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- Fitness landscape models: Fisher’s model, multivariate phenotype fitness models
- stochastic multitype models for the population genetics and demography of populations undergoing selection mutation drift and migration
- quantiative genetics: mutation selection balance, Qst/Fst comparisons
- frequent mathematical tools: differential equations (ODE,PDE), stochastic differential equations and diffusion, probabilistic geometry (fitness landscape), generating functions, random matrix theory. Discrete/continuous time, individual/genotype based simulations.
- Distribution of mutation fitness effects in context (epistasis, environment dependence etc.)
- Evolutionary and demographic dynamics of populations away from equilibrium: abrupt change, moving optimum in space or time. Mainly asexual models so far (clonal interference), with mutation, selection and genetic drift.
- Selective sweeps and distribution of allele frequencies over time: biallelic, multiallelic loci, dominance
- Try to produce testable predictions for experimental evolution: stochastic growth processes, mutation effects, adaptation trajectories, fluctuation tests, evolutionary rescue.
- Evolution of life history traits and trade – offs in simple ecological contexts (first), but with an explicit genetic basis for life history traits: virulence/transmission, birth/death etc.
- Impact of various factors on the speed and probability of successful adaptation to a new environment vs. extinction : epistasis, demographic stochasticity, environmental variation, mutation rate and effects distribution, strength of the environmental stress, initial maladaptation and standing variance, migration from a source etc.
- neutrality test on quantiative traits from common garden experiments (Qst/Fst comparisons)
- empirically studying stochastic birth and death processes,
- kill curves and antibiotic dose effects on bacterial birth and death rates
- rescue probability and dynamics
- distribution of antibiotic resistance and its cost.
R codes for multivariate Qst / Fst comparisons: here (.rar file).
This .rar archive has the R code for multivariate Qst / Fst analysis from Martin et al.(2008) and an example application on Galba truncatula data from Chapuis et al. (2008).
Supervised PhD theses
Yoann Anciaux (2017), with Ophélie Ronce: text here
Noémie Harmand (2017) with Thomas Lenormand text here
Florian Lavigne (ongoing) with Lionel Roques
Martin G., S. P. Otto, T. Lenormand (2006). “Selection for recombination in structured populations”.Genetics 172 : 593–609. here.
Martin G. & T. Lenormand (2006). “A general multivariate extension of Fisher’s Geometric model and the distribution of mutation fitness effects across species.” Evolution, 60(5) : 893–907. here.
Martin G., S.F. Elena, T. Lenormand (2007). « Distributions of epistasis in microbes fit predictions from a fitness landscape model. » Nature Genetics 39, 555 – 560 . here.
Martin G., E. Chapuis & J. Goudet (2008). « Multivariate Qst - Fst comparisons : a neutrality test for the evolution of the G-matrix in structured populations. » Genetics, 180:2135 – 2149. here.
Chapuis E., Martin G. & Goudet J. (2008) « Effects of Selection and Drift on G Matrix Evolution in a Heterogeneous Environment: A Multivariate Q(st)-F-st Test With the Freshwater Snail Galba truncatula » . Genetics 180: 2151-2161.
Martin G., S. Gandon (2010) « Lethal mutagenesis and evolutionary epidemiology ». Phil. Trans. Roy. Soc. 365 : 1953 – 1963. here.
Martin G., R. Aguilee, J. Ramsayer, O. Kaltz, and O. Ronce. (2012). “The probability of evolutionary rescue: towards a comparison of theory and evolution experiments”. Phil. Trans. R. Soc. Lond. B 368. here.
Martin G. (2014).“Fisher’s Geometrical Model Emerges as a Property of Complex Integrated Phenotypic Networks”. Genetics. here.
Martin G. & Lambert A. (2015) “A Simple, Semi-Deterministic Approximation to the Distribution of Selective Sweeps in Large Populations”. Theoretical Population Biology. here.
Martin G. & Roques L. (2016) “The Non-stationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation”. Genetics. here.
Gill M.E., Hamel, F., Martin, G. & Roques L. (2017) “Mathematical properties of a class of integro-differential models from population genetics.” SIAM J. Appl. Math. here
Harmand N., Gallet R., Jabbour-Zahab R., Martin G. & Lenormand T. (2017) “Fisher’s geometrical model and the mutational patterns of antibiotic resistance across dose gradients”. Evolution. here.
Roques L., Garnier J., Martin G. (2017) “Beneficial mutation selection dynamics in finite asexual populations: a free boundary approach”. Scientific Reports. here
Anciaux Y., Chevin L.M., Ronce O., Martin G. (2018) Evolutionary rescue over a fitness landscape”. Genetics. here.
Harmand N., Gallet R., Martin G. & Lenormand T. (2018) “Evolution of bacteria specialization along an antibiotic dose gradient”. Evolution Letters. in press.