,000-11,000) C. moreletii present, highlighting Calakmul as an important region for this species. Because covariates enable insights into population responses to local environmental conditions, N-mixture models applied to spotlight count data result in particularly insightful estimates of crocodylian detection and abundance.

Counting Cats: The integration of expert and citizen science data for unbiased inference of population abundance

Free-roaming animal populations are hard to count, and professional experts are a limited resource. There is vast untapped potential in the data collected by nonprofessional scientists who volunteer their time to population monitoring, but citizen science (CS) raises concerns around data quality and biases. A particular concern in abundance modeling is the presence of false positives that can occur due to misidentification of nontarget species. Here, we introduce Integrated Abundance Models (IAMs) that integrate citizen and expert data to allow robust inference of population abundance meanwhile accounting for biases caused by misidentification. We used simulation experiments to confirm that IAMs successfully remove the inflation of abundance estimates caused by false-positive detections and can provide accurate estimates of both bias and abundance. We illustrate the approach with a case study on unowned domestic cats, which are commonly confused with owned, and infer their abundance by analyzing a combination of CS data and expert data. Our case study finds that relying on CS data alone, either through simple summation or via traditional modeling approaches, can vastly inflate abundance estimates. IAMs provide an adaptable framework, increasing the opportunity for further development of the approach, tailoring to specific systems and robust use of CS data.

Time-for-space substitution in N-mixture models for estimating population trends: a simulation-based evaluation

N-mixture models usually rely on a meta-population design, in which repeated counts of individuals in multiple sampling locations are obtained over time. The time-for-space substitution (TSS) in N-mixture models allows to estimate population abundance and trend of a single population, without spatial replication. This application could be of great interest in ecological studies and conservation programs; however, its reliability has only been evaluated on a single case study. Here we perform a simulation-based evaluation of this particular application of N-mixture modelling. We generated count data, under 144 simulated scenarios, from a single population surveyed several times per year and subject to different dynamics. We compared simulated abundance and trend values with TSS estimates. TSS estimates are overall in good agreement with real abundance. Trend and abundance estimation is mainly affected by detection probability and population size. After evaluating the reliability of TSS, both against real world data, and simulations, we suggest that this particular application of N-mixture model could be reliable for monitoring abundance in single populations of rare or difficult to study species, in particular in cases of species with very narrow geographic ranges, or known only for few localities.

Abundance estimation of unmarked animals based on camera-trap data

The rapid improvement of camera traps in recent decades has revolutionized biodiversity monitoring. Despite clear applications in conservation science, camera traps have seldom been used to model the abundance of unmarked animal populations. We sought to summarize the challenges facing abundance estimation of unmarked animals, compile an overview of existing analytical frameworks, and provide guidance for practitioners seeking a suitable method. When a camera records multiple detections of an unmarked animal, one cannot determine whether the images represent multiple mobile individuals or a single individual repeatedly entering the camera viewshed. Furthermore, animal movement obfuscates a clear definition of the sampling area and, as a result, the area to which an abundance estimate corresponds. Recognizing these challenges, we identified 6 analytical approaches and reviewed 927 camera-trap studies published from 2014 to 2019 to assess the use and prevalence of each method. Only about 5% of the studies used any of the abundance-estimation methods we identified. Most of these studies estimated local abundance or covariate relationships rather than predicting abundance or density over broader areas. Next, for each analytical approach, we compiled the data requirements, assumptions, advantages, and disadvantages to help practitioners navigate the landscape of abundance estimation methods. When seeking an appropriate method, practitioners should evaluate the life history of the focal taxa, carefully define the area of the sampling frame, and consider what types of data collection are possible. The challenge of estimating abundance of unmarked animal populations persists; although multiple methods exist, no one method is optimal for camera-trap data under all circumstances. As analytical frameworks continue to evolve and abundance estimation of unmarked animals becomes increasingly common, camera traps will become even more important for informing conservation decision-making.

Visual Head Counts: A Promising Method for Efficient Monitoring of Diamondback Terrapins

Determining the population status of the diamondback terrapin (Malaclemys terrapin spp.) is challenging due to their ecology and limitations associated with traditional sampling methods. Visual counting of emergent heads offers a promising, efficient, and non-invasive method for generating abundance estimates of terrapin populations across broader spatial scales than has been achieved using capture–recapture, and can be used to quantify determinants of spatial variation in abundance. We conducted repeated visual head count surveys along the shoreline of Wellfleet Bay in Wellfleet, Massachusetts, and analyzed the count data using a hierarchical modeling framework designed specifically for repeated count data: the N-mixture model. This approach allows for simultaneous modeling of imperfect detection to generate estimates of true terrapin abundance. Detection probability was lowest when temperatures were coldest and when wind speed was highest. Local abundance was on average higher in sheltered sites compared to exposed sites and declined over the course of the sampling season. We demonstrate the utility of pairing visual head counts and N-mixture models as an efficient method for estimating terrapin abundance and show how the approach can be used to identifying environmental factors that influence detectability and distribution.

Multiyear monitoring of bird communities in chlorpyrifos-treated orchards in Spain and the United Kingdom: Spatial and temporal trends in species composition, abundance, and site fidelity

The relationship between agricultural practices and the welfare of wild birds has gained increased attention over the last decades. To assess the potential effects of chlorpyrifos on the bird community, a multiyear, multisite monitoring program was carried out in treated cider orchards (in the United Kingdom) and treated citrus orchards (in Spain). Constant-effort mist netting was used over several consecutive years in the United Kingdom (2012-2014) and Spain (2010-2012). The general structure of the bird community and the presence of breeding species were analyzed. Twelve and 11 bird species (out of 81 and 45 trapped) in Spain and the United Kingdom, respectively, exceeded the 2% dominance value. For a selection of 6 species in citrus and 4 in cider orchards, N-mixture models were fitted to the number of trapped birds. The abundance of most species was strongly and significantly affected by seasonality. No species showed any indication of reduction in population size over the years. The results of this extensive field program support the indications that chlorpyrifos spray applications present a low risk to the bird community over the years. Environ Toxicol Chem 2019;38:616-629. © 2018 The Authors. Environmental Toxicology and Chemistry Published by Wiley Periodicals, Inc. on behalf of SETAC.