Professor Byron Morgan
Past Head of Statistics and past Director of School. Co-Director of the National Centre for Statistical Ecology.
- Statistical Ecology
- Capture recapture
- Integrated population modelling
- Applications of Hidden Markov Models
- Models for Butterflies and moths
- N-mixture models
Past president of the British and Irish Region of the International Biometric Society. Past president of the International Biometric Society. Honorary life member of the International Biometric Society. Fellow of the Learned Society of Wales.
Showing 50 of 152 total publications in the Kent Academic Repository. View all publications.
Dennis, E., Brereton, T., Morgan, B., Fox, R., Shortall, C., Prescott, T. and Foster, S. (2019). Trends and indicators for quantifying moth abundance and occupancy in Scotland. Journal of Insect Conservation [Online]. Available at: https://doi.org/10.1007/s10841-019-00135-z.Moths form an important part of Scotland’s biodiversity and an up-to-date assessment of their status is needed given their value as a diverse and species-rich taxon, with various ecosystem roles, and the known decline of moths within Britain. We use long-term citizen-science data to produce species-level trends and multi-species indicators for moths in Scotland, to assess population (abundance) and distribution (occupancy) changes.
Abundance trends for moths in Scotland are produced using Rothamsted Insect Survey count data, and, for the first time, occupancy models are used to estimate occupancy trends for moths in Scotland, using opportunistic records from the National Moth Recording Scheme. Species-level trends are combined to produce abundance and occupancy indicators. The associated uncertainty is estimated using a parametric bootstrap approach, and comparisons are made with alternative published approaches.
Overall moth abundance (based on 176 species) in Scotland decreased by 20% for 1975-2014 and by 46% for 1990-2014. The occupancy indicator, based on 230 species, showed a 16% increase for 1990-2014. Alternative methods produced similar indicators and conclusions, suggesting robustness of the results, although rare species may be under-represented in our analyses. Species abundance and occupancy trends were not clearly correlated; in particular species with negative population trends showed varied occupancy responses. Further research into the drivers of moth population changes is required, but increasing occupancy is likely to be driven by a warming summer climate facilitating range expansion, whereas population declines may be driven by reductions in habitat quality, changes in land management practices and warmer, wetter winters.
Besbeas, P. and Morgan, B. (2019). Exact inference for integrated population modelling. Biometrics [Online]. Available at: https://doi.org/10.1111/biom.13045.Integrated population modelling is widely used in statistical ecology. It allows data from population time series and independent surveys to be analysed simultaneously. In classical analysis the time-series likelihood component can be conveniently approximated using Kalman filter methodology. However, the natural way to model systems which have a discrete state space is to use hidden Markov models (HMMs). The proposed method avoids the Kalman filter approximations and Monte Carlo simulations. Subject to possible numerical sensitivity analysis, it is exact, flexible, and allows the use of standard techniques of classical inference. We apply the approach to data on Little owls, where
the model is shown to require a one-dimensional state space, and Northern lapwings, with a two-dimensional state space. In the former example the method identifies a parameter redundancy which changes the perception of the data needed to estimate immigration in integrated population modelling. The latter example may be analysed using either first- or second-order HMMs, describing numbers of one-year olds and adults or adults only, respectively. The use of first-order chains is found to be more efficient, mainly due to the smaller number of one-year olds than adults in this application. For the lapwing modelling it is necessary to group the states in order to reduce the large dimension of the state space. Results check with Bayesian and Kalman filter analyses, and avenues for future research are identified.
Dennis, E., Morgan, B., Fox, R., Roy, D. and Brereton, T. (2019). Functional data analysis of multi-species abundance and occupancy data sets. Ecological Indicators [Online] 104:156-165. Available at: https://doi.org/10.1016/j.ecolind.2019.04.070.Multi-species indicators are widely used to condense large, complex amounts of information on multiple separate species by forming a single index to inform research, policy and management. Much detail is typically lost when such indices are constructed. Here we investigate the potential of Functional Data Analysis, focussing upon Functional Principal ComponentAnalysis (FPCA), which can be easily carried out using standard R programs, as a tool for displaying features of the underlying information. Illustrations are provided using data from the UK Butterflies for the New Millennium and UK Butterfly Monitoring Scheme databases. The FPCAs conducted result in a huge simplification in terms of dimensional reduction, allowing species occupancy and abundance to be reduced to two and three dimensions, respectively. We show that a functional principal component arises for both occupancy and abundance analyses that distinguishes between species that increase or decrease over time, and that it differs from percentage trend, which is a simplification of complex temporal changes. We find differences in species patterns of occupancy and abundance, providing a warning against routinely combining both types of index within multi-species indicators, for example when using occupancy as a proxy for abundance when sufficient abundance data are not available. By identifying the differences between species, figures displaying functional principal component scores are much more informative than the simple bar plots of percentages of significant trends that often accompany multi-species indicators. Informed by the outcomes of the FPCA, we make recommendations for accompanying visualisations for multi-species indicators, and discuss how these are likely to be context and audience specific. We show that, in the absence of FPCA, using mean species occupancy and total abundance can provide additional, accessible information to complement species-level trends. At the simplest level, we suggest using jitter plots to display variation in species-level trends. We recommend the routine augmentation of multi-species indicators in the future with additional statistical procedures and figures, to serve as an aid to improve communication and understanding of biodiversity metrics, as well as reveal potentially hidden patterns of behaviourand guide additional directions for investigation.
Dennis, E., Morgan, B., Brereton, T., Roy, D. and Fox, R. (2017). Using citizen science butterfly counts to predict species population trends. Conservation Biology [Online]. Available at: http://dx.doi.org/10.1111/cobi.12956.Citizen scientists are increasingly engaged in gathering biodiversity information, but trade-offs are often required between public engagement goals and reliable data collection. We compare population estimates derived from the first four years (2011-2014) of a short-duration citizen science project (Big Butterfly Count, BBC), to those from long-running, standardized monitoring data collected by experienced observers (UK Butterfly Monitoring Scheme, UKBMS), for 18 widespread butterfly species. BBC data are gathered during an annual, three-week period, whereas UKBMS sampling takes place over six months each year. An initial comparison with UKBMS data restricted to the three-week BBC period revealed that species population changes were significantly correlated between the two sources. The short-duration sampling season renders BBC counts susceptible to bias caused by inter-annual phenological variation in the timing of species’ flight periods. BBC counts were found to be described well by measures for phenology and sampling effort. Annual estimates of species abundance and population trends predicted from models including BBC data and weather covariates as a proxy for phenology correlated significantly with those derived from UKBMS data. In validating the BBC counts, we show, for the first time, that citizen science data, obtained using a simple sampling protocol, can produce comparable estimates of insect species abundance to standardized monitoring data. Although caution is urged in extrapolating from this UK study of a small number of common, conspicuous insects, we demonstrate that mass-participation citizen science can simultaneously contribute to public engagement and biodiversity monitoring. Mass-participation citizen science is not an adequate replacement for standardised biodiversity monitoring but may have a role in extending and complementing it (e.g. by sampling different land-use types), as well as serving to reconnect an increasingly urban human population with nature.
Besbeas, P. and Morgan, B. (2017). Variance estimation for integrated population models. Advances in Statistical Analysis [Online]. Available at: http://dx.doi.org/10.1007/s10182-017-0304-5.Abstract State-space models are widely used in ecology. However, it is well known that in practice it can be difficult to estimate both the process and observation variances that occur in such models. We consider this issue for integrated population models,which incorporate state-space models for population dynamics. To some extent, the mechanism of integrated population models protects against this problem, but it can still arise, and two illustrations are provided, in each of which the observation variance is estimated as zero. In the context of an extended case study involving data on British Grey herons, we consider alternative approaches for dealing with the problem when it occurs. In particular, we consider penalised likelihood, a method based on fitting splines and a method of pseudo-replication, which is undertaken via a simple bootstrap procedure. For the case study of the paper, it is shown that when it occurs, an estimate of zero observation variance is unimportant for inference relating to the model parameters of primary interest. This unexpected finding is supported by a simulation study.
Cowen, L., Besbeas, P., Morgan, B. and Schwarz, C. (2017). Hidden Markov Models for Extended Batch Data. Biometrics [Online]. Available at: http://dx.doi.org/10.1111/biom.12701.Batch marking provides an important and efficient way to estimate the survival probabilities and population sizes of wild animals. It is particularly useful when dealing with animals that are difficult to mark individually. For the first time, we provide the likelihood for extended batch-marking experiments. It is often the case that samples contain individuals that remain unmarked, due to time and other constraints, and this information has not previously been analyzed. We provide ways of modeling such information, including an open N-mixture approach. We demonstrate that models for both marked and unmarked individuals are hidden Markov models; this provides a unified approach, and is the key to developing methods for fast likelihood computation and maximization. Likelihoods for marked and unmarked individuals can easily be combined using integrated population modeling. This allows the simultaneous estimation of population size and immigration, in addition to survival, as well as efficient estimation of standard errors and methods of model selection and evaluation, using standard likelihood techniques. Alternative methods for estimating population size are presented and compared. An illustration is provided by a weather-loach data set, previously analyzed by means of a complex procedure of constructing a pseudo likelihood, the formation of estimating equations, the use of sandwich estimates of variance, and piecemeal estimation of population size. Simulation provides general validation of the hidden Markov model methods developed and demonstrates their excellent performance and efficiency. This is especially notable due to the large numbers of hidden states that may be typically required
Lahoz-Monfort, J., Harris, M., Wanless, S., Freeman, S. and Morgan, B. (2017). Bringing It All Together: Multi-species Integrated Population Modelling of a Breeding Community. Journal of Agricultural, Biological, and Environmental Statistics [Online] 22:140-160. Available at: http://dx.doi.org/10.1007/s13253-017-0279-4.Integrated population models (IPMs) combine data on different aspects of demography with time-series of population abundance. IPMs are becoming increasingly popular in the study of wildlife populations, but their application has largely been restricted to the analysis of single species. However, species exist within communities: sympatric species are exposed to the same abiotic environment, which may generate synchrony in the fluctuations of their demographic parameters over time. Given that in many environments conditions are changing rapidly, assessing whether species show similar demographic and population responses is fundamental to quantifying interspecific differences in environmental sensitivity and highlighting ecological interactions at risk of disruption. In this paper, we combine statistical approaches to study populations, integrating data along two different dimensions: across species (using a recently proposed framework to quantify multi-species synchrony in demography) and within each species (using IPMs with demographic and abundance data).We analyse data from three seabird species breeding at a nationally important long-term monitoring site. We combine demographic datasets with island-wide population counts to construct the first multi-species Integrated Population Model to consider synchrony. Our extension of the IPM concept allows the simultaneous estimation of demographic parameters, adult abundance and multi-species synchrony in survival and productivity, within a robust statistical framework. The approach is readily applicable to other taxa and habitats.
Dennis, E., Morgan, B., Roy, D. and Brereton, T. (2017). Urban indicators for UK butterflies. Ecological Indicators [Online] 76:184-193. Available at: http://dx.doi.org/10.1016/j.ecolind.2017.01.009.Most people live in urban environments and there is a need to produce abundance indices to assist policy and management of urban greenspaces and gardens. While regional indices are produced, with the exception of birds, studies of the differences between urban and rural areas are rare. We explore these differences for UK butterflies, with the intention to describe changes that are relevant to people living in urban areas, in order to better connect people with nature in support of conservation, provide a measure relevant to human well-being, and assess the biodiversity status of the urban environment.
Transects walked under the UK Butterfly Monitoring Scheme are classified as urban or rural, using a classification for urban morphological zones. We use models from the Generalised Abundance Index family to produce urban and rural indices of relative abundance for UK butterfly species. Composite indices are constructed for various subsets of species. For univoltine and bivoltine species, where we are able to fit phenomenological models, we estimate measures of phenology and identify urban/rural differences. Trends in relative abundance over the period 1995–2014 are more negative in urban areas compared to rural areas for 25 out of 28 species. For the composite indices, all trends are negative, and they are significantly more negative for urban areas than for rural areas. Analysis of phenological parameters shows butterflies tend to emerge earlier in urban than in rural areas. In addition, some fly longer in urban than in rural areas, whereas in other cases the opposite is the case, and hypotheses are proposed to account for these features.
Investigating new urban/rural indicators has revealed national declines that are stronger for urban areas. For continued monitoring, there is a need for an urban butterfly indicator, and for this to be evaluated and reported annually. We explain how this may be interpreted, and the relevance for other monitoring schemes. The results of this paper, including the phenological findings, shed new light on the potentially deleterious effects of urbanisation and climate change, which require suitable monitoring and reporting to support policy and management, for example of urban greenspaces and gardens.
Besbeas, P., McCrea, R. and Morgan, B. (2017). Integrated population model selection in ecology. In prep.
Dennis, E., Morgan, B., Freeman, S., Ridout, M., Brereton, T., Fox, R., Powney, G. and Roy, D. (2017). Efficient occupancy model-fitting for extensive citizen-science data. PLoS ONE [Online]. Available at: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0174433.Appropriate large-scale citizen-science data present important new opportunities for biodiversity modelling, due in part to the wide spatial coverage of information. Recently proposed occupancy modelling approaches naturally incorporate random effects in order to account for annual variation in the composition of sites surveyed. In turn this leads to Bayesian analysis and model fitting, which are typically extremely time consuming. Motivated by presence-only records of occurrence from the UK Butterflies for the New Millennium data base, we present an alternative approach, in which site variation is described in a standard way through logistic regression on relevant environmental covariates. This allows efficient occupancy model-fitting using classical inference, which is easily achieved using standard computers. This is especially important when models need to be fitted each year, typically for many different species, as with British butterflies for example. Using both real and simulated data we demonstrate that the two approaches, with and without random effects, can result in similar conclusions regarding trends. There are many advantages to classical model-fitting, including the ability to compare a range of alternative models, identify appropriate covariates and assess model fit, using standard tools of maximum likelihood. In addition, modelling in terms of covariates provides opportunities for understanding the ecological processes that are in operation. We show that there is even greater potential; the classical approach allows us to construct regional indices simply, which indicate how changes in occupancy typically vary over a species’ range. In addition we are also able to construct dynamic occupancy maps, which provide a novel, modern tool for examining temporal changes in species distribution. These new developments may be applied to a wide range of taxa, and are valuable at a time of climate change. They also have the potential to motivate citizen scientists.
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 capture–recapture 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 capture–recapture 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.
Dennis, E., Morgan, B., Freeman, S., Brereton, T. and Roy, D. (2016). A generalised abundance index for seasonal invertebrates. Biometrics [Online]. Available at: http://dx.doi.org/10.1111/biom.12506.At a time of climate change and major loss of biodiversity, it is important to have efficient tools for monitoring populations. In this context, animal abundance indices play an important role. In producing indices for invertebrates, it is important to account for variation in counts within seasons. Two new methods for describing seasonal variation in invertebrate counts have recently been proposed; one is nonparametric, using generalized additive models, and the other is parametric, based on stopover models. We present a novel generalized abundance index which encompasses both parametric and nonparametric approaches. It is extremely efficient to compute this index due to the use of concentrated likelihood techniques. This has particular relevance for the analysis of data from long-term extensive monitoring schemes with records for many species and sites, for which existing modeling techniques can be prohibitively time consuming. Performance of the index is demonstrated by several applications to UK Butterfly Monitoring Scheme data. We demonstrate the potential for new insights into both phenology and spatial variation in seasonal patterns from parametric modeling and the incorporation of covariate dependence,
which is relevant for both monitoring and conservation. Associated R code is available on the journal website.
Matechou, E., McCrea, R., Morgan, B., Nash, D. and Griffiths, R. (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.
GÃ¡lvez, N., Guillera-Arroita, G., Morgan, B. and Davies, Z. (2016). Cost-efficient effort allocation for camera-trap occupancy surveys of mammals. Biological Conservation [Online] 204:350-359. Available at: http://dx.doi.org/10.1016/j.biocon.2016.10.019.Camera-traps are increasingly used to survey threatened mammal species and are an important tool for estimating habitat occupancy. To date, cost-efficient occupancy survey effort allocation studies have focused on trade-offs between number of sample units (SUs) and sampling occasions, with simplistic accounts of associated costs which do not reflect camera-trap survey realities. Here we examine camera-trap survey costs as a function of the number of SUs, survey duration and camera-traps per SU, linking costs to precision in occupancy estimation. We evaluate survey effort trade-offs for hypothetical species representing different levels of occupancy (?) and detection (p) probability to identify optimal design strategies. We apply our cost function to three threatened species as worked examples. Additionally, we use an extensive camera-trap data set to evaluate independence between multiple camera traps per SU. The optimal number of sampling occasions that result in minimum cost decrease as detection probability increases, irrespective of whether the species is rare (? <0.25) or common (? >0.5). The most expensive survey scenarios occur for elusive (p <0.25) species with a large home range (>10 km2), where the survey is conducted on foot. Minimum survey costs for elusive species can be achieved with fewer sampling occasions and multiple cameras per SU. Multiple camera-traps set within a single SU can yield independent species detections. We provide managers and researchers with guidance for conducting cost-efficient camera-trap occupancy surveys. Efficient use of survey budgets will ultimately contribute to the conservation of threatened and data deficient mammals.
Matechou, E., Nicholls, G., Morgan, B., Collazo, J. and Lyons, J. (2016). Bayesian analysis of Jolly-Seber type models; Incorporating heterogeneity in arrival and departure. Environmental and Ecological Statistics [Online]:1-17. Available at: http://doi.org/10.1007/s10651-016-0352-0.We propose the use of finite mixtures of continuous distributions in modelling
the process by which new individuals, that arrive in groups, become part of a
wildlife population. We demonstrate this approach using a data set of migrating semipalmated
sandpipers (Calidris pussila) for which we extend existing stopover models
to allow for individuals to have different behaviour in terms of their stopover duration
at the site. We demonstrate the use of reversible jump MCMC methods to derive
posterior distributions for the model parameters and the models, simultaneously. The
algorithm moves between models with different numbers of arrival groups as well as
between models with different numbers of behavioural groups. The approach is shown
to provide new ecological insights about the stopover behaviour of semipalmated sandpipers
but is generally applicable to any population in which animals arrive in groups
and potentially exhibit heterogeneity in terms of one or more other processes.
Buckland, S. and Morgan, B. (2016). 50-Year Anniversary of Papers by Cormack, Jolly and Seber. Statistical Science [Online] 31:141. Available at: http://dx.doi.org/10.1214/16-STS555.
Dennis, E., Morgan, B., Freeman, S., Roy, D. and Brereton, T. (2015). Dynamic models for longitudinal butterfly data. Journal of Agricultural, Biological, and Environmental Statistics [Online] 21:1-21. Available at: http://dx.doi.org/10.1007/s13253-015-0216-3.There has been recent interest in devising stochastic models for seasonal insects, which
respond rapidly to climate change. Fitted to count data, these models are used to construct
indices of abundance, which guide conservation and management. We build upon Dennis et
al. (2014, under review) to produce dynamic models, which provide succinct descriptions of
data from all years simultaneously. They produce estimates of key life-history parameters
such as annual productivity and survival.
Analyses for univoltine species, with only one generation each year, extend to bivoltine
species, with two annual broods. In the latter case we estimate the productivities of each
generation separately, and also devise extended indices which indicate the contributions
made from different generations.
We demonstrate the performance of the models using count data for UK butterfly species,
and compare with current procedures which use generalized additive models. We may incor-
orate relevant covariates within the model, and illustrate using northing and measures of
temperature. Consistent patterns are demonstrated for multiple species. This generates a
variety of hypotheses for further investigation, which have the potential to illuminate features
of butterfly phenology and demography which are at present poorly understood.
Dennis, E., Morgan, B. and Ridout, M. (2015). Computational aspects of N-mixture models. Biometrics [Online] 71:237-246. Available at: http://dx.doi.org/10.1111/biom.12246.The N-mixture model is widely used to estimate the abundance of a population in the presence of unknown
detection probability from only a set of counts subject to spatial and temporal replication (Royle, 2004, Biometrics 60,105–115). We explain and exploit the equivalence of N-mixture and multivariate Poisson and negative-binomial models, which provides powerful new approaches for fitting these models. We show that particularly when detection probability and the number of sampling occasions are small, infinite estimates of abundance can arise. We propose a sample covariance as a diagnostic for this event, and demonstrate its good performance in the Poisson case. Infinite estimates may be missed in practice, due to numerical optimization procedures terminating at arbitrarily large values. It is shown that the use of a bound, K, for an infinite summation in the N-mixture likelihood can result in underestimation of abundance, so that default values of K in computer packages should be avoided. Instead we propose a simple automatic way to choose K. The methods are illustrated by analysis of data on Hermann’s tortoise Testudo hermanni.
Hubbard, B., Cole, D. and Morgan, B. (2014). Parameter Redundancy in Capture-Recapture-Recovery Models. Statistical Methodology [Online] 17:17-29. Available at: https://doi.org/10.1016/j.stamet.2012.11.005.In principle it is possible to use recently-derived procedures to determine whether or not all the parameters of particular complex ecological models can be estimated using classical methods of statistical inference. If it is not possible to estimate all the parameters a model is parameter redundant. Furthermore, one can investigate whether derived results hold for such models for all lengths of study, and also how the results might change for specific data sets. In this paper we show how to apply these approaches to entire families of capture-recapture and capture-recapture-recovery models. This results in comprehensive tables, providing the definitive parameter redundancy status for such models. Parameter redundancy can also be caused by the data rather than the model, and how to investigate this is demonstrated through two applications, one to recapture data on dippers, and one to recapture-recovery data on great cormorants.
Cole, D., Morgan, B., McCrea, R., Pradel, R., Gimenez, O. and Choquet, R. (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 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.
Guillera-Arroita, G., Ridout, M. and Morgan, B. (2014). Two-stage sequential Bayesian study design for species estimation. Journal of Agricultural, Biological, and Environmental Statistics [Online] 19:278-291. Available at: http://dx.doi.org/10.1007/s13253-014-0171-4.A problem of interest for ecology and conservation is that of determining the best al-
location of survey effort in studies aimed at estimating the proportion of sites occupied
by a species. Many species are difficult to detect and often remain undetected during
surveys at sites where they are present. Hence, for the estimator of species occupancy
to be unbiased, detectability needs to be taken into account. In such studies there is a
trade-off between sampling more sites and expending more survey effort within each
site. This design problem has not been addressed to date with an explicit consideration
of the uncertainty in assumed parameter values. In this article we apply sequential and
Bayesian design techniques and show how a simple two-stage design can significantly
improve the efficiency of the study. We further investigate the optimal allocation of
survey effort between the two study stages, given a prior distribution for the parame-
ter values. We address this problem using asymptotic approximations and then explore
how the results change when the sample size is small, considering second-order approx-
imations and highlighting the value of simulations as a tool for study design. Given the
efficiency gain, we recommend following the sequential design approach for species
occupancy estimation. This article has supplementary material online.
Cowen, L., Besbeas, P., Morgan, B. and Schwarz, C. (2014). A comparison of abundance estimates from extended batch-marking and Jolly-Seber type experiments. Ecology and Evolution [Online] 4:210-218. Available at: http://dx.doi.org/10.1002/ece3.899.Little attention has been paid to the use of multi-sample batch-marking studies,
as it is generally assumed that an individual’s capture history is necessary for
fully efficient estimates. However, recently, Huggins et al. (2010) present a
pseudo-likelihood for a multi-sample batch-marking study where they used
estimating equations to solve for survival and capture probabilities and then
derived abundance estimates using a Horvitz–Thompson-type estimator. We
have developed and maximized the likelihood for batch-marking studies. We
use data simulated from a Jolly–Seber-type study and convert this to what
would have been obtained from an extended batch-marking study. We compare
our abundance estimates obtained from the Crosbie–Manly–Arnason–Schwarz
(CMAS) model with those of the extended batch-marking model to determine
the efficiency of collecting and analyzing batch-marking data. We found that
estimates of abundance were similar for all three estimators: CMAS, Huggins,
and our likelihood. Gains are made when using unique identifiers and employ-
ing the CMAS model in terms of precision; however, the likelihood typically
had lower mean square error than the pseudo-likelihood method of Huggins
et al. (2010). When faced with designing a batch-marking study, researchers
can be confident in obtaining unbiased abundance estimators. Furthermore,
they can design studies in order to reduce mean square error by manipulating
capture probabilities and sample size.
Lahoz-Monfort, J., Harris, M., Morgan, B., Freeman, S. and Wanless, S. (2014). Exploring the consequences of reducing survey effort for detecting individual and temporal variability in survival. Journal of Applied Ecology [Online] 51:534-543. Available at: http://dx.doi.org/10.1111/1365-2664.12214.1. Long-term monitoring programmes often involve substantial input of skilled staff time. In
mark–recapture studies, considerable effort is usually devoted to both marking and recaptur-
ing/resighting individuals. Given increasing budgetary constraints, it is essential to streamline
field protocols to minimize data redundancy while still achieving targets such as detecting
trends or ecological effects.
2. We evaluated different levels of field effort investment in marking and resighting individu-
als by resampling existing mark–recapture–recovery data to construct plausible scenarios of
changes in field protocols. We demonstrate the method with 26 years data from a common
guillemot Uria aalge monitoring programme at a major North Sea colony. We also assess the
impact of stopping the ringing of chicks on our ability to study population demography using
integrated population models (IPM) fitted to data including information on breeding adults.
Different data sets were removed artificially to explore the ability to compensate for missing
3. Current ringing effort at this colony appears adequate but resighting effort could be
halved while still maintaining the capacity to monitor first-year survival and detect the effect
of hatch date on survival prospects.
4. The IPM appears robust for estimating survival, productivity or abundance of the breed-
ing population, but has limited capacity to recover year-specific first-year survival when chick
data are omitted. If productivity were not monitored, the inclusion of chick data would be
essential to estimate it, albeit imprecisely.
5. Synthesis and applications. Post-study evaluation can help streamline existing long-term
environmental monitoring programmes. To our knowledge, this study is the first use of data
thinning of existing mark–recapture–recovery data to identify potential field effort reductions.
We also highlight how alternative monitoring scenarios can be evaluated with integrated pop-
ulation models when data are collected on different aspects of demography and abundance.
When effort reduction is necessary, both approaches provide decision-support tools for
adjusting field protocols to collect demographic data. The framework has broad applicability
to other taxa and demographic parameters, provided suitable long-term data are available,
and we discuss its use in different contexts.
Gimenez, O., Buckland, S., Morgan, B., Bertrand, S., Choquet, R., Dray, S., Etienne, M., Fewster, R., Gosselin, F., MÃ©rigotB., Monestiez, P., Morales, J., Mortier, F., Munoz, F., Ovaskainen, O., Pavoine, S., Pradel, R., Schurr, F., Thomas, L., Thuiller, W., Trenkel, V., de Valpine, P., Rexstad, E. and Bez, N. (2014). Statistical ecology comes of age. Biology Letters [Online] 10. Available at: http://dx.doi.org/10.1098/rsbl.2014.0698.The desire to predict the consequences of global environmental change has
been the driver towards more realistic models embracing the variability and
uncertainties inherent in ecology. Statistical ecology has gelled over the past
decade as a discipline that moves away from describing patterns towards
modelling the ecological processes that generate these patterns. Following
the fourth International Statistical Ecology Conference (1 –4 July 2014) in
Montpellier, France, we analyse current trends in statistical ecology. Impor-
tant advances in the analysis of individual movement, and in the modelling
of population dynamics and species distributions, are made possible by the
increasing use of hierarchical and hidden process models. Exciting research
perspectives include the development of methods to interpret citizen science
data and of efficient, flexible computational algorithms for model fitting. Stat-
istical ecology has come of age: it now provides a general and mathematically
rigorous framework linking ecological theory and empirical data.
Besbeas, P. and Morgan, B. (2014). Goodness-of-fit of integrated population models using calibrated simulation. Methods in Ecology and Evolution [Online] 5:1373-1382. Available at: http://dx.doi.org/10.1111/2041-210X.12279.1. Integrated population modelling is proving to be an important and useful technique in statistical ecology.
However, there is currently no simple formal method for judging how well models fit data, when potentially sev-
eral different data sets described by different structured models are being analysed in combination.
2. We propose and evaluate a new approach, of calibrated simulation. Here, comparative data sets are obtained
from simulating data when model parameter values are obtained from the assumed asymptotic normal distribu-
tion of the maximum-likelihood estimators from the real data. The approach is motivated and justified by Baye-
sian P-values. Calibration of the resulting statistics is achieved as repeated data sets are easily simulated from the
fitted model. The method requires the specification of model discrepancy measures, and we show how different
measures can highlight different aspects of fit.
3. Calibration is only strictly necessary if the statistics proposed may appear to be extreme.
4. The approach of using calibrated simulation to check the goodness-of-fit of integrated population models is
demonstrated by application to data sets on lapwings and herons. In each case, there are two data sets involved
in the integrated analysis, and for each component data set, discrepancy measures of goodness-of-fit are
obtained. For the lapwing application, as replication is efficient, it is possible to calibrate the procedure simply by
using additional simulations. The heron application is shown to be feasible, but is substantially harder to cali-
brate, due to the presence of productivity thresholds that need to be estimated using profile likelihood methods.
We demonstrate the importance of taking more than one discrepancy measure for time-series data. Avenues for
future research are outlined. This article has supplementary materials on line.
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 ring–recovery 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.
Lahoz-Monfort, J., Morgan, B., Harris, M., Daunt, F., Wanless, S. and Freeman, S. (2013). Breeding together: modelling synchrony in productivity in a seabird community. Ecology [Online] 94:3-10. Available at: http://dx.doi.org/10.1890/12-0500.1.With environmental conditions changing rapidly, there is a need to move
beyond single-species models and consider how communities respond to environmental
drivers. We present a modeling approach that allows estimation of multispecies synchrony in
productivity, or its components, and the contribution of environmental covariates as
synchronizing and desynchronizing agents.
We apply the model to long-term breeding success data for five seabird species at a North
Atlantic colony. Our Bayesian analysis reveals varying degrees of synchrony in overall
productivity, with a common signal indicating a significant decline in productivity between
1986 and 2009. Productivity in seabirds reflects conditions in the marine ecosystem so the
estimated synchronous component is a useful indicator of local marine environment health.
For the two species for which we have most data, the environmental contribution to overall
productivity synchrony is driven principally by effects operating at the chick stage rather than
during incubation. Our results emphasize the importance of studying together species that
coexist in a community. The framework, which accommodates interspecific clutch-size
variation, is readily applicable to any species assemblage in any ecosystem where long-term
productivity data are available.
Matechou, E., Morgan, B., Pledger, S., Collazo, J. and Lyons, J. (2013). Integrated analysis of capture-recapture-resighting data and counts of unmarked birds at stop-over sites. Journal of Agricultural, Biological, and Environmental Statistics [Online] 18:120-135. Available at: http://dx.doi.org/10.1007/s13253-013-0127-0.The models presented in this paper are motivated by a stop-over study of semipalmated sandpipers, Callidris pussila. Two sets of data were collected at the stop-over site: a capture-recapture-resighting data set and a vector of counts of unmarked birds. The two data sets are analysed simultaneously by combining a new model for the capture-recapture-resighting data set with a binomial likelihood for the counts. The aim of the analysis is to estimate the total number of birds that used the site and the average duration of stop-over. The combined analysis is shown to be highly efficient when just 1% of birds are recaptured, and is recommended for similar investigations.
Jackson, H., Morgan, B. and Groombridge, J. (2013). How closely do measures of mitochondrial DNA control region diversity reflect recent trajectories of population decline in birds?. Conservation Genetics [Online] 14:1291-1296. Available at: http://dx.doi.org/10.1007/s10592-013-0514-7.Monitoring levels of genetic diversity in wild- life species is important for understanding population sta- tus and trajectory. Knowledge of the distribution and level of genetic diversity in a population is essential to inform conservation management, and help alleviate detrimental genetic impacts associated with recent population bottle- necking. Mitochondrial DNA (mtDNA) markers such as the control region have become a common means of sur- veying for within-population genetic diversity and detect- ing signatures of recent population decline. Nevertheless, little attention has been given to examining the mtDNA control region’s sensitivity and performance at detecting instances of population decline. We review genetic studies of bird populations published since 1993 that have used the mtDNA control region and reported haplotype diversity, number of haplotypes and nucleotide diversity as measures of within-population variability. We examined the extent to which these measures reflect differences in known demo- graphic parameters such as current population size, severity of any recent bottleneck and IUCN Red List status.Overall, significant relationships were observed between two measures of genetic diversity (haplotype diversity and the number of haplotypes), and population size across a number of comparisons. Both measures gave a more accurate reflection of recent population history in com- parison to nucleotide diversity, for which no significant associations were found. Importantly, levels of diversity only correlated with demographic declines where popula- tion sizes were known to have fallen below 500 individu- als. This finding suggests that measures of mtDNA control region diversity should be used with a degree of caution when inferring demographic history, particularly bottle- neck events at population sizes above N = 500.
Matechou, E., Pledger, S., Efford, M., Morgan, B. and Thomson, D. (2013). Estimating age-specific survival when age is unknown: open population capture–recapture models with age structure and heterogeneity. Methods in Ecology and Evolution [Online] 4:654-664. Available at: http://dx.doi.org/10.1111/2041-210X.12061.Summary
When studying senescence in wildlife populations, we are often limited by the sparseness of the available information on the ages of the individuals under study. Additionally, heterogeneity between individuals can be substantial. Ignoring this heterogeneity can lead to biased estimates of the population parameters of interest and can mask senescence.
This article demonstrates the use of a recently developed capture–recapture model for extracting age-dependent estimates of survival probabilities for individuals of unknown age and extends the model by allowing for heterogeneity in survival and capture probabilities using finite mixtures.
Using simulation, we show that the estimates of age-dependent survival probabilities when age is unknown can be biased when heterogeneity in capture probabilities is not modelled, in contrast to the case of time-dependent survival probabilities when the estimates are robust to similar violations of model assumptions.
The methods are demonstrated using a long-term data set of female brushtail possums (Trichosurus vulpecula Kerr) for which age-specific models for survival probabilities indicating senescence are strongly favoured. We found no evidence of heterogeneity in survival but strong evidence of heterogeneity in capture probabilities.
These models have a wide range of applications for estimating age dependence in survival when the age is unknown as they can be applied to any capture–recapture data set, as long as it is collected over a period which is longer, and preferably considerably so, than the life span of the species studied.
Matechou, E., Morgan, B., Pledger, S., Collazo, J. and Lyons, J. (2013). Integrated Analysis of Capture–Recapture–Resighting Data and Counts of Unmarked Birds at Stop-Over Sites. Journal of Agricultural, Biological, and Environmental Statistics [Online] 18:120-135. Available at: http://dx.doi.org/10.1007/s13253-013-0127-0.The models presented in this paper are motivated by a stop-over study of semipalmated sandpipers, Calidris pusilla. Two sets of data were collected at the stop-over site: a capture–recapture–resighting data set and a vector of counts of unmarked birds. The two data sets are analyzed simultaneously by combining a new model for the capture–recapture–resighting data set with a binomial likelihood for the counts. The aim of the analysis is to estimate the total number of birds that used the site and the average duration of stop-over. The combined analysis is shown to be highly efficient, even when just 1 % of birds are recaptured, and is recommended for similar investigations. This article has supplementary material online.
Besbeas, P. and Morgan, B. (2012). Kalman filter initialization for integrated population modelling. Journal of the Royal Statistical Society: Series C [Online] 61:151-162. Available at: http://dx.doi.org/10.1111/j.1467-9876.2011.01012.x.In integrated population modelling in ecology, where data from multiple surveys are analysed simultaneously, the Kalman filter may be used to approximate a component likelihood for a state space model of population count data. We evaluate a new method for initiating this Kalman filter, based on a stable age distribution. The new method is illustrated and compared with alternative approaches by application to data on the grey heron. The new method is simple to use, extends naturally to the case of multivariate time series of count data and performs well in a simulation study.
McCrea, R., Morgan, B., Brown, D. and Robinson, R. (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., 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.
Viallefont, A., Besbeas, P., Morgan, B. and McCrea, R. (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.
Cole, D., Morgan, B., Catchpole, E. and Hubbard, B. (2012). Parameter redundancy in mark-recovery models. Biometrical Journal [Online] 54:507-523. Available at: http://dx.doi.org/10.1002/bimj.201100210.We provide a definitive guide to parameter redundancy in mark-recovery models, indicating, for a wide range of models, in which all the parameters are estimable, and in which models they are not. For these parameter-redundant models, we identify the parameter combinations that can be estimated. Simple, general results are obtained, which hold irrespective of the duration of the studies. We also examine the effect real data have on whether or not models are parameter redundant, and show that results can be robust even with very sparse data. Covariates, as well as time- or age-varying trends, can be added to models to overcome redundancy problems. We show how to determine, without further calculation, whether or not parameter-redundant models are still parameter redundant after the addition of covariates or trends.
Besbeas, P. and Morgan, B. (2012). A threshold model for heron productivity. Journal of Agricultural, Biological, and Environmental Statistics [Online] 17:128-141. Available at: http://dx.doi.org/10.1007/s13253-011-0080-8.We demonstrate the potential of conditionally Gaussian state-space models in integrated
population modeling, when certain model parameters may be functions of previous
observations. The approach is applied to a heron census, and the data are best
described by a model with three population-size thresholds which determine the population
productivity. The model provides an explanation of how the population rebounds
rapidly after major falls in size, which are characteristic of the data. By contrast, a
simple logarithmic regression of productivity on population size was not significant.
The results are of ecological interest, and suggest hypotheses for further investigation.
Besbeas, P. and Morgan, B. (2012). Kalman filter initialisation for integrated population modelling. Journal of the Royal Statistical Society: Series C (Applied Statistics) [Online] 61:151-162. Available at: http://dx.doi.org/10.1111/j.1467-9876.2011.01012.x.In integrated population modelling in ecology, where data from multiple surveys are
analysed simultaneously, the Kalman filter may be used to approximate a component likelihood
for a state space model of population count data.We evaluate a new method for initiating this
Kalman filter, based on a stable age distribution. The new method is illustrated and compared
with alternative approaches by application to data on the grey heron.The new method is simple
to use, extends naturally to the case of multivariate time series of count data and performs well
in a simulation study.
Guillera-Arroita, G., Ridout, M., Morgan, B. and Linkie, M. (2012). Models for species-detection data collected along transects in the presence of abundance-induced heterogeneity and clustering in the detection process. Methods in Ecology and Evolution [Online] 3:358-367. Available at: http://dx.doi.org/10.1111/j.2041-210X.2011.00159.x.1. Models have been devised previously that allow the estimation of abundance from detection data
of unmarked individuals while accounting for imperfect detection, but these are restricted to models
for discrete sampling protocols, i.e. replicated detection ? non-detection or count data. Furthermore,
these models assume that the detections from each individual are independent; however, there
are cases in which this assumption is likely to be violated. For example, in surveys along transects,
clustering in the signs left by each individual could be expected.
2. Here, we propose models to estimate abundance from species-detection data collected continu-
ously along transects considering two cases: (i) independent detections and (ii) clustering within the
detections of each individual. We account for clustering by describing the detection process as a
Markov-modulated Poisson process. We study the properties of the estimators via simulation,
assessing the impact of unmodelled detection clustering.
3. We show that bias may be induced in the estimator of abundance if clustering in individual detec-
tions is not accounted for and how an estimator with better coverage properties is obtained if clus-
tering is modelled. We demonstrate that both abundance and the clustering pattern can be well
estimated simultaneously, given enough data.
4. To illustrate our approach, we fit the models to tiger pugmark detection data from transect sur-
veys in Kerinci Seblat National Park in Sumatra. The analysis suggested strong abundance-induced
heterogeneity in detections when clustering was disregarded, but the evidence reduced drastically
when clustering was accounted for. This example illustrates how unmodelled clustering can affect
the estimation of abundance.
5. Estimates of abundance need to be reliable to ensure that conservation and management inter-
ventions are not misguided. Provided certain model assumptions are met, abundance can be esti-
mated from detection data of unmarked individuals. This requires an adequate description of the
detection process, or otherwise, bias may be induced in the abundance estimator. The models and
discussion provided here deal with the issue of clustering within the detections of individuals and
are of relevance for ecologists interested in methodological developments for the estimation of ani-
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.
McCrea, R. and Morgan, B. (2014). Analysis of Capture-Recapture Data. Chapman and Hall/CRC Press.
Newman, K., Buckland, S., Morgan, B., King, R., Borchers, D., Cole, D., Besbeas, P., Gimenez, O. and Thomas, L. (2014). Modelling Population Dynamics: Model Formulation, Fitting and Assessment Using State-Space Methods. Springer.Provides unifying framework for estimating the abundance of open populations that are subject to births, deaths and movement in and out of the population
Going beyond the estimation of abundance, teaches ways of determining the reasons for variation in abundance over time and survival probabilities
Ecologists and wildlife managers will learn to model dynamics in annual cycles for populations of large vertebrates, including discrete time models
This book gives a unifying framework for estimating the abundance of open populations: populations subject to births, deaths and movement, given imperfect measurements or samples of the populations. The focus is primarily on populations of vertebrates for which dynamics are typically modelled within the framework of an annual cycle, and for which stochastic variability in the demographic processes is usually modest. Discrete-time models are developed in which animals can be assigned to discrete states such as age class, gender, maturity, population (within a metapopulation), or species (for multi-species models).
The book goes well beyond estimation of abundance, allowing inference on underlying population processes such as birth or recruitment, survival and movement. This requires the formulation and fitting of population dynamics models. The resulting fitted models yield both estimates of abundance and estimates of parameters characterizing the underlying processes.
Morgan, B. and Viallefont, A. (2013). Ornithological data. In: Encyclopedia of Environmetrics 2nd Edition. Wile. Available at: https://doi.org/10.1002/978047005733.9 vao017.This article introduces the different types of ornithological data, obtained either at the population level (count data, occupancy data) or at the individual level (capture–mark–recapture data, radiotracking data, and geolocation data), as well as references to the modeling/analysis techniques appropriate for each type of data. It also gives a list of organizations and web sites through which such data can be made available, as well as an extensive list of references to up-to-date articles and books.
Dennis, E., Morgan, B., Freeman, S., Ridout, M., Brereton, T., Fox, R. and Roy, D. (2015). The Construction of Spatial Distribution Maps and Regional Occupancy Indices from Opportunistic Records. University of Kent.A major advantage of opportunistic citizen-science data is the wide spatial and temporal coverage it provides, relative to long-standing monitoring data obtained from transect sampling, for example. Opportunistic schemes are used to form atlases for many taxa, but only broad trends between multi-year survey periods have typically been studied. Optimal methods for analysing opportunistic data are required, with the aim of greater understanding changes in species’ distributions. We apply occupancy models to opportunistic data in order to create spatial maps and regional indices.
Besbeas, P. and Morgan, B. (2015). Pseudo Replication for Integrated Population Models. University of Kent Technical Report.State-space models are widely used in ecology. However it is well known that in practice it can be difficult to separate process and observation variances. We consider this issue for integrated population modelling. To some extent the mechanism of such models protects against this problem, but it can still arise, and two illustrations are provided, in each of which the measurement variance is estimated as zero. In the context of an extended case study involving data on British Grey herons we consider alternative approaches for dealing with the problem when it occurs. In particular we consider penalised likelihood and introduce a method of pseudo replication. We recommend the use of pseudo replication, which is undertaken via a simple bootstrap procedure. For the case study of the paper it is shown that when it occurs, an estimate of zero measurement variance may not be important for inference relating to the model parameters of primary interest. The wider implications of the work are discussed.
Yu, C. (2015). The Use of Mixture Models in Capture-Recapture.Mixture models have been widely used to model heterogeneity. In this thesis, we focus on the use of mixture models in capture--recapture, for both closed populations and open populations.
We provide both practical and theoretical investigations. A new model is proposed for closed populations and the practical difficulties of model fitting for mixture models are demonstrated for open populations.
As the number of model parameters can increase with the number of mixture components, whether we can estimate all of the parameters using the method of maximum likelihood is an important issue. We explore this using formal methods and develop general rules to ensure that all parameters are estimable.
Hubbard, B. (2014). Parameter Redundancy With Applications in Statistical Ecology.This thesis is concerned with parameter redundancy in statistical ecology models. If it is not possible to estimate all the parameters, a model is termed parameter redundant. Parameter redundancy commonly occurs when parameters are confounded in the model so that the model could be reparameterised in terms of a smaller number of parameters. In principle, it is possible to use symbolic algebra to determine whether or not all the parameters of a certain ecological model can be estimated using classical methods of statistical inference.
We examine a variety of different ecological models: We begin by exploring models based on marking a number of animals and observing the same animals at future time points. These observations can either be when the animal is marked and then
recovered dead in mark-recovery modelling, or when the animal is marked and then recaptured alive in capture-recapture modelling. We also explore capture-recapture-recovery models where both dead recoveries and alive recaptures can be observed in the same study. We go on to explore occupancy models which are used to obtain
estimates of the probability of presence, or absence, for living species by the use of repeated detection surveys, where these models have the advantage that individuals are not required to be marked. A variety of different occupancy models are examined included the addition of season-dependent parameters, group-dependent parameters and species-dependent, along with other models.
We investigate parameter redundancy by deriving general results for a variety of different models where the model's parameter dependencies can be relaxed suited to different studies. We also analyse how the results change for specific data sets and how sparse data influence whether or not a model is parameter redundant using procedures written in Maple. This theory on parameter redundancy is vital for the correct use of these ecological models so that valid statistical inference can be made.
Freeman, S., Isaac, N., Besbeas, P., Dennis, E. and Morgan, B. (2019). A Generic Method for Estimating and Smoothing Multispecies Biodiversity Indices, Robust to Intermittent Data. University of Kent.Biodiversity indicators provide a powerful and convenient way to summarise extensive, complex ecological data sets and are important in influencing government policy on biodiversity and conservation. Typically, component data consist of time-varying indices for each of a number of different species. There currently exists a wide range of different biodiversity indicators, but their derivation from these indices varies and they suffer from a range of statistical shortcomings. In this paper we describe a state-space formulation for new multispecies biodiversity indicators, based on rates of change in the abundance or occupancy11probability of the contributing individual species. Our formulation is flexible and applicable to a wide range of taxa. It possesses a number of desirable features, including:
1) it provides a natural way to incorporate the sporadic unavailability of data;
2) it can incorporate variation between years and species in the precision with which the individual species’ indices are estimated, and
3) it allows the direct incorporation of smoothing over time. Furthermore, the same algorithm can be adopted for cases based on count (abundance) or ‘presence-absence’ (geographical range or distribution) data - only the subsequent interpretation differs. Model fitting is straightforward in either Bayesian or classical implementations, the latter following from efficient hidden Markov modelling. The procedure removes the need for bootstrapping, which can be prohibitive when huge volumes of data are available. We illustrate these desirable properties through the use of simulated data, and by applying our method to a suite of national-scale data sets from the UK.
Dennis, E., Kery, M., Morgan, B., Coray, A., Schaub, M. and Baur, B. (2019). Integrated Modeling of Insect Population Dynamics at Two Temporal Scales. University of Kent.1. Population size of species with birth-pulse life-cycles varies both within and between seasons, but most population dynamics models ignore the former and assume that a population can be characterised adequately by a single number within a season. However, within-season dynamics can be too substantial to be ignored when modelling dynamics between seasons. Typical examples are insect populations or migratory animals. Numerous models for only between-season dynamics exist, but very few have combined dynamics at both temporal scales.
2. We extend the models of Dennis et al. (2016b) in two directions: we adapt them for a generation time >1 year and fit them as an integrated population model for multiple data types, by maximising a joint likelihood for time-series of population counts of unmarked individuals and capture-recapture data from a smaller sample of sites with marked individuals. We analyse annual monitoring data for the endangered flightless beetle Iberodorcadion fuliginator from 17 populations in the Upper Rhine Valley for 1998–2016, with a 2-year life cycle. Standard tools of classical statistics are used for model fitting and comparison and a concentrated likelihood approach provides computational efficiency.
3. The additional information introduced by the capture-recapture data makes the population model more robust and also enables true, rather than relative, abundance to be estimated. Fitting a dynamic stopover model provides estimates of survival and phenology parameters within a season, as well as productivity between seasons. For I. fuliginator, we demonstrate a population decline since 1998 and how this links with productivity, which is affected by temperature. A delayed mean emergence date in recent years is also shown.
4. A main point of interest in our work is the focus on the two temporal scales at which perhaps most animal populations vary: in the short-term, a population is seldom ever truly closed even within a single season, and in the long term (between seasons) it never is. Hence models such as ours may serve as a template for a very general description of population dynamics in many species. This includes rare species with limited data sets, for which there is a general lack of population dynamic models, yet conservation actions may greatly benefit from this kind of models.