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Posts

Highly dimensional non-local non-linear PDEs

2 minute read

Published:

Phenotypic diversity in Hemerocallis. Plants can be caracterised by many different traits, all of which can be assigned numerical values: Flower colour, Specific Leaf Area (SLA), seed mass, Plant nitrogen fixation capacity, Leaf shape, Flower sex, plant woodiness. Source: H Cui et al. 2019.

portfolio

publications

Topology and habitat assortativity drive neutral and adaptive diversification in spatial graphs

Published in N/A, 2021

In review @ Communication Biology. This paper establishes the link between landscape complexity and diversification using an eco-evolutionary model on graphs.

Recommended citation: Boussange Victor and Pellissier Loic (2021) "Topology and habitat assortativity drive neutral and adaptive diversification in spatial graphs." bioRxiv. https://www.biorxiv.org/content/10.1101/2021.07.06.451404v1

talks

Solving non-local nonlinear Partial Differential Equations in high dimensions with HighDimPDE.jl

Published:

Abstract

Non-local nonlinear Partial Differential Equations arise in a variety of fields in Biology and are used for modelling e.g. morphogeneis, cancer evolution or gene regulatory networks. They are also present in many models of evolution, for example in population genetics with the non-local Fisher KPP equation, or in quantitative genetics where populations are structured with quantitative traits.

Using graph-based metrics to assess the effect of landscape topography on diversification

Published:

Abstract

Biodiversity is unevenly distributed across the Earth, and empirical studies suggest that landscape features have a crucial role in shaping such patterns. Montane regions or riverine systems sustain high levels of species diversity, indicating that topography and habitat complexity are major drivers of biodiversity. Nonetheless, there exists a gap between theory and observations. The complexity of the eco-evolutionary processes that shape species’ evolution blur our understanding on how exactly diversification mechanisms are influenced by landscapes. Recently, insights from an eco-evolutionary model where landscapes are represented as a graphs - that capture landscape topographical complexity - revealed that simple graph properties have a major influence on the diversification processes. In particular, the theory demonstrates how heterogeneity in degree, characteristic length and habitat assortativity differently affect neutral and adaptive diversification. In this talk, we propose a simple methodology to project real landscapes on graphs, and illustrate how to characterize large geographical areas by using graph-based topography metrics. Because they connect differentiation patterns to generating eco-evolutionary mechanisms and landscape features, such metrics could improve our understanding of the origin of spatial biodiversity gradients.

Graph topology and habitat assortativity drive phenotypic differentiation in an eco-evolutionary model

Published:

Abstract

Biodiversity results from differentiation mechanisms that are largely influenced by the features of the landscape over which populations are distributed. Notably, landscape connectivity and habitat heterogeneity constrain the movement and survival of individuals, thereby promoting differentiation through drift and local adaptation. Nonetheless, the complex topology of landscapes can blur our understanding on how they regulate differentiation. Here, we construct from first principles a stochastic, individual based model where the landscape is explicitly represented as a graph. We investigate both analytically and with simulations how the graph topology and the underlying spatial habitat configuration affect differentiation at the population level. Differentiation emerges from differences in local populations’ phenotypes, which consist of neutral and adaptive traits that are co-evolving. Using a macroscopic description of the dynamics developed in ref. [1] we demonstrate that a simple quantity, the habitat assortativity of the graph, conditions local adaptation. This has non-trivial consequences on differentiation mechanisms, and we show that habitat assortativity can amplify or dampen neutral differentiation depending on the migration regime. The approach undertaken provides a rigorous framework to study macroscopic patterns emerging from microscopic processes developing over complex structures.

teaching

Taste of research internship

Taste of research internship, ETH Zürich, D-USYS, 2020

I was the mentor of a student from Polytech Nice-Sophia, working on a project aimed at sing machine learning to understand economic development, called “Using machine learning to understand economic development”.