Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

For point patterns observed in natura, spatial heterogeneity is more the rule than the exception. In numerous applications, this can be mathematically handled by the flexible class of log Gaussian Cox processes (LGCPs); in brief, a LGCP is a Cox process driven by an underlying log Gaussian random field (log GRF). This allows the representation of point aggregation, point vacuum and intermediate situations, with more or less rapid transitions between these different states depending on the properties of GRF. Very often, the covariance function of the GRF is assumed to be stationary. In this article, we give two examples where the sizes (that is, the number of points) and the spatial extents of point clusters are allowed to vary in space. To tackle such features, we propose parametric and semiparametric models of non-stationary LGCPs where the non-stationarity is included in both the mean function and the covariance function of the GRF. Thus, in contrast to most other work on inhomogeneous LGCPs, second-order intensity-reweighted stationarity is not satisfied and the usual two step procedure for parameter estimation based on e.g. composite likelihood does not easily apply. Instead we propose a fast three step procedure based on composite likelihood. We apply our modelling and estimation framework to analyse datasets dealing with fish aggregation in a reservoir and with dispersal of biological particles

When group dispersal and Allee effect shape metapopulation dynamics

The dispersal ability of a species will be critical for how population dynamics are realized in spatially structured systems. To date, the effect of group dispersal on metapopulation dynamics is poorly understood. Here, we investigate how group dispersal and Allee effects shape metapopulation dynamics identifying conditions in which group dispersal can be an advantage over independent dispersal. We approach this question by building and analysing a Markovian random walk for metapopulation dynamics including group dispersal and Allee effect. This Markovian random walk is analogous to the discrete-time Stochastic Patch Occupancy Model (SPOM). We find that intermediate group sizes may lead to larger and more sustainable metapopulations in the presence of an Allee effect. Hence, understanding how group size variation and realized (meta) population dynamics are linked offers an exciting future venue for research that is expected to yield key insights into the ecology and evolution of populations occupying spatially structured environments.Peer reviewe

Dating and localizing an invasion from post-introduction data and a coupled reaction-diffusion-absorption model

Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in particular in the intents of reconstructing the past dynamics of the alien organisms and predicting their future spatial extents. Partial differential equations offer a rich and flexible modeling framework that has been applied to a large number of invasions. In this article, we are specifically interested in dating and localizing the introduction that led to an invasion using mathematical modeling, post-introduction data and an adequate statistical inference procedure. We adopt a mechanistic-statistical approach grounded on a coupled reaction-diffusion-absorption model representing the dynamics of an organism in an heterogeneous domain with respect to growth. Initial conditions (including the date and site of the introduction) and model parameters related to diffusion, reproduction and mortality are jointly estimated in the Bayesian framework by using an adaptive importance sampling algorithm. This framework is applied to the invasion of \textit{Xylella fastidiosa}, a phytopathogenic bacterium detected in South Corsica in 2015, France

The impact of within-herd genetic variation upon inferred transmission trees for foot-and-mouth disease virus

Full-genome sequences have been used to monitor the fine-scale dynamics of epidemics caused by RNA viruses. However, the ability of this approach to confidently reconstruct transmission trees is limited by the knowledge of the genetic diversity of viruses that exist within different epidemiological units. In order to address this question, this study investigated the variability of 45 foot-and-mouth disease virus (FMDV) genome sequences (from 33 animals) that were collected during 2007 from eight premises (10 different herds) in the United Kingdom. Bayesian and statistical parsimony analysis demonstrated that these sequences exhibited clustering which was consistent with a transmission scenario describing herd-to-herd spread of the virus. As an alternative to analysing all of the available samples in future epidemics, the impact of randomly selecting one sequence from each of these herds was used to assess cost-effective methods that might be used to infer transmission trees during FMD outbreaks. Using these approaches, 85% and 91% of the resulting topologies were either identical or differed by only one edge from a reference tree comprising all of the sequences generated within the outbreak. The sequence distances that accrued during sequential transmission events between epidemiological units was estimated to be 4.6 nucleotides, although the genetic variability between viruses recovered from chronic carrier animals was higher than between viruses from animals with acute-stage infection: an observation which poses challenges for the use of simple approaches to infer transmission trees. This study helps to develop strategies for sampling during FMD outbreaks, and provides data that will guide the development of further models to support control policies in the event of virus incursions into FMD free countries

A Bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data

We describe a statistical framework for reconstructing the sequence of transmission events between observed cases of an endemic infectious disease using genetic, temporal and spatial information. Previous approaches to reconstructing transmission trees have assumed all infections in the study area originated from a single introduction and that a large fraction of cases were observed. There are as yet no approaches appropriate for endemic situations in which a disease is already well established in a host population and in which there may be multiple origins of infection, or that can enumerate unobserved infections missing from the sample. Our proposed framework addresses these shortcomings, enabling reconstruction of partially observed transmission trees and estimating the number of cases missing from the sample. Analyses of simulated datasets show the method to be accurate in identifying direct transmissions, while introductions and transmissions via one or more unsampled intermediate cases could be identified at high to moderate levels of case detection. When applied to partial genome sequences of rabies virus sampled from an endemic region of South Africa, our method reveals several distinct transmission cycles with little contact between them, and direct transmission over long distances suggesting significant anthropogenic influence in the movement of infected dogs

Classification basée sur des mélanges de modèles hiérarchiques bivariés

International audienceLes approches probabilistes basées sur les modèles de mélange sont de plus en plus utilisées en classification automatique car elles fournissent un cadre formel pour résoudre des problèmes pratiques qui se posent en classification, tels que la détermination du nombre de classes, et permettent d'estimer l'incertitude associée à la classification. Les limites de ces méthodes résident principalement dans le choix de la loi de probabilité des composantes du mélange, qui dépend du type de données et va contraindre la forme des classes. Peu de modèles de mélange ont été étudiés dans le cas multivarié, et il est difficile d'adapter la méthode d'estimation d'une distribution à une autre. Nous proposons une généralisation des méthodes de classification basées sur des modèles de mélange qui : - s'adapte rapidement à des données de type différents (continues, discrètes, binaires, surdispersées), - permet d'obtenir des formes de classe et des structures de corrélation variées, - permet de traiter des données multivariées comportant des observations de plusieurs types. Pour cela nous considérons un modèle hiérarchique, dans lequel la couche cachée est issue d'un mélange de lois gaussiennes bivariées et la couche d'observation est obtenue par une distribution bivariée dont le choix dépend du type de données observées. L'estimation du modèle se fait par un algorithme MCEM

Using early data to estimate the actual infection fatality ratio from COVID-19 in France (Running title: Infection fatality ratio from COVID-19)

The first cases of COVID-19 in France were detected on January 24, 2020. The number of screening tests carried out and the methodology used to target the patients tested do not allow for a direct computation of the real number of cases and the mortality rate.In this report, we develop a 'mechanistic-statistical' approach coupling a SIR ODE model describing the unobserved epidemiological dynamics, a probabilistic model describing the data acquisition process and a statistical inference method. The objective of this model is not to make forecasts but to estimate the real number of people infected with COVID-19 during the observation window in France and to deduce the mortality rate associated with the epidemic.Main results. The actual number of infected cases in France is probably much higher than the observations: we find here a factor x 15 (95%-CI: 4-33), which leads to a 5.2/1000 mortality rate (95%-CI: 1.5 / 1000-11.7/ 1000) at the end of the observation period. We find a R0 of 4.8, a high value which may be linked to the long viral shedding period of 20 days

Strain Diversity and Spatial Distribution Are Linked to Epidemic Dynamics in Host Populations*

The inherently variable nature of epidemics renders predictions of when and where infection is expected to occur challenging. Differences in pathogen strain composition, diversity, fitness, and spatial distribution are generally ignored in epidemiological modeling and are rarely studied in natural populations, yet they may be important drivers of epidemic trajectories. To examine how these factors are linked to epidemics in natural host populations, we collected epidemiological and genetic data from 15 populations of the powdery mildew fungus, Podosphaera plantaginis, on Plantago lanceolata in the angstrom land Islands, Finland. In each population, we tracked spatiotemporal disease progression throughout one epidemic season and coupled our survey of infection with intensive field sampling of the pathogen. We found that strain composition varied greatly among populations in the landscape. Within populations, strain composition was driven by the sequence of strain activity: early-active strains reached higher abundances, leading to consistent strain compositions over time. Co-occurring strains also varied in their contribution to the growth of the local epidemic, and these fitness inequalities were linked to epidemic dynamics: a higher proportion of hosts became infected in populations containing strains that were more similar in fitness. Epidemic trajectories in the populations were also linked to strain diversity and spatial dynamics: higher infection rates occurred in populations containing higher strain diversity, while spatially clustered epidemics experienced lower infection rates. Together, our results suggest that spatial and/or temporal variation in the strain composition, diversity, and fitness of pathogen populations are important factors generating variation in epidemiological trajectories among infected host populations.Peer reviewe

Assessing the Aerial Interconnectivity of Distant Reservoirs of Sclerotinia sclerotiorum

Many phytopathogenic fungi are disseminated as spores via the atmosphere from short to long distances. The distance of dissemination determines the extent to which plant diseases can spread and novel genotypes of pathogens can invade new territories. Predictive tools including models that forecast the arrival of spores in areas where susceptible crops are grown can help to more efficiently manage crop health. However, such models are difficult to establish for fungi with broad host ranges because sources of inoculum cannot be readily identified. Sclerotinia sclerotiorum, the pandemic agent of white mold disease, can attack >400 plant species including economically important crops. Monitoring airborne inoculum of S. sclerotiorum in several French cropping areas has shown that viable ascospores are present in the air almost all the time, even when no susceptible crops are nearby. This raises the hypothesis of a distant origin of airborne inoculum. The objective of the present study was to determine the interconnectivity of reservoirs of S. sclerotiorum from distant regions based on networks of air mass movement. Viable airborne inoculum of S. sclerotiorum was collected in four distinct regions of France and 498 strains were genotyped with 16 specific microsatellite markers and compared among the regions. Air mass movements were inferred using the HYSPLIT model and archived meteorological data from the global data assimilation system (GDAS). The results show that up to 700 km could separate collection sites that shared the same haplotypes. There was low or no genetic differentiation between strains collected from the four sites. The rate of aerial connectivity between two sites varied according to the direction considered. The results also show that the aerial connectivity between sites is a better indicator of the probability of the incoming component (PIC) of inoculum at a given site from another one than is geographic distance. We identified the links between specific sites in the trajectories of air masses and we quantified the frequencies at which the directional links occurred as a proof-of-concept for an operational method to assess the arrival of airborne inoculum in a given area from distant origins

Regression-based ranking of pathogen strains with respect to their contribution to natural epidemics

Peer reviewe