Adaptation in a heterogeneous environment II: to be three or not to be.

We propose a model to describe the adaptation of a phenotypically structured population in a H-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of this model. We show that the large-time behaviour of the solution (persistence or extinction) depends on the sign of a principal eigenvalue, [Formula: see text], and we study the dependency of [Formula: see text] with respect to H. This analysis sheds new light on the effect of increasing the number of patches on the persistence of a population, which has implications in agroecology and for understanding zoonoses; in such cases we consider a pathogenic population and the patches correspond to different host species.

Seed predation-induced Allee effects, seed dispersal and masting jointly drive the diversity of seed sources during population expansion.

The environmental factors affecting plant reproduction and effective dispersal, in particular biotic interactions, have a strong influence on plant expansion dynamics, but their demographic and genetic consequences remain an understudied body of theory. Here, we use a mathematical model in a one-dimensional space and on a single reproductive period to describe the joint effects of predispersal seed insect predators foraging strategy and plant reproduction strategy (masting) on the spatio-temporal dynamics of seed sources diversity in the colonisation front of expanding plant populations. We show that certain foraging strategies can result in a higher seed predation rate at the colonisation front compared to the core of the population, leading to an Allee effect.

A research agenda for scaling up agroecology in European countries.

A profound transformation of agricultural production methods has become unavoidable due to the increase in the world's population, and environmental and climatic challenges. Agroecology is now recognized as a challenging model for agricultural systems, promoting their diversification and adaptation to environmental and socio-economic contexts, with consequences for the entire agri-food system and the development of rural and urban areas. Through a prospective exercise performed at a large interdisciplinary institute, INRAE, a research agenda for agroecology was built that filled a gap through its ambition and interdisciplinarity.

Adaptation in a heterogeneous environment I: persistence versus extinction.

Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens is a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under the effects of mutation, selection and migration in a two-patch environment, each patch being associated with a different phenotypic optimum. We consider two types of growth functions that depend on the n-dimensional phenotypic trait: either local and linear or nonlocal nonlinear.

Towards unified and real-time analyses of outbreaks at country-level during pandemics.

The management of public health and the preparedness for health emergencies partly rely on the collection and analysis of surveillance data, which become crucial in the context of an emergency such as the pandemic caused by COVID-19. For COVID-19, typically, numerous national and global initiatives have been set up from this perspective. Here, we propose to develop a shared vision of the country-level outbreaks during a pandemic, by enhancing, at the international scale, the foundations of the analysis of surveillance data and by adopting a unified and real-time approach to monitor and forecast the outbreak across time and across the world.

COVID-19 mortality dynamics: The future modelled as a (mixture of) past(s).

Discrepancies in population structures, decision making, health systems and numerous other factors result in various COVID-19-mortality dynamics at country scale, and make the forecast of deaths in a country under focus challenging. However, mortality dynamics of countries that are ahead of time implicitly include these factors and can be used as real-life competing predicting models. We precisely propose such a data-driven approach implemented in a publicly available web app timely providing mortality curves comparisons and real-time short-term forecasts for about 100 countries.

Impact of Lockdown on the Epidemic Dynamics of COVID-19 in France.

The COVID-19 epidemic was reported in the Hubei province in China in December 2019 and then spread around the world reaching the pandemic stage at the beginning of March 2020. Since then, several countries went into lockdown. Using a mechanistic-statistical formalism, we estimate the effect of the lockdown in France on the contact rate and the effective reproduction number of the COVID-19.

Using Early Data to Estimate the Actual Infection Fatality Ratio from COVID-19 in France.

The number of screening tests carried out in France and the methodology used to target the patients tested do not allow for a direct computation of the actual number of cases and the infection fatality ratio (IFR). The main objective of this work is to estimate the actual number of people infected with COVID-19 and to deduce the IFR during the observation window in France. We develop a `mechanistic-statistical' approach coupling a SIR epidemiological model describing the unobserved epidemiological dynamics, a probabilistic model describing the data acquisition process and a statistical inference method.

Population persistence under high mutation rate: From evolutionary rescue to lethal mutagenesis.

Populations may genetically adapt to severe stress that would otherwise cause their extirpation. Recent theoretical work, combining stochastic demography with Fisher's geometric model of adaptation, has shown how evolutionary rescue becomes unlikely beyond some critical intensity of stress. Increasing mutation rates may however allow adaptation to more intense stress, raising concerns about the effectiveness of treatments against pathogens.

Beneficial mutation-selection dynamics in finite asexual populations: a free boundary approach.

Using a free boundary approach based on an analogy with ice melting models, we propose a deterministic PDE framework to describe the dynamics of fitness distributions in the presence of beneficial mutations with non-epistatic effects on fitness. Contrarily to most approaches based on deterministic models, our framework does not rely on an infinite population size assumption, and successfully captures the transient as well as the long time dynamics of fitness distributions. In particular, consistently with stochastic individual-based approaches or stochastic PDE approaches, it leads to a constant asymptotic rate of adaptation at large times, that most deterministic approaches failed to describe.

The Nonstationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation.

Various models describe asexual evolution by mutation, selection, and drift. Some focus directly on fitness, typically modeling drift but ignoring or simplifying both epistasis and the distribution of mutation effects (traveling wave models). Others follow the dynamics of quantitative traits determining fitness (Fisher's geometric model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift.

Modelling Population Dynamics in Realistic Landscapes with Linear Elements: A Mechanistic-Statistical Reaction-Diffusion Approach.

We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D) landscape crossed by linear one-dimensional (1D) corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid "2D/1D model", i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape.

Linking niche theory to ecological impacts of successful invaders: insights from resource fluctuation-specialist herbivore interactions.

Theories of species coexistence and invasion ecology are fundamentally connected and provide a common theoretical framework for studying the mechanisms underlying successful invasions and their ecological impacts. Temporal fluctuations in resource availability and differences in life-history traits between invasive and resident species are considered as likely drivers of the dynamics of invaded communities. Current critical issues in invasion ecology thus relate to the extent to which such mechanisms influence coexistence between invasive and resident species and to the ability of resident species to persist in an invasive-dominated ecosystem.

Allee effect promotes diversity in traveling waves of colonization.

Most mathematical studies on expanding populations have focused on the rate of range expansion of a population. However, the genetic consequences of population expansion remain an understudied body of theory. Describing an expanding population as a traveling wave solution derived from a classical reaction-diffusion model, we analyze the spatio-temporal evolution of its genetic structure.

Success rate of a biological invasion in terms of the spatial distribution of the founding population.

We analyze the role of the spatial distribution of the initial condition in reaction-diffusion models of biological invasion. Our study shows that, in the presence of an Allee effect, the precise shape of the initial (or founding) population is of critical importance for successful invasion. Results are provided for one-dimensional and two-dimensional models.

A statistical-reaction-diffusion approach for analyzing expansion processes.

In this article, we propose a method for analyzing the spatial variations in the range expansion of the pine processionary moth (PPM), an invasive species in France. Based on binary measurements - the presence or absence of PPM nests - the proposed method allows us to infer the local effect of the environment on PPM population expansion. This effect is estimated at each position x using a parameter F(x) that corresponds to the local PPM fitness.

Patchy patterns due to group dispersal.

The presence of multiple foci in population patterns may be due to various processes arising in the population dynamics. Group dispersal, which has been lightly investigated for airborne species, is one of these processes. We built a stochastic model generating the dispersal of groups of particles.

Spreading speeds in slowly oscillating environments.

In this paper, we derive exact asymptotic estimates of the spreading speeds of solutions of some reaction-diffusion models in periodic environments with very large periods. Contrarily to the other limiting case of rapidly oscillating environments, there was previously no explicit formula in the case of slowly oscillating environments. The knowledge of these two extremes permits to quantify the effect of environmental fragmentation on the spreading speeds.

Modelling the impact of an invasive insect via reaction-diffusion.

An exotic, specialist seed chalcid, Megastigmus schimitscheki, has been introduced along with its cedar host seeds from Turkey to southeastern France during the early 1990s. It is now expanding in plantations of Atlas Cedar (Cedrus atlantica). We propose a model to predict the expansion and impact of this insect.

Biological invasions: deriving the regions at risk from partial measurements.

We consider the problem of forecasting the regions at higher risk for newly introduced invasive species. Favourable and unfavourable regions may indeed not be known a priori, especially for exotic species whose hosts in native range and newly-colonised areas can be different. Assuming that the species is modelled by a logistic-like reaction-diffusion equation, we prove that the spatial arrangement of the favourable and unfavourable regions can theoretically be determined using only partial measurements of the population density: (1) a local 'spatio-temporal' measurement, during a short time period and, (2) a 'spatial' measurement in the whole region susceptible to colonisation.

Mathematical analysis of the optimal habitat configurations for species persistence.

We study a reaction-diffusion model in a binary environment made of habitat and non-habitat regions. Environmental heterogeneity is expressed through the species intrinsic growth rate coefficient. It was known that, for a fixed habitat abundance, species survival depends on habitat arrangements.

Species persistence decreases with habitat fragmentation: an analysis in periodic stochastic environments.

This paper presents a study of a nonlinear reaction-diffusion population model in fragmented environments. The model is set on R(N), with periodic heterogeneous coefficients obtained using stochastic processes. Using a criterion of species persistence based on the notion of principal eigenvalue of an elliptic operator, we provided a precise numerical analysis of the interactions between habitat fragmentation and species persistence.

Analysis of the periodically fragmented environment model: I--species persistence.

This paper is concerned with the study of the stationary solutions of the equation [Equation: see text] where the diffusion matrix A and the reaction term f are periodic in x. We prove existence and uniqueness results for the stationary equation and we then analyze the behaviour of the solutions of the evolution equation for large times. These results are expressed by a condition on the sign of the first eigenvalue of the associated linearized problem with periodicity condition.