Dr Rachel McCrea
Rachel completed a research fellowship in 2016, funded by the Natural Environment Research Council. The emphasis of this project was on developing individual level statistical models that make it possible to understand the wealth of detailed data being collected on a huge range of animal populations.
Rachel is a member of the School’s Athena SWAN Committee and Director of Studies for the Year in Data Analytics programme.
Rachel is an applied statistician working closely with ecologists as well as statisticians, developing new statistical methodology for the modelling of ecological data. She has worked extensively with capture-recapture data (and co-authored a book Analysis of capture-recapture data) and is particularly interested in the potential of multi-state models. Her research has included the development of goodness-of-fit assessment and model selection strategies for complex data sets. Modelling population dynamics, integrated population modelling and survey design are also current areas of interest.
Current PhD students are:
- Sotiris Prevenas (joint with Cristiano Villa) - Computational methodologies for state-space models: a big data challenge
- Ulrike Naumann - Modelling changes in abundance of species over space and time in island ecosystems
- Ming Zhou (with Eleni Matechou and Diana Cole) - Statistical development of ecological removal models
Recently completed projects that Rachel has supervised:
- Dr Hannah Worthington (now a Lecturer in Statistics at the University of St Andrews) - The statistical development of integrated multi-state stopover models
- Dr Anita Jeyam (now a Postdoctoral Research Associate at the University of Edinburgh) - Statistical development of ecological removal models
Rachel has advised many PhD students from the Durrell Institute of Conservation and Ecology, University of Kent.
- Associate Editor for Journal of the Royal Statistical Society Series C (Applied Statistics)
- Associate Editor for Methods in Ecology and Evolution
- Chair of the Scientific Programme Committee of the International Statistical Ecology Conference 2018 and Co-Chair for ISEC 2020
- Secretary of the British and Irish Region of the International Biometric Conference (from November 2018)
- Member of the Durrell Institute of Conservation and Ecology
- Director of the National Centre for Statistical Ecology (NCSE)
Zhou, M. et al. (2019). Removal models accounting for temporary emigration. Biometrics [Online] 75:24-35. Available at: https://doi.org/10.1111/biom.12961.Removal of protected species from sites scheduled for development is often a legal requirement in order to minimize the loss of biodiversity. The assumption of closure in the classic removal model will be violated if individuals become temporarily undetectable, a phenomenon commonly exhibited by reptiles and amphibians. Temporary emigration can be modeled using a multievent framework with a partial hidden process, where the underlying state process describes the movement pattern of animals between the survey area and an area outside of the study. We present a multievent removal model within a robust design framework which allows for individuals becoming temporarily unavailable for detection. We demonstrate how to investigate parameter redundancy in the model. Results suggest the use of the robust design and certain forms of constraints overcome issues of parameter redundancy. We show which combinations of parameters are estimable when the robust design reduces to a single secondary capture occasion within each primary sampling period. Additionally, we explore the benefit of the robust design on the precision of parameters using simulation. We demonstrate that the use of the robust design is highly recommended when sampling removal data. We apply our model to removal data of common lizards, Zootoca vivipara, and for this application precision of parameter estimates is further improved using an integrated model.
Lewis-Phillips, J. et al. (2019). Pond management enhances the local abundance and species richness of farmland bird communities. Agriculture, Ecosystems & Environment [Online] 273:130-140. Available at: https://doi.org/10.1016/j.agee.2018.12.015.Agricultural intensification and the associated loss of non-cropped habitats have caused a major decline in UK farmland bird populations since the 1970s. As a consequence, there is an urgent need to implement effective conservation and habitat restoration measures in agricultural landscapes. Over the last 40â50 years, due to the cessation of traditional management practices, the majority of UK farmland ponds have become highly terrestrialised, resulting in major reductions in the diversity and abundance of aquatic plant and invertebrate assemblages. Recent research undertaken at farmland ponds in early summer, has shown restored open-canopy, macrophyte-dominated ponds support an increased abundance and diversity of farmland birds, compared to non-managed, overgrown ponds.
Here, we expand on this previous research with a year-long field study to assess the implications of pond management for farmland birds by comparing bird diversity, abundance and activity at managed open-canopy ponds with those at unmanaged overgrown ponds. Driven strongly by pond management and connectivity to semi-natural landscape features such as hedgerows and woodland patches, bird abundance and species richness, as well as foraging and parental behaviour, were all significantly higher at managed open-canopy ponds. Further, a wider landscape analysis found that terrestrial land-use patterns in the vicinity of the ponds were not significant predictors of bird communities at the pond sites.
In light of the numerous potential benefits to conservation-listed birds and other wildlife, we conclude that farmland pond management has been undervalued as a conservation measure to assist farmland birds. Consequently, we conclude that future agri-environment schemes, should more fully embrace farmland ponds.
Worthington, H. et al. (2018). Estimation of population size when capture probability depends on individual state. Journal of Agricultural, Biological, and Environmental Statistics [Online]. Available at: https://doi.org/10.1007/s13253-018-00347-x.We develop a multi-state model to estimate the size of a closed population from
captureârecapture studies. We consider the case where captureârecapture data are not of
a simple binary form, but where the state of an individual is also recorded upon every
capture as a discrete variable. The proposed multi-state model can be regarded as a
generalisation of the commonly applied set of closed population models to a multi-state
form. The model allows for heterogeneity within the capture probabilities associated with
each state while also permitting individuals to move between the different discrete states.
A closed-form expression for the likelihood is presented in terms of a set of sufficient
statistics. The link between existing models for capture heterogeneity is established,
and simulation is used to show that the estimate of population size can be biased when
movement between states is not accounted for. The proposed unconditional approach is
also compared to a conditional approach to assess estimation bias. The model derived
in this paper is motivated by a real ecological data set on great crested newts, Triturus
Yeo, L., McCrea, R. and Roberts, D. (2017). A novel application of mark-recapture to examine behaviour associated with the online trade in elephant ivory. PeerJ [Online] 5:e3048. Available at: https://doi.org/10.7717/peerj.3048.The illegal trade in elephant ivory is driving the unlawful killing of elephants such that populations are now suffering unsustainable reductions. The internet is increasingly being used as a platform to conduct illegal wildlife trade, including elephant ivory. As a globally accessible medium the internet is as highly attractive to those involved in the illegal trade as it is challenging to regulate. Characterising the online illegal wildlife (ivory) trade is complex, yet key to informing enforcement activities. We applied mark-recapture to investigate behaviour associated with the online trade in elephant ivory on eBay UK as a generalist online marketplace. Our results indicate that trade takes place via eBay UK, despite its policy prohibiting this, and that two distinct trading populations exist, characterised by the pattern of their ivory sales. We suggest these may represent a large number of occasional (or non-commercial) sellers and a smaller number of dedicated (or commercial) sellers. Directing resource towards reducing the volume of occasional sales, such as through education, would enable greater focus to be placed upon characterising the extent and value of the illegal, âcommercialâ online ivory trade. MRC has the potential to characterise the illegal trade in ivory and diverse wildlife commodities traded using various online platforms.
Besbeas, P., McCrea, R. and Morgan, B. (2017). Integrated population model selection in ecology. In prep.
Jeyam, A. et al. (2017). A test of positive association for detecting heterogeneity in capture for capture-recapture data. Journal of Agricultural, Biological, and Environmental Statistics [Online] 23:1-19. Available at: https://doi.org/10.1007/s13253-017-0315-4.The CormackâJollyâSeber (CJS) model assumes that all marked animals have equal recapture probabilities at each sampling occasion, but heterogeneity in capture often occurs and should be taken into account to avoid biases in parameter estimates. Although diagnostic tests are generally used to detect trap-dependence or transience and assess the overall fit of the model, heterogeneity in capture is not routinely tested for. In order to detect and identify this phenomenon in a CJS framework, we propose a test of positive association between previous and future encounters using GoodmanâKruskalâs gamma. This test is based solely on the raw capture histories and makes no assumption on model structure. The development of the test is motivated by a dataset of Sandwich terns (Thalasseus sandvicensis), and we use the test to formally show that they exhibit heterogeneity in capture. We use simulation to assess the performance of the test in the detection of heterogeneity in capture, compared to existing and corrected diagnostic goodness-of-fit tests, Leslieâs test of equal catchability and Carothersâ extension of the Leslie test. The test of positive association is easy to use and produces good results, demonstrating high power to detect heterogeneity in capture. We recommend using this new test prior to model fitting as the outcome will guide the model-building process and help draw more accurate biological conclusions. Supplementary materials accompanying this paper appear online.
Cole, D. and McCrea, R. (2016). Parameter Redundancy in Discrete State-Space and Integrated Models. Biometrical Journal [Online] 58:1071-1090. Available at: http://dx.doi.org/10.1002/bimj.201400239.Discrete state-space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrisation of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as non-identifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state-space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state-space models using discrete analogues of methods for continuous state-space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant.
McCrea, R., Morgan, B. and Gimenez, O. (2016). A new strategy for diagnostic model assessment in capture-recapture. Journal of the Royal Statistical Society: Series C (Applied Statistics) [Online] 66:815-831. Available at: http://dx.doi.org/10.1111/rssc.12197.Common to both diagnostic tests used in captureârecapture and score tests is the idea that starting from a simple base model it is possible to interrogate data to determine whether more complex parameter structures will be supported. Current recommendations advise that diagnostic tests are performed as a precursor to a model selection step. We show that certain well-known diagnostic tests for examining the fit of captureârecapture models to data are in fact score tests. Because of this direct relationship we investigate a new strategy for model assessment which combines the diagnosis of departure from basic model assumptions with a step-up model selection, all based on score tests. We investigate the power of such an approach to detect common reasons for lack of model fit and compare the performance of this new strategy with the existing recommendations by using simulation. We present motivating examples with real data for which the extra flexibility of score tests results in an improved performance compared with diagnostic tests.
Matechou, E. et al. (2016). Open models for removal data. Annals of Applied Statistics [Online]. Available at: http://dx.doi.org/10.1214/16-AOAS949.Individuals of protected species, such as amphibians and reptiles, often need to be removed from sites before development commences. Usually, the population is considered to be closed. All individuals are assumed to i) be present and available for detection at the start of the study period and ii) remain at the site until the end of the study, unless they are detected. However, the assumption of population closure is not always valid. We present new removal models which allow for population renewal through birth and/or immigration, and population depletion through sampling as well as through death/emigration. When appropriate, productivity may be estimated and a Bayesian approach allows the estimation of the probability of total population depletion. We demonstrate the performance of the models using data on common lizards, Zootoca vivipara, and great crested newts, Triturus cristatus.
Hudson, M. et al. (2016). In-situ itraconazole treatment improves survival rate during an amphibian chytridiomycosis epidemic. Biological Conservation [Online] 195:37-45. Available at: http://dx.doi.org/10.1016/j.biocon.2015.12.041.The emerging infectious disease, amphibian chytridiomycosis caused by the fungus Batrachochytrium dendrobatidis (Bd), threatens hundreds of amphibian species globally. In the absence of field-based mitigation methods, the Amphibian Conservation Action Plan advocates captive assurance programmes to prevent extinction from this infectious disease. Unfortunately, with the cooperation of the entire global zoo community, the International Union for the Conservation of Nature Amphibian Ark estimates only 50 species could be saved. Clearly, if catastrophic losses are to be averted, alternative mitigation techniques need to be developed. There has been an absence of trialling laboratory proven interventions for chytridiomycosis in field settings, which must change in order to allow informed management decisions for highly threatened amphibian populations. We tested the in-situ treatment of individual mountain chicken frogs (Leptodactylus fallax) using the antifungal drug, itraconazole. Multi-state markârecapture analysis showed increased probability of survival and loss of Bd infection for treated frogs compared to untreated animals. There was evidence of a prophylactic effect of treatment as, during the treatment period, infection probability was lower for treated animals than untreated animals. Whilst long term, post-treatment increase in survival was not observed, a deterministic population model estimated antifungal treatment would extend time to extinction of the population from 49 to 124 weeks, an approximated 60% increase. In-situ treatment of individuals could, therefore, be a useful short-term measure to augment other conservation actions for amphibian species threatened by chytridiomycosis or to facilitate population survival during periods of high disease risk.
King, R. and McCrea, R. (2014). A generalised likelihood framework for partially observed captureârecaptureârecovery models. Statistical Methodology [Online] 17:30-45. Available at: http://dx.doi.org/10.1016/j.stamet.2013.07.004.We provide a closed form likelihood expression for multi-state captureârecaptureârecovery data when the state of an individual may be only partially observed. The corresponding sufficient statistics are presented in addition to a matrix formulation which facilitates an efficient calculation of the likelihood. This likelihood framework provides a consistent and unified framework with many standard models applied to captureârecaptureârecovery data as special cases.
McCrea, R., Morgan, B. and Pradel, R. (2014). Diagnostic goodness-of-fit tests for joint recapture and recovery data. Journal of Agricultural, Biological, and Environmental Statistics [Online] 19:338-356. Available at: http://dx.doi.org/10.1007/s13253-014-0174-1.
Cole, D. et al. (2014). Does Your Species Have Memory? Analysing Capture-Recapture Data with Memory Models. Ecology and Evolution [Online] 4:2124-2133. Available at: http://dx.doi.org/10.1002/ece3.1037.1. We examine memory models for multi-site capture-recapture data. This is an important topic,as animals may exhibit behaviour that is more complex than simple first-order Markov movement between sites, when it is necessary to devise and fit appropriate models to data.
2. We consider the Arnason-Schwarz model for multi-site capture-recapture data, which incorporates just first-order Markov movement, and also two alternative models that allow for memory, the Brownie model and the Pradel model. We use simulation to compare two alternative tests which may be undertaken to determine whether models for multi-site capture-recapture data need to incorporate memory.
3. Increasing the complexity of models runs the risk of introducing parameters that cannot be estimated, irrespective of how much data are collected, a feature which is known as parameter redundancy. Rouan et al (JABES, 2009, pp 338-355) suggest a constraint that may be applied to overcome parameter redundancy when it is present in multi-site memory models. For this case, we apply symbolic methods to derive a simpler constraint, which allows more parameters to be estimated, and give general results not limited to a particular configuration. We also consider the effect sparse data can have on parameter redundancy, and recommend minimum sample sizes.
4. Memory models for multi-site capture-recapture data can be highly complex, and difficult to fit to data. We emphasise the importance of a structured approach to modelling such data, by considering a priori which parameters can be estimated, which constraints are needed in order for estimation to take place, and how much data need to be collected. We also give guidance on the amount of data needed to use two alternative families of tests for whether models for multi-site capture-recapture data need to incorporate memory.
McCrea, R., Morgan, B. and Cole, D. (2013). Age-dependent mixture models for recovery data on animals marked at unknown age. Journal of the Royal Statistical Society: Series C (Applied Statistics) [Online] 62:101-113. Available at: http://dx.doi.org/10.1111/j.1467-9876.2012.01043.x.Data are often collected from wild animals that have been marked at unknown
age. As a result, standard probability models, fitted by maximum likelihood, cannot incorporate age dependence in probabilities of annual survival.We propose and fit new mixture models to ringârecovery data on birds ringed of unknown age, in which it is possible to incorporate age dependence in survival. It is shown that it is important to analyse simultaneously data on animals marked as young, and of known age, as otherwise the mixture model is parameter redundant. The potential of the approach is illustrated by a new analysis of data on mallards, Anas platyrhynchos, and the wider performance of the approach is demonstrated through simulation.The models provide a way of analysing correctly large numbers of historical data sets.
Viallefont, A. et al. (2012). Estimating survival and transition rates from aggregate sightings of animals. Journal of Ornithology [Online] 152:381-391. Available at: http://dx.doi.org/10.1007/s10336-010-0588-7.We compare and contrast two methods for fitting probability models to data which arise when animals are marked in batches, without individual identification, and live in several different sites or states. The methods are suitable for populations in which animals are marked at birth and then resighted over several sites/states, for small animals going through several growth stages (insects, amphibiae, etc.), as well as for the follow-up of animals released after laboratory colour-marking, for example. The methods we consider include a multi-state model for resightings of batch-marked animals, allowing us to estimate survival, transitions, and sighting probabilities. One method is based on the EM algorithm, and the second uses the Kalman filter for computing likelihoods. The methods are illustrated on real data from a cohort of Great Cormorants Phalacrocorax carbo, and their performance is evaluated using simulation. We recommend identifying the batches, for instance in the case of sites, by using a different colour on each site at the time of marking, and in general the use of the Kalman filter rather than the EM-based approach.
Hayman, D. et al. (2012). Endemic Lagos bat virus infection in Straw-coloured fruit bats. Epidemiology and Infection 140:2163-2171.
McCrea, R., Morgan, B. and Bregnballe, T. (2012). Model comparison and assessment for multi-state capture-recapture-recovery data. Journal of Ornithology [Online] 152:293-303. Available at: http://dx.doi.org/10.1007/s10336-010-0611-z.The work of this paper is motivated by a study of Great Cormorants, Phalacrocorax carbo sinensis, in Denmark. The dataset is complex, involving birds in different states living in and moving between neighbouring colonies. As a consequence, the set of probability models that might describe the data is large. In order to choose between the models, we present a score test approach for moving efficiently between the members of a model set with many members. We then provide a new measure for testing the absolute goodness-of-fit of the selected model to the data. This measure may be used when a model is multi-state/multi-site, and involves age- and time-dependence, as well as integrated recovery and recapture data, which is needed for the application. An illustration is provided by data from a single colony only, but with two breeding states, and an additional emigrated state.
McCrea, R. (2012). Sufficient statistic likelihood construction for age- and time- dependent multi-state joint recapture and recovery data. Statistics and Probability Letters [Online] 82:357-359. Available at: http://dx.doi.org/10.1016/j.spl.2011.10.020.Two closed-form likelihoods for multi-state joint recapture and recovery data were proposed in King and Brooks (2003); the first incorporated dependence on time and cohort whilst the second included dependence on age and cohort. However, when multi-state joint recapture and recovery data are modelled, it is likely that dependence on age and time will both be potentially of interest and therefore the most useful model formulation will incorporate both of these parameter structures. Within this article the likelihood function required for such a model is derived in terms of a set of sufficient statistics.
Hayman, D. et al. (2012). Straw-coloured fruit bat demography in Ghana. Journal of Mammalogy 93:1393-1404.
McCrea, R. et al. (2012). Conditional modelling of ring-recovery data. Methods in Ecology and Evolution [Online] 3:823-831. Available at: http://dx.doi.org/10.1111/j.2041-210X.2012.00226.x.1. Ring-recovery data can be used to obtain estimates of survival probability which is a key demo-
graphic parameter of interest for wild animal populations. Conditional modelling of ring-recovery
data is needed when cohort numbers are unavailable or unreliable. It is often necessary to include in
such analysis a recovery probability that is declining as a function of time, and failure to do this can
result in biased estimates of annual survival.
2. Corresponding estimates of survival probability need to be reliable in order for correct conclu-
sions to be drawn regarding the effects of climate change.
3. We show that standard logistic modelling of a decline in recovery probability is unsatisfactory,
and propose and investigate a range of alternative procedures.
4. Methods are illustrated by application to a recovery data set on grey herons. The model selected
is a scaled-logistic model, and it is shown to provide a unifying analysis of several data sets collected
on different common bird species. The model makes specific predictions, providing potential new
insights and avenues for ecological research. The wider performance of this model is evaluated
5. In this study, we propose a new scaled-logistic model for the analysis of ring-recovery data with-
out cohort numbers, which incorporates a reporting probability that declines over time. The model
is shown to perform well in simulation studies and for both a single real data set and several real
data sets in combination. Its use has the potential to reduce bias in estimates of wild animal survival
that currently do not incorporate such reporting probabilities. Alternative models are shown to
possess undesirable features.
McCrea, R. and Morgan, B. (2011). Multistate mark-recapture model selection using score tests. Biometrics [Online] 67:234-241. Available at: http://dx.doi.org/10.1111/j.1541-0420.2010.01421.x.Although multistate mark-recapture models are recognized as important, they lack a simple model-selection procedure. This article proposes and evaluates a step-up approach to select appropriate models for multistate mark-recapture data using score tests. Only models supported by the data require fitting, so that over-complicated model structures with too many parameters do not need to be considered. Typically only a small number of models are fitted, and the procedure is also able to identify parameter-redundant and near-redundant models. The good performance of the technique is demonstrated using simulation, and the approach is illustrated on a three-region Canada goose data set. In this case, it identifies a new model that is much simpler than the best model previously considered for this application.
Gnone, G. et al. (2011). Distribution, abundance and movements of the bottlenose dolphin in the Pelagos sanctuary MPA. Aquatic Conservation-Marine and Freshwater Ecosystems [Online] 21:372-388. Available at: http://dx.doi.org/10.1002/aqc.1191.1. The Pelagos Sanctuary is the largest marine protected area of the Mediterranean Sea (87 500?km2), and is located in the north-west part of the basin. The presence of the bottlenose dolphin in this area is well documented but its distribution and abundance are not well known.
2. The present study collected and analysed data from 10 different research groups operating in the Pelagos Sanctuary from 1994 to 2007. Photo-identification data were used to analyse the displacement behaviour of the dolphins and to estimate their abundance through markârecapture modelling.
3. Results show that the distribution of bottlenose dolphin is confined to the continental shelf within the 200?m isobath, with a preference for shallow waters of less than 100?m depth.
4. Bottlenose dolphins seem to be more densely present in the eastern part of the sanctuary and along the north-west coast of Corsica.
5.Bottlenose dolphins show a residential attitude with excursions usually within a distance of 80?km (50?km on average). A few dolphins exhibit more wide-ranging journeys, travelling up to 427?km between sub-areas.
6.The displacement analysis identified two (sub)populations of bottlenose dolphins, one centred on the eastern part of the sanctuary and the other one around the west coast of Corsica.
7. In 2006, the eastern (sub)population was estimated to comprise 510â552 individuals, while 368â429 individuals were estimated in the Corsican (sub)population. It was estimated that in total, 884â1023 bottlenose dolphins were living in the Pelagos Sanctuary MPA in the same year.
8. The designation of a number of Special Areas of Conservation (SACs) under the Habitats Directive is discussed as a possible tool to protect the bottlenose dolphin in the Pelagos Sanctuary and in the whole of the Mediterranean Sea.
Brown, D., McCrea, R. and Morgan, B. (2011). Incorporating covariates in the analysis of capture re-encounter data. Proceedings of the International Statistical Institute Congress.
Griffiths, R., Sewell, D. and McCrea, R. (2010). Dynamics of a declining amphibian metapopulation: survival, dispersal and the impact of climate. Biological Conservation [Online] 143:485-491. Available at: http://dx.doi.org/10.1016/j.biocon.2009.11.017.Climate can interact with population dynamics in complex ways. In this study we describe how climatic factors influenced the dynamics of an amphibian metapopulation over 12 years through interactions with survival, recruitment and dispersal. Low annual survival of great crested newts (Triturus cristatus) was related to mild winters and heavy rainfall, which impacted the metapopulation at the regional level. Consequently, survival varied between years but not between subpopulations. Despite this regional effect, the four subpopulations were largely asynchronous in their dynamics. Three out of the four subpopulations suffered reproductive failure in most years, and recruitment to the metapopulation relied on one source. Variation in recruitment and juvenile dispersal was therefore probably driving asynchrony in population dynamics. At least one subpopulation went extinct over the 12 year period. These trends are consistent with simulations of the system, which predicted that two subpopulations had an extinction risk of >50% if adult survival fell below 30% in combination with low juvenile survival. Intermittent recruitment may therefore only result in population persistence if compensated for by relatively high adult survival. Mild winters may consequently reduce the viability of amphibian metapopulations. In the face of climate change, conservation actions may be needed at the local scale to compensate for reduced adult survival. These would need to include management to enhance recruitment, connectivity and dispersal.
McCrea, R. et al. (2010). Multi-site integrated population modelling. Journal of Agricultural, Biological, and Environmental Statistics [Online] 15:539-561. Available at: http://dx.doi.org/10.1007/s13253-010-0027-5.We examine the performance of a method of integrated population modelling for the joint analysis of different types of demographic data on individuals that exist in, and move between, different sites. The value of the approach is demonstrated by a simulation study which shows substantial improvement in parameter estimation when site-specific census data are combined with demographic data. The multivariate normal approximation to a multi-state mark-recapture likelihood is evaluated, and the performance of a diagonal variance-covariance matrix for the approximation is also examined. The work is motivated by a study of great cormorants. Analysis of the cormorant data suggests that breeders survive better than non-breeders, and also that probabilities of recruitment to breeding have been declining over time for all the colonies of the study. Supplementary material, including notes on the computation of standard errors and extended simulation results, are available online.
McCrea, R. and Morgan, B. (2014). Analysis of capture-recapture data. Chapman and Hall/CRC Press.
King, R. and McCrea, R. (2019). Capture-recapture methods and models: Estimating population size. in: Handbook of Statistics: Integrated population Biology and Modeling. Elsevier.This book chapter describes ecological capture-recapture studies and associated models often fitted to capture-recapture data to obtain estimates of total population size. Such estimates can be important for numerous reasons, including for example, conservation and management purposes. We focus on different forms of heterogeneity that may affect the propensity of individuals to be observed within the study period. Failing to account for such heterogeneity can lead to significant bias in the population estimates. We consider different types of heterogeneity corresponding to recorded (discrete-valued) covariates/characteristics of individuals that are observed within the study period; in addition to unobserved heterogeneity in the form of mixture distributions. The different models are motivated and discussed, including the specification of the likelihood functions, before being applied to a real dataset. Finally we conclude with a discussion including the modern challenges which are arising due to technological advances.
Borysiewicz, R. et al. (2008). An integrated analysis of multisite recruitment, mark-recapture-recovery and multisite census data. in: Thomson, D. L., Cooch, E. G. and Conroy, M. J. eds. Modeling Demographic Processes in Marked Populations. New York: Springer, pp. 579-591. Available at: http://dx.doi.org/10.1007/978-0-387-78151-8.
Besbeas, P., Borysiewicz, R. and Morgan, B. (2008). Completing the ecological jigsaw. in: Thomson, D. L., Cooch, E. G. and Conroy, M. J. eds. Modeling Demographic Processes in Marked Populations. New York: Springer, pp. 513-539. Available at: http://dx.doi.org/10.1007/978-0-387-78151-8.
McCrea, R. (2018). Review of new book exploring capture-recapture methodology for social science and medical data. Biometrical Journal 60:865-866.
Worthington, H. et al. (2019). Estimating Abundance from Multiple Sampling Capture-Recapture Data via a Multi-State Multi-Period Stopover Model. Annals of Applied Statistics.Capture-recapture studies often involve collecting data on numerous capture occasions over a relatively short period of time. For many study species, this process is repeated, for example annually, resulting in capture information spanning multiple sampling periods. To account for the different temporal scales, the robust design class of models have traditionally been applied providing a frame-work in which to analyse all of the available capture data in a single likelihood expression. However, these models typically require strong
constraints, either the assumption of closure within a sampling period (the closed robust design) or conditioning on the number of individuals captured within a sampling period (the open robust design). For real datasets these assumptions may not be appropriate. We develop a general modelling structure that requires neither assumption by explicitly modelling the movement of individuals into the population both within and between the sampling periods, which in turn permits the estimation of abundance within a single consistent framework. The exibility of the novel model structure is further demonstrated by including the computationally challenging case of multi-state data where there is individual time-varying discrete covariate information. We derive an efficient likelihood expression for the new multi-state multi-period stopover model using the hidden Markov model framework. We demonstrate the signfiï¿½cant improvement in parameter estimation using our new modelling approach in terms of both the multi-period and multi-state components through both a simulation study and a real dataset relating to the protected species of great crested newts, Triturus cristatus."