Fitting N-mixture models to count data with unmodeled heterogeneity: Bias, diagnostics, and alternative approaches

Assessing trends in population size of three unmarked species: A comparison of a multi-species N-mixture model and random encounter models

Estimation of changes in abundances and densities is essential for the research, management, and conservation of animal populations. Recently, technological advances have facilitated the surveillance of animal populations through the adoption of passive sensors, such as camera traps (CT). Several methods, including the random encounter model (REM), have been developed for estimating densities of unmarked populations but require additional information. Hierarchical abundance models, such as the N-mixture model (NMM), can estimate abundances without performing additional fieldwork but do not explicitly estimate the area effectively sampled. This obscures the interpretation of its densities and requires its users to focus on relative measures of abundance instead. Hence, the main objective of our study is to evaluate if REM and NMM yield consistent results qualitatively. Therefore, we compare relative trends: (i) between species, (ii) between years and (iii) across years obtained from annual density/abundance estimates of three species (fox, wild boar and red deer) in central Spain monitored by a camera trapping network for five consecutive winter periods. We reveal that NMM and REM provided density estimates in the same order of magnitude for wild boar, but not for foxes and red deer. Assuming a Poisson detection process in the NMM was important to control for inflation of abundance estimates for frequently detected species. Both methods consistently ranked density/abundance across species (between species trend), but did not always agree on relative ranks of yearly estimates within a single population (between years trend), nor on its linear population trends across years (across years trend). Our results suggest that relative trends are generally consistent when the range of variability is large, but can become inconsistent when the range of variability is smaller.

Simulation-based assessment of the performance of hierarchical abundance estimators for camera trap surveys of unmarked species

Knowledge on animal abundances is essential in ecology, but is complicated by low detectability of many species. This has led to a widespread use of hierarchical models (HMs) for species abundance, which are also commonly applied in the context of nature areas studied by camera traps (CTs). However, the best choice among these models is unclear, particularly based on how they perform in the face of complicating features of realistic populations, including: movements relative to sites, multiple detections of unmarked individuals within a single survey, and low detectability. We conducted a simulation-based comparison of three HMs (Royle-Nichols, binomial N-mixture and Poisson N-mixture model) by generating groups of unmarked individuals moving according to a bivariate Ornstein-Uhlenbeck process, monitored by CTs. Under a range of simulated scenarios, none of the HMs consistently yielded accurate abundances. Yet, the Poisson N-mixture model performed well when animals did move across sites, despite accidental double counting of individuals. Absolute abundances were better captured by Royle-Nichols and Poisson N-mixture models, while a binomial N-mixture model better estimated the actual number of individuals that used a site. The best performance of all HMs was observed when estimating relative trends in abundance, which were captured with similar accuracy across these models.

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.

Accounting for detection probability with overestimation by integrating double monitoring programs over 40 years

In the context of wildlife population declines, increasing computer power over the last 20 years allowed wildlife managers to apply advanced statistical techniques that has improved population size estimates. However, respecting the assumptions of the models that consider the probability of detection, such as N-mixture models, requires the implementation of a rigorous monitoring protocol with several replicate survey occasions and no double counting that are hardly adaptable to field conditions. When the logistical, economic and ecological constraints are too strong to meet model assumptions, it may be possible to combine data from independent surveys into the modelling framework in order to understand population dynamics more reliably. Here, we present a state-space model with an error process modelled on the log scale to evaluate wintering waterfowl numbers in the Camargue, southern France, while taking a conditional probability of detection into consideration. Conditional probability of detection corresponds to estimation of a detection probability index, which is not a true probability of detection, but rather conditional on the difference to a particular baseline. The large number of sites (wetlands within the Camargue delta) and years monitored (44) provide significant information to combine both terrestrial and aerial surveys (which constituted spatially and temporally replicated counts) to estimate a conditional probability of detection, while accounting for false-positive counting errors and changes in observers over the study period. The model estimates abundance indices of wintering Common Teal, Mallard and Common Coot, all species abundant in the area. We found that raw counts were underestimated compared to the predicted population size. The model-based data integration approach as described here seems like a promising solution that takes advantage of as much as possible of the data collected from several methods when the logistic constraints do not allow the implementation of a permanent monitoring and analysis protocol that takes into account the detectability of individuals.

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.

Space-for-time is not necessarily a substitution when monitoring the distribution of pelagic fishes in the San Francisco Bay-Delta

Occupancy models are often used to analyze long-term monitoring data to better understand how and why species redistribute across dynamic landscapes while accounting for incomplete capture. However, this approach requires replicate detection/non-detection data at a sample unit and many long-term monitoring programs lack temporal replicate surveys. In such cases, it has been suggested that surveying subunits within a larger sample unit may be an efficient substitution (i.e., space-for-time substitution). Still, the efficacy of fitting occupancy models using a space-for-time substitution has not been fully explored and is likely context dependent. Herein, we fit occupancy models to Delta Smelt (Hypomesus transpacificus) and Longfin Smelt (Spirinchus thaleichthys) catch data collected by two different monitoring programs that use the same sampling gear in the San Francisco Bay-Delta, USA. We demonstrate how our inferences concerning the distribution of these species changes when using a space-for-time substitution. Specifically, we found the probability that a sample unit was occupied was much greater when using a space-for-time substitution, presumably due to the change in the spatial scale of our inferences. Furthermore, we observed that as the spatial scale of our inferences increased, our ability to detect environmental effects on system dynamics was obscured, which we suspect is related to the tradeoffs associated with spatial grain and extent. Overall, our findings highlight the importance of considering how the unique characteristics of monitoring programs influences inferences, which has broad implications for how to appropriately leverage existing long-term monitoring data to understand the distribution of species.

Sharing detection heterogeneity information among species in community models of occupancy and abundance can strengthen inference

The estimation of abundance and distribution and factors governing patterns in these parameters is central to the field of ecology. The continued development of hierarchical models that best utilize available information to inform these processes is a key goal of quantitative ecologists. However, much remains to be learned about simultaneously modeling true abundance, presence, and trajectories of ecological communities.Simultaneous modeling of the population dynamics of multiple species provides an interesting mechanism to examine patterns in community processes and, as we emphasize herein, to improve species-specific estimates by leveraging detection information among species. Here, we demonstrate a simple but effective approach to share information about observation parameters among species in hierarchical community abundance and occupancy models, where we use shared random effects among species to account for spatiotemporal heterogeneity in detection probability.We demonstrate the efficacy of our modeling approach using simulated abundance data, where we recover well our simulated parameters using N-mixture models. Our approach substantially increases precision in estimates of abundance compared with models that do not share detection information among species. We then expand this model and apply it to repeated detection/non-detection data collected on six species of tits (Paridae) breeding at 119 1 km2 sampling sites across a P. montanus hybrid zone in northern Switzerland (2004-2020). We find strong impacts of forest cover and elevation on population persistence and colonization in all species. We also demonstrate evidence for interspecific competition on population persistence and colonization probabilities, where the presence of marsh tits reduces population persistence and colonization probability of sympatric willow tits, potentially decreasing gene flow among willow tit subspecies.While conceptually simple, our results have important implications for the future modeling of population abundance, colonization, persistence, and trajectories in community frameworks. We suggest potential extensions of our modeling in this paper and discuss how leveraging data from multiple species can improve model performance and sharpen ecological inference.

Nest density drives productivity in chestnut-collared longspurs: Implications for grassland bird conservation

Grassland birds are declining faster than any other avian guild in North America and are increasingly a focus of conservation concern. Adaptive, outcome-based management of rangelands could do much to mitigate declines. However, this approach relies on quantitative, generalizable habitat targets that have been difficult to extrapolate from the literature. Past work relies heavily on individual versus population response, and direct response to management (e.g. grazing) versus response to outcomes. We compared individual and population-level responses to vegetation conditions across scales to identify quantitative targets of habitat quality for an imperiled grassland songbird, the chestnut-collared longspur (Calcarius ornatus) in northern Montana, USA during 2017-2018. We estimated nest density and nest survival within 9-ha survey plots using open N-mixture and nest survival models, respectively, and evaluated relationships with plot- and nest-site vegetation conditions. Plot-scale conditions influenced nest density, whereas nest survival was unaffected by any measured condition. Nest-site and plot-scale vegetation measurements were only weakly correlated, suggesting that management targets based on nest sites only would be incomplete. While nest survival is often assumed to be the key driver of bird productivity, our results suggest that nest density and plot-scale conditions are more important for productivity of longspurs at the core of the breeding distribution. Habitat outcomes for grassland birds should incorporate nest density and average conditions at scale(s) relevant to management (e.g. paddock or pasture).

The Rapid Rise of Next-Generation Natural History

Many ecologists have lamented the demise of natural history and have attributed this decline to a misguided view that natural history is outdated and unscientific. Although there is a perception that the focus in ecology and conservation have shifted away from descriptive natural history research and training toward hypothetico-deductive research, we argue that natural history has entered a new phase that we call “next-generation natural history.” This renaissance of natural history is characterized by technological and statistical advances that aid in collecting detailed observations systematically over broad spatial and temporal extents. The technological advances that have increased exponentially in the last decade include electronic sensors such as camera-traps and acoustic recorders, aircraft- and satellite-based remote sensing, animal-borne biologgers, genetics and genomics methods, and community science programs. Advances in statistics and computation have aided in analyzing a growing quantity of observations to reveal patterns in nature. These robust next-generation natural history datasets have transformed the anecdotal perception of natural history observations into systematically collected observations that collectively constitute the foundation for hypothetico-deductive research and can be leveraged and applied to conservation and management. These advances are encouraging scientists to conduct and embrace detailed descriptions of nature that remain a critically important component of the scientific endeavor. Finally, these next-generation natural history observations are engaging scientists and non-scientists alike with new documentations of the wonders of nature. Thus, we celebrate next-generation natural history for encouraging people to experience nature directly.

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.

Mosquito surveillance and disease outbreak risk models to inform mosquito-control operations in Europe

Surveillance programs are needed to guide mosquito-control operations to reduce both nuisance and the spread of mosquito-borne diseases. Understanding the thresholds for action to reduce both nuisance and the risk of arbovirus transmission is becoming critical. To date, mosquito surveillance is mainly implemented to inform about pathogen transmission risks rather than to reduce mosquito nuisance even though lots of control efforts are aimed at the latter. Passive surveillance, such as digital monitoring (validated by entomological trapping), is a powerful tool to record biting rates in real time. High-quality data are essential to model the risk of arbovirus diseases. For invasive pathogens, efforts are needed to predict the arrival of infected hosts linked to the small-scale vector to host contact ratio, while for endemic pathogens efforts are needed to set up region-wide highly structured surveillance measures to understand seasonal re-activation and pathogen transmission in order to carry out effective control operations.

Using an individual-based model to assess common biases in lek-based count data to estimate population trajectories of lesser prairie-chickens

Researchers and managers are often interested in monitoring the underlying state of a population (e.g., abundance), yet error in the observation process might mask underlying changes due to imperfect detection and availability for sampling. Additional heterogeneity can be introduced into a monitoring program when male-based surveys are used as an index for the total population. Often, male-based surveys are used for avian species, as males are conspicuous and more easily monitored than females. To determine if male-based lek surveys capture changes or trends in population abundance based on female survival and reproduction, we developed a virtual ecologist approach using the lesser prairie-chicken (Tympanuchus pallidicinctus) as an example. Our approach used an individual-based model to simulate lek counts based on female vital rate data, included models where detection and lek attendance probabilities were <1, and was analyzed using both unadjusted counts and an N-mixture model to compare estimates of population abundance and growth rates. Using lek counts to estimate population growth rates without accounting for detection probability or density-based lek attendance consistently biased population growth rates and abundance estimates. Our results therefore suggest that lek-based surveys used without accounting for lek attendance and detection probability may miss important trends in population changes. Rather than population-level inference, lek-based surveys not accounting for lek attendance and detection probability may instead be better for inferring broad-scale range shifts of lesser prairie-chicken populations in a presence/absence framework.

The effect of urbanization on the functional and scale-sensitive diversity of bird assemblages in Central India

Diversity changes can be evaluated at various spatial scales, and the relationship between changes in diversity at the local, landscape and regional scales is not evident. The overall patterns of functional and beta diversity of bird assemblages were evaluated along a five-stage urbanization gradient, censused over the months of January to April in the years 2010–2013, in and around Amravati city, Deccan Plateau, Central India. We expected the abundance of large and predatory species to decline along the gradient, and urbanization to homogenize species richness at the landscape level. Overall, 112,829 birds belonging to 89 species were identified in the region, and species richness decreased from the rural forest (73 species) to more urbanized areas (lowest at the centre of Amravaty city with 29 species). Along the urbanization gradient, bird assemblages contained more small species, and the share of frugivorous and omnivorous species also increased, while that of insectivorous species decreased. Diversity partitioning indicated that of the overall pattern, local (alpha) diversity accounted for 50.1% of the total (gamma) diversity, and urbanization stages another 36.2%; the contribution of within-stage, local diversity was rather small (2.7%), indicating fairly homogeneous assemblages.

N-mixture models reliably estimate the abundance of small vertebrates

Accurate measures of species abundance are essential to identify conservation strategies. N-mixture models are increasingly used to estimate abundance on the basis of species counts. In this study we tested whether abundance estimates obtained using N-mixture models provide consistent results with more traditional approaches requiring capture (capture-mark recapture and removal sampling). We focused on endemic, threatened species of amphibians and reptiles in Italy, for which accurate abundance data are needed for conservation assessments: the Lanza’s Alpine salamander Salamandra lanzai, the Ambrosi’s cave salamander Hydromantes ambrosii and the Aeolian wall lizard Podarcis raffonei. In visual counts, detection probability was variable among species, ranging between 0.14 (Alpine salamanders) and 0.60 (cave salamanders). For all the species, abundance estimates obtained using N-mixture models showed limited differences with the ones obtained through capture-mark-recapture or removal sampling. The match was particularly accurate for cave salamanders in sites with limited abundance and for lizards, nevertheless non-incorporating heterogeneity of detection probability increased bias. N-mixture models provide reliable abundance estimates that are comparable with the ones of more traditional approaches, and offer additional advantages such as a smaller sampling effort and no need of manipulating individuals, which in turn reduces the risk of harming animals and spreading diseases.