, The Influence of Spatial Inhomogeneities on Neutral Models of Geographical Variation IV. Discontinuities in the Population Density and Migration Rate, In: Theoretical Population Biology, vol.563, pp.337-347, 1999.
, Deconstructing isolation-by-distance: The genomic consequences of limited dispersal, PLOS Genetics, vol.138, pp.1006911-1553, 2017.
, Traveling waves for a bistable equation with nonlocal diffusion, EN. In: Advances in Differential Equations, vol.20910, pp.887-936, 2015.
, Stopping Times and Tightness, The Annals of Probability, vol.6, issue.2, pp.335-340, 1978.
DOI : 10.1214/aop/1176995579
URL : http://doi.org/10.1214/aop/1176995579
, Occupation and local times for skew Brownian motion with applications to dispersion across an interface, The Annals of Applied Probability, vol.21, issue.1, pp.183-214, 2011.
DOI : 10.1214/10-AAP691
URL : http://doi.org/10.1214/10-aap691
, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, Courier Corporation, vol.55, 1964.
, The great migration and African-American genomic diversity, PLoS genetics, vol.125, p.1006059, 2016.
DOI : 10.1371/journal.pgen.1006059
URL : http://doi.org/10.1371/journal.pgen.1006059
, Inference in two dimensions: allele frequencies versus lengths of shared sequence blocks, Theoretical population biology, pp.105-119, 2013.
, The effect of a barrier to gene flow on patterns of geographic variation
, A fast, powerful method for detecting identity by descent, The American Journal of Human Genetics, vol.88, issue.2, pp.173-182, 2011.
, Neutral evolution in spatially continuous populations, Theoretical population biology 61, pp.31-48, 2002.
, About scaling behavior of random balls models, Proceed. 6th Int. Conf. on Stereology, Spatial Statistics and Stochastic Geometry, 2006.
, Self-similar Random Fields and Rescaled Random Balls Models, Journal of Theoretical Probability, vol.123, issue.12, pp.1110-1141, 2010.
DOI : 10.1017/S0027763000003627
, A new model for evolution in a spatial continuum, Electronic Journal of Probability, vol.157, pp.162-216, 2010.
, A New Model for Evolution in a Spatial Continuum, Electronic Journal of Probability, vol.15, issue.0, pp.162-216, 2010.
DOI : 10.1214/EJP.v15-741
, Modeling evolution in a spatial continuum, Journal of Statistical Mechanics: Theory and Experiment, pp.1-01002, 2013.
, Large scale behaviour of the spatial Lambda-Fleming?Viot process, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 49, pp.374-401, 2013.
, Encyclopedia of Mathematics and its Applications, Teugels. Regular variation, vol.27, pp.0-521, 1989.
, Convergence of probability measures. Second Wiley Series in Probability and Statistics, pp.0-471, 1999.
, Stochastic flows associated to coalescent processes, Probability Theory and Related Fields 126, pp.261-288, 2003.
DOI : 10.1007/s00440-003-0264-4
URL : https://hal.archives-ouvertes.fr/hal-00103962
, Uniqueness for diffusions with piecewise constant coefficients, Probability Theory and Related Fields, pp.557-572, 1987.
, Is the Gibraltar Strait a barrier to gene flow for the bat Myotis myotis (Chiroptera: Vespertilionidae)?, In: Molecular ecology, vol.911, pp.1761-1772, 2000.
, Existence of traveling waves in the fractional bistable equation, Archiv der Mathematik, vol.239, issue.5
DOI : 10.1016/j.physd.2009.10.011
, Computationally Efficient Composite Likelihood Statistics for Demographic Inference, Molecular biology and evolution 33, pp.591-593, 2015.
DOI : 10.1007/s00285-010-0329-9
URL : https://academic.oup.com/mbe/article-pdf/33/2/591/17472123/msv255.pdf
, Reaction-diffusion equations for interacting particle systems, Journal of Statistical Physics, vol.44, pp.3-4, 1986.
, ??l??ments d'une th??orie g??n??rale des cha??nes simples constantes de Markoff, Annales scientifiques de l'École Normale Supérieure, pp.61-111, 1940.
DOI : 10.24033/asens.883
, One-dimensional stepping stone models, sardine genetics and Brownian local time, The Annals of Applied Probability, vol.18, issue.1, pp.334-358, 2008.
DOI : 10.1214/07-AAP451
URL : http://doi.org/10.1214/07-aap451
, Probability models for DNA sequence evolution, 2008.
DOI : 10.1007/978-1-4757-6285-3
, Probability: theory and examples. Fourth Cambridge Series in Statistical and Probabilistic Mathematics, pp.978-978, 2010.
DOI : 10.1017/CBO9780511779398
, The Brownian net and selection in the spatial $\Lambda $-Fleming-Viot process, Electronic Journal of Probability, vol.22, issue.0, 2015.
DOI : 10.1214/17-EJP61
, Markov processes: characterization and convergence, pp.0-471, 1986.
, Branching Brownian motion and selection in the spatial $\Lambda$-Fleming???Viot process, The Annals of Applied Probability, vol.27, issue.5, 2015.
DOI : 10.1214/16-AAP1245
, Drift, draft and structure: some mathematical models of evolution, Stochastic Models in Biological Sciences
DOI : 10.4064/bc80-0-7
, Some mathematical models from population genetics Lectures from the 39th Probability Summer School held in Saint- Flour Ecole d'Eté de Probabilités de Saint-Flour. [Saint-Flour Probability Summer School, Lecture Notes in Mathematics, vol.2012, pp.978-981, 2009.
, Coalescing Markov labelled partitions and a continuous sites genetics model with infinitely many types, Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, pp.339-358, 1997.
, Rescaling limits of the spatial Lambda- Fleming-Viot process with selection, 2014.
, DIFFUSION PROCESSES IN GENETICS, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp.227-246, 1950.
DOI : 10.1007/978-3-319-16856-2_8
, A Pain in the Torus: Some Difficulties with Models of Isolation by Distance, The American Naturalist, vol.109, issue.967, pp.359-368, 1975.
DOI : 10.1086/283003
, THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES, Annals of Eugenics, vol.7, issue.4, pp.355-369, 1937.
DOI : 10.1111/j.1469-1809.1937.tb02153.x
, A central limit theorem for the spatial $\Lambda $-Fleming-Viot process with selection, Electronic Journal of Probability, vol.22, issue.0, pp.1-68, 2017.
DOI : 10.1214/16-EJP20
URL : https://hal.archives-ouvertes.fr/hal-01612042
, The Himalayas as a Directional Barrier to Gene Flow, The American Journal of Human Genetics, vol.80, issue.5, pp.884-894, 2007.
DOI : 10.1086/516757
, Partially reflected Brownian motion: a stochastic approach to transport phenomena, In: Focus on Probability Theory. Nova Sci. Publ, pp.135-169, 2006.
, Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation, Journal of Magnetic Resonance, vol.248, pp.153-163, 2014.
DOI : 10.1016/j.jmr.2014.07.013
URL : https://hal.archives-ouvertes.fr/hal-01111053
, Brownian motion and stochastic flow systems, 1985.
, On skew Brownian motion, The Annals of Probability 9, pp.309-313, 1981.
, Brownian motions on a half line, Illinois Journal of Mathematics, vol.7, pp.181-231, 1963.
, A functional limit theorem for locally perturbed random walks, Probability and Mathematical Statistics 36, pp.353-368, 2016.
, Limit theorems for stochastic processes
, Stepping-stone model of population, In: Annual Report of the National Institute of Genetics, vol.3, pp.62-63, 1953.
, Diffusion models in population genetics, Journal of Applied Probability, vol.153, issue.02, pp.177-232, 1964.
DOI : 10.2307/2405451
, Evolutionary Rate at the Molecular Level, Nature, vol.16, issue.5129, pp.624-626, 1968.
DOI : 10.1016/0926-6593(66)90068-3
, The neutral theory of molecular evolution, 1984.
, Remarks on the spatial distribution of a reproducing population, Journal of applied probability, pp.577-583, 1977.
, The coalescent, Stochastic processes and their applications, pp.235-248, 1982.
DOI : 10.1016/0304-4149(82)90011-4
, Oxford Studies in Probability, Kingman. Poisson processes, vol.3, pp.0-19, 1993.
, A reduction of continuous square-integrable martingales to Brownian motion, In: Lecture notes in Math, vol.190, pp.19-31, 1971.
, Limit theorems for sequences of jump Markov processes approximating ordinary differential processes, Journal of Applied Probability, vol.82, pp.344-356, 1971.
, Approximation of population processes CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), vol.36, pp.0-89871, 1981.
, The stepping stone model of population structure and the decrease of genetic correlation with distance, Genetics, vol.494, p.561, 1964.
, Inference of human population history from individual whole-genome sequences, Nature, vol.52, issue.7357, pp.493-496, 2011.
DOI : 10.1101/SQB.1987.052.01.094
, On the constructions of the skew Brownian motion, Probability Surveys, vol.3, issue.0, pp.413-466, 2006.
DOI : 10.1214/154957807000000013
URL : https://hal.archives-ouvertes.fr/inria-00000785
, One ??? dimensional stochastic differential equations involving the local times of the unknown process, In: Stochastic analysis and applications, vol.52, issue.53
DOI : 10.1215/kjm/1250523691
, One ??? dimensional stochastic differential equations involving the local times of the unknown process, In: Stochastic analysis and applications, vol.52, issue.53
DOI : 10.1215/kjm/1250523691
, Two continuum-sites stepping stone models in population genetics with delayed coalescence, 2009.
, Composite likelihood methods, Contemporary mathematics 80, pp.221-239, 1988.
, Random walk: a modern introduction
, Les Mathématiques de l'Hérédité, Masson et Cie, 1948.
, Ten years of landscape genetics, Trends in Ecology & Evolution, vol.28, issue.10, pp.614-621, 2013.
DOI : 10.1016/j.tree.2013.05.012
, On a Brownian motion with a hard membrane, Statistics & Probability Letters, vol.113, pp.62-70, 2016.
DOI : 10.1016/j.spl.2016.02.005
URL : http://arxiv.org/pdf/1511.01043
, Stochastic pde's arising from the long range contact and long range voter processes, Probability theory and related fields 102, pp.519-545, 1995.
, Clines with partial panmixia, Theoretical population biology 81, pp.45-68, 2012.
DOI : 10.1016/j.tpb.2011.09.006
, Clines with partial panmixia in an unbounded unidimensional habitat, Theoretical Population Biology, vol.82, issue.1
DOI : 10.1016/j.tpb.2012.02.008
, Clines with partial panmixia across a geographical barrier, Theoretical Population Biology, vol.109, pp.28-43, 2016.
DOI : 10.1016/j.tpb.2016.01.002
, Clines with Variable Migration, Genetics, vol.834, pp.867-886, 1976.
, Clines with Asymmetric Migration, Genetics, vol.884, pp.813-827, 1978.
, The influence of spatial inhomogeneities on neutral models of geographical variation. I. Formulation, In: Theoretical Population Biology, vol.333, pp.291-310, 1988.
, The influence of spatial inhomogeneities on neutral models of geographical variation. II. The semi-infinite linear habitat, In: Theoretical Population Biology, vol.333, pp.311-343, 1988.
, Estimate of the mutation rate per nucleotide in humans, Genetics, vol.1561, pp.297-304, 2000.
, The Population Reference Sample, POPRES: a resource for population, disease, and pharmacological genetics research, The American Journal of Human Genetics, vol.833, pp.347-358, 2008.
, The Influence of Spatial Inhomogeneities on Neutral Models of Geographical Variation III. Migration across a Geographical Barrier, Theoretical Population Biology, vol.43, issue.2
DOI : 10.1006/tpbi.1993.1010
, A central limit theorem for Markov processes that move by small steps, The Annals of Probability, pp.1065-1074, 1974.
, Markovian learning processes, In: SIAM Review, vol.162, pp.143-162, 1974.
, Approximation of stochastic processes by Gaussian diffusions, and applications to Wright-Fisher genetic models Special issue on mathematics and the social and biological sciences, In: SIAM Journal on Applied Mathematics, vol.292, pp.225-242, 1975.
, Limit theorems for stationary distributions, In: Advances in Applied Probability, vol.73, pp.561-575, 1975.
, Ergodicity of diffusion and temporal uniformity of diffusion approximation, Journal of Applied Probability, vol.142, pp.399-404, 1977.
, Random walks with barriers, Nature physics, vol.76, pp.508-514, 2011.
, A splitting technique for Harris recurrent Markov chains, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.29, issue.2, pp.309-318, 1978.
DOI : 10.1007/BF00534764
, Clines with partial panmixia across a geographical barrier in an environmental pocket, Theoretical Population Biology, vol.110, pp.1-11, 2016.
DOI : 10.1016/j.tpb.2016.03.003
, Length distributions of identity by descent reveal finescale demographic history, The American Journal of Human Genetics, vol.915, pp.809-822, 2012.
, Diffusion processes with generalized drift coefficients, Theory of Probability & Its Applications, pp.62-78, 1979.
, Stochastic differential equations with generalized drift vector, Theory of Probability & Its Applications 24, pp.332-347, 1979.
, Inference of historical migration rates via haplotype sharing, Bioinformatics, vol.131, issue.2, pp.180-188, 2013.
DOI : 10.1007/s00439-011-1072-z
URL : https://academic.oup.com/bioinformatics/article-pdf/29/13/i180/6436673/btt239.pdf
, The Geography of Recent Genetic Ancestry across Europe, PLoS Biology, vol.12, issue.9
DOI : 10.1371/journal.pbio.1001555.s021
, Inferring recent demography from isolation by distance of long shared sequence blocks " . en, p.76810, 2016.
, Central limit theorems for local martingales, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.14, issue.3, pp.269-286, 1980.
DOI : 10.1016/B978-1-4832-0022-4.50006-5
, FAST-TRACK: A southern California freeway is a physical and social barrier to gene flow in carnivores, Molecular Ecology, vol.157, pp.1733-1741, 2006.
, Estimating barriers to gene flow from distorted isolation by distance patterns, 2017.
DOI : 10.1101/205484
, Likelihood and Approximate Likelihood Analyses of Genetic Structure in a Linear Habitat: Performance and Robustness to Model Mis-Specification, Molecular Biology and Evolution, vol.24, issue.12, pp.2730-2745, 2007.
DOI : 10.1093/molbev/msm206
URL : https://hal.archives-ouvertes.fr/halsde-00321541
, Analysis of Genetic Inheritance in a Family Quartet by
, The reduction in fitness from genetic drift at heterotic loci in small populations, Genetical Research, vol.30, issue.02, pp.2-257, 1970.
DOI : 10.1017/S0016672300001580
, Genetic differentiation and estimation of gene flow from F-statistics under isolation by distance, Genetics, vol.1454, pp.1219-1228, 1997.
, Continuous martingales and Brownian motion
, Results for the Stepping Stone Model for Migration in Population Genetics, The Annals of Probability, vol.4, issue.5, pp.699-728, 1976.
DOI : 10.1214/aop/1176995980
, Asymptotic properties of the equilibrium probability of identity in a geographically structured population, Advances in Applied Probability, vol.49, issue.02, pp.268-282, 1977.
DOI : 10.2307/1425929
, A Comparison of Three Indirect Methods for Estimating Average Levels of Gene Flow, pp.1349-1368, 1989.
, Brownian motion and stochastic calculus, 1991.
, Fractional integrals and derivatives. Theory and applications, Edited and with a foreword by S. M. Nikol'skii, Translated from the 1987 Russian original, Revised by the authors, pp.2-88124, 1993.
, Stochastic Equations for Diffusion Processes in a Bounded Region, Theory of Probability & Its Applications, pp.264-274, 1961.
, Gene flow and selection in a cline, Genetics, vol.754, pp.733-756, 1973.
, Gene flow and the geographic structure of natural populations, Science, vol.236, issue.4803
DOI : 10.1126/science.3576198
, The Great Wall of China: a physical barrier to gene flow?, In: Heredity, vol.903, pp.212-219, 2003.
, The spatial Lambda-Fleming???Viot process: An event-based construction and a lookdown representation, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 51, pp.570-598, 2015.
DOI : 10.1214/13-AIHP571
, A diffusion with a discontinuous local time, pp.37-45, 1978.
, An introduction to stochastic partial differential equations, Lecture Notes in Math, vol.1180, pp.265-439, 1986.
DOI : 10.1007/BFb0074920
, Isolation by distance, Genetics, vol.282, p.114, 1943.
, Landscape barriers reduce gene flow in an invasive carnivore: geographical and local genetic structure of American mink in Scotland, Molecular Ecology, vol.84, issue.No. 21, pp.1601-1615, 2009.
DOI : 10.4141/A03-001