Tristan Roget’s research while affiliated with Institut Montpelliérain Alexander Grothendieck and other places

Signs of ageing become apparent only late in life, after organismal development is finalized. Ageing, most notably, decreases an individual’s fitness. As such, it is most commonly perceived as a non-adaptive force of evolution and considered a by-product of natural selection. Building upon the evolutionarily conserved age-related Smurf phenotype, we propose a simple mathematical life-history trait model in which an organism is characterized by two core abilities: reproduction and homeostasis. Through the simulation of this model, we observe (1) the convergence of fertility’s end with the onset of senescence, (2) the relative success of ageing populations, as compared to non-ageing populations, and (3) the enhanced evolvability (i.e. the generation of genetic variability) of ageing populations. In addition, we formally demonstrate the mathematical convergence observed in (1). We thus theorize that mechanisms that link the timing of fertility and ageing have been selected and fixed over evolutionary history, which, in turn, explains why ageing populations are more evolvable and therefore more successful. Broadly speaking, our work suggests that ageing is an adaptive force of evolution.

Signs of ageing become apparent only late in life, after organismal development is finalized. Ageing, most notably, decreases an individual’s fitness. As such, it is most commonly perceived as a non-adaptive force of evolution and considered a by-product of natural selection. Building upon the evolutionarily conserved age-related Smurf phenotype, we propose a simple mathematical life-history trait model in which an organism is characterized by two core abilities: reproduction and homeostasis. Through the simulation of this model, we observe 1) the convergence of fertility’s end with the onset of senescence, 2) the relative success of ageing populations, as compared to non-ageing populations, and 3) the enhanced evolvability (i.e. the generation of genetic variability) of ageing populations. In addition, we formally demonstrate the mathematical convergence observed in 1). We thus theorize that mechanisms that link the timing of fertility and ageing have been selected and fixed over evolutionary history, which, in turn, explains why ageing populations are more evolvable and therefore more successful. Broadly speaking, our work suggests that ageing is an adaptive force of evolution.

Signs of ageing become apparent only late in life, after organismal development is finalized. Ageing, most notably, decreases an individual’s fitness. As such, it is most commonly perceived as a non-adaptive force of evolution and considered a by-product of natural selection. Building upon the evolutionarily conserved age-related Smurf phenotype, we propose a simple mathematical life-history trait model in which an organism is characterized by two core abilities: reproduction and homeostasis. Through the simulation of this model, we observe 1) the convergence of fertility’s end with the onset of senescence, 2) the relative success of ageing populations, as compared to non-ageing populations, and 3) the enhanced evolvability (i.e. the generation of genetic variability) of ageing populations. In addition, we formally demonstrate the mathematical convergence observed in 1). We thus theorize that mechanisms that link the timing of fertility and ageing have been selected and fixed over evolutionary history, which, in turn, explains why ageing populations are more evolvable and therefore more successful. Broadly speaking, our work suggests that ageing is an adaptive force of evolution.

Signs of ageing become apparent only late in life, after organismal development is finalized. Ageing, most notably, decreases an individual’s fitness. As such, it is most commonly perceived as a non-adaptive force of evolution and considered a by-product of natural selection. Building upon the evolutionarily conserved age-related Smurf phenotype, we propose a simple mathematical life-history trait model in which an organism is characterized by two core abilities: reproduction and homeostasis. Through the simulation of this model, we observe 1) the convergence of fertility’s end with the onset of senescence, 2) the relative success of ageing populations, as compared to non-ageing populations, and 3) the enhanced evolvability (i.e. the generation of genetic variability) of ageing populations. In addition, we formally demonstrate the mathematical convergence observed in 1). We thus theorize that mechanisms that link the timing of fertility and ageing have been selected and fixed over evolutionary history, which, in turn, explains why ageing populations are more evolvable and therefore more successful. Broadly speaking, our work suggests that ageing is an adaptive force of evolution.

Signs of ageing become apparent only late in life, after organismal development is finalized. Ageing, most notably, decreases an individual’s fitness. As such, it is most commonly perceived as a non-adaptive force of evolution and considered a by-product of natural selection. Building upon the evolutionarily conserved age-related Smurf phenotype, we propose a simple mathematical life-history trait model in which an organism is characterized by two core abilities: reproduction and homeostasis. Through the simulation of this model, we observe 1) the convergence of fertility’s end with the onset of senescence, 2) the relative success of ageing populations, as compared to non-ageing populations, and 3) the enhanced evolvability (i.e. the generation of genetic variability) of ageing populations. In addition, we formally demonstrate the mathematical convergence observed in 1). We thus theorize that mechanisms that link the timing of fertility and ageing have been selected and fixed over evolutionary history, which, in turn, explains why ageing populations are more evolvable and therefore more successful. Broadly speaking, our work suggests that ageing is an adaptive force of evolution.

We study the long time behavior of an asymmetric size-structured measure-valued growth-fragmentation branching process that models the dynamics of a population of cells taking into account physiological and morphological asymmetry at division. We show that the process exhibits a Malthusian behavior; that is that the global population size grows exponentially fast and that the trait distribution of individuals converges to some stable distribution. The proof is based on a generalization of Lyapunov function techniques for non-conservative semi-groups. We then investigate the fluctuations of the growth rate with respect to the parameters guiding asymmetry. In particular, we exhibit that, under some special assumptions, symmetric division is sub-optimal in a Darwinian sense.

We study the long time behavior of an asymmetric size-structured measure-valued growth-fragmentation branching process that models the dynamics of a population of cells taking into account physiological and morphological asymmetry at division. We show that the process exhibits a Malthusian behavior; that is that the global population size grows exponentially fast and that the trait distribution of individuals converges to some stable distribution. The proof is based on a generalization of Lyapunov function techniques for non-conservative semi-groups. We then investigate the fluctuations of the growth rate with respect to the parameters guiding asymmetry. In particular, we exhibit that, under some special assumptions, asymmetric division is optimal in a Darwinian sense.

Ageing’s sensitivity to natural selection has long been discussed because of its apparent negative effect on an individual’s fitness. Thanks to the recently described (Smurf) 2-phase model of ageing (Tricoire and Rera in PLoS ONE 10(11):e0141920, 2015) we propose a fresh angle for modeling the evolution of ageing. Indeed, by coupling a dramatic loss of fertility with a high-risk of impending death—amongst other multiple so-called hallmarks of ageing—the Smurf phenotype allowed us to consider ageing as a couple of sharp transitions. The birth–death model (later called bd-model) we describe here is a simple life-history trait model where each asexual and haploid individual is described by its fertility period $x_b$ and survival period $x_d$. We show that, thanks to the Lansing effect, the effect through which the “progeny of old parents do not live as long as those of young parents”, $x_b$ and $x_d$ converge during evolution to configurations $x_b-x_d\approx 0$ in finite time. To do so, we built an individual-based stochastic model which describes the age and trait distribution dynamics of such a finite population. Then we rigorously derive the adaptive dynamics models, which describe the trait dynamics at the evolutionary time-scale. We extend the Trait Substitution Sequence with age structure to take into account the Lansing effect. Finally, we study the limiting behaviour of this jump process when mutations are small. We show that the limiting behaviour is described by a differential inclusion whose solutions $x(t)=(x_b(t),x_d(t))$ reach the diagonal $\lbrace x_b=x_d\rbrace$ in finite time and then remain on it. This differential inclusion is a natural way to extend the canonical equation of adaptive dynamics in order to take into account the lack of regularity of the invasion fitness function on the diagonal $\lbrace x_b=x_d\rbrace$.

This thesis is divided into two parts connected by the same thread. It concerns the theoretical study and the application of mathematical models describing population dynamics. The individuals reproduce and die at rates which depend on age a and phenotypic trait. The trait is fixed duringthe life of the individual. It is modified over generations by mutations appearing during reproduction. Natural selection is modeled by introducing a density-dependent mortality rate describing competition for resources.In the first part, we study the long-term behavior of a selection-mutation partial differential equation with age structure describing such a large population. By studying the spectral properties of a family of positive operators on a measures space, we show the existence of stationary measures that can admit Dirac masses in traits maximizing fitness. When these measures admit a continuous density, we show the convergence of the solutions towards this (unique) stationary state.The second part of this thesis is motivated by a problem from the biology of aging. We want to understand the appearance and maintenance during evolution of a senescence marker observed in the species Drosophila melanogaster. For this, we introduce an individual-based model describing the dynamics of a population structured by age and by the following life history trait: the age of reproduction ending and the one where the mortality becomes non-zero. We also model the Lansing effect, which is the effect through which the “progeny of old parents do not live as long as those of young parents”. We show, under large population and rare mutation assumptions, that the evolution brings these two traits to coincide. For this, we are led to extend the canonical equation of adaptive dynamics to a situation where the fitness gradient does not admit sufficient regularity properties. The evolution of the trait is no longer described by the (unique) trajectory of an ordinary differential equation but by a set of trajectories solutions of a differential inclusion.

Ageing's sensitivity to natural selection has long been discussed because of its apparent negative effect on individual's fitness. Thanks to the recently described (Smurf) 2-phase model of ageing we were allowed to propose a fresh angle for modeling the evolution of ageing. Indeed, by coupling a dramatic loss of fertility with a high-risk of impending death - amongst other multiple so-called hallmarks of ageing - the Smurf phenotype allowed us to consider ageing as a couples of sharp transitions. The bd model we describe here is a simple life-history trait model where each asexual and haploid individual is described by its fertility period $x_b$ and survival period $x_d$. We show that, thanks to the Lansing effect, $x_b$ and $x_d$ converge during evolution to configurations $x_b-x_d\approx 0$. This guarantees that a certain proportion of the population maintains the Lansing effect which in turn, confers higher evolvability to individuals. \\To do so, we build an individual-based stochastic model which describes the age and trait distribution dynamics of such a finite population. Then we rigorously derive the adaptive dynamics models, which describe the trait dynamics at the evolutionary time-scale. First, we extend the Trait substitution sequence with age structure to take into account the Lansing effect. Finally, we study the limiting behaviour of this jump process when mutations are small. We show that the limiting behaviour is described by a differential inclusion whose solutions $x(t)=(x_b(t),x_d(t))$ reach in finite time the diagonal $\lbrace x_b=x_d\rbrace$ and then stay on it. This differential inclusion is a natural way to extend the canonical equation of adaptive dynamics in order to take into account the lack of regularity of the invasion fitness function on the diagonal $\lbrace x_b=x_d\rbrace$.