Offre de thèse
Biais dans les études évolutionnaires induits par les observations rares et applications aux données paléontologiques
Date limite de candidature
31-08-2026
Date de début de contrat
01-10-2026
Directeur de thèse
CHAMPAGNAT Nicolas
Encadrement
This PhD project is part of a collaboration between Sylvain Billiard, theoretical ecologist in University of Lille, and Nicolas Champagnat, applied mathematician in University of Lorraine. In particular, the PhD project is interdisciplinary, and joint meetings between the two supervisors and the PhD student will be organised regularly, half in Lille and Nancy. The PhD student will also make longer stays in Lille to progress on the biological aspect of the PhD.
Type de contrat
école doctorale
équipe
PROBAS STATScontexte
A key ingredient in this analysis will be played by parameters scaling: in addition to the rate of observation which will converge to zero, we also need to consider evolutionary models where extinction is certain. This is the case for standard IBM, but simplified models of evolution like TSS do not allow for extinction. Hence, we will need to consider a modified version of the TSS where extinction is possible, considering for example a similar process as the one of [CL07]. The asymptotic analysis then requires to tune carefully the rate of observation with respect to the time to extinction of the population. Two main mathematical question will be considered: 1) in a regime of large population, this will require to use tools from the theory of large deviations; 2) in a small population regime, we will need to use spectral theoretic tools from the theory of quasi-stationary distributions (QSD) [MV12,KS+11] to characterize the population state before extinction and the rate of extinction. In the simplest models, the PhD student will seek for results as explicit as possible. In more complex models like structured population models or the TSS, the main part of the analysis will be numerical.spécialité
Mathématiqueslaboratoire
IECL - Institut Elie Cartan de Lorraine
Mots clés
biologie évolutive, dynamiques adaptatives, modélisation stochastique de dynamiques de populations, conditionnement de dynamiques de populations, limites d'échelle
Détail de l'offre
Les biais d'observation et d'échantillonnage sont omniprésents en écologie, en évolution et en épidémiologie. En paléontologie, il est bien connu que la rareté des observations introduit un fort biais dans les mesures de l'abondance des espèces. Cependant, bien que les questions d'évolution soient au cœur de la paléontologie, très peu de travaux abordent la possibilité d'un biais induit par la rareté des observations sur l'adaptation même des espèces observées. Ce biais peut avoir une forte influence sur les partons paléontologiques, mais il est difficile à décrire. Nous proposons une approche fondée sur des modèles stochastiques issus de la théorie de la dynamique adaptative, combinés à un processus d'observation de Poisson dont le taux est proportionnel à la taille de la population, afin d'analyser la dynamique du processus conditionné a etre observé avant son extinction, dans un régime d'observations rares. L'objectif est d'évaluer le biais introduit par cette condition sur la dynamique évolutive et d'examiner s'il peut expliquer certaines caractéristiques des données paléontologiques, telles que la présence de longues périodes de stase ou « l'effet Lilliput ». Les paramètres et limites d'échelle joueront un rôle clé dans cette analyse : l'analyse asymptotique nécessite d'ajuster soigneusement le taux d'observation par rapport au temps d'extinction de la population. Deux questions mathématiques principales seront abordées : 1) dans un régime de grande population, il sera nécessaire de recourir à des outils issus de la théorie des grandes déviations ; 2) dans un régime de petite population, il faudra utiliser des outils de la théorie spectrale.
Keywords
evolutionary biology, adaptive dynamics, stochastic modeling of population processes, conditioning of population dynamics, parameter scalings
Subject details
Observation and sampling bias are ubiquitous in ecology, evolution and epidemiology. In paleontology, the rareness of observations is known to introduce a strong bias in measurements of species abundances. However, even though questions of evolution are central in paleontology, very few works address the possibility of a bias induced by the rareness of observations on the adaptation itself of observed species. This bias may have strong influence on the paleontological patterns, but is hard to describe. We propose an approach based on stochastic models from the theory of adaptive dynamics combined with a Poisson observation process with a rate proportional to the population size, to analyse the dynamics of the process conditionally on being observed before its extinction, in a regime of rare observations. The goal is to evaluate the bias introduced by this conditioning on the evolutionary dynamics and to examine if it can explain features of paleontological records such as the presence of periods of long stasis or the so-called “lilliput effect”. A key ingredient in this analysis will be played by parameters scaling: the asymptotic analysis requires to tune carefully the rate of observation with respect to the time to extinction of the population. Two main mathematical question will be considered: 1) in a regime of large population, this will require to use tools from the theory of large deviations; 2) in a small population regime, we will need to use spectral theoretic tools from the theory of quasi-stationary distributions to characterize the population state before extinction and the rate of extinction.
Profil du candidat
Le candidat doit posséder des compétences et des connaissances en écologie théorique, notamment en dynamique adaptative, ainsi qu'en modélisation stochastique de la dynamique des populations et dans les outils probabilistes de base associés. Une expérience, ou la volonté d'acquérir des compétences, en analyse numérique des modèles stochastiques sera très appréciée. Un intérêt pour les projets pluridisciplinaires et la volonté d'apprendre le langage scientifique d'une autre discipline sont également les bienvenus.
Candidate profile
The candidate should have skills and knowledge in theoretical ecology, in particular adaptive dynamics, and in stochastic modeling of population dynamics and the basic related probabilitic tools. An experience, or a willingness to develop skills, in numerical analysis of stochastic models will be highly appreciated. An interest in pluridisciplinary projects and willingness to learn the scientific language of another discipline is also welcome.
Référence biblio
[CL07] Nicolas Champagnat. Amaury Lambert. Evolution of discrete populations and the canonical diffusion of adaptive dynamics. Ann. Appl. Probab. 17(1), 102–155, 2007.
[CM11] N. Champagnat and S. Méléard. Polymorphic evolution sequence and evolutionary branching. Probab. Theory Relat. Fields, 151:45–94, 2011.
[DL96] U. Dieckmann and R. Law. The dynamical theory of coevolution: a derivation from stochastic
ecological processes. J. Math. Biol., 34(5-6):579–612, 1996.
[Fo16] Michael Foote; On the measurement of occupancy in ecology and paleontology. Paleobiology
42(4), 707–729, 2016. doi: https://doi.org/10.1017/pab.2016.24
[MBB13] Philip D. Mannion, Roger B.J. Benson, Richard J. Butler, Vertebrate palaeobiodiversity patterns and the impact of sampling bias, Palaeogeography, Palaeoclimatology, Palaeoecology 372, 1–4, 2013.
[MV12] Sylvie Méléard, Denis Villemonais. Quasi-stationary distributions and population processes,
Probability Surveys 9, 340–410, 2012.
[MGM+96] J.A.J. Metz, S.A.H. Geritz, G. Meszéena, F.J.A. Jacobs and J.S. van Heerwaarden. Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In
Stochastic and spatial structures of dynamical systems (Amsterdam, 1995), Konink. Nederl.
Akad. Wetensch. Verh. Afd. Natuurk. Eerste Reeks, 45, pp. 183–231. North-Holland, Amsterdam, 1996.
[KS+11] Klebaner, F. C., Sagitov, S., Vatutin, V. A., Haccou, P., Jagers, P. Stochasticity in the adaptive
dynamics of evolution: the bare bones. Journal of biological dynamics 5(2), 147–162, 2011.
[SJL82] Philip W. Signor, III, Jere H. Lipps, 1982. Sampling bias, gradual extinction patterns and
catastrophes in the fossil record. Geological Implications of Impacts of Large Asteroids and Comets on the Earth, Leon T. Silver, Peter H. Schultz
[SS97] Solow AR, Smith W. On fossil preservation and the stratigraphic ranges of taxa. Paleobiology
23(3), 271–277, 1997. doi:10.1017/S0094837300019680
[St10] Tanja Stadler, Sampling-through-time in birth–death trees, Journal of Theoretical Biology
267(3), 396–404, 2010.
[SL16] Starrfelt J, Liow LH. How many dinosaur species were there? Fossil bias and true richness estimated using a Poisson sampling model. Philos Trans R Soc Lond B Biol Sci. 371(1691):20150219,
2016. doi: 10.1098/rstb.2015.0219.