A Bayesian inference framework to reconstruct transmission trees using epidemiological and genetic data

The accurate identification of the route of transmission taken by an infectious agent through a host population is critical to understanding its epidemiology and informing measures for its control. However, reconstruction of transmission routes during an epidemic is often an underdetermined problem: data about the location and timings of infections can be incomplete, inaccurate, and compatible with a large number of different transmission scenarios. For fast-evolving pathogens like RNA viruses, inference can be strengthened by using genetic data, nowadays easily and affordably generated. However, significant statistical challenges remain to be overcome in the full integration of these different data types if transmission trees are to be reliably estimated. We present here a framework leading to a bayesian inference scheme that combines genetic and epidemiological data, able to reconstruct most likely transmission patterns and infection dates. After testing our approach with simulated data, we apply the method to two UK epidemics of Foot-and-Mouth Disease Virus (FMDV): the 2007 outbreak, and a subset of the large 2001 epidemic. In the first case, we are able to confirm the role of a specific premise as the link between the two phases of the epidemics, while transmissions more densely clustered in space and time remain harder to resolve. When we consider data collected from the 2001 epidemic during a time of national emergency, our inference scheme robustly infers transmission chains, and uncovers the presence of undetected premises, thus providing a useful tool for epidemiological studies in real time. The generation of genetic data is becoming routine in epidemiological investigations, but the development of analytical tools maximizing the value of these data remains a priority. Our method, while applied here in the context of FMDV, is general and with slight modification can be used in any situation where both spatiotemporal and genetic data are available

Modélisation stochastique de la croissance et du développement du système racinaire de jeunes pêchers. I. Estimation et validation du modèle

Nous avons étudié le développement racinaire de jeunes semis de pêcher (Prunus persica variété GF 305). Pour ce faire, 45 arbres ont été cultivés pendant 6 semaines sur perlite. Tous les 5 jours, 5 plants ont été dépotés. La longueur et la distance à la base de l'axe qui le porte ont été mesurées pour chacun de leurs axes racinaires. La croissance de chaque axe a été modélisée par une fonction puissance de son âge. Les courbes de croissance d'un même ordre de ramification sont affines. Le coefficient d'affinité dépend de ce que nous avons appelé la «vigueur» de la racine. Le processus de ramification a été modélisé par un processus de Poisson temporel à paramètre aléatoire (mixed Poisson). L'étude statistique du modèle montre une variabilité importante de la vigueur pour les axes d'ordre 2, 3 et 4. De l'ordre 1 vers l'ordre 4, la croissance évolue progressivement du type indéfini vers le type défini, et la vitesse de croissance diminue. Parallèlement, l'intensité du processus de ramification diminue. Ce modèle nous permet de décrire en moyenne et en variabilité les cinétiques de variables globales comme la longueur totale ou le nombre de racines d'un ordre donné. Il nous a aussi permis d'évaluer la sensibilité de ce type de modèle au choix des lois ou distributions des variables aléatoires utilisées pour décrire la variabilité observée.Stochastic modeling of growth and development of the root system of young peach tree seedlings. I. Estimation and validation of the model. The growth and branching of the root system of young peach tree seedlings (Prunus persica cultivar GF 305) have been studied. Forty-five seedlings were grown on perlite during 6 weeks. Five plants were dug out every 5 days and their root axes length and position measured. The growth of each axis has been modeled using a power function depending on its age. For a given branching order, the growth curves of all the axes are proportional. The proportionality coefficient depends on a root growth potential ("vigor"). The branching process has been modeled using a temporal Poisson point process with random parameter (mixed Poisson). The estimation procedure has shown a great variability of the root growth potential for the branching orders number 2, 3 and 4. From order 1 to order 4, root growth evolved from an indefinite type to a definite type and the growth rate decreased. Similarly, the intensity of the branching process decreased from order 1 to order 3. Our model allowed us to describe the mean and variability of the kinetics of global state variables such as total root length and total root number of a given branching order. It also allowed us to analyse the sensitivity of such a model to the choice of laws of the random variables used to describe the observed variabilities

Parametric estimation of a boolean segment process with stochastic restoration estimation

We propose a stochastic restoration estimation (SRE) algorithm to estimate the parameters of the length distribution of a boolean segment process. A boolean segment process is a stochastic process obtained by considering the union of independent random segments attached to random points independently scattered on the plane. Each iteration of the SRE algorithm has two steps: first, censored segments are restored; second, based on these restored data, parameter estimations are updated. With a usually straightforward implementation, this algorithm is particularly interesting when censoring effects are difficult to take into account. We illustrate this method in two situations where the parameter of interest is either the mean of the segment length distribution or the variance of its logarithm. Its application to vine shoot length distribution estimation is presented. © 2000 American Statistical Association, Institute of Mathematical Statistics, and Inreiface Foundation of North America.link_to_subscribed_fulltex

Land heterogeneity stimulates intake rate during grazing trips

International audienc

Modélisation probabiliste de la disposition dans le plan horizontal des racines adventives autour de la tige de maïs (Zea mays L)

La disposition spatiale des racines primaires du maïs autour de la tige est décrite par un modèle statistique basé sur un processus de Gibbs et un processus markovien. L'hypothèse de base sur laquelle repose le modèle porte sur la définition d'un potentiel d'interaction entre paires de racines situées sur un même entre-nœud et sur 2 entre-nœuds successifs. La disposition des racines sur un entre-nœud donné est alors dépendante d'un potentiel global défini comme la somme de ces potentiels d'interaction et d'un potentiel principal, lié au nombre de racines de l'entre-noeud. Il nous permet ainsi de résumer et de quantifier les observations angulaires sur les entre-nœuds 2-6 au travers d'un faible nombre de paramètres significatifs (23). L'étude effectuée a montré une bonne adéquation des résultats du modèle avec les données observées. On montre que les positions des racines situées sur un même entre-noeud comme celles situées sur 2 entre-nœuds successifs ne sont pas indépendantes. Le potentiel d'interaction de 2 racines situées sur 2 entre-nœuds successifs est d'environ 75% du potentiel d'interaction entre 2 racines du même entre-nœud tant en intensité maximale qu'en portée.Probabilistic modeling of primary root arrangement in the horizontal plane around the maize stem. The spatial arrangement of the maize roots around the stem in the horizontal plane is described by way of a statistical model. Based upon a Gibbs process and a markovian hypothesis, it allows us to summarize and quantify the angular observations on internodes 2-6 through a small number of significant parameters (23). The basic assumption of the model is that an interaction potential between 2 roots on a single internode and between 2 roots on 2 successive internodes can be defined. For 2 roots on the same internode (respectively 2 successive internodes) separated by an angle θ, the interaction potential is defined as if |θ| < a (resp < c), V (θ) = 0 if |θ| ≥ a (resp ≥ c). The parameters a, b, c and d depend on the internodes. The parameter a (resp c) characterizes the range of the interaction, b (resp d) its intensity. The disposition of the roots of an internode is then dependent upon the total potential, defined as the sum of the interaction potentials and of a principal term depending on the number of roots on the internode. Simulation studies show a good fit between the results of the model and the actual data. This is the case for the distribution of the number of roots on each internode (fig 3 and table III). Angular distributions between actual and simulated data have also been compared. These are the angle between 2 successive roots on a single internode (figs 4 and 5) and the radio α/β where 2 β is the angle between 2 successive roots on a single internode and a is the angle of the bissectrix of β and a root on the next internode whose position is between the 2 preceeding roots. It is shown that both roots on the same internode and on 2 successive internodes are interacting (table II). More particularly, the interaction potential between 2 roots on successive internodes is about 75% of the interaction potential between 2 roots on the same internode

Modélisation probabiliste de la disposition dans le plan horizontal des racines adventives autour de la tige de maïs (Zea mays L)

La disposition spatiale des racines primaires du maïs autour de la tige est décrite par un modèle statistique basé sur un processus de Gibbs et un processus markovien. L'hypothèse de base sur laquelle repose le modèle porte sur la définition d'un potentiel d'interaction entre paires de racines situées sur un même entre-nœud et sur 2 entre-nœuds successifs. La disposition des racines sur un entre-nœud donné est alors dépendante d'un potentiel global défini comme la somme de ces potentiels d'interaction et d'un potentiel principal, lié au nombre de racines de l'entre-noeud. Il nous permet ainsi de résumer et de quantifier les observations angulaires sur les entre-nœuds 2-6 au travers d'un faible nombre de paramètres significatifs (23). L'étude effectuée a montré une bonne adéquation des résultats du modèle avec les données observées. On montre que les positions des racines situées sur un même entre-noeud comme celles situées sur 2 entre-nœuds successifs ne sont pas indépendantes. Le potentiel d'interaction de 2 racines situées sur 2 entre-nœuds successifs est d'environ 75% du potentiel d'interaction entre 2 racines du même entre-nœud tant en intensité maximale qu'en portée.Probabilistic modeling of primary root arrangement in the horizontal plane around the maize stem. The spatial arrangement of the maize roots around the stem in the horizontal plane is described by way of a statistical model. Based upon a Gibbs process and a markovian hypothesis, it allows us to summarize and quantify the angular observations on internodes 2-6 through a small number of significant parameters (23). The basic assumption of the model is that an interaction potential between 2 roots on a single internode and between 2 roots on 2 successive internodes can be defined. For 2 roots on the same internode (respectively 2 successive internodes) separated by an angle θ, the interaction potential is defined as if |θ| < a (resp < c), V (θ) = 0 if |θ| ≥ a (resp ≥ c). The parameters a, b, c and d depend on the internodes. The parameter a (resp c) characterizes the range of the interaction, b (resp d) its intensity. The disposition of the roots of an internode is then dependent upon the total potential, defined as the sum of the interaction potentials and of a principal term depending on the number of roots on the internode. Simulation studies show a good fit between the results of the model and the actual data. This is the case for the distribution of the number of roots on each internode (fig 3 and table III). Angular distributions between actual and simulated data have also been compared. These are the angle between 2 successive roots on a single internode (figs 4 and 5) and the radio α/β where 2 β is the angle between 2 successive roots on a single internode and a is the angle of the bissectrix of β and a root on the next internode whose position is between the 2 preceeding roots. It is shown that both roots on the same internode and on 2 successive internodes are interacting (table II). More particularly, the interaction potential between 2 roots on successive internodes is about 75% of the interaction potential between 2 roots on the same internode