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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.

N-mixture models provide an appealing alternative to mark–recapture models, in that they allow for estimation of detection probability and population size from count data, without requiring that individual animals be identified. There is, however, a cost to using the N-mixture models: inference is very sensitive to the model’s assumptions. We consider the effects of three violations of assumptions that might reasonably be expected in practice: double counting, unmodeled variation in population size over time, and unmodeled variation in detection probability over time. These three examples show that small violations of assumptions can lead to large biases in estimation. The violations of assumptions we consider are not only small qualitatively, but are also small in the sense that they are unlikely to be detected using goodness-of-fit tests. In cases where reliable estimates of population size are needed, we encourage investigators to allocate resources to acquiring additional data, such as recaptures of marked individuals, for estimation of detection probabilities.

N-mixture models describe count data replicated in time and across sites in terms of abundance N and detectability p. They are popular because they allow inference about N while controlling for factors that influence p without the need for marking animals. Using a capture-recapture perspective, we show that the loss of information that results from not marking animals is critical, making reliable statistical modeling of N and p problematic using just count data. One cannot reliably fit a model in which the detection probabilities are distinct among repeat visits as this model is overspecified. This makes uncontrolled variation in p problematic. By counter example, we show that even if p is constant after adjusting for covariate effects (the \"constant p\" assumption) scientifically plausible alternative models in which N (or its expectation) is non-identifiable or does not even exist as a parameter, lead to data that are practically indistinguishable from data generated under an N-mixture model. This is particularly the case for sparse data as is commonly seen in applications. We conclude that under the constant p assumption reliable inference is only possible for relative abundance in the absence of questionable and/or untestable assumptions or with better quality data than seen in typical applications. Relative abundance models for counts can be readily fitted using Poisson regression in standard software such as R and are sufficiently flexible to allow controlling for p through the use covariates while simultaneously modeling variation in relative abundance. If users require estimates of absolute abundance, they should collect auxiliary data that help with estimation of p.

AIM: During the past decade ecologists have attempted to estimate the parameters of species distribution models by combining locations of species presence observed in opportunistic surveys with spatially referenced covariates of occurrence. Several statistical models have been proposed for the analysis of presence‐only data, but these models have largely ignored the effects of imperfect detection and survey bias. In this paper I describe a model‐based approach for the analysis of presence‐only data that accounts for errors in the detection of individuals and for biased selection of survey locations. INNOVATION: I develop a hierarchical, statistical model that allows presence‐only data to be analysed in conjunction with data acquired independently in planned surveys. One component of the model specifies the spatial distribution of individuals within a bounded, geographic region as a realization of a spatial point process. A second component of the model specifies two kinds of observations, the detection of individuals encountered during opportunistic surveys and the detection of individuals encountered during planned surveys. MAIN CONCLUSIONS: Using mathematical proof and simulation‐based comparisons, I demonstrate that biases induced by errors in detection or biased selection of survey locations can be reduced or eliminated by using the hierarchical model to analyse presence‐only data in conjunction with counts observed in planned surveys. I show that a relatively small number of high‐quality data (from planned surveys) can be used to leverage the information in presence‐only observations, which usually have broad spatial coverage but may not be informative of both occurrence and detectability of individuals. Because a variety of sampling protocols can be used in planned surveys, this approach to the analysis of presence‐only data is widely applicable. In addition, since the point‐process model is formulated at the level of an individual, it can be extended to account for biological interactions between individuals and temporal changes in their spatial distributions.

Numerous modelling techniques exist to estimate abundance of plant and animal populations. The most accurate methods account for multiple complexities found in ecological data, such as observational biases, spatial autocorrelation, and species correlations. There is, however, a lack of user‐friendly and computationally efficient software to implement the various models, particularly for large data sets. We developed the spAbundance R package for fitting spatially explicit Bayesian single‐species and multi‐species hierarchical distance sampling models, N‐mixture models, and generalized linear mixed models. The models within the package can account for spatial autocorrelation using Nearest Neighbour Gaussian Processes and accommodate species correlations in multi‐species models using a latent factor approach, which enables model fitting for data sets with large numbers of sites and/or species. We provide three vignettes and three case studies that highlight spAbundance functionality. We used spatially explicit multi‐species distance sampling models to estimate density of 16 bird species in Florida, USA, an N‐mixture model to estimate black‐throated blue warbler (Setophaga caerulescens) abundance in New Hampshire, USA, and a spatial linear mixed model to estimate forest above‐ground biomass across the continental USA. spAbundance provides a user‐friendly, formula‐based interface to fit a variety of univariate and multivariate spatially explicit abundance models. The package serves as a useful tool for ecologists and conservation practitioners to generate improved inference and predictions on the spatial drivers of abundance in populations and communities.

There is increasing need for methods that integrate multiple data types into a single analytical framework as the spatial and temporal scale of ecological research expands. Current work on this topic primarily focuses on combining capture–recapture data from marked individuals with other data types into integrated population models. Yet, studies of species distributions and trends often rely on data from unmarked individuals across broad scales where local abundance and environmental variables may vary. We present a modeling framework for integrating detection–nondetection and count data into a single analysis to estimate population dynamics, abundance, and individual detection probabilities during sampling. Our dynamic population model assumes that site-specific abundance can change over time according to survival of individuals and gains through reproduction and immigration. The observation process for each data type is modeled by assuming that every individual present at a site has an equal probability of being detected during sampling processes. We examine our modeling approach through a series of simulations illustrating the relative value of count vs. detection-nondetection data under a variety of parameter values and survey configurations. We also provide an empirical example of the model by combining long-term detection-nondetection data (1995–2014) with newly collected count data (2015–2016) from a growing population of Barred Owl (Strix varia) in the Pacific Northwest to examine the factors influencing population abundance over time. Our model provides a foundation for incorporating unmarked data within a single framework, even in cases where sampling processes yield different detection probabilities. This approach will be useful for survey design and to researchers interested in incorporating historical or citizen science data into analyses focused on understanding how demographic rates drive population abundance.

Aim As climate change increases the frequency and severity of droughts in many regions, conservation during drought is becoming a major challenge for ecologists. Droughts are multidimensional climate events whose impacts may be moderated by changes in temperature, water availability or food availability, or some combination of these. Simultaneously, other stressors such as extensive anthropogenic landscape modification may synergize with drought. Useful observational models for guiding conservation decision‐making during drought require multidimensional, dynamic representations to disentangle possible drought impacts, and consequently, they will require large, highly resolved data sets. In this paper, we develop a two‐stage predictive framework for assessing how drought impacts vary with species, habitats and climate pathways. Location Central Valley, California, USA. Methods We used a two‐stage counterfactual analysis combining predictive linear mixed models and N‐mixture models to characterize the multidimensional impacts of drought on 66 bird species. We analysed counts from the eBird participatory science data set between 2010 and 2019 and produced species‐ and habitat‐specific estimates of the impact of drought on relative abundance. Results We found that while fewer than a quarter (16/66) of species experienced abundance declines during drought, nearly half of all species (27/66) changed their habitat associations during drought. Among species that shifted their habitat associations, the use of natural habitats declined during drought while use of developed habitat and perennial agricultural habitat increased. Main Conclusions Our findings suggest that birds take advantage of agricultural and developed land with artificial irrigation and heat‐buffering microhabitat structure, such as in orchards or parks, to buffer drought impacts. A working lands approach that promotes biodiversity and mitigates stressors across a human‐induced water gradient will be critical for conserving birds during drought.

Time‐to‐detection (TTD) occupancy models are increasingly used to study site occupancy of organisms. Occupancy is a reduced representation of abundance (distinguishing only between 0 and >0 individuals), which is also often a quantity of interest. In this paper, we present a novel framework for TTD occupancy models that address limitations of existing approaches. Our approach incorporates factors that accommodate detection heterogeneity among sites/visits and inter‐visit dependency, allowing for the relaxation of some restrictive assumptions inherent in previous models. As a result, our framework offers a robust and versatile tool for analysing various ecological data sets. We employ a maximum likelihood approach to estimate model parameters and conduct inference for the proposed TTD occupancy models. A key feature of these models is the introduction of a community parameter. This parameter characterizes the similarity of detectabilities, ranging from complete independence to complete identity, across multiple site visits. This framework disentangles the detection rate, abundance and occupancy, similar to the popular N‐mixture model. For situations where abundance estimation is not the primary goal, a family of mixed gamma exponential TTD models is developed, which generally exhibit more stable numerical properties compared to N‐mixture type TTD models. The performance of the proposed models and some reduced models is evaluated through simulation studies. The results indicate that the N‐mixture TTD model tends to considerably overestimate the occupancy probability when the community parameter is less than one, a condition necessary to satisfy the strict closure population assumption. On the other hand, the standard exponential TTD occupancy model underestimates the occupancy probability in the presence of unobserved detection heterogeneity and inter‐visit dependency. An analysis of 63 bird species in the Karoo region of South Africa demonstrates the enhanced flexibility of the proposed TTD occupancy models for data fitting. This paper demonstrates the importance of employing more flexible and general models to accurately capture the complexities of ecological systems or survey data. We provide R‐code to fit all considered models to data. The proposed TTD model framework contributes to enhancing our understanding of species occupancy distributions.

We designed a participatory monitoring program for the capercaillie population in the French Pyrenees based on lek censuses conducted during the breeding season. This program was implemented by a consortium of stakeholders interested in the conservation of French galliforms. The program, carried out since 2010, relied on a dual frame sampling approach: The first sampled frame was the list of all known leks in the study area. We distinguished two types of known leks: leks known to be active before the onset of the program (with at least one cock detected since 2000) and leks with an indeterminate activity status at the time of the onset of the program. The monitoring program also accounted for the existence of leks that were unknown due mainly to incomplete expert knowledge. We therefore built a complementary area frame by discretizing the study area into a set of 4-km² grid cells. These cells were then sampled and searched to find unknown leks. When unknown leks were found, cock censuses were organized. An additional field experiment allowed us to estimate the detection probability of unknown leks during these cell searches. We then fitted two hierarchical models: (i) An N-mixture model fitted to the lek census data set allowed us to estimate the mean number of cocks on the three types of leks (known active, known indeterminate, and unknown leks); and (ii) another model fitted to the cell search data set allowed us to estimate the number of unknown leks in the studied mountain range. By multiplying the estimated mean numbers of cocks associated with the three types of leks by the number of leks of each type (an estimated value in the case of unknown leks), we obtained estimates of the total numbers of cocks on all leks at different spatial scales in the study area every 2 years. Our model suggests that the capercaillie cock population was stable from 2010 to 2017 over the whole range but decreased slightly in the foothill area and western part, a decrease that worsened in 2018–2019.

Understanding how and why animals use the environments where they occur is both foundational to behavioral ecology and essential to identify critical habitats for species conservation. However, some behaviors are more difficult to observe than others, which can bias analyses of raw observational data. To our knowledge, no method currently exists to model how animals use different environments while accounting for imperfect behavior-specific detection probability. We developed an extension of a binomial N-mixture model (hereafter the behavior N-mixture model) to estimate the probability of a given behavior occurring in a particular environment while accounting for imperfect detection. We then conducted a simulation to validate the model's ability to estimate the effects of environmental covariates on the probabilities of individuals performing different behaviors. We compared our model to a naïve model that does not account for imperfect detection, as well as a traditional N-mixture model. Finally, we applied the model to a bird observation data set in northwest Costa Rica to quantify how three species behave in forests and farms. Simulations and sensitivity analyses demonstrated that the behavior N-mixture model produced unbiased estimates of behaviors and their relationships with predictor variables (e.g., forest cover, habitat type). Importantly, the behavior N-mixture model accurately characterized uncertainty, unlike the naïve model, which often suggested erroneous effects of covariates on behaviors. When applied to field data, the behavior N-mixture model suggested that Hoffmann's woodpecker (Melanerpes hoffmanii) and Inca dove (Columbina inca) behaved differently in forested versus agricultural habitats, while turquoise-browed motmot (Eumomota superciliosa) did not. Thus, the behavior N-mixture model can help identify habitats that are essential to a species' life cycle (e.g., where individuals nest, forage) that nonbehavioral models would miss. Our model can greatly improve the appropriate use of behavioral survey data and conclusions drawn from them. In doing so, it provides a valuable path forward for assessing the conservation value of alternative habitat types.