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SummaryWe propose a new method to estimate the ratio between the basic reproduction numbers of a newly emerged variant and the one currently dominating. We use public data of two kinds: the proportions of the daily infected from each strain obtained from a random sample that has been sequenced, and the epidemic curves of total infections and recoveries. Our method is based on a new discrete-time SIR model with two strains, considered both in the deterministic and stochastic versions. In the deterministic case we use maximum likelihood, while in the stochastic setting, since we need to reconstruct the missing incidence and prevalence information of the new variant, we decided to use a hierarchical Bayesian hidden Markov model. This new methodology is applied to data from the Piedmont Italian region in December-January 2022, when the Omicron variant started to be observed and quickly became prevalent. With both approaches, we obtain an estimate of the contagiousness ratio that is consistent with other studies specifically designed for the aim.

In this work, we propose a model that can be used to infer the behaviour of multiple animals. Our proposal is defined as a set of hidden Markov models that are based on the sticky hierarchical Dirichlet process, with a shared base-measure, and a step and turn with an attractive point (STAP) emission distribution. The latent classifications are representative of the behaviour assumed by the animals, which is described by the STAP parameters. Given the latent classifications, the animals are independent. As a result of the way we formalize the distribution over the STAP parameters, the animals may share, in different behaviours, the set or a subset of the parameters, thereby allowing us to investigate the similarities between them. The hidden Markov models, based on the Dirichlet process, allow us to estimate the number of latent behaviours for each animal, as a model parameter. This proposal is motivated by a real data problem, where the global positioning system (GPS) coordinates of six Maremma Sheepdogs have been observed. Among the other results, we show that four dogs share most of the behaviour characteristics, while two have specific behaviours.

Simple Summary Efficiently addressing human-large carnivore conflicts is a conservation issue of increasing relevance, especially in human-dominated landscapes where impact on rural economies generates negative attitudes towards large carnivores and their conservation. We quantified patterns of bear impact on farms and the costs of compensation from 2005 to 2015 in the Abruzzo Lazio and Molise National Park (central Italy), an historical stronghold of the relict and highly imperiled Apennine brown bear population, where the park authority has been adopting conflict management approaches since the 1960s. Although the compensation program is rather costly (1490 ± 589 €/bear/year), the park policy has been increasingly integrated with prevention incentives, managing to effectively avert further increases in bear damages during the study period. Concurrently, local residents generally share a positive attitude towards bears, and the number of illegally killed bears decreased in the last decade. Despite this, our findings indicate there is still room for improvement in local conflict management, and that a more efficient use of conservation funds would benefit from increased monitoring, integrated prevention, conditional compensation, and participatory processes. Lessons learned from areas of historical coexistence between humans and large carnivores provide critical insights to design successful management strategies in areas of recent and future recolonisation by large carnivores. Abstract Human-carnivore conflicts are a major conservation issue. As bears are expanding their range in Europe’s human-modified landscapes, it is increasingly important to understand, prevent, and address human-bear conflicts and evaluate mitigation strategies in areas of historical coexistence. Based on verified claims, we assessed costs, patterns, and drivers of bear damages in the relict Apennine brown bear population in the Abruzzo Lazio and Molise National Park (PNALM), central Italy. During 2005–2015, 203 ± 71 (SD) damage events were verified annually, equivalent to 75,987 ± 30,038 €/year paid for compensation. Most damages occurred in summer and fall, with livestock depredation, especially sheep and cattle calves, prevailing over other types of damages, with apiaries ranking second in costs of compensation. Transhumant livestock owners were less impacted than residential ones, and farms that adopted prevention measures loaned from the PNALM were less susceptible to bear damages. Livestock farms chronically damaged by bears represented 8 ± 3% of those annually impacted, corresponding to 24 ± 6% of compensation costs. Further improvements in the conflict mitigation policy adopted by the PNALM include integrated prevention, conditional compensation, and participatory processes. We discuss the implications of our study for Human-bear coexistence in broader contexts.

The description of the pattern of livestock movements between herds provides essential information for both improving risk-based surveillance and to understand the likely spread of infectious diseases. This study provides a description of the temporal pattern of pig movements recorded in Italy on a 4-year period (2013–2016). Data, provided by the National Livestock registry, were described by social network analysis and the application of a walk-trap algorithm for community detection. Our results show a highly populated community located in Northern Italy, which is the focal point of the Italian industrial pig production and as a general pattern an overall decline of medium and backyard farms and an increase in the number of large farms, in agreement with the trend observed by other EU pig-producing countries. A seasonal pattern of all the parameters evaluated, including the number of active nodes in both the intensive and smaller production systems, emerged: that is characterized by a higher number of movements in spring and autumn, linked with the breeding and production cycle as pigs moved from the growing to the finishing phase and with periods of increased slaughtering at Christmas and Easter. The same pattern was found when restricting the analysis to imported pig batches. Outbreaks occurring during these periods would have a greater impact on the spread of infectious diseases; therefore, targeted surveillance may be appropriate. Finally, potential super-spreader nodes have been identified and represent 0.47% of the total number of pig holdings (n = 477). Those nodes are present during the whole study period with a similar ranking in their potential of being super-spreaders. Most of them were in Northern Italy, but super-spreaders with high mean out-degree centrality were also located in other Regions. Seasonality, communities and super-spreaders should be considered when planning surveillance activity and when applying disease control strategies.

GPS technology is currently easily accessible to researchers, and many animal movement datasets are available. Two of the main features that a model which describes an animal's path can possess are directional persistence and attraction to a point in space. In this work, we propose a new approach that can have both characteristics. Our proposal is a hidden Markov model with a new emission distribution. The emission distribution models the two aforementioned characteristics, while the latent state of the hidden Markov model is needed to account for the behavioral modes. We show that the model is easy to implement in a Bayesian framework. We estimate our proposal on the motivating data that represent GPS locations of a Maremma Sheepdog recorded in Australia. The obtained results are easily interpretable and we show that our proposal outperforms the main competitive model.

SummaryWe here propose a hierarchical Bayesian model to infer RNA synthesis, processing, and degradation rates from sequencing data, based on an ordinary differential equation system that models the RNA life cycle. We parametrize the latent kinetic rates, that rule the system, with a novel functional form, and estimate their parameters through 6 Dirichlet process mixture models. Owing to the complexity of this approach, we are able to simultaneously perform inference, clustering and model selection. We apply our method to investigate transcriptional and post-transcriptional responses of murine fibroblasts to the activation of proto-oncogene Myc. Our approach uncovers simultaneous regulations of the rates, which had not previously been observed in this biological system.

The predictive probability of success of a future clinical trial is a key quantitative tool for decision-making in drug development. It is derived from prior knowledge and available evidence, and the latter typically comes from the accumulated data on the clinical endpoint of interest in previous clinical trials. However, a surrogate endpoint could be used as primary endpoint in early development and, usually, no or limited data are collected on the clinical endpoint of interest. We propose a general, reliable, and broadly applicable methodology to predict the success of a future trial from surrogate endpoints, in a way that makes the best use of all the available evidence. The predictions are based on an informative prior, called surrogate prior, derived from the results of past trials on one or several surrogate endpoints. If available, in a Bayesian framework, this prior could be combined with data from past trials on the clinical endpoint of interest. Two methods are proposed to address a potential discordance between the surrogate prior and the data on the clinical endpoint. We investigate the patterns of behavior of the predictions in a comprehensive simulation study, and we present an application to the development of a drug in Multiple Sclerosis. The proposed methodology is expected to support decision-making in many different situations, since the use of predictive markers is important to accelerate drug developments and to select promising drug candidates, better and earlier.

Brown bears (Ursus arctos marsicanus) in the Apennines, central Italy, survive in a precarious conservation status but the reproductive performance of the population has never been formally assessed. Each year, from 2006 to 2014, we conducted surveys of females with cubs (FWC) to estimate the minimum number of female bears that reproduced and annual productivity in this bear population. We discriminated unique family groups based on simultaneity of sightings, presence of individually recognizable bears, and ad hoc distance-based rules developed using Global Positioning System relocations from 11 adult female bears in our study population. To estimate the true number of FWC from unique counts, we applied 2 estimators (Chao2, Capwire) known to handle heterogeneity in sighting probabilities relatively well at small sample sizes. Annually, we estimated 1–6 ( = 3.9 ± 1.5 SD) unique FWC and tallied a minimum of 3–11 ( = 7.4 ± 3.0 SD) cubs in the population. No temporal trend in FWC was observed and the...

CircSpaceTime is the only R package, currently available, that implements Bayesian models for spatial and spatio-temporal interpolation of circular data. Such data are often found in applications w...

We introduce a Bayesian multivariate hierarchical framework to estimate a space-time model for a joint series of monthly extreme temperatures and amounts of precipitation. Data are available for 360 monitoring stations over 60 years, with missing data affecting almost all series. Model components account for spatio-temporal correlation and annual cycles, dependence on covariates and between responses. Spatio-temporal dependence is modeled by the nearest neighbor Gaussian process (GP), response multivariate dependencies are represented by the linear model of coregionalization and effects of annual cycles are included by a circular representation of time. The proposed approach allows imputation of missing values and interpolation of climate surfaces at the national level. It also provides a characterization of the so called Italian ecoregions, namely broad and discrete ecologically homogeneous areas of similar potential as regards the climate, physiography, hydrography, vegetation and wildlife. To now, Italian ecoregions are hierarchically classified into 4 tiers that go from 2 Divisions to 35 Subsections and are defined by informed expert judgments. The current climatic characterization of Italian ecoregions is based on bioclimatic indices for the period 1955–2000.

Exotic animal diseases are transboundary hazards, characterized by their capability to cover global distances, affecting animal health and welfare with significant economic losses. Their prevention is complex and requires the dynamic management of potential entry points, transmission pathways, and preventative barriers. The well-timed detection of an undefined or unexpected (exotic or re-emerging) threat could minimize the consequences due to onward transmission. As a fit for purpose framework, OIE developed the import risk assessment i.e. a risk assessment model focusing on the entrance of an exotic disease into a geographical area with naive hosts. In this paper, we propose an improvement of the model by integrating it with Social Network Analysis (SNA) accounting for within-country animal movements. Our integrated model has been used as a combined tool to better estimate the spatial probability of the introduction of at least one affected animal in Italian provinces using Bluetongue (BT) as an example. Starting from international country-specific BT prevalence data, the model estimated the probability of introduction to Italy via two different routes of release i.e. the import of infected animals or the release of infected vectors either associated with imported livestock or through windborne dispersion from Africa. The conventional OIE model estimating the probability of BT entering Italy assuming the same release probability for every Italian province was paralleled by a model integrated with outputs from SNA to account for different release probability among provinces based on animal movements. The conventional model predicted a remarkable homogeneity in the risk among the provinces with some peaks only visible during the warmest months. The model incorporating the network analysis predicted the highest risk to be in the North Eastern region of Italy but also highlighted the likely occurrence in a couple of Southern provinces, an output mirroring past occurrence of BT in Italy. Moreover, the sensitivity analysis highlighted the main role for a couple of model parameters i.e. the probability for a vector to become infected and the vaccine coverage, thus suggesting that an extra effort in vaccine campaigns could be envisaged. The ability to measure animal movements by SNA can allow the identification of geographical risk hot spots and therefore the risk-based targeting of the surveillance system.

Modelling the range of prominent vectors of pathogens is a common technique used for planning surveys, building exposure assessment estimations or addressing the impact of future climate scenarios. In most cases the recorded distribution of a target species is used together several environmental variables to capture its potential distribution, ignoring the availability of adequate hosts for the arthropod. In this study we used satellite-recorded, Fourier transformed, environmental variables of ground temperature and vegetation (NDVI) and a large dataset of records of the tick Ixodes ricinus and their hosts. The aim is to evaluate the influence of the contact rates of the ticks with the different hosts and how they impact on the raw, environmental-based distribution of the tick. These effects may alter the estimations of the distribution of the tick under future climate scenarios. This study demonstrated that the relative contribution of the hosts supporting the feeding of the tick life stages dramatically altered the expected distribution of the tick. In the study case, results support that both Passeriformes (Aves) and Rodentia-Soricomorpha contribute in different ways to the colonization of the tick along a large latitudinal gradient. However, Artiodactyla are the main supporters of the tick and enhance its presence in the fringe of its distribution area. Thus, complete data on the distribution of each host contributing to the tick's life cycle and their relative importance for the tick, should be included in the assessment of exposure by arthropods. Other results of the study suggested that more information could be obtained exploring the association of the arthropod to the variables in the environmental niche, instead of the classic approach based on a crude evaluation on the geographical space (maps).

Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animal behavior. ¶ In this work, we propose a new model for interpreting the animal movent as a mixture of characteristic patterns, that we interpret as different behaviors. The probability that the animal is behaving according to a specific pattern, at each time instant, is nonparametrically estimated using the Logistic-Gaussian process. Owing to a new formalization and the way we specify the coregionalization matrix of the associated multivariate Gaussian process, our model is invariant with respect to the choice of the reference element and of the ordering of the probability vector components. We fit the model under a Bayesian framework, and show that the Markov chain Monte Carlo algorithm we propose is straightforward to implement. ¶ We perform a simulation study with the aim of showing the ability of the estimation procedure to retrieve the model parameters. We also test the performance of the information criterion we used to select the number of behaviors. The model is then applied to a real dataset where a wolf has been observed before and after procreation. The results are easy to interpret, and clear differences emerge in the two phases.

The modelling of animal movement is an important ecological and environmental issue. It is well-known that animals change their movement patterns over time, according to observable and unobservable factors. To trace the dynamics of behaviors, to identify factors influencing these dynamics and unobserved characteristics driving intra-subjects correlations, we introduce a time-dependent mixed effects projected normal regression model. A set of animal-specific parameters following a hidden Markov chain is introduced to deal with unobserved heterogeneity. For the maximum likelihood estimation of the model parameters, we outline an expectation–maximization algorithm. A large-scale simulation study provides evidence on model behavior. The data analysis approach based on the proposed model is finally illustrated by an application to a dataset, which derives from a population of Talitrus saltator from the beach of Castiglione della Pescaia (Italy).

We consider modeling of angular or directional data viewed as a linear variable wrapped onto a unit circle. In particular, we focus on the spatio-temporal context, motivated by a collection of wave directions obtained as computer model output developed dynamically over a collection of spatial locations. We propose a novel wrapped skew Gaussian process which enriches the class of wrapped Gaussian process. The wrapped skew Gaussian process enables more flexible marginal distributions than the symmetric ones arising under the wrapped Gaussian process and it allows straightforward interpretation of parameters. We clarify that replication through time enables criticism of the wrapped process in favor of the wrapped skew process. We formulate a hierarchical model incorporating this process and show how to introduce appropriate latent variables in order to enable efficient fitting to dynamic spatial directional data. We also show how to implement kriging and forecasting under this model. We provide a simulation example as a proof of concept as well as a real data example. Both examples reveal consequential improvement in predictive performance for the wrapped skew Gaussian specification compared with the earlier wrapped Gaussian version.

Winds from the North-West quadrant and lack of precipitation are known to lead to an increase of PM10 concentrations over a residential neighborhood in the city of Taranto (Italy). In 2012 the local government prescribed a reduction of industrial emissions by 10% every time such meteorological conditions are forecasted 72 hours in advance. Wind forecasting is addressed using the Weather Research and Forecasting (WRF) atmospheric simulation system by the Regional Environmental Protection Agency. In the context of distributions-oriented forecast verification, we propose a comprehensive model-based inferential approach to investigate the ability of the WRF system to forecast the local wind speed and direction allowing different performances for unknown weather regimes. Ground-observed and WRF-forecasted wind speed and direction at a relevant location are jointly modeled as a 4-dimensional time series with an unknown finite number of states characterized by homogeneous distributional behavior. The proposed model relies on a mixture of joint projected and skew normal distributions with time-dependent states, where the temporal evolution of the state membership follows a first order Markov process. Parameter estimates, including the number of states, are obtained by a Bayesian MCMC-based method. Results provide useful insights on the performance of WRF forecasts in relation to different combinations of wind speed and direction.

We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, that is, circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or skewed cluster-specific distributions for the circular variable. Furthermore, we relax the independence assumption between the circular and linear components observed at the same time. Such an assumption is generally used to alleviate the computational burden involved in the parameter estimation step, but it is hard to justify in empirical applications. We carry out a simulation study using different data-generation schemes to investigate model behavior, focusing on well recovering the hidden structure. Finally, the model is used to fit a real data example on a bivariate time series of wind speed and direction. Copyright © 2015 John Wiley & Sons, Ltd.

Disease incursion and transmission modelling can play an important role in elucidating important pathways and dynamics of transboundary diseases. It is an important pre-requisite for preparedness and rapid response. A model framework has been developed which makes use of global datasets to predict the probability of entry of exotic animal pathogens to European Union (EU) member states (MSs) via some of the most likely routes of introduction: legal trade of livestock and meat products, illegal trade of red meat, wild animal dispersion, windborne vector dispersion and human introduction of pets. The model was designed to be applicable for a wide range of pathogens, many of which have limited data. We demonstrate its application through four case study pathogens: African swine fever, Classical swine fever, Bluetongue and classical rabies. The model results highlight the differences in probability between EU MSs; the absolute values for entry via a given route differed across MSs whilst different pathogens were predicted as having the highest probability of entry for the same route across MSs. Scenario analyses suggested that the probability of entry was heavily influenced by the pathogen prevalence in the country of origin and the extent to which EU MSs pose a risk to each other; the greatest risk was predominantly from countries within the EU. While we believe the input data are obtained from high quality sources, there are still big issues with regards uncertainty in some areas, in particular with regards to prevalence of pathogens in vector populations and consistency of reporting of pathogen prevalence in animals across all countries of the world. Thus, it is inevitable that there is a high degree of uncertainty associated with the absolute values. However, the main strength of the model is the broad range of analyses over pathogens, EU MSs and routes of entry. The model is also relatively easy to update with new data and a web based visualisation tool has been developed which allows users to interrogate the results of the model. As such, we believe that the model proposed here can be a useful quantitative complement to current qualitative early warning systems, helping to drive risk-based surveillance activities, by providing detailed quantitative comparisons to indicate which pathogens are most likely to enter the EU, by which route and into which areas within Europe.

The effects of scuba diving activities on coralligenous concretions builders in the Mediterranean Sea are reported for a non-marine protected area (non-MPA). Five erect bryozoan species, which are particularly vulnerable due to their fragile structure, were investigated: Adeonella calveti , Myriapora truncata , Pentapora fascialis , Reteporella grimaldii , and Smittina cervicornis . These species were sampled at frequently and rarely visited diving sites to the maximum depths reachable with the most common recreational diving certifications (i.e., 40 m). To do this, a non-destructive photographic sampling technique was used to minimize any impact on the benthic communities. For each sample, the number of colonies, their width, coverage, type of injury and degree of exposure were quantified using image analysis software. The number of species differed between the frequently and rarely visited diving sites, and frequently visited sites had significantly lower number of colonies and reduced colony width. Species-specific response to stress was associated with colony morphology and skeleton rigidity. Both the type of injury and colony position within the coralligenous habitat were affected by the presence of scuba divers. A linear model was proposed to analyse the response of bryozoans to scuba diving pressure. The results reported here suggest that P. fascialis and R. grimaldii could serve as robust species indicators of diving stress.

Circular data arise in many areas of application. Recently, there has been interest in looking at circular data collected separately over time and over space. Here, we extend some of this work to the spatio-temporal setting, introducing space-time dependence. We accommodate covariates, implement full kriging and forecasting, and also allow for a nugget which can be time dependent. We work within a Bayesian framework, introducing suitable latent variables to facilitate Markov chain Monte Carlo (MCMC) model fitting. The Bayesian framework enables us to implement full inference, obtaining predictive distributions for kriging and forecasting. We offer comparison between the less flexible but more interpretable wrapped Gaussian process and the more flexible but less interpretable projected Gaussian process. We do this illustratively using both simulated data and data from computer model output for wave directions in the Adriatic Sea off the coast of Italy.

In this work, we deal with a bivariate time series of wind speed and direction. Our observed data have peculiar features, such as informative missing values, non-reliable measures under a specific condition and interval-censored data, that we take into account in the model specification. We analyze the time series with a non-parametric Bayesian hidden Markov model, introducing a new emission distribution based on the invariant wrapped Poisson, the Poisson and the hurdle density, suitable to model our data. The model is estimated on simulated datasets and on the real data example that motivated this work.

In this paper, we propose a discrete circular distribution obtained by extending the wrapped Poisson distribution. This new distribution, the Invariant Wrapped Poisson (IWP), enjoys numerous advantages: simple tractable density, parameter-parsimony and interpretability, good circular dependence structure and easy random number generation thanks to known marginal/conditional distributions. Existing discrete circular distributions strongly depend on the initial direction and orientation, i.e. a change of the reference system on the circle may lead to misleading inferential results. We investigate the invariance properties, i.e. invariance under change of initial direction and of the reference system orientation, for several continuous and discrete distributions. We prove that the introduced IWP distribution satisfies these two crucial properties. We estimate parameters in a Bayesian framework and provide all computational details to implement the algorithm. Inferential issues related to the invariance properties are discussed through numerical examples on artificial and real data.

The effect of temperature increase on the stock of the deep-sea pink shrimp (Parapenaeus longirostris) was analysed along the western coasts of Italy (North Tyrrhenian–Ligurian Sea: Geographical Sub-Area 9). This crustacean is currently one of the most important commercial species of the trawl fisheries in the Mediterranean Sea. Landings of the species in the North Tyrrhenian–Ligurian Sea have grown consistently during the last years following a rapid increase in the stock size. Since the deep-sea pink shrimp stock is exploited on the same fishing ground of other heavily overexploited stocks in a full mixed and poorly selective fishery, its condition seems to be largely independent of the current fishing exploitation pattern suggesting a positive role of climate change on the dynamic of the stock. To test this hypothesis we investigated the effect of sea surface temperature (SST) on density and distribution of P. longirostris by means of general additive models (GAMs). Two different models were developed for the whole stock and for the recruits (CL The best GAM for the whole stock explained 67.1% of the total deviance, showing a clear increase in density in concomitance with the expansion of the stock northward. We found a significant positive effect of the min SST of all seasons, as expected considering that P. longirostris spawn all year round, with the highest influence played by summer min SST, either in the same or previous year. The best model for recruits explained 64.9% of the total deviance. Recruitment increased linearly with the density of spawners showing a positive temporal trend and an expansion northward. The observed trend in recruitment appeared significantly linked to minimum SST in summer and during the autumn of the previous year, with a positive effect on shrimp density over 23.5 °C and 14 °C respectively. The climate-related changes in recruitment appeared to be the key process driving the dynamics of the stock, involving either higher production or survival in the planktonic stages, or owing to changes in the quality/quantity of nursery habitats.

When a large amount of spatial data is available computational and modeling challenges arise and they are often labeled as “big n problem”. In this work we present a brief review of the literature. Then we focus on two approaches, respectively based on stochastic partial differential equations and integrated nested Laplace approximation, and on the tapering of the spatial covariance matrix. The fitting and predictive abilities of using the two methods in conjunction with Kriging interpolation are compared in a simulation study.