Project description
New methods for the analysis of multi-scale models from evolutionary biology
A theory based on Hamilton-Jacobi equations has been successful in analysing linear asexual reproduction, but it faces challenges when applied to nonlinear sexual reproduction. The ERC-funded MUSEUM project aims to develop methods for analysing unconventional multi-scale integro-differential equations in evolutionary biology and their connections to stochastic processes. These equations, which feature non-standard nonlinear integral terms, often exhibit solutions that concentrate around one or more evolving points, particularly in a small variance regime and over long time scales. The project will analyse nonlinear reproduction models for sexual reproduction. Additionally, it will investigate long-time limits of stochastic individual-based models to better understand the stochastic effects that emerge in small subpopulations.
Objective
The goal of MUSEUM is to develop robust methods for the asymptotic analysis of unconventional multi-scale integro-differential equations from evolutionary biology and their connection with stochastic processes. These equations involve nonstandard nonlinear integral terms and, under specific conditions of small variance and long time, exhibit solutions that concentrate around one or multiple evolving points.
We will develop new methods for the asymptotic analysis of models with nonlinear reproduction operators, in the regime of small variance. In these models, the nonlinearity of the reproduction operator comes from sexual reproduction, involving two parents, as opposed to asexual reproduction, which only involves one parent and which can be modeled by linear operators. Both of these reproductive modes are relevant to many living organisms. A recent theory, that encompasses Hamilton-Jacobi equations offers robust methods for the asymptotic analysis of integro-differential models with linear asexual reproduction. However, these methods, relying on comparison principles and viscosity solution theory, prove inadequate in the case of nonlinear sexual reproduction. Nonlinear reproduction operators introduce new features, yet their analysis remains considerably underdeveloped. Their treatment requires a conceptual leap.
Addressing stochastic effects in small subpopulations, we will also analyse large population and long time limits of stochastic individual-based models in the small variance regime. In this way, we will palliate the inadequacies of Hamilton-Jacobi approximations.
The methods that we will develop through this project will offer theoretical biologists the opportunity to go beyond their current possibilities and explore new frontiers.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been human-validated.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been human-validated.
- natural sciences biological sciences evolutionary biology
- natural sciences mathematics applied mathematics statistics and probability
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
- natural sciences mathematics applied mathematics mathematical model
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2024-COG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
75794 PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.