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.
By Nick Barton
By Quentin Griette
By Ada Altieri
By Mete Demircigil
By Elisa Thébault
By Sebastian Schreiber
By Jean-François Arnoldi
By Michael Scott
By Florence Bansept
By Apolline Louvet
By Aliene MacPherson
By Vincent Bansaye
By Sébastien Lion
By Philipp Messer
By Raphael Forien
By Nicolas Vauchelet
By David MacLeod
By Cheryl Mentuda
By Léo Girardin
By Coralie Fritsch
By Adrian Lam
By Diana Fusco
By Léonard Dekens
By Oana Carja
By Sepideh Mirrahimi
By Olivier Cotto
By Benoît Henry
By Himani Sachdeva
By Florian Patout
By Ignacio Madrid Canales
By Denis Roze
By Gaël Raoul
By Julien Berestycki
By Sylvie Ferrari
By Mikhail Gromov
By Mikhail Gromov
By Mikhail Gromov
By Vasilis Dakos
