arXiv subjects

Florence Débarre

Publications and source records attributed to Florence Débarre.

8 recordsLinked to original sources

arXiv2026

Stochastic dynamics at the back of a gene drive eradication wave

Gene drive alleles bias their own inheritance to offspring. They can fix in a wild-type population in spite of a fitness cost, and even lead to the eradication of the target population if the fitness cost is high. However, this outcome may be prevented or delayed if areas previously cleared by the drive are recolonised by wild-type individuals. Here, we investigate the conditions under which these stochastic wild-type recolonisation events are likely and when they are unlikely to occur in one spatial dimension. More precisely, we examine the conditions ensuring that the last individual carrying a wild-type allele is surrounded by a large enough number of drive homozygous individuals, resulting in a very low chance of wild-type recolonisation. To do so, we make a deterministic approximation of the distribution of drive alleles within the wave, and we split the distribution of wild-type alleles into a deterministic part and a stochastic part. Our analytical and numerical results suggest that the probability of wild-type recolonisation events increases with lower fitness of drive individuals and with smaller local carrying capacity. Numerical simulations show that these results extend to two spatial dimensions. The role of the migration rate however, is less clear but has a lower impact. We further demonstrate that, in the event of wild-type recolonization, the probability of subsequent drive reinvasion decreases with smaller values of the intrinsic growth rate of the population. Overall, our study paves the way for further analysis of wild-type recolonisation at the back of eradication traveling waves.

q-bio.PE↗

arXiv2024

No evidence of systematic proximity ascertainment bias in early COVID-19 cases in Wuhan Reply to Weissman (2024)

In a short text published as Letter to the Editor of the Journal of the Royal Statistical Society Series A, Weissman (2024) argues that the finding that early COVID-19 cases without an ascertained link to Wuhan's Huanan Seafood Wholesale market resided on average closer to the market than cases epidemiologically linked to it, reveals "major proximity ascertainment bias". Here we show that Weissman's conclusion is based on a flawed premise, and that there is no such "internal evidence" of major bias. The pattern can indeed be explained by places of infection not being limited to residential neighbourhoods, and by stochasticity -- i.e., without requiring any ascertainment bias.

physics.soc-ph↗

arXiv2024

Confirmation of the centrality of the Huanan market among early COVID-19 cases

The centrality of Wuhan's Huanan market in maps of December 2019 COVID-19 case residential locations, established by Worobey et al. (2022a), has recently been challenged by Stoyan and Chiu (2024, SC2024). SC2024 proposed a statistical test based on the premise that the measure of central tendency (hereafter, "centre") of a sample of case locations must coincide with the exact point from which local transmission began. Here we show that this premise is erroneous. SC2024 put forward two alternative centres (centroid and mode) to the centre-point which was used by Worobey et al. for some analyses, and proposed a bootstrapping method, based on their premise, to test whether a particular location is consistent with it being the point source of transmission. We show that SC2024's concerns about the use of centre-points are inconsequential, and that use of centroids for these data is inadvisable. The mode is an appropriate, even optimal, choice as centre; however, contrary to SC2024's results, we demonstrate that with proper implementation of their methods, the mode falls at the entrance of a parking lot at the market itself, and the 95% confidence region around the mode includes the market. Thus, the market cannot be rejected as central even by SC2024's overly stringent statistical test. Our results directly contradict SC2024's and -- together with myriad additional lines of evidence overlooked by SC2024, including crucial epidemiological information -- point to the Huanan market as the early epicentre of the COVID-19 pandemic.

physics.soc-ph↗

arXiv2023

Pulled, pushed or failed: the demographic impact of a gene drive can change the nature of its spatial spread

Understanding the temporal spread of gene drive alleles -- alleles that bias their own transmission -- through modeling is essential before any field experiments. In this paper, we present a deterministic reaction-diffusion model describing the interplay between demographic and allelic dynamics, in a one-dimensional spatial context. We focused on the traveling wave solutions, and more specifically, on the speed of gene drive invasion (if successful). We considered various timings of gene conversion (in the zygote or in the germline) and different probabilities of gene conversion (instead of assuming 100$\%$ conversion as done in a previous work). We compared the types of propagation when the intrinsic growth rate of the population takes extreme values, either very large or very low. When it is infinitely large, the wave can be either successful or not, and, if successful, it can be either pulled or pushed, in agreement with previous studies (extended here to the case of partial conversion). In contrast, it cannot be pushed when the intrinsic growth rate is vanishing. In this case, analytical results are obtained through an insightful connection with an epidemiological SI model. We conducted extensive numerical simulations to bridge the gap between the two regimes of large and low growth rate. We conjecture that, if it is pulled in the two extreme regimes, then the wave is always pulled, and the wave speed is independent of the growth rate. This occurs for instance when the fitness cost is small enough, or when there is stable coexistence of the drive and the wild-type in the population after successful drive invasion. Our model helps delineate the conditions under which demographic dynamics can affect the spread of a gene drive.

math.AP↗

arXiv2021

Demographic feedbacks can hamper the spatial spread of a gene drive

This paper is concerned with a reaction--diffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring). In our model, the gene drive has a negative effect on the fitness of individuals carrying it, and is therefore susceptible of decreasing the total carrying capacity of the population locally in space. This tends to generate an opposing demographic advection that the gene drive has to overcome in order to invade. While previous reaction--diffusion models neglected this aspect, here we focus on it and try to predict the sign of the traveling wave speed. It turns out to be an analytical challenge, only partial results being within reach, and we complete our theoretical analysis by numerical simulations. Our results indicate that taking into account the interplay between population dynamics and population genetics might actually be crucial, as it can effectively reverse the direction of the invasion and lead to failure. Our findings can be extended to other bistable systems, such as the spread of cytoplasmic incompatibilities caused by Wolbachia.

math.AP↗

arXiv2021

The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection

Emerging epidemics and local infection clusters are initially prone to stochastic effects that can substantially impact the epidemic trajectory. While numerous studies are devoted to the deterministic regime of an established epidemic, mathematical descriptions of the initial phase of epidemic growth are comparatively rarer. Here, we review existing mathematical results on the epidemic size over time, and derive new results to elucidate the early dynamics of an infection cluster started by a single infected individual. We show that the initial growth of epidemics that eventually take off is accelerated by stochasticity. These results are critical to improve early cluster detection and control. As an application, we compute the distribution of the first detection time of an infected individual in an infection cluster depending on the testing effort, and estimate that the SARS-CoV-2 variant of concern Alpha detected in September 2020 first appeared in the United Kingdom early August 2020. We also compute a minimal testing frequency to detect clusters before they exceed a given threshold size. These results improve our theoretical understanding of early epidemics and will be useful for the study and control of local infectious disease clusters.

q-bio.PE↗

arXiv2019

Catch me if you can: a spatial model for a brake-driven gene drive reversal

Population management using artificial gene drives (alleles biasing inheritance, increasing their own transmission to offspring) is becoming a realistic possibility with the development of CRISPR-Cas genetic engineering. A gene drive may however have to be stopped. "Antidotes" (brakes) have been suggested, but have been so far only studied in well-mixed populations. Here, we consider a reaction--diffusion system modeling the release of a gene drive (of fitness $1-a$) and a brake (fitness $1-b$, $b\leq a$) in a wild-type population (fitness $1$). We prove that, whenever the drive fitness is at most $1/2$ while the brake fitness is close to $1$, coextinction of the brake and the drive occurs in the long run. On the contrary, if the drive fitness is greater than $1/2$, then coextinction is impossible: the drive and the brake keep spreading spatially, leaving in the invasion wake a complicated spatio-temporally heterogeneous genetic pattern. Based on numerical experiments, we argue in favor of a global coextinction conjecture provided the drive fitness is at most $1/2$, irrespective of the brake fitness. The proof relies upon the study of a related predator--prey system with strong Allee effect on the prey. Our results indicate that some drives may be unstoppable, and that, if gene drives are ever deployed in nature, threshold drives, that only spread if introduced in high enough frequencies, should be preferred.

math.AP↗

arXiv2018

The split-and-drift random graph, a null model for speciation

We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this Markov chain is governed by two types of events: vertex duplication, where at constant rate a pair of vertices is sampled uniformly and one of these vertices loses its incident edges and is rewired to the other vertex and its neighbors; and edge removal, where each edge disappears at constant rate. Besides the number of vertices $n$, the model has a single parameter $r_n$. Using a coalescent approach, we obtain explicit formulas for the first moments of several graph invariants such as the number of edges or the number of complete subgraphs of order $k$. These are then used to identify five non-trivial regimes depending on the asymptotics of the parameter $r_n$. We derive an explicit expression for the degree distribution, and show that under appropriate rescaling it converges to classical distributions when the number of vertices goes to infinity. Finally, we give asymptotic bounds for the number of connected components, and show that in the sparse regime the number of edges is Poissonian.

math.PR↗