Je travaille au Département
de mathématiques et de statistique de l'Université
de Montréal
depuis plusieurs années où j'ai enseigné la théorie des
probabilités, les mathématiques appliquées et l'analyse. Mes
intérêts de recherche se situent en génétique de population
mathématique et en théorie évolutive des jeux. J'utilise
comme outils la modélisation mathématique, les processus
stochastiques, les méthodes statistiques et l'analyse
dynamique.
Si vous voulez en savoir davantage, veuillez consulter la
liste de contributions ci-dessous.
Vous pouvez me contacter à l'adresse courriel suivante:
sabin.lessard(at)umontreal.ca
I have been
working in the Département de
mathématiques et de statistique at Université
de Montréal for many years where I taught probability
theory, applied mathematics and analysis. My research
interests are in mathematical population genetics and
evolutionary game theory. As tools I use mathematical
modeling, stochastic processes, statistical methods and
dynamical analysis.
If you want to know more, please consult the list of
contributions below.
You can reach me at the following email address:
sabin.lessard(at)umontreal.ca
Livres / Books
Lessard,
S. 2023. Les rudiments du calcul stochastique, Ellipses,
Paris.
Lessard, S. 2023. Processus stochastiques, 2e édition,
Ellipses,
Paris.
Lessard, S. 2020. Probabilités
pour débutants, Ellipses,
Paris.
Lessard, S. 2017. Initiation
à la théorie des probabilités, Ellipses,
Paris.
Lessard, S. 2016. Analyse
mathématique : premiers pas, Ellipses,
Paris.
Lessard, S. 2014. Processus stochastiques,
Ellipses,
Paris.
Lessard, S. and Monga, E. 1993. Statistique: Concepts et méthodes, Les Presses de
l'Université de Montréal, Montréal, et Masson Éditeur, Paris.
Lessard, S. (Éditeur) 1990. Mathematical
and
Statistical Developments of Evolutionary Theory, NATO
ASI Series C: Mathematical and Physical Sciences, Volume 299,
Kluwer Academic Publishers, Dordrecht, The Netherlands.
Karlin, S. and Lessard, S. 1986. Theoretical Studies on Sex Ratio Evolution,
Monographs in Population Biology, Volume 22, Princeton
University Press, Princeton, New Jersey.
Articles / Papers
https://portal-portail.nserc-crsng.gc.ca/p/ccvview-visionnercvc.aspx?ccvID=954f51b2-038f-4de0-8b6c-91d6dd49c5ed&appID=aa3ac839-8cbc-4f36-9ec1-3dbed20da8ac&cc_ccv=0
95. Kroumi, D. and Lessard, S. 2023. Evolutionary game with
stochastic payoffs in a finite island modelhttps://arxiv.org/pdf/2311.00
, Journal of Dynamics and Games (submitted) (arXiv:2311.00269)
94. Li, C., Feng, T.J., Zheng, X.D., Lessard, S. and Tao, Y.
2023. Noise-induced stochastic Nash equilibrium, Physical
Review Letters (submitted) (https://arxiv.org/abs/2310.16501)
93. Kroumi, D. and Lessard, S. 2023. Stochastic
viability in an island model with partial dispersal:
Approximation by a diffusion process in the limit of a large
number of islands, Theoretical Population Biology
(submitted) (arXiv:2311.00275)
92. Martin, É. and Lessard, S. 2023. Assortment by group
founders always promotes the evolution of cooperation under
global selection but can oppose it under local selection, Dynamic
Games and Applications,
https://doi.org/10.1007/s13235-023-00514-x (pdf)
91. Lessard, S. and Ewens, W.J. 2022. On the sign of the
average effect of an allele, Theoretical Population
Biology148, 46-48. (pdf)
90. Feng, T.J., Li, C., Zheng, X.D., Lessard, S. and Tao, Y.
2022. Stochastic replicator dynamics and evolutionary
stability, Physical Review E 105, 044403.
(pdf)
89. Feng, T.J., Mei,
J., Li, C., Zheng, X.D., Lessard, S. and Tao, Y. 2022.
Stochastic evolutionary stability in matrix games with random
payoffs, Physical Review E105, 034303. (pdf)
88. Kroumi, D. and Lessard, S. 2022. Average
abundancy of cooperation in multi-player games with random
payoffs, Journal ofMathematical
Biology85, 27 (pdf)
87. Kroumi, D., Martin, É. and Lessard, S. 2022. Evolution of cooperation
with respect to fixation probabilities in multi-player games
with random payoffs, Theoretical Population Biology145,
1-21. (pdf)
86. Feng, T.J., Mei, J., Wang, R.W., Lessard, S., Tao, Y. and
Zheng, X.D. 2022.Noise-induced
quasi-heteroclinic cycle in a rock-paper-scissors
game with random payoffs, Dynamic Games and
Applications12, 1-13. (pdf)
85. Lessard, S., Li, C., Zheng, X.D. and Tao, Y. 2021.
Inclusive fitness and Hamilton’s rule in a stochastic
environment, Theoretical
Population Biology142, 91-99. (pdf)
84. Kroumi, D., Martin, É., Li, C. and Lessard, S. 2021.
The effect of variability in payoffs on
conditions for the evolution of cooperation in a small
population,
Dynamic Games and
Applications11, 803-834. (pdf)
83. Kroumi, D. and Lessard, S. 2021. The effect of
variability in payoffs on average abundance in two-player
linear games under symmetric mutation, Journal of
Theoretical Biology 513, 110569. (pdf)
82. Li, C. and Lessard, S. 2021. The effect of the opting-out
strategy on conditions for selection to favor the evolution of
cooperation in a finite population, Journal of Theoretical
Biology510, 110543. (pdf) 81. Li, C. and
Lessard, S. 2020. Randomized matrix game in a finite
population: effect of stochastic fluctuations in the payoffs
on the evolution of cooperation, Theoretical Population
Biology134,
77-91. (pdf)
80. Soares, C. and Lessard, S. 2020. First-order effect of frequency-dependent
selection on fixation probability in an age-structured
population with application to a public goods game,Theoretical Population Biology133, 80-96. (pdf)
79. Griffiths, R.C.,
Jenkins, P.A. and Lessard, S. 2019. Corrigendum to “A
coalescent dual process for a Wright-Fisher diffusion with
recombination and its application to haplotype partitioning”
[Theor. Popul. Biol.112
(2016) 126-138], Theoretical
Population Biology130, 203. (pdf)
78. Li, C., Zheng, X.D., Feng, T.J., Wang, M.Y., Lessard, S.
and Tao, Y. 2019. Weak selection can filter environmental
noise in the evolution of animal behavior, Physical Review
E 100, 052411.
(pdf)
77. Soares, C. and
Lessard, S. 2019. Diffusion approximation for an
age-class-structured population under viability and fertility
selection with application to fixation probability of an
advantageous mutant, Journal
of Mathematical Biology 79, 2069-2110. (pdf)
76. Lessard, S. and Ewens, W.J. 2019. The left-hand side of
the Fundamental Theorem of Natural Selection: a reply, Journal of Theoretical
Biology472,
77-83. (pdf)
75.
Zheng, X.D., Li, C., Lessard, S. and Tao, Y. 2018.
Environmental noise could promote stochastic local stability
of behavioral diversity evolution, Physical Review
Letters 128, 218101. (pdf)
74. Lessard, S. and Soares, C. 2018. Frequency-dependent
growth in class-structured populations: continuous dynamics in
the limit of weak selection, Journal of Mathematical Biology 77, 229-259. (pdf)
73.
Zheng, X.D., Li, C., Lessard, S. and Tao, Y. 2017.
Evolutionary stability concepts in a stochastic environment,
Physical Review E96, 032414. (pdf)
72. Griffiths, R.C.,
Jenkins, P.A. and Lessard, S. 2016. A coalescent dual process
for a Wright-Fisher diffusion with recombination and its
application to haplotype partitioning, Theoretical Population
Biology112,
126-138. (pdf)
71. Durand, G. and Lessard, S. 2016. Fixation probability in a
two-locus intersexual selection model, Theoretical Population
Biology109,
75-87. (pdf)
70. Lessard, S. and Soares, C. 2016. Definition of fitness in
age-structured populations: Comparison in the haploid case, Journal of Theoretical
Biology391,
65-73. (pdf)
69.
Kroumi, D. and Lessard, S. 2015. Strong migration limit for
games in structured populations: Applications to dominance
hierarchy and set structure, Games6, 318-346. (pdf)
68. Ewens, W. J. and Lessard, S. 2015. On the interpretation
and relevance of the Fundamental Theorem of Natural Selection, Theoretical Population
Biology104,
59-67. (pdf)
67. Kroumi, D. and Lessard, S. 2015. Evolution of cooperation
in a multidimensional phenotype space, Theoretical Population
Biology102,
60-75. (pdf)
66. Kroumi, D. and Lessard, S. 2015. Conditions for
cooperation to be more abundant than defection in a
hierarchically structured population, Dynamic Games and
Applications5,
239-262. (pdf)
65. Kermany, A.R. and
Lessard, S. 2012. Effect of epistasis and linkage on
fixation probability in three-locus models: an ancestral
recombination-selection graph approach, Theoretical
Population Biology82, 131-145. (pdf)
64. Lessard, S. and Kermany, A.R. 2012. Fixation
probability in a two-locus model by the ancestral
recombination-selection graph, Genetics190,
691-707. (pdf)
63. Lessard, S. 2011. Evolution of cooperation in finite
populations, In: Evolutionary Game Dynamics (Karl
Sigmund, Editor), Proceedings of Symposia in Applied
Mathematics, American Mathematical Society, Providence, Rhode
Island, 143-171. (pdf)
62. Lessard, S. 2011. On the robustness of the extension of
the one-third law of evolution to the multi-player game, Dynamic
Games and Applications1, 408-418. (pdf)
61. Lessard, S.
2011. Effective game matrix and inclusive payoff in
group-structured populations, Dynamic Games and
Applications1,
301-318. (pdf)
60. Lessard, S. 2010. Recurrence equations for
the probability distribution of sample configurations in exact
population genetics models, Journal of Applied Probability
47, 732-751. (pdf)
59. Lessard, S. and Lahaie, P. 2009. Fixation probability
with multiple alleles and projected average allelic effect on
selection, Theoretical
Population Biology75, 266-277 (pdf)
58. Lessard, S. 2009. Diffusion approximations for one-locus
multi-allele kin selection, mutation and random drift in
group-structured populations: a unifying approach to selection
models in population genetics, Journal of Mathematical Biology59,
659-696. (pdf)
57. Ladret, V. and Lessard, S. 2008. Evolutionary game dynamics
in a finite asymmetric two-deme population and emergence of
cooperation, Journal of
Theoretical Biology255,
137-151. (pdf)
56. Larribe, F. and Lessard, S. 2008. A
composite-conditional-likelihood approach for gene mapping based
on linkage disequilibrium in windows of marker loci, Statistical Applications in
Genetics and Molecular Biology7, Issue 1, Article 27, 31
pages. (pdf)
55. Lessard, S. 2007. An exact sampling formula for the
Wright-Fisher model and a conjecture about the finite-island
model, Genetics177, 1249-1254. (pdf)
54. Ladret, V. and Lessard, S. 2007. Fixation probability for a
beneficial allele and a mutant strategy in a linear game under
weak selection in a finite island model, Theoretical Population Biology72, 409-425. (pdf)
53. Lessard, S. 2007. Cooperation is less likely to evolve in a
finite population with a highly skewed distribution of family
size, Proceedings of the
Royal Society B274,
1861-1865. (pdf)
52. Lessard, S. and Ladret, V. 2007. The probability of fixation
of a single mutant in an exchangeable selection model, Journal of Mathematical Biology54, 721-744. (pdf)
51. Wakeley, J. and Lessard, S. 2006. Corridors for migration
between large subdivided populations, and the structured
coalescent, Theoretical Population Biology70,
412-420. (pdf)
50. Lessard, S. 2006. ESS theory now: Overview, Theoretical Population Biology69, 231-233. (pdf)
49. Lessard, S. 2005. Kin selection is implicated in partial
sib-mating populations with constant viability differences
before mating, Genetics171, 407-413. (pdf)
48. Griffiths, R. and Lessard, S. 2005. Ewens' sampling formula
and related formulae: combinatorial proofs, extensions to
variable population size and applications to ages of alleles, Theoretical Population Biology68, 167-177. (pdf)
47. Lessard, S. 2005. Long-term stability from fixation
probabilities in finite populations: New perspectives for ESS
theory, Theoretical Population
Biology68,
19-27. (pdf)
46. Lessard, S. and Rocheleau, G. 2004. Kin selection and
coefficients of relatedness in family-structured populations, Theoretical Population Biology66, 287-306. (pdf)
45. Courteau, J. and Lessard, S. 2004. Sex ratio evolution
through group selection using diffusion approximation, Journal of Mathematical Biology48, 340-356. (pdf)
44. Lessard, S. and Wakeley, J. 2004. The two-locus
ancestral graph in a subdivided population: convergence as
the number of demes grows in the island model, Journal of Mathematical Biology48, 275-292. (pdf)
43. Wakeley, J. and Lessard, S. 2003. Theory of the effects of
population structure and sampling on patterns of linkage
disequilibrium applied to genomic data from humans, Genetics164, 1043-1053. (pdf)
42. Lessard, S. and Rocheleau, G. 2003. Change in frequency of a
rare mutant allele: a general formula and applications to
partial inbreeding models,
Journal of Mathematical Biology46, 71-94. (pdf)
41. Tao, Y. and Lessard, S. 2002. Frequency-dependent selection
in sexual family-structured populations, Journal of Theoretical Biology217, 525-534. (pdf)
40. Lessard, S. 2002. The theory of optimal sex ratio, Comments on Theoretical Biology 7, 315-354.
39. Larribe, F., Lessard, S. and Schork, N.J. 2002. Gene mapping
via the ancestral recombination graph, Theoretical Population Biology62, 215-229. (pdf)
38. Lessard, S. 2001. William D. Hamilton: A tribute, Theoretical Population Biology59, 7-9. (pdf)
37. Lemire, M. and Lessard, S. 2001. Equilibrium structure and
stability analysis in a frequency-dependent, two-population
diploid model, Journal of
Mathematical Biology 43,
1-21. (pdf)
36. Lemire, M., Lessard, S. and Tao, Y. 2000. Evolutionary
stability in two-sex two-locus models, Selection1, 193-203.
35. Courteau, J. and Lessard, S. 2000. Optimal sex ratios in
structured populations, Journal
of Theoretical Biology207, 157-175. (pdf)
34. Tao, Y. and Lessard, S. 2000. Fundamental theorem of natural
selection and frequency-dependent selection: Analysis of the
diploid matrix game model, Journal
of Theoretical Biology206, 17-25. (pdf)
33. Mahdi, S. and Lessard, S. 2000. Variability in centred
house-of-cards mutation models, IMA Journal of Mathematics Applied in Medicine and Biology17, 1-15. (pdf)
32. Tao, Y., Lessard, S. and Lemire, M. 2000. Evolutionarily
stable strategy in a sex- and frequency-dependent selection
model, Journal of Theoretical
Bilogy204,
191-200. (pdf)
31. Rocheleau, G. and Lessard, S. 2000. Stability analysis of
the partial self-mating selection model, Journal of Mathematical Biology40, 541-574. (pdf)
30. Courteau, J. and Lessard, S. 1999. Stochastic effects in LMC
models, Theoretical
Population Biology55,
127-136. (pdf)
29. Lessard, S. 1997. Fisher's fundamental theorem of natural
selection revisited, Theoretical
Population Biology 52,
119-136. (pdf)
28. Lemire, M. and Lessard, S. 1997. On the non-existence of an
optimal migration rate, Journal
of Mathematical Biology35, 657-682. (pdf)
27. Mahdi, S. and Lessard, S. 1996. Convergence of covariance
structures in additive Gaussian polygenic models, Biometrics52, 833-845. (pdf)
26. Lessard, S. 1996. La sélection de parentèle (kin selection),
In: Dictionnaire du
Darwinisme et de l'Évolution (Patrick Tort, Éditeur),
Presses Universitaires de France, Paris, 3893-3902.
25. Castilloux, A.M. and Lessard, S. 1995. The fundamental
theorem of natural selection in Ewens' sense: Case of many loci, Theoretical Population Biology48, 306-315. (pdf)
24. Lessard, S. and Castilloux, A.M. 1995. The fundamental
theorem of natural selection in Ewens' sense: Case of fertility
selection, Genetics141, 733-742. (pdf)
23. Lessard, S. and Mahdi, S. 1995. Convergence de la
variabilité dans les modèles polygéniques gaussiens, Genetics Selection Evolution 27, 395-421. (pdf)
22. Lessard, S. 1994. Adaptive topography in fertility-viability
selection models: The haplodiploid case, Theoretical Population Biology 46, 344-362. (pdf)
21. Lessard, S. 1993. Adaptive topography in fertility-viability
selection models: An alternative to inclusive fitness in kin
selection models, Theoretical
Population Biology 43,
281-309. (pdf)
20. Lessard, S. 1992. Relatedness and inclusive fitness with
inbreeding, Theoretical
Population Biology 42,
284-307. (pdf)
19. Lessard, S.1991. Statistical models for sex ratio evolution,
In: Statistical Methods in
Biological and Medical Sciences (C.R. Rao and R.
Chakraborty, Editors), Handbook of Statistics, Volume 8, North-Holland, New-york,
347-372.
18. Lessard, S. 1990. Evolutionary stability: One concept,
several meanings, Theoretical
Population Biology 37,
159-170. (pdf)
17. Lessard, S. 1990. Évolution du rapport numérique des sexes
et modèles dynamiques connexes, In: Mathematical and Statistical Developments of
Evoltionary Theory (S. Lessard, Editor), NATO ASI
Series C: Mathematical and Physical Sciences, Volume 299, Kluwer Academic
Publishers, Dordrecht, The Netherlands, 269-325.
16. Lessard, S. 1990. Population Genetics of Sex Allocation, In:
Some Mathematical Questions in
Biology - Sex Allocation and Sex Change: Experiments and Models (M.
Mangel, Editor), Lectures on Mathematics in the Life Sciences,
Volume 22, The American
Mathematical Society, Providence, Rhode Island, 109-126.
15. Lessard, S. 1989. Resource allocation in Mendelian
populations: Further in ESS theory, In: Mathematical Evolutionary Theory
(M.W. Feldman, Editor), Princeton University Press,
Princeton, New Jersey, 207-246.
14. Lessard, S. 1989. The mathematics of resource allocation in
population biology I. Interspecific competition, Applied Mathematics and
Computation 32,
207-226. (pdf)
13. Lessard, S. 1988. Le Q.I. et l'hérédité, ou les pièges de la
statistique - Partie II: Héritabilité et analyse de variance, La Gazette des Sciences
Mathématiques du Québec12, 3-19.
12. Lessard, S. 1988. Le Q.I. et l'hérédité, ou les pièges de la
statistique - Partie I: Tests d'aptitude et analyse factorielle, La Gazette des Sciences
Mathématiques du Québec11, 3-30.
11. Lessard, S. 1987. The role of recombination and selection in
the modifier theory of sex ratio distortion, Theoretical Population Biology 31, 339-358. (pdf)
10. Lessard, S. 1986. Evolutionary principles for general
frequency-dependent two-phenotype models in sexual populations, Journal of Theoretical Biology 119, 329-344. (pdf)
9. Lessard, S. 1985. The role of recombination in the modifier
theory of autosomal segregation distortion, Theoretical Population Biology 28, 133-149. (pdf)
8. Lessard, S. 1985. Notions de stratégie et de stabilité en
théorie de l'évolution, La
Gazette des Sciences Mathématiques du Québec 9, 13-32.
7. Karlin, S. and Lessard, S. 1984. On the optimal sex-ratio: A
stability analysis based on a characterization for one-locus
multiallele viability models, Journal
of Mathematical Biology20, 15-38. (pdf)
6. Lessard, S. 1984. Evolutionary dynamics in
frequency-dependent two-phenotype models, Theoretical Population Biology25, 210-234. (pdf)
5. Karlin, S. and Lessard, S. 1983. On the optimal sex-ratio, Proceedings of the National
Academy of Sciences USA80, 5931-5935.
4. Lessard, S. and Karlin, S. 1982. A criterion for
stability-instability at fixation states involving an eigenvalue
one with applications in population genetics, Theoretical Population Biology22, 108-126. (pdf)
3. Lessard, S. 1981. Is the between-population variance
negligible in the total variance of heterozygosity? Theoretical Population Biology20, 394-410. (pdf)
2. Lessard, S. 1981. La loi forte des grands nombres pour
certaines classes de variables aléatoires faiblement
dépendantes, Revue Roumaine
de Mathématiques Pures et Appliquées 26, 1355-1366.
1. Lessard, S. 1980. Une double généralisation du théorème de
Fejèr-Lebesgue, Canadian
Mathematical Bulletin23,
29-35.
Thèses / Thesis
Sur quelques problèmes de
convergence ponctuelle, Thése de doctorat, Université
de Montréal, 1978, 59 pages. Superviseur: Richard Duncan
Sur les affinités entre la
théorie des martingales et la théorie ergodique,
Mémoire de maîtrise, Université de Montréal, 1974, 66 pages.
Superviseur: Richard Duncan
Critiques de
livres / Book reviews
Histoire d'un génome: Population et génétique dans l'est du
Québec, sous la direction de Gérard Bouchard et Marc De
Brackeleer, Presses de l'Université du Québec, 1991, 607 pages.
In Cahiers Québécois de
Démographie21,
1993, 207-212.
The Theory of Evolution and Dynamical Systems, par J. Hofbauer
and K. Sigmund, Cambridge University Press, 1988, 341 pages. In
American Scientist79, 1991, 180.
Stagiaires postdoctoraux / Postdoctoral
fellows
CHEN, Yu-Ting, Evolution of cooperation in graph-structured
populations, 2013-2014.
KERMANY, Amir, Ancestral recombination-selection graph and
evolution of recombination, stagiaire postdoctoral, 2009-2011.
LADRET, Véronique, Théorie de la coalescence et probabilité de
fixation, 2004-2006.
LI, Cong, Evolution of cooperation in
evolutionary games with the opting-out strategy and under
random environmental noise, 2020.
SOARES, Cintia, Évolution dans des populations structurées en
classes, 2019. KROUMI, Dhaker, Étude de quelques populations
structurées : processus de coalescence et abondance d’une
stratégie, 2016.
LARRIBE, Fabrice, Cartographie génétique fine par le graphe de
recombinaison ancestral, 2003.
ROCHELEAU, Ghislain, Modèles de sélection avec consanguinité,
2003.
LEMIRE, Mathieu, Sur les stratégies stables au cours de
l’évolution, 2001.
COURTEAU, Josiane, Sex-ratio optimal dans des populations
structurées, 1997.
CARRIER, Vincent, Modèles de sélection sexuelle à deux espèces,
1996.
MAHDI, Smail, Convergence de la variabilité de caractères
génétiques quantitatifs, 1994.
Étudiant(e)s de maîtrise / Master's students
MARTIN, Éloi, Évolution de la coopération dans des populations
structurées en groupes avec assortativité partielle, 2024.
ELGBEILI, Guillaume, Probabilité et temps
de fixation à l’aide de processus ancestraux, 2013.
SAIDI, Lamiae,
Applications du processus ancestral avec recombinaison et
conversion en génétique statistique, 2013.
LAHAIE, Philippe, Probabilité de fixation dans des modèles
génétiques de populations à plusieurs allèles, 2008.
LASALLE-IALONGO, David, Processus de coalescence dans une
population subdivisée avec possibilité de coalescences
multiples, 2008.
MARTIN, Géraldine, Mesures d’apparentement pour des modèles de
sélection avec interactions dans une population structurée en
groupes, 2009.
VILLANDRE, Luc, Effet de l'échantillonnage non proportionnel de
cas et de témoins sur une méthode de vraisemblance maximale pour
l'estimation de la position d'une mutation sous sélection, 2009.
LANGEVIN, Samuel, Probabilité de fixation dans des modèles de
sélection avec consanguinité, 2006.
ROCHELEAU, Ghislain, Modèles de sélection avec autofécondation
partielle et modèles connexes,1997.
CASTILLOUX, Anne-Marie, Le théorème fondamental de la sélection
naturelle, 1995.
LEMIRE, Mathieu, Modèles de migration en génétique des
populations, 1994.
Stagiaires de recherche d'été du premier
cycle / Undergraduate Summer Internships
MARTIN, Éloi, Dilemme du prisonnier avec
paiements aléatoires dans un modèle de Moran, 2020.
DURAND, Guillermo, Utilisation du graphe ancestral de
sélection-recombinaison dans un modèle à deux loci avec
sélection sexuelle, 2014.
ROBITAILLE-GROU, Marie-Christine, Processus ancestral avec
conversion génique, 2013.
