Many populations can somehow adapt to rapid environmental changes. To understand this fast evolution, we investigate the genealogy of individuals inside those populations. More precisely, we use a deterministic model to describe the phenotypic density of a population under selection when the fitness optimum moves at constant speed. We study the inside dynamics of this population using the neutral fractions approach. We then define a Markov process characterizing the distribution of ancestral phenotypic lineages inside the equilibrium. This construction yields qualitative as well as quantitative properties on the phenotype of typical ancestors. In particular, we show that in asexual populations typical ancestors of present individuals carried traits much closer to the fitness optimum than most individuals alive at the same time. We also investigate more deeply the asymptotic regime of small mutation effects. In this regime, we obtain an explicit formula for the typical ancestral lineage using the description of the solutions of Hamilton Jacobi equation as a minimizer of an optimization problem. In addition, we compare our deterministic results on lineages with the lineages of stochastic models.
De Nick Barton
De Quentin Griette
De Ada Altieri
De Mete Demircigil
De Elisa Thébault
De Jean-François Arnoldi
De Michael Scott
De Florence Bansept
De Apolline Louvet
De Vincent Bansaye
De Sébastien Lion
De Philipp Messer
De Raphael Forien
De Nicolas Vauchelet
De David MacLeod
De Cheryl Mentuda
De Léo Girardin
De Coralie Fritsch
De Adrian Lam
De Diana Fusco
De Léonard Dekens
De Oana Carja
De Sepideh Mirrahimi
De Olivier Cotto
De Benoît Henry
De Himani Sachdeva
De Florian Patout
De Ignacio Madrid Canales
De Denis Roze
De Julien Berestycki
De Sylvie Ferrari
De Vasilis Dakos
