The paper Hidden Markov Models for Extended Batch Data by Laura L. E. Cowen, Panagiotis Besbeas, Byron J. T. Morgan and Carl J. Schwarz has been published online early in Biometrics

Summary. 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 analysed. We provide ways of modelling 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 maximisation. Likelihoods for marked and unmarked individuals can easily be combined using integrated population modelling. 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 analysed 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 demonstratestheir excellent performance and efficiency. This is especially notable due to the large numbers of hidden states that may be typically required​

The following paper has been recently published in PLOS ONE and is available online at: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0174433

Efficient occupancy model-fitting for extensive citizen-science data

Emily B. Dennis, Byron J.T. Morgan, Stephen N. Freeman, Martin S. Ridout, Tom M. Brereton, Richard Fox, Gary D. Powney & David B. Roy

Abstract:

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.

Emily and Byron (with David Roy and Tom Brereton) have had the paper Urban indicators for UK butterflies published in Ecological Indicators. The paper is available at:

http://www.sciencedirect.com/science/article/pii/S1470160X17300092

The paper has been covered in the press including:

https://www.theguardian.com/environment/2017/feb/16/urban-butterfly-declines-69-compared-to-45-drop-countryside

http://www.dailymail.co.uk/sciencetech/article-4229306/Paving-gardens-hits-city-butterflies.html

https://www.kent.ac.uk/news/environment/12510/the-statistics-behind-the-urban-decline-of-butterflies

Abstract:

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.

Diana and Rachel’s Paper, Parameter redundancy in discrete state-space and integrated models, is available online early in the Biometrical Journal at http://onlinelibrary.wiley.com/doi/10.1002/bimj.201400239/abstract

Abstract: 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 parametrization 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.