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1. Understanding whether a species still persists, or the timing of its extinction is challenging, however, such knowledge is fundamental for effective species management. 2. For the vast majority of species our understanding of their existence is based solely on sighting data that can range from museum specimens and clear photographs, through vocalisations, to markings and oral accounts. 3. Here we review the methods that have been developed to infer the extinction of species from a sighting record, providing an understanding of their assumptions and applications. We have also produced an RShiny package which can be used to implement some of the methods presented in the article. 4. While there are a number of potential areas that could be further developed, the methods reviewed provide a useful tool for inferring species extinction.

In this discussion response, we consider some practical implications of the authors’ consideration of the no-highest-order interaction (NHOI) model for multiple systems estimation, which permits the authors to derive the explicit (albeit untestable) identifying assumption related to the unobserved (or missing) individuals. In particular, we discuss several aspects, from the standard process of model selection to potential poor predictive performance due to over-fitting and the implications of data reduction. We discuss these aspects in relation to the case study presented by the authors relating to the number of civilian casualties within the Kosovo war, and conduct further preliminary simulations to investigate these issues further. The results suggest that the NHOI models considered, despite having a potentially useful theoretical result in relation to the underlying identifying assumption, may perform poorly in practice.

State-space models are an increasingly common and important tool in the quantitative ecologists’ armoury, particularly for the analysis of time-series data. This is due to both their flexibility and intuitive structure, describing the different individual processes of a complex system, thus simplifying the model specification step. State-space models are composed of two processes (a) the system (or state) process that describes the dynamics of the true underlying state of the system over time; and (b) the observation process that links the observed data with the current true state of the system at that time. Specification of the general model structure consists of considering each distinct ecological process within the system and observation processes, which are then automatically combined within the state-space structure. There is typically a trade-off between the complexity of the model and the associated model-fitting process. Simpler model specifications permit the application of simpler model-fitting tools; whereas more complex model specifications, with nonlinear dynamics and/or non-Gaussian stochasticity often require more sophisticated model-fitting algorithms to be applied. We provide a brief overview of general state-space models before focusing on the different model-fitting tools available. In particular for different general state-space model structures we discuss established model-fitting tools that are available. We also offer practical guidance for choosing a specific fitting procedure.

Precise and accurate estimates of abundance and demographic rates are primary quantities of interest within wildlife conservation and management. Such quantities provide insight into population trends over time and the associated underlying ecological drivers of the systems. This information is fundamental in managing ecosystems, assessing species conservation status and developing and implementing effective conservation policy. Observational monitoring data are typically collected on wildlife populations using an array of different survey protocols, dependent on the primary questions of interest. For each of these survey designs, a range of advanced statistical techniques have been developed which are typically well understood. However, often multiple types of data may exist for the same population under study. Analyzing each data set separately implicitly discards the common information contained in the other data sets. An alternative approach that aims to optimize the shared information contained within multiple data sets is to use a “model-based data integration” approach, or more commonly referred to as an “integrated model.” This integrated modeling approach simultaneously analyzes all the available data within a single, and robust, statistical framework. This paper provides a statistical overview of ecological integrated models, with a focus on integrated population models (IPMs) which include abundance and demographic rates as quantities of interest. Four main challenges within this area are discussed, namely model specification, computational aspects, model assessment and forecasting. This should encourage researchers to explore further and develop new practical tools to ensure that full utility can be made of IPMs for future studies.

Mark–recapture surveys are commonly used to monitor translocated populations globally. Data gathered are then used to estimate demographic parameters, such as abundance and survival, using Jolly–Seber (JS) models. However, in translocated populations initial population size is known and failure to account for this may bias parameter estimates, which are important for informing conservation decisions during population establishment. Here, we provide methods to account for known initial population size in JS models by incorporating a separate component likelihood for translocated individuals, using a maximum‐likelihood estimation, with models that can be fitted using either R or MATLAB. We use simulated data and a case study of a threatened lizard species with low capture probability to demonstrate that unconstrained JS models may overestimate the size of translocated populations, especially in the early stages of post‐release monitoring. Our approach corrects this bias; we use our simulations to demonstrate that overestimates of population size between 78% and 130% can occur in the unconstrained JS models when the detection probability is below 0.3 compared to 1%–8.9% for our constrained model. Our case study did not show an overestimate; however accounting for the initial population size greatly reduced error in all parameter estimates and prevented boundary estimates. Adopting the corrected JS model for translocations will help managers to obtain more robust estimates of the population sizes of translocated animals, better informing future management including reinforcement decisions, and ultimately improving translocation success.

Batch marking is common and useful for many capture-recapture studies where individual marks cannot be applied due to various constraints such as timing, cost, or marking difficulty. When batch marks are used, observed data are not individual capture histories but a set of counts including the numbers of individuals first marked, marked individuals that are recaptured, and individuals captured but released without being marked (applicable to some studies) on each capture occasion. Fitting traditional capture-recapture models to such data requires one to identify all possible sets of capture-recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this paper, we propose a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in central Madagascar.

State-space models are an increasingly common and important tool in the quantitative ecologists’ armoury, particularly for the analysis of time-series data. This is due to both their flexibility and intuitive structure, describing the different individual processes of a complex system, thus simplifying the model specification step. State-space models are composed of two processes (a) the system (or state) process that describes the dynamics of the true underlying state of the system over time; and (b) the observation process that links the observed data with the current true state of the system at that time. Specification of the general model structure consists of considering each distinct ecological process within the system and observation processes, which are then automatically combined within the state-space structure. There is typically a trade-off between the complexity of the model and the associated model-fitting process. Simpler model specifications permit the application of simpler model-fitting tools; whereas more complex model specifications, with nonlinear dynamics and/or non-Gaussian stochasticity often require more sophisticated model-fitting algorithms to be applied. We provide a brief overview of general state-space models before focusing on the different model-fitting tools available. In particular for different general state-space model structures we discuss established model-fitting tools that are available. We also offer practical guidance for choosing a specific fitting procedure.

Understanding the factors that facilitate or constrain establishment of populations in novel environments is crucial for conservation biology and the study of adaptive radiation. Important questions include: (1) Does the timing of colonization relative to stochastic events, such as climatic perturbations, impact the probability of successful establishment? (2) To what extent does community context (e.g., the presence of competitors) change the probability of establishment? (3) How do sources of intrapopulation variance, such as sex differences, affect success at an individual level during the process of establishment? Answers to these questions are rarely pursued in a field‐experimental context or on the same time scales (months to years) as the processes of colonization and establishment. We introduced slender anole lizards (Anolis apletophallus) to eight islands in the Panama Canal and tracked them over multiple generations to investigate the factors that mediate establishment success. All islands were warmer than the mainland (ancestral) environment, and some islands had a native competitor. We transplanted half of these populations only 4 months before the onset of a severe regional drought and the other half 2 years (two generations) before the drought. We found that successful establishment depended on both the intensity of interspecific competition and the timing of colonization relative to the drought. The islands that were colonized shortly before the drought went functionally extinct by the second generation, and regardless of time before the drought, the populations on islands with interspecific competition declined continuously over the study period. Furthermore, the effect of the competitor interacted with sex, with males suffering, and females benefitting, from the presence of a native competitor. Our results reveal that community context and the timing of colonization relative to climactic events can combine to determine establishment succes

Batch marking is common and useful for many capture-recapture studies where individual marks cannot be applied due to various constraints such as timing, cost, or marking difficulty. When batch marks are used, observed data are not individual capture histories but a set of counts including the numbers of individuals first marked, marked individuals that are recaptured, and individuals captured but released without being marked (applicable to some studies) on each capture occasion. Fitting traditional capture-recapture models to such data requires one to identify all possible sets of capture-recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this paper, we propose a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in central Madagascar.

Hidden Markov models (HMMs) are being widely used in the field of ecological modeling, however determining the number of underlying states in an HMM remains a challenge. Here we examine a special case of capture-recapture models for open populations, where some animals are observed but it is not possible to ascertain their state (partial observations), whilst the other animals' states are assigned without error (complete observations). We propose a mixture test of the underlying state structure generating the partial observations, which assesses whether they are compatible with the set of states observed in the complete observations. We demonstrate the good performance of the test using simulation and through application to a data set of Canada Geese.

Recently, multiple systems estimation (MSE) has been applied to estimate the number of victims of human trafficking in different countries. The estimation procedure consists of a log-linear analysis of a contingency table of population registers and covariates. As the number of potential models increases exponentially with the number of registers and covariates, it is practically impossible to fit and compare all models. Therefore, the model search needs to be restricted to a small subset of all potential models. This paper addresses principles and criteria for model assessment and selection for MSE of human trafficking with special attention to sparsity which is typical to human trafficking data. The concepts are illustrated on data from Slovakia and Romania.

Recently, multiple systems estimation (MSE) has been applied to estimate the number of victims of human trafficking in different countries. The estimation procedure consists of a log-linear analysis of a contingency table of population registers and covariates. As the number of potential models increases exponentially with the number of registers and covariates, it is practically impossible to fit and compare all models. Therefore, the model search needs to be restricted to a small subset of all potential models. This paper addresses principles and criteria for model assessment and selection for MSE of human trafficking with special attention to sparsity which is typical to human trafficking data. The concepts are illustrated on data from Slovakia and Romania.

Abundance estimation, for both human and animal populations, informs policy decisions and population management. Capture-recapture and multiple sources data share a common structure; the population can be partially enumerated and individuals are identifiable. Consequently, the analytical methods were developed simultaneously. However, whilst ecological models have been developed to describe highly complex, biologically realistic scenarios, for example modeling population changes through time and combining different forms of data, multiple systems estimation has changed comparatively less so. In this paper we provide a brief description of the historical development of ecological and epidemiological capture-recapture and discuss the associated underlying differences that have led to model divergence. We identify three key areas where ecological modeling methods may inform and improve multiple systems estimation.

Long-term capture-recapture studies provide an opportunity to investigate the population dynamics of long-lived species through individual maturation and adulthood and/or time. We consider capture-recapture data collected on cohorts of female gray seals (Halichoerus grypus) born during the 1990s and later observed breeding on the Isle of May, Firth of Forth, Scotland. Female gray seals can live for 30+ years but display individual variability in their maturation rates and so recruit into the breeding population across a range of ages. Understanding the partially hidden process by which individuals transition from immature to breeding members, and in particular the identification of any changes to this process through time, are important for understanding the factors affecting the population dynamics of this species. Age-structured capture-recapture models can explicitly relate recruitment, and other demographic parameters of interest, to the age of individuals and/or time. To account for the monitoring of the seals from several birth cohorts we consider an age-structured model that incorporates a specific cohort-structure. Within this model we focus on the estimation of the distribution of the age of recruitment to the breeding population at this colony. Understanding this recruitment process, and identifying any changes or trends in this process, will offer insight into individual year effects and give a more realistic recruitment profile for the current UK gray seal population model. The use of the hidden Markov model provides an intuitive framework following the evolution of the true underlying states of the individuals. The model breaks down the different processes of the system: recruitment into the breeding population; survival; and the associated observation process. This model specification results in an explicit and compact expression for the model with associated efficiency in model fitting. Further, this framework naturally leads to extensions to more com

Removal models were proposed over 80 years ago as a tool to estimate unknown population size. More recently, they are used as an effective tool for management actions for the control of non desirable species, or for the evaluation of translocation management actions. Although the models have evolved over time, in essence, the protocol for data collection has remained similar: at each sampling occasion attempts are made to capture and remove individuals from the study area. Within this paper we review the literature of removal modelling and highlight the methodological developments for the analysis of removal data, in order to provide a unified resource for ecologists wishing to implement these approaches. Models for removal data have developed to better accommodate important features of the data and we discuss the shift in the required assumptions for the implementation of the models. The relative simplicity of this type of data and associated models mean that the method remains attractive and we discuss the potential future role of this technique.

Hidden Markov models (HMMs) are being widely used in the field of ecological modeling, however determining the number of underlying states in an HMM remains a challenge. Here we examine a special case of capture-recapture models for open populations, where some animals are observed but it is not possible to ascertain their state (partial observations), whilst the other animals' states are assigned without error (complete observations). We propose a mixture test of the underlying state structure generating the partial observations, which assesses whether they are compatible with the set of states observed in the complete observations. We demonstrate the good performance of the test using simulation and through application to a data set of Canada Geese.