Doctoral contract Complex invasion fronts in ecology (M/F)

Job Description

Thesis Subject

The program offers a PhD in mathematics applied to ecology and mathematical modeling for ecology. It will be an interdisciplinary PhD in which mathematical theories will be tested against experimental data and enriched by this process. The objective is to train a scientist with a solid background in the analysis of partial differential equations and with the ability to meet the needs of ecologists in terms of modeling and model analysis.
The three tasks of the PhD are interconnected by the shared observation that new mathematical methods are required to analyze the models describing the ecosystems currently of interest to ecology. Anthropogenic disturbances of natural environments (climate change, biodiversity collapse) trigger cascading changes in the composition and configuration of ecosystems. The arrivals, departures, extinctions, and evolutions of species are interconnected processes that ecology now seeks to understand through the lens of these interconnections, rather than in spite of them.
Pest invasions in agriculture, recolonization by symbiotic systems such as plants and their microbial or mycorrhizal fungal communities, and the expansion of the ranges of genetically modified species are increasingly pressing issues, whether in understanding the consequences of environmental deregulation or in devising countermeasures. Rooted in specific problems arising from previous work by project members, these invasion front issues form the three tasks of the PhD. In the long term, it will then be possible to combine the three tasks for a broad approach to biocontrol problems in agroecology, utilizing microbial or mycorrhizal mutualisms in plants and genetically well-understood natural enemies of pests.
The deterministic mathematical modeling of these invasion fronts gives rise to complex reaction-diffusion systems. This complexity is particularly evident in the absence of the comparison principle (the principle that two solutions of the system that are initially ordered will remain so forever). This principle is a key tool in the classical theory of reaction-diffusion equations, allowing for the description of the persistence, extinction, and propagation properties of their solutions. In its absence, new and incompletely understood phenomena may emerge. The most famous examples are Turing instabilities for activator-inhibitor systems and periodic cycles for predator-prey systems. Furthermore, systems of reaction-diffusion equations produce a wide variety of propagation fronts with complex behavior.
In addition to the pulled fronts and pushed fronts already present in scalar equations, these systems of equations feature fronts “locked” onto mobile environmental improvements, fronts “non-locally pulled” by mobile environmental deteriorations, mutualistic fronts in which one species pulls and another pushes, and structured fronts that evolve as they propagate from a pulled regime to a pushed regime or vice versa. J. Garnier and L. Girardin are working on these new invasion regimes.
Since the seminal work of the 20th century, reaction-diffusion equations have inspired experimental models. In a series of studies, É. Vercken compared the theory of pulled and pushed invasion fronts to controlled laboratory invasions for an insect model.
Based on this interdisciplinary expertise, the project aims to contribute to the analysis of propagation phenomena in complex ecological models. The project will yield positive benefits for each discipline: on the one hand, the development of new analytical methods; on the other, access to new predictions and insights into experimental results and field observations.
Task 1: Invasion of yellows disease and its aphid vector in a periodic sugar beet field
Task 2: Co-invasion of symbiotic species pairs
Task 3: Experimental and theoretical invasion of a haplodiploid population and its eco-evolutionary dynamics

Your Work Environment

The doctoral student will be affiliated with the InfoMaths doctoral school (ED 512) and based at the ICJ (UMR 5208) in Lyon. Supervision will be divided as follows: J. Garnier 30% (CNRS, Univ. Savoie Mont-Blanc, HDR, co-supervisor, primary supervisor for Task 2, secondary supervisor for Tasks 1 and 3), L. Girardin 40% (CNRS, Univ. Claude Bernard Lyon 1, co-supervisor, primary supervisor for Task 1, secondary supervisor for Tasks 2 and 3), É. Vercken 30% (INRAE, Univ. Côte d'Azur, HDR, co-supervisor, primary supervisor for Task 3, secondary supervisor for Tasks 1 and 2).

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

CNRS

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