rGAI: An R package for fitting the generalized abundance index to seasonal count data.

The generalized abundance index (GAI) provides a useful tool for estimating relative population sizes and trends of seasonal invertebrates from species' count data and offers potential for inferring which external factors may influence phenology and demography through parametric descriptions of seasonal variation. We provide an R package that extends previous software with the ability to include covariates when fitting parametric GAI models, where seasonal variation is described by either a mixture of Normal distributions or a stopover model which provides estimates of life span. The package also generalizes the models to allow any number of broods/generations in the target population within a defined season. The option to perform bootstrapping, either parametrically or nonparametrically, is also provided. The new package allows models to be far more flexible when describing seasonal variation, which may be dependent on site-specific environmental factors or consist of many broods/generations which may overlap, as demonstrated by two case studies. Our open-source software, available at https://github.com/calliste-fagard-jenkin/rGAI, makes these extensions widely and freely available, allowing the complexity of GAI models used by ecologists and applied statisticians to increase accordingly.

A general framework for modeling population abundance data.

Time-series data resulting from surveying wild animals are often described using state-space population dynamics models, in particular with Gompertz, Beverton-Holt, or Moran-Ricker latent processes. We show how hidden Markov model methodology provides a flexible framework for fitting a wide range of models to such data. This general approach makes it possible to model abundance on the natural or log scale, include multiple observations at each sampling occasion and compare alternative models using information criteria. It also easily accommodates unequal sampling time intervals, should that possibility occur, and allows testing for density dependence using the bootstrap. The paper is illustrated by replicated time series of red kangaroo abundances, and a univariate time series of ibex counts which are an order of magnitude larger. In the analyses carried out, we fit different latent process and observation models using the hidden Markov framework. Results are robust with regard to the necessary discretization of the state variable. We find no effective difference between the three latent models of the paper in terms of maximized likelihood value for the two applications presented, and also others analyzed. Simulations suggest that ecological time series are not sufficiently informative to distinguish between alternative latent processes for modeling population survey data when data do not indicate strong density dependence.

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 required.

Using citizen science butterfly counts to predict species population trends.

Citizen scientists are increasingly engaged in gathering biodiversity information, but trade-offs are often required between public engagement goals and reliable data collection. We compared population estimates for 18 widespread butterfly species derived from the first 4 years (2011-2014) of a short-duration citizen science project (Big Butterfly Count [BBC]) with those from long-running, standardized monitoring data collected by experienced observers (U.K. Butterfly Monitoring Scheme [UKBMS]). BBC data are gathered during an annual 3-week period, whereas UKBMS sampling takes place over 6 months each year. An initial comparison with UKBMS data restricted to the 3-week BBC period revealed that species population changes were significantly correlated between the 2 sources. The short-duration sampling season rendered BBC counts susceptible to bias caused by interannual phenological variation in the timing of species' flight periods. The BBC counts were positively related to butterfly 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. Overall, citizen science data obtained using a simple sampling protocol produced comparable estimates of butterfly species abundance to data collected through standardized monitoring methods. Although caution is urged in extrapolating from this U.K. study of a small number of common, conspicuous insects, we found that mass-participation citizen science can simultaneously contribute to public engagement and biodiversity monitoring. Mass-participation citizen science is not an adequate replacement for standardized biodiversity monitoring but may extend and complement it (e.g., through sampling different land-use types), as well as serving to reconnect an increasingly urban human population with nature.

Efficient occupancy model-fitting for extensive citizen-science data.

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.

Bringing It All Together: Multi-species Integrated Population Modelling of a Breeding Community.

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. Supplementary materials accompanying this paper appear on-line. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary materials for this article are available at 10.1007/s13253-017-0279-4.

A generalized 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 rôle. 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.

Computational aspects of N-mixture models.

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.

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.

Does your species have memory? Analyzing capture-recapture data with memory models.

We examine memory models for multisite capture-recapture data. This is an important topic, as animals may exhibit behavior that is more complex than simple first-order Markov movement between sites, when it is necessary to devise and fit appropriate models to data. We consider the Arnason-Schwarz model for multisite 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 multisite capture-recapture data need to incorporate memory. 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 multisite 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. Memory models for multisite capture-recapture data can be highly complex and difficult to fit to data. We emphasize the importance of a structured approach to modeling 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 multisite capture-recapture data need to incorporate memory.

A comparison of abundance estimates from extended batch-marking and Jolly-Seber-type experiments.

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 employing 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.

Breeding together: modeling synchrony in productivity in a seabird community.

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.

Parameter redundancy in mark-recovery models.

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.

Expression of neuregulin 4 splice variants in normal human tissues and prostate cancer and their effects on cell motility.

The neuregulin 4 gene encodes at least five different variants (designated A1, A2, B1, B2 and B3) produced as a result of alternative splicing. We have determined their sites of expression in normal human adult tissues using isoform-specific antibodies. Their expression is cell type specific and differs in subcellular location suggesting that they may have varied functions in these contexts. We have shown in a panel of prostate cancers that each form is present to differing degrees, and that principal component analysis indicates that there are three patterns of expression. Some isoforms were positively correlated with high prostate-specific antigen levels and others were inversely associated with Gleason score. Synthetic, refolded A forms promoted lamellipodia and filopodia formation in cells expressing the ErbB4 (CTa) receptor and stimulated cell motility in wound healing assays. The data suggest that the different forms have varied sites of expression and function, and this includes effects on cell architecture and motility.

Multistate mark-recapture model selection using score tests.

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.

Continuous covariates in mark-recapture-recovery analysis: a comparison of methods.

Time varying, individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured. We examine three methods to incorporate time varying, individual covariates of the survival probabilities into the analysis of data from mark-recapture-recovery experiments: deterministic imputation, a Bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history, and a conditional approach considering only the events for which the associated covariate data are completely observed (the trinomial model). After describing the three methods, we compare results from their application to the analysis of the effect of body mass on the survival of Soay sheep (Ovis aries) on the Isle of Hirta, Scotland. Simulations based on these results are then used to make further comparisons. We conclude that both the trinomial model and Bayesian imputation method perform best in different situations. If the capture and recovery probabilities are all high, then the trinomial model produces precise, unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate. In contrast, the Bayesian imputation method performs substantially better when capture and recovery probabilities are low, provided that the specified model of the covariate is a good approximation to the true data-generating mechanism.

Estimating population size and hidden demographic parameters with state-space modeling.

Recent research has shown how process variability and measurement error in ecological time series can be separated using state-space modeling techniques to combine individual-based data with population counts. We extend the current maximum likelihood approaches to allow the incorporation of sex- and age-dependent counts and provide an application to data from a population of Soay sheep living on the St. Kilda archipelago. We then empirically evaluate the performance and potential of the method by sequentially omitting portions of the data available. We show that the use of multivariate time series extends the power of the state-space modeling approach. The variance of measurement error was found to be smaller for males and the sex ratio of lambs to be skewed toward females and constant over time. Our results indicated that demographic parameters estimated using state-space modeling without relevant individual-based data were in close agreement with those obtained from mark-recapture-recovery analyses alone. Similarly, estimates of population size obtained when the corresponding count observations were unavailable were close to those from the entire data set. We conclude that the approach illustrated here has great potential for estimating hidden demographic parameters, planning studies on population monitoring, and estimating both historical and future population size.

The number and transmission of [PSI] prion seeds (Propagons) in the yeast Saccharomyces cerevisiae.

BACKGROUND: Yeast (Saccharomyces cerevisiae) prions are efficiently propagated and the on-going generation and transmission of prion seeds (propagons) to daughter cells during cell division ensures a high degree of mitotic stability. The reversible inhibition of the molecular chaperone Hsp104p by guanidine hydrochloride (GdnHCl) results in cell division-dependent elimination of yeast prions due to a block in propagon generation and the subsequent dilution out of propagons by cell division. PRINCIPAL FINDINGS: Analysing the kinetics of the GdnHCl-induced elimination of the yeast [PSI+] prion has allowed us to develop novel statistical models that aid our understanding of prion propagation in yeast cells. Here we describe the application of a new stochastic model that allows us to estimate more accurately the mean number of propagons in a [PSI+] cell. To achieve this accuracy we also experimentally determine key cell reproduction parameters and show that the presence of the [PSI+] prion has no impact on these key processes. Additionally, we experimentally determine the proportion of propagons transmitted to a daughter cell and show this reflects the relative cell volume of mother and daughter cells at cell division. CONCLUSIONS: While propagon generation is an ATP-driven process, the partition of propagons to daughter cells occurs by passive transfer via the distribution of cytoplasm. Furthermore, our new estimates of n(0), the number of propagons per cell (500-1000), are some five times higher than our previous estimates and this has important implications for our understanding of the inheritance of the [PSI+] and the spontaneous formation of prion-free cells.

Exploring individual quality in a wild population of red deer.

1. A wide range of measures are used to quantify 'individual quality', with the term often used but not defined. 2. Here we use detailed data from a population of red deer (Cervus elaphus) to assess whether frequently used measures of individual quality are well correlated, and therefore likely to lead to comparable ecological and evolutionary insight in analyses. 3. Correlations between measures were usually small, indicating that individuals may be considered high quality for one trait, but low quality for another. 4. By using principal component analysis, we illustrate that there are potentially many varied individual life-history tactics within a population. 5. This variation in tactics makes it challenging to characterize individual quality as a simple scalar; measures of heterogeneity in ecological studies should therefore be both species and question specific.

A note on simplifying likelihoods for site occupancy models.

We show how a simple reparameterization can reduce the number of parameters that need to be estimated by numerical maximum likelihood in site occupancy models. Three examples are provided.