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.Comment: added Proposition 2.4 and formal proofs of Proposition 2.3 and 2.

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.Comment: Reply to Stoyan and Chiu (arXiv:2208.10106

Thickness dependence of the superconducting critical temperature in heavily doped Si:B epilayers

International audienceWe report on the superconducting properties of a series of heavily doped Si:B epilayers grown by gas immersion laser doping with boron content (nB) ranging from ∼3 × 1020 cm−3 to ∼6 × 1021cm−3 and thickness (d) varying between ∼20 nm and ∼210 nm. We show that superconductivity is only observed for nB values exceeding a threshold value (nc,S ) which scales as nc,S ∝ 1/d. The critical temperature (Tc) then rapidly increases with nB, largely exceeding the theoretical values which can be estimated by introducing the electron-phonon coupling constant (λe-ph) deduced from ab initio calculations into the McMillan equation. Surprisingly Tc(nB,d) is fully determined by the boron dose (nB × d) and can be well approximated by a simple Tc(nB,d) ≈ Tc,0[1 − A/(nB.d)] law, with Tc,0 ∼ 750 mK and A ∼ 8(±1) × 1015 cm−2

Evolutionary Epidemiology of Drug-Resistance in Space

The spread of drug-resistant parasites erodes the efficacy of therapeutic treatments against many infectious diseases and is a major threat of the 21st century. The evolution of drug-resistance depends, among other things, on how the treatments are administered at the population level. “Resistance management” consists of finding optimal treatment strategies that both reduce the consequence of an infection at the individual host level, and limit the spread of drug-resistance in the pathogen population. Several studies have focused on the effect of mixing different treatments, or of alternating them in time. Here, we analyze another strategy, where the use of the drug varies spatially: there are places where no one receives any treatment. We find that such a spatial heterogeneity can totally prevent the rise of drug-resistance, provided that the size of treated patches is below a critical threshold. The range of parasite dispersal, the relative costs and benefits of being drug-resistant compared to being drug-sensitive, and the duration of an infection with drug-resistant parasites are the main factors determining the value of this threshold. Our analysis thus provides some general guidance regarding the optimal spatial use of drugs to prevent or limit the evolution of drug-resistance

Data from: Fitness costs in spatially structured environments

The clustering of individuals that results from limited dispersal is a double-edged sword: while it allows for local interactions to be mostly among related individuals, it also results in increased local competition. Here I show that, because they mitigate local competition, fitness costs such as reduced fecundity or reduced survival are less costly in spatially structured environments than in non spatial settings. I first present a simple demographic example to illustrate how spatial structure weakens selection against fitness costs. Then, I illustrate the importance of disentangling the evolution of a trait from the evolution of potential associated costs, using an example taken from a recent study investigating the effect of spatial structure on the evolution of host defense. In this example indeed, the differences between spatial and non-spatial selection gradients are due to differences in the fitness costs, thereby undermining interpretations of the results made in terms of the trait only. This illustrates the need to consider fitness costs as proper traits in both theoretical and empirical studies

Fidelity of parent-offspring transmission and the evolution of social behavior in structured populations

International audienceThe theoretical investigation of how spatial structure affects the evolution of social behavior has mostly been done under the assumption that parent-offspring strategy transmission is perfect, i.e., for genetically transmitted traits, that mutation is very weak or absent. Here, we investigate the evolution of social behavior in structured populations under arbitrary mutation probabilities. We consider populations of fixed size N , struc-tured such that in the absence of selection, all individuals have the same probability of reproducing or dying (neutral reproductive values are the all same). Two types of individuals, A and B , corresponding to two types of social behavior, are competing; the fidelity of strategy transmission from parent to offspring is tuned by a parameter µ. Social interactions have a direct effect on individual fecundities. Under the assumption of small phe-notypic differences (implying weak selection), we provide a formula for the expected frequency of type A individuals in the population, and deduce conditions for the long-term success of one strategy against another. We then illustrate our results with three common life-cycles (Wright-Fisher, Moran Birth-Death and Moran Death-Birth), and specific population structures (graph-structured populations). Qualitatively, we find that some life-cycles (Moran Birth-Death, Wright-Fisher) prevent the evolution of altruistic behavior, confirming previous results obtained with perfect strategy transmission. We also show that computing the expected frequency of al-truists on a regular graph may require knowing more than just the graph's size and degree

Debarre_2015_Evolution

Zipped folder containing the scripts to re-run and plot all the figures presented in the article

Living, competing and evolving in a heterogeneous environment

Tout observateur peut constater la diversité des milieux sur Terre. La compréhension des liens entre cette diversité des habitats et la biodiversité est l'un des thèmes centraux en Écologie, en Évolution et en Biologie de la conservation. Je m'intéresse dans cette thèse aux conséquences écologiques (à court terme) et évolutives (à plus long terme) de la structuration spatiale et de l'hétérogénéité de l'environnement. Je développe et analyse plusieurs modèles mathématiques, combinant différents formalismes théoriques (dynamiques adaptatives, génétique des populations, génétique quantitative). Ces modèles permettent d'explorer les conséquences de l'hétérogénéité spatiale de l'environnement sur (1) les conditions de persistance des populations ; (2) la coexistence entre différents phénotypes et (3) la dynamique évolutive des populations. Je montre ainsi l'importance (i) de l'intensité et de la place de la migration dans le cycle de vie ; (ii) du type de structure spatiale (explicite ou implicite, continu ou discret) ; (iii) de la forme du compromis évolutif, et donc des coûts d'adaptation à une autre ressource ; et enfin (iv) des éventuels rétrocontrôles démographiques. J'illustre à l'aide des interactions entre hôtes et parasites l'importance des hétérogénéités spatiales. Un premier exemple concerne leur utilisation dans la gestion des pharmacorésistances ou des résistances aux insecticides : une répartition hétérogène du traitement permet d'éviter la propagation de parasites ou de nuisibles résistants. Un second exemple, enfin, illustre comment les hétérogénéités dues à l'auto-structuration spatiale influencent l'évolution de stratégies de défense des hôtes, et permettent l'évolution de défenses altruistes.Any observer can notice the diversity of habitats on Earth. Understanding the links betweenthis diversity of habitats and biodiversity is a core topic in Ecology, Evolution andConservation Biology.In this thesis, I study the ecological (short-term) and evolutionary (long-term) consequencesof spatial structuring and environmental heterogeneities. I develop and analyzeseveral mathematical models, which combine different theoretical frameworks (adaptivedynamics, population genetics, and quantitative genetics). I explore the consequences ofspatial heterogeneities on (1) the conditions for population persistence; (2) the coexistenceof different phenotypes, and (3) evolutionary dynamics of populations. I show that theresults depend on (i) the life-cycle, and in particular whether migration influences local regulation;(ii) the choice of the spatial structure (explicit or implicit, continuous or discrete);(iii) the shape of the trade-off, and hence the costs of adaptation to another resource, andfinally (iv) the potential demographical feedbacks.I use the specific case of hosts and parasites interactions to illustrate the importanceof spatial heterogeneities. As a first example, I show that a heterogeneous application oftreatments can help prevent the spread of resistant parasites or pests. Secondly, I show howspatial heterogeneities due to self-structuring influence the evolution of host defense strategies,and allow for the evolution of altruistic defense strategies

Imperfect Strategy Transmission Can Reverse the Role of Population Viscosity on the Evolution of Altruism

International audiencePopulation viscosity, i.e., low emigration out of the natal deme, leads to high within-deme relatedness, which is beneficial to the evolution of altruistic behavior when social interactions take place among deme-mates. However, a detrimental side effect of low emigration is the increase in competition among related individuals. The evolution of altruism depends on the balance between these opposite effects. This balance is already known to be affected by details of the life cycle; we show here that it further depends on the fidelity of strategy transmission from parents to their offspring. We consider different life cycles and identify thresholds of parent–offspring strategy transmission inaccuracy, above which higher emigration can increase the frequency of altruists maintained in the population. Predictions were first obtained analytically assuming weak selection and equal deme sizes and then confirmed with stochastic simulations relaxing these assumptions. Contrary to what happens with perfect strategy transmission from parent to offspring, our results show that higher emigration can be favorable to the evolution of altruism

FDebarre_JEB-2621_FigsS1-4

Supplementary figures