arXiv subjects

Camille Coron

Publications and source records attributed to Camille Coron.

13 recordsLinked to original sources

arXiv2025

Using low-cost sensors to improve NO2 concentration maps derived from physico-chemical models

Urban air quality is a major concern today. Concentrations of pollutants, such as nitrogen dioxide, must be monitored to ensure that they do not exceed hazardous thresholds. For this reason, scarse reference stations, which are generally managed by air quality monitoring associations, are located in major cities. Two recent approaches enable fine-scale mapping of pollutant concentrations. The first relies on deterministic physico-chemical models that incorporate the street network and compute concentration estimates on a grid, producing spatial maps. The second is based on the emergence of low-cost sensors, which enable monitoring organizations to increase the density of their measurement networks. However, these sensors are unreliable and require regular and important calibration. We propose to combine these approaches and improve maps generated by deterministic models by integrating data from multiple sensor networks. Specifically, we model the bias of deterministic models and estimate its parameters using measurements, through a Bayesian nested framework. Our approach simultaneously enables the calibration of low-cost sensors and the correction of deterministic models outputs. This method, although general, is applied to the city of Rouen (France), combining outputs of the physico-chemical model SIRANE (Soulhac et al. 2011) and the measurements provided both by 4 reference monitoring stations and 10 low-cost sensors during December 2022. Results show that the method indeed corrects the concentration maps, reducing the root mean squared error by approximately 12.4%, and that low-cost sensors play an essential role in this correction.

stat.AP↗

arXiv2025

Debiasing physico-chemical models in air quality monitoring by combining different pollutant concentration measures

Air quality monitoring requires to produce accurate estimation of nitrogen dioxide or fine particulate matter concentration maps, at different moments. A typical strategy is to combine different types of data. On the one hand, concentration maps produced by deterministic physicochemical models at urban scale, and on the other hand, concentration measures made at different points, different moments, and by different devices. These measures are provided first by a small number of reference stations, which give reliable measurements of the concentration, and second by a larger number of micro-sensors, which give biased and noisier measurements. The proposed approach consists in modeling the bias of the physicochemical model and estimating the parameters of this bias using all the available concentration measures. Our model relies on a partition of the geographical space of interest into different zones within which the bias is assumed to be modeled by a single affine transformation of the actual concentration. Our approach allows to improve the concentration maps provided by the deterministic models but also to understand the behavior of micro-sensors and their contribution in improving air quality monitoring. We introduce the model, detail its implementation and experiment it through numerical results using datasets collected in Grenoble (France).

stat.AP↗

arXiv2025

Genetic contribution of advantaged ancestors in the biparental Moran model -- finite selection

We study a population of $N$ individuals evolving according to a biparental Moran model with two types, one being advantaged compared to the other. The advantage is conferred by a Mendelian mutation, which reduces the death probability of individuals carrying it. We assume that a proportion $a$ of individuals initially carry this mutation, which therefore eventually gets fixed with high probability. After a long time, we sample a gene uniformly from the population, at a new locus, independent of the locus under selection, and calculate the probability that this gene originated from one of the initially advantaged individuals, when the population size is large. Our theorem provides quantitative insights, such as the observation that under strong viability selection, if only $1\%$ of the individuals are initially advantaged, up to $19\%$ of the population's genome will originate from them after a long time.

math.PR↗

arXiv2024

A periodic Kingman model for the balance between mutation and selection

We consider a periodic extension of the classical Kingman non-linear model (Kingman, 1978) for the balance between selection and mutation in a large population. In the original model, the fitness distribution of the population is modeled by a probability measure on the unit interval evolving through a simple dynamical system in discrete time: selection acts through size-biasing, and the mutation probability and distribution are kept fixed through time. A natural extension of Kingman model is given by a periodic mutation environment; in this setting, we prove the convergence of the fitness distribution along subsequences and find an explicit criterion in terms of the Perron eigenvalue of an appropriately chosen matrix to decide whether an atom emerges at the largest fitness, a phenomenon usually called condensation.

math.PR↗

arXiv2024

Genetic contribution of an advantaged mutant in the biparental Moran model -- finite selection

We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The advantage is due to a mutation, transmitted in a Mendelian way from parent to child that reduces the death probability of individuals carrying it. We assume that initially this mutation is carried by a proportion a of individuals in the population. Once the mutation is fixed, a gene is sampled uniformly in the population, at a locus independent of the locus under selection. We then give the probability that this gene initially comes from an advantaged individual, i.e. the genetic contribution of these individuals, as a function of a and when the population size is large.

math.PR↗

arXiv2022

Genetic contribution of an advantaged mutant in the biparental Moran model

We consider a population of haploid individuals reproducing sexually, i.e. for which the genome of each individual is a random mixture of the genome of its two parents. We assume that initially one individual carries a mutation at one locus, and that individuals carrying this mutation have an advantage regarding genome transmission. Our aim is to study the long time effect of this mutation on the genetic composition of the population, when population size is large.

math.PR↗

arXiv2022

Genetics of the biparental Moran model

Our goal is to study the genetic composition of a population in which each individual has 2 parents, who contribute equally to the genome of their ospring. We use a biparental Moran model, which is characterized by its xed number N of individuals. We x an individual and consider the proportions of the genomes of all individuals living n time steps later, that come from this individual. We rst prove that when n goes to innity, these proportions all converge almost surely towards the same random variable. We then rigorously prove that when N then goes to innity, this random variable multiplied by N (i.e. the stationary weight of any ancestor in the whole population) converges in law towards the mixture of a Dirac measure in 0 and an exponential law with parameter 1/2, and that the weights of several given ancestors are independent.

math.PR↗

arXiv2017

Estimation of species relative abundances and habitat preferences using opportunistic data

We develop a new statistical procedure to monitor, with opportunist data, relative species abundances and their respective preferences for dierent habitat types. Following Giraud et al. (2015), we combine the opportunistic data with some standardized data in order to correct the bias inherent to the opportunistic data collection. Our main contributions are (i) to tackle the bias induced by habitat selection behaviors, (ii) to handle data where the habitat type associated to each observation is unknown, (iii) to estimate probabilities of selection of habitat for the species. As an illustration, we estimate common bird species habitat preferences and abundances in the region of Aquitaine (France).

stat.AP↗

arXiv2017

Perpetual integrals convergence and extinctions in population dynamics

In this article we use a criterion for the integrability of paths of one-dimensional diffusion processes from which we derive new insights on allelic fixation in several situations. This well known criterion involves a simple necessary and sufficient condition based on scale function and speed measure. We provide a new simple proof for this result and also obtain explicit bounds for the moments of such integrals. We also extend this criterion to non-homogeneous processes by use of Girsanov's transform. We apply our results to multi-type population dynamics: using the criterion with appropriate time changes, we characterize the behavior of proportions of each type before population extinction in different situations.

math.PR↗

arXiv2017

A stochastic model for speciation by mating preferences

Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the population size. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations.

q-bio.PE↗

arXiv2015

Capitalising on Opportunistic Data for Monitoring Species Relative Abundances

With the internet, a massive amount of information on species abundance can be collected under citizen science programs. However, these data are often difficult to use directly in statistical inference, as their collection is generally opportunistic, and the distribution of the sampling effort is often not known. In this paper, we develop a general statistical framework to combine such "opportunistic data" with data collected using schemes characterized by a known sampling effort. Under some structural assumptions regarding the sampling effort and detectability, our approach allows to estimate the relative abundance of several species in different sites. It can be implemented through a simple generalized linear model. We illustrate the framework with typical bird datasets from the Aquitaine region, south-western France. We show that, under some assumptions, our approach provides estimates that are more precise than the ones obtained from the dataset with a known sampling effort alone. When the opportunistic data are abundant, the gain in precision may be considerable, especially for the rare species. We also show that estimates can be obtained even for species recorded only in the opportunistic scheme. Opportunistic data combined with a relatively small amount of data collected with a known effort may thus provide access to accurate and precise estimates of quantitative changes in relative abundance over space and/or time.

stat.AP↗

arXiv2013

Slow-fast stochastic diffusion dynamics and quasi-stationary distributions for diploid populations

We are interested in the long-time behavior of a diploid population with sexual reproduction, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with competition, cooperation and Mendelian reproduction. This stochastic process is indexed by a scaling parameter $K$ that goes to infinity, following a large population assumption. When the birth and natural death parameters are of order $K$, the sequence of stochastic processes indexed by $K$ converges toward a slow-fast dynamics. We indeed prove the convergence toward 0 of a fast variable giving the deviation of the population from Hardy-Weinberg equilibrium, while the sequence of slow variables giving the respective numbers of occurrences of each allele converges toward a 2-dimensional diffusion process that reaches $(0,0)$ almost surely in finite time. We obtain that the population size and the proportion of a given allele converge toward a generalized Wright-Fisher diffusion with varying population size and diploid selection. Using a non trivial change of variables, we next study the absorption of this diffusion and its long time behavior conditioned on non-extinction. In particular we prove that this diffusion starting from any non-trivial state and conditioned on not hitting $(0,0)$ admits a unique quasi-stationary distribution. We finally give numerical approximations of this quasi-stationary behavior in three biologically relevant cases: neutrality, overdominance, and separate niches.

math.PR↗

arXiv2012

Stochastic modeling of density-dependent diploid populations and extinction vortex

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long term genetic behaviour of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly non-neutral allele in the absence of mutations, which involves finding the unique sub-polynomial solution of a nonlinear 3-dimensional recurrence relationship. This equation is simplified to a 1-order relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.

math.PR↗