This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

**Appendix 1.** Supplemental simulation study results.

**Table S1.** Parameter values used to simulate spatial capture–recapture datasets.

**Table S2.** Average number of individuals detected per simulation (*n*) with 95% confidence intervals in parentheses and the proportion of individuals detected once, twice, etc. over 10 sampling occasions.

**Table S3.** Properties of spatial capture–recapture abundance estimates.

**Table S4.** Properties of spatial capture–recapture movement scale, *σ*_{move}, estimates.

**Table S5.** Properties of spatial capture–recapture detection probability at zero distance from the detector, *g*0, estimates.

**Table S6.** Properties of spatial capture–recapture detection scale, *σ*_{d}, estimates.

**Table S7.** Properties of spatial capture–recapture random walk bias (*ρ*), persistence (*γ*), and turning angle (*ω*) estimates.

**Table S8.** Properties of spatial capture–recapture random walk bias, *β*, estimates.

**Figure S1.** One individual's simple random walk across the simulation state space during 10 sampling occasions.

**Figure S2.** The movement distribution for the individual from Figure 1 between the first and second sampling occasions.

**Figure S3.** Ratios of the likelihoods of individuals' future locations under spatial capture–recapture models with activity centre and random walk movement models.

**Figure S4.** Calibration of individuals' forecasted locations over 10 future sampling occasions (denoted by each panel's label) under spatial capture–recapture models with activity centre (red) and random walk (blue) movement models.

**Figure S5.** One individual's biased random walk across the simulation state space during 10 sampling occasions.

**Figure S6.** The movement distribution for the individual from Figure 6 between the first and second sampling occasions.

**Figure S7.** Ratios of the likelihoods of individuals' future locations under spatial capture–recapture models with activity centre and biased random walk movement models (top) and random walk and biased random walk movement models (bottom).

**Figure S8.** Calibration of individuals' forecasted locations over 10 future sampling occasions (denoted by each panel's label) under spatial capture–recapture models with activity centre (red), random walk (green), and biased random walk (blue) movement models.

**Figure S9.** One individual's correlated random walk across the simulation state space during 10 sampling occasions.

**Figure S10.** The movement distribution for the individual from Figure 9 between the second and third sampling occasions.

**Figure S11.** Ratios of the likelihoods of individuals' future locations under spatial capture–recapture models with activity centre and correlated random walk movement models (top) and random walk and correlated random walk movement models (bottom).

**Figure S12.** Calibration of individuals' forecasted locations over 10 future sampling occasions (denoted by each panel's label) under spatial capture–recapture models with activity centre (red), random walk (green), and correlated random walk (blue) movement models.

**Figure S13.** Ratios of the likelihoods of individuals' future locations under spatial capture–recapture models with activity centre and simple random walk movement models.

**Figure S14.** Calibration of individuals' forecasted locations over 10 future sampling occasions (denoted by each panel's label) under spatial capture–recapture models with activity centre and simple random walk movement models.

**Figure S15.** Ratios of the likelihoods of individuals' future locations under spatial capture–recapture models with activity centre and simple random walk movement models.

**Figure S16.** Calibration of individuals' forecasted locations over 10 future sampling occasions (denoted by each panel's label) under spatial capture–recapture models with activity centre and simple random walk movement models.

**Figure S17.** Ratios of the likelihoods of individuals' future locations under spatial capture–recapture models with activity centre and simple random walk movement models.

**Figure S18.** Calibration of individuals' forecasted locations over 10 future sampling occasions (denoted by each panel's label) under spatial capture–recapture models with activity centre and simple random walk movement models.

**Figure S19.** Ratios of the likelihoods of individuals' future locations under spatial capture–recapture models with activity centre and simple random walk movement models.

**Figure S20.** Calibration of individuals' forecasted locations over 10 future sampling occasions (denoted by each panel's label) under spatial capture–recapture models with activity centre and simple random walk movement models.

**Appendix 2.** Supplemental north Atlantic right whale results.

**Figure S1.** Average expected (left) and realized (right) density of North Atlantic right whales off the Atlantic coast of Florida, Georgia, and South Carolina between 1 December 2009 and 31 March 2010.

**Figure S2.** Associations between North Atlantic right whale density and movement and depth (left), sea surface temperature (middle), and wind speed (right).

**Figure S3.** Estimated immigration, *τ*, (top) and persistence, *φ*, (bottom) rates and 95% confidence intervals for North Atlantic right whales in the southeastern United States from 1 December 2009 to 31 March 2010.

**Figure S4.** Estimated detection probability for a North Atlantic right whale given its distance from the closest aerial survey trackline.

Wildlife movement is an important process affecting individual space use, migration, encounter rates with predators, prey and anthropogenic threats, population dynamics and gene flow (Matthiopoulos et al., 2015; Morales et al., 2010; Nathan et al., 2008). Therefore, wildlife managers and conservationists often seek to understand wildlife movement to manage habitat features and anthropogenic activities in areas and times where wildlife are expected to be (Runge et al., 2014). Commonly, researchers outfit animals with telemetry or GPS tags to record the animals' movements through time (Cagnacci et al., 2010). However, recent developments in spatial capture–recapture (SCR) allow researchers to model the movement of uniquely identifiable individuals without telemetry or GPS tags (McClintock et al., 2021).

Objectives of individual wildlife movement modelling often include imputing an individual's trajectory (i.e. sequence of locations) between locations collected by GPS tags; estimating movement velocities, turning rates and points or habitat features of attraction and repulsion; and inferring an individual's behavioural state sequence (Hooten et al., 2017). Researchers make inferences on these subjects using hidden Markov models, state space models and diffusion processes (Hooten et al., 2017; Patterson et al., 2017). However, inference is often restricted to a small number of individuals, because costs and logistical constraints limit the number of tagged individuals, that is individuals that are outfitted with GPS or telemetry tags. Additionally, although many studies have focused on predicting the future distribution of wildlife populations (e.g. Hazen et al., 2017), few have focused on forecasting individuals' future movements given their past locations and estimated movement rates (but see Randon et al., 2022). Such forecasts could be useful in further studying the individuals or mitigating threats to them.

The movements of all individuals in a population, not just tagged individuals, may be critically important to understand and forecast, especially in endangered species facing spatially and temporally varying threats. SCR models have been used to estimate wildlife density, habitat selection and space use from data collected from untagged individuals (Royle, Sollman, et al., 2013). Open population SCR models have been used to estimate the movement of individuals' activity centres, that is home range centres (Gardner et al., 2010; Glennie et al., 2019). Bischof et al. (2020) forecasted the annual population size and distribution of wolverines based on the annual activity centre movement, recruitment and mortality rates estimated with an open population SCR model. Additionally, McClintock et al. (2021) proposed a framework for integrating random walk (RW) movement models with SCR. These integrated SCR movement models have been implemented primarily in Bayesian frameworks. For instance, Gardner et al. (2022) simulated data from and fit SCR models integrated with correlated RW and Langevin movement models; Hostetter et al. (2022) estimated polar bear density and movement with SCR models integrated with simple and correlated RWs; and Chandler et al. (2021) estimated white‐tailed deer density and movement with SCR models integrated with biased RWs. Integrated SCR movement models could also allow researchers to forecast the movements of individuals.

We describe a SCR model integrated with hidden Markov models for simple, biased and correlated RWs using a maximum likelihood estimation framework. Our model differs from other maximum likelihood‐based SCR models (Efford & Schofield, 2020; Glennie et al., 2019) by modelling the movement of individuals rather than their activity centres and by permitting bias and correlation in movement direction and speed. As with the conventional activity centre model used in SCR analyses, the biased RW accounts for the bias of an individual's movement toward a point of attraction, an important property of some species' movement behaviours. Each RW exhibits another important property of animal movement: serial correlation of an individual's locations. Additionally, the correlated RW exhibits serial correlation of an individual's speed and direction. We show through a simulation study that these models can be fit to relatively sparse data characteristic of SCR studies. We also evaluate model performance in estimating abundance and forecasting movements of individuals. Finally, we estimate North Atlantic right whale (*Eubalaena glacialis*) population size, population dynamics and movement in the coastal waters of the southeastern United States using integrated SCR movement models.

Consider a study region, ** S**, containing an unknown number of individuals,

We formulate a SCR model using a hidden Markov model to account for the partially observed movement trajectories of individuals through subregions of ** S** and a thinned Poisson point process describing the number of individuals observed at least once. The hidden Markov model contains three components: the initial state distribution,

In all models described hereafter, the state‐dependent detection process, ** P**(

In a simple RW movement model, the states of the hidden Markov model have one‐to‐one correspondence with subregions in ** S**, meaning the model will have

In a biased RW movement model, an individual's state describes the subregion in which it is located and the subregion in which the activity centre or source of bias is located. Therefore, such a hidden Markov model will have *m*^{2} states. We formulate ** δ** such that an activity centre is distributed equivalently to the initial location in the simple RW described above. Then, given an activity centre is located in

In a correlated RW movement model, an individual's state describes both the current and previous subregions in which it has been located. In the case of a second‐order correlated RW, a hidden Markov model will have *m*^{2} states. We formulate ** δ** identically to our formulation in the biased RW, except here, instead of an individual's activity centre being uniformly distributed, its location prior to its initial location is uniformly distributed. Elements of

In this SCR model, the hidden Markov model describes processes for the movement and detection of individuals in the population of interest, and a Poisson point process describes the number of individuals in the population, that is abundance, and their expected distribution at the beginning of the time series, $\left(\mathrm{exp}\left({\beta}_{0}+{\mathit{Z}}_{1}\mathit{\beta}\right),\mathrm{exp}\left({\beta}_{0}+{\mathit{Z}}_{2}\mathit{\beta}\right),\dots ,\mathrm{exp}\left({\beta}_{0}+{\mathit{Z}}_{m}\mathit{\beta}\right)\right)$, where *β*_{0} is an intercept effect. Following Borchers and Efford (2008) and Glennie et al. (2019), we formulate the model likelihood conditional on *n* individuals being observed at least once. The probability of an individual being observed at least once, *p**, is $1-\mathit{\delta}\left({\prod}_{t=1}^{T-1}\mathit{P}\left({\mathit{y}}_{i,t}=0\right)\mathit{\Gamma}\right)\mathit{P}\left({\mathit{y}}_{i,T}=0\right)\mathit{\epsilon}$. The likelihood of *n* individuals being observed at least once under the Poisson point process is $\frac{{\left(D{p}^{*}\right)}^{n}\mathrm{exp}\left(-D{p}^{*}\right)}{n!}$, where *D* is the expected population abundance, that is the parameter that estimates *N*. The full model likelihood follows as:

We wrote likelihood functions in R and C++ using the Rcpp package and use numerical optimization for maximum likelihood estimation (Eddelbuettel & Francois, 2011; Eddelbuettel & Sanderson, 2014; R Core Team, 2019).

The location of an individual during an occasion can be estimated using the forward–backward algorithm (Zucchini et al., 2016). Let *α*_{i,t} be the forward probabilities, and *γ*_{i,t} be the backward probabilities for individual *i* on occasion *t* where*α*_{i,t} and *γ*_{i,t} are vectors of length *m*, and the *j*‐th elements are the relative probabilities that individual *i* is located in *s*_{j} on occasion *t* given individual *i*'s encounter history before and including occasion *t* and its encounter history after occasion *t*, respectively. The dot product of *α*_{i,t} and *γ*_{i,t} is the likelihood of individual *i*'s encounter history, *L*_{i}. The distribution of the individual's location given its entire encounter history is the elementwise product of *α*_{i,t} and *γ*_{i,t} scaled to sum to one, $\frac{\left({\mathit{\alpha}}_{i,t}\circ {\mathit{\gamma}}_{i,t}\right)}{{L}_{i}}$. It follows that the realized population density on occasion *t* is ${\sum}_{i=1}^{n}\frac{\left({\mathit{\alpha}}_{i,t}\circ {\mathit{\gamma}}_{i,t}\right)}{{L}_{i}}+D\left(1-{p}^{*}\right)\frac{\left({\mathit{\alpha}}_{n+1,t}\circ {\mathit{\gamma}}_{n+1,t}\right)}{{L}_{n+1}}$ and the average realized population density over all sampling occasions is $\frac{1}{T}{\sum}_{t=1}^{T}\left({\sum}_{i=1}^{n}\left(\frac{\left({\mathit{\alpha}}_{i,t}\circ {\mathit{\gamma}}_{i,t}\right)}{{L}_{i}}\right)+D\left(1-{p}^{*}\right)\frac{\left({\mathit{\alpha}}_{n+1,t}\circ {\mathit{\gamma}}_{n+1,t}\right)}{{L}_{n+1}}\right)$, where *α*_{n + 1,t} and *γ*_{n + 1,t} are the forward and backward probabilities for an individual that was never observed. Additionally, *L*_{n + 1} is the likelihood of an individual that was never observed, $\mathit{\delta}\left({\prod}_{t=1}^{T-1}\mathit{P}\left({\mathit{y}}_{i,t}=0\right)\mathit{\Gamma}\right)\mathit{P}\left({\mathit{y}}_{i,T}=0\right)\mathit{\epsilon}$. The expected population density, which does not explicitly account for individuals' encounter histories, on occasion *t* is the product of expected abundance, the initial state vector and *t* – 1 state transition matrices, $D\mathit{\delta}{\mathit{\Gamma}}^{t-1}$. The average expected density over all sampling occasions is $\frac{1}{T}{\sum}_{t=1}^{T}D\mathit{\delta}{\mathit{\Gamma}}^{t-1}$. Each expression of density results in a vector whose *j*‐th element is the estimated number of individuals in state *j* over the time period of interest.

Given the observed data and estimated parameters from the model described above, individuals' future locations can be forecast. The first step in forecasting locations is to estimate an individual's location at time *T*, the last sampling occasion. Here, we use the forward–backward algorithm to estimate the distribution of the location of individual *i*, which was observed at least once over the previous *T* occasions (Zucchini et al., 2016). At time *T*, *γ*_{i,T} is ** ε**, therefore this distribution is

We simulated 1000 closed population SCR data sets under three scenarios. In the first scenario, individuals moved according to a simple RW; in the second, individuals moved according to a biased RW; and in the third, individuals moved according to a correlated RW. In each scenario, a population of 100 individuals was simulated with a uniform initial density. The study region, ** S**, was square, 1600 unit

The North Atlantic right whale is an endangered large whale species that inhabits the coastal waters of the eastern United States and Canada. Some right whales migrate to the coastal waters of the southeastern United States, hereafter referred to as the Southeast, each winter (Gowan et al., 2019; Krzystan et al., 2018). Throughout their range, right whales are at risk of being struck and killed or severely injured by vessels; therefore, understanding and predicting their movements could provide valuable information to managers working to mitigate the threat of vessel strikes (Crum et al., 2019; van der Hoop et al., 2014). We fit open SCR models to right whale encounter history data collected from aerial surveys off the Southeast between 1 December 2009 and 31 March 2010 (see Gowan et al., 2021; Gowan & Ortega‐Ortiz, 2014 for detailed descriptions of data collection). We divided our study region (Appendix 2 in Figure S1) into 772 100 km^{2} sub‐regions for the model. We augmented the models described in the model formulation section with two additional unobservable states, one for individuals that had yet to immigrate to the Southeast and another for individuals that had already emigrated from the Southeast or had died, although we expect deaths were rare as right whale annual survival exceeds 0.95 (Pace et al., 2017). The probability that an individual not in the Southeast immigrated to the Southeast, *τ*, was modelled as a quadratic function of *t*, the number of days since 1 December, ${\tau}_{t}=\frac{1}{1+\mathrm{exp}\left(-\left({\beta}_{0}+{\beta}_{1}*t+{\beta}_{2}*{t}^{2}\right)\right)}$. The probability that an individual in the Southeast remained in the Southeast, *φ*, was modelled as a linear function of the number of days since 1 December, ${\phi}_{t}=\frac{1}{1+\mathrm{exp}\left(-\left({\beta}_{3}+{\beta}_{4}*t\right)\right)}$. The model permitted migration during one state transition every 10 days, and the population was closed on all other transitions. We modelled daily movement according to activity centre, simple and correlated RW movement models where movement was an exponentially declining function of distance. In the activity centre model, individuals' activity centres could move every 10 days and were independent of past activity centres. We simplified the correlated RW model to shorten computation time by accounting only for correlation in movement direction and classifying movements into four categories, north, south, east and west. For each movement model, we tested a null model without environmental covariates and a model that included quadratic effects of depth and sea surface temperature and a linear effect of wind speed, $f\left({d}_{\text{move},j,k},{\mathit{Z}}_{k}\mathit{\beta}\right)=\mathrm{exp}\left(-\frac{{d}_{\text{move},j,k}}{{\sigma}_{\text{move}}}+{\beta}_{5}*\mathrm{ss}{\mathrm{t}}_{k}+{\beta}_{6}*\mathrm{ss}{\mathrm{t}}_{k}^{2}+{\beta}_{7}*\text{dept}{\mathrm{h}}_{k}+{\beta}_{8}*\text{dept}{\mathrm{h}}_{k}^{2}+{\beta}_{9}*w{s}_{k}\right)$. We fit models to the full dataset and used AIC for model comparison (Burnham & Anderson, 2002). Additionally, we fit models to a reduced dataset, which omitted every 10th sampling occasion starting with the seventh occasion, that is the seventh, 17th, 27th, etc. To evaluate the forecasting skill of each model, we generated forecasts for the locations of all individuals, previously observed and unobserved, on the omitted occasions based on the models' parameter estimates and the data collected preceding each omitted occasion. We compared models' forecast skill by comparing the likelihood of omitted data under forecasts from each model.

SCR models estimated abundance with relative bias ≤5% in most cases, regardless of movement model specification (Table 1). Mean square error of abundance estimates was the smallest in cases where the specified movement model matched the model used to simulate the data (Table 1). Models that matched the simulating model also predicted future locations of individuals with the highest likelihood, and their forecasts were well calibrated, that is the confidence level of forecast regions matched the proportion of locations that fell within them (Figure 1).

When individuals' movements were simulated according to a simple RW, forecasts from the activity centre model became less likely relative to the simple RW forecasts as time since the last sampling occasion increased (Appendix 1 in Figure S3). Additionally, forecast regions generated by the activity centre model contained fewer locations of individuals than expected and this miscalibration worsened over time (Appendix 1 in Figure S4).

When individuals' movements were simulated according to a biased RW, the likelihoods of the activity centre and simple RW forecasts were similar and lower than the likelihood of the biased RW forecast on the first forecasted occasion. Following the first forecasted occasion, the likelihoods of the activity centre forecasts remained the same across time relative to the biased RW forecasts, whereas the likelihoods of the simple RW forecasts decreased over time relative to the biased RW forecasts (Appendix 1 in Figure S7). Forecasted regions generated by the activity centre model contained fewer locations of individuals than expected, while those generated by the simple RW model contained more locations than expected. This miscalibration increased with time (Appendix 1 in Figure S8).

When individuals' movements were simulated according to a correlated RW, the likelihoods of the activity centre forecasts decreased sharply over time relative to the correlated RW forecasts, while the likelihoods of the simple RW forecasts decreased over the first few occasions and then plateaued relative to the correlated RW forecasts (Appendix 1 in Figure S11). Forecast regions generated by the activity centre and simple RW models contained fewer locations of individuals than expected. This miscalibration was worse in the activity centre model and worsened with time under both models (Appendix 1 in Figure S12).

Aerial surveys were conducted on 77 days between 1 December 2009 and 31 March 2010 and observed 214 individual right whales at least once. Individuals were observed an average of 4.1 times (range: 1–17). Abundance estimates were smallest for models with an activity centre movement model and largest for models with a simplified correlated RW movement model (Table 2). The correlated RW movement model received the most support in the data followed by the simple RW and then the activity centre movement model (Table 2). However, data omitted from the reduced data set were more likely under forecasts generated by the simple RW than under the correlated RW (Table 2). The correlated and simple RW models estimated that right whales moved 26–35 km per day on average (Table 2). Models that included the effects of environmental covariates on movement received considerably greater support in the data and generated better forecasts than models without environmental covariates (Figure 2). These models all estimated that right whales moved to areas of lower wind speeds and depths around 20 m (Appendix 2 in Figure S2). The simple RW and activity centre models estimated that right whales moved to areas with sea surface temperatures around 14°C, while the correlated RW model produced unreasonable estimates of the association between right whale movements and sea surface temperature (Appendix 2 in Figure S2).

We describe a maximum likelihood estimator for a SCR model integrated with RW movement models and a framework to forecast future locations of wildlife. Our simulation study and right whale case study demonstrate the value of using more realistic and complex movement models than static activity centre models. Incorporating complex space use or movement models into SCR can reduce bias in abundance estimates (Chandler et al., 2021; Royle, Chandler, Sun, et al., 2013). Likewise, the RW movement models improved estimation of abundance and forecast skill in most cases. The activity centre model outperformed only the simple RW model when analysing data generated from a biased RW. Additionally, in our right whale case study, RW models received considerably more support in the data and predicted out‐of‐sample data with higher likelihood than did activity centre models.

Integrating SCR and movement models can address many questions important to ecology and conservation (McClintock et al., 2021). Here, we are interested in where the individuals in a population will be located in the near‐term future. A SCR model addresses the question of how many individuals are in the population, while a hidden Markov model provides means to forecast each individual's location given their encounter histories and the estimated model parameters (Royle, Chandler, Gazenski, et al., 2013; Zucchini et al., 2016). Such an integrated model allows for the estimation and forecasting of individuals' locations, regardless of whether they have been previously observed or tagged.

This application could be especially useful in monitoring and mitigating threats to endangered species, like the right whale. Right whales are at risk of vessel strikes throughout their range, and many management and outreach activities are used to mitigate this threat (Crum et al., 2019; van der Hoop et al., 2014). Forecasting right whale movements could provide valuable information to plan and prioritize activities, such as dynamically enforced speed restrictions and broadcast notices to mariners. Additionally, forecasts could inform where monitoring effort should be allocated to observe individuals that have yet to be observed or track individuals of interest, such as reproductive females in the right whale population. However, when a species' movements are associated with temporally dynamic environmental covariates, forecasts of those covariates will be needed and will introduce an additional source of uncertainty (Payne et al., 2017). Movement forecasts should also be evaluated with out‐of‐sample data. In our right whale case study the correlated RW model with environmental covariates received the most support in the data according to AIC. However, that model estimated unreasonably high densities during one 10‐day period in a few subregions at the edge of the study region. These subregions were not surveyed and had high and low sea surface temperatures, which resulted in the model estimating an unreasonable association between right whale movement and sea surface temperature (Appendix 2 in Figure S2). The likelihood of out‐of‐sample data under forecasts from each model exposed this artefact, as the simple RW forecasts clearly outperformed forecasts of the correlated RW.

Our simulation study demonstrated that integrated SCR movement models have the potential to produce properly calibrated forecasts of individuals' future movements based only on sparse SCR data. However, mismatches between the forecasting and simulating models led to poorly calibrated forecasts that performed increasingly poorly as the forecast extended farther into the future. Therefore, we advise testing multiple realistic movement models and comparing their performance in out‐of‐sample prediction before using a model's forecasts. In some cases, SCR data alone may not provide enough information to fit a realistic movement model. For instance, the correlated RW model estimated the *γ* and *ω* parameters, which describe the correlation of movement trajectories, with low precision in our simulation study (Appendix 1), and the correlated RW model fit to right whale data predicted right whale movements worse than the simple RW model. In such cases, additional information such as tagging data, which can increase the number of recaptures on consecutive sampling occasions, or individuals' directions and speeds of travel at the time of observation, which can be used to infer past and future locations, may need to be included in the analysis (Gardner et al., 2022; McClintock et al., 2021).

Forecasts are also affected by the uncertainty regarding individuals' current locations. This uncertainty increases as the amount of time since an individual was last observed increases, as the effectiveness and coverage of the detection process decrease, and as the scale of an individual's movement increases. Therefore, forecasts will be most informative for individuals that were observed recently, in systems that are subject to consistent and efficient sampling, and for species that move short distances. Hidden Markov models propagate the uncertainty regarding individuals' locations through their forecasts and account for the stochastic nature of the movement process. When none of the aforementioned conditions are met, the region in which an individual is forecasted to be located may be too large to be meaningful. In our right whale case study, forecasts may only be useful for a few days after an individual is observed, because individuals were estimated to move over 25 km per day on average. Still, females with calves, the demographic group of greatest importance to the population, are observed frequently in the Southeast (Gowan et al., 2019; Krzystan et al., 2018). Forecasts of their movements would likely be of greatest interest and could be information rich due to the frequency of their sightings.

In addition to describing an approach to forecast the movements of wildlife, we describe a maximum likelihood estimator for integrated SCR movement models. Most studies that integrated SCR and movement models have used a Bayesian approach, although Glennie et al. (2019) described a simple RW for activity centres, and Dupont et al. (2021) model the movements of tagged individuals with biased RWs, both using maximum likelihood estimation. We found that our models computed considerably faster when implemented with maximum likelihood estimation than with a Bayesian framework. However, maximum likelihood estimation may require a sparse matrix implementation when modelling movement at finer spatial scales, because the computation required for our implementation is proportional to the square of the number of subregions or states in the model (Zucchini et al., 2016). Additionally, a Bayesian approach may be easier and more flexible to implement, especially with software such as NIMBLE, which allows user‐defined functions to be used in the model (de Valpine et al., 2017; Hostetter et al., 2022; Turek et al., 2021).

Much effort has been expended to project the distribution of wildlife populations in the long‐term future (Payne et al., 2017), while only Randon et al. (2022) have developed near‐term forecasting of wildlife movements. Integrated SCR movement models have only recently been developed and have many potential applications, including near‐term movement forecasting. These models can forecast the movements of all individuals in a population of interest, whether they have been tagged, previously observed, or neither. In study systems with consistent and efficient SCR sampling, forecasts can provide valuable information to improve wildlife monitoring and threat mitigation activities.

Nathan J. Crum conceived the ideas and designed the methods with support from Timothy A. Gowan and Kandethody M. Ramachandran. Nathan J. Crum analysed the data with support from Timothy A. Gowan. Nathan J. Crum led the writing. All authors contributed to the review and revision of the manuscript.

We thank the aerial survey teams from Clearwater Marine Aquarium Research Institute, Florida Fish and Wildlife Conservation Commission and New England Aquarium for collecting the right whale data. We thank the North Atlantic Right Whale Consortium for curating and providing the photo ID data used in the right whale analysis. We thank Florent Bled, Brett McClintock and two anonymous reviewers for their helpful reviews of this manuscript. Funding for aerial surveys was provided by NOAA Fisheries, US Coast Guard, US Navy, US Army Corps of Engineers and Georgia Department of Natural Resources. Funding for the analysis was provided by NOAA Fisheries (NA16NMF4720319) and the Save the Manatee Trust Fund.

The authors declare no conflicts of interest.

The peer review history for this article is available at

The R package, scrrw, used for the simulation study is available via Zenodo