Open models for removal data

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

A generalised abundance index for seasonal invertebrates

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

Dynamic models for longitudinal butterfly data

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

Hidden Markov Models for Extended Batch Data

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 require

Cost-efficient effort allocation for camera-trap occupancy surveys of mammals

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 (? 0.5). The most expensive survey scenarios occur for elusive (p 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

Fast Bayesian inference for large occupancy datasets

In recent years, the study of species’ occurrence has benefited from the increased availability of large-scale citizen-science data. Whilst abundance data from standardized monitoring schemes are biased towards well-studied taxa and locations, opportunistic data are available for many taxonomic groups, from a large number of locations and across long timescales. Hence, these data provide opportunities to measure species’ changes in occurrence, particularly through the use of occupancy models, which account for imperfect detection. These opportunistic datasets can be substantially large, numbering hundreds of thousands of sites, and hence present a challenge from a computational perspective, especially within a Bayesian framework. In this paper, we develop a unifying framework for Bayesian inference in occupancy models that account for both spatial and temporal autocorrelation. We make use of the P´olyaGamma scheme, which allows for fast inference, and incorporate spatio-temporal random effects using Gaussian processes (GPs), for which we consider two efficient approximations: Subset of Regressors and Nearest neighbour GPs. We apply our model to data on two UK butterfly species, one common and widespread and one rare, using records from the Butterflies for the New Millennium database, producing occupancy indices spanning 45 years. Our framework can be applied to a wide range of taxa, providing measures of variation in species’ occurrence, which are used to assess biodiversity change

Functional data analysis of multi-species abundance and occupancy data sets

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

Modeling the bacterial protein toxin, pneumolysin, in its monomeric and oligomeric form

Pneumolysin is a member of the family of related bacterial thiol-activated toxins, which share structural similarities and a proposed common cytolytic mechanism. Currently the molecular mechanism of membrane damage caused by these toxins remains a matter of controversy. A prerequisite for defining this mechanism is a detailed knowledge of the monomeric and oligomeric pneumolysin structures. We present for the first time details of the monomeric structure of a thiol-activated toxin, pneumolysin. Electron microscope images of metal-shadowed pneumolysin monomers show an asymmetric molecule composed of four domains. We have studied the conformation of pneumolysin monomer by low resolution hydrodynamic bead modeling procedures. The bead model dimensions and shape are derived solely from the electron micrographs. The bead model has been evaluated in terms of the predicted solution properties, which in turn have been compared to the experimental values of the sedimentation coefficient, s(20,w)0, obtained by analytical ultracentrifugation and the intrinsic viscosity, [eta]. Pneumolysin oligomers, observed as ring- and arc-shaped structures, were also examined by electron microscopy. Metal shadowing and negative staining methods were used to establish the overall dimensions of the oligomer and were used to produce a morphological model for the oligomer, incorporating monomer subunits based on the hydrodynamic bead model

Trends and indicators for quantifying moth abundance and occupancy in Scotland

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

Statistical ecology comes of age

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. Important 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. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.Peer reviewe