G. Yule, A mathematical theory of evolution, based on the conclusions of dr, Philosophical Transactions of the Royal Society of London B B213, p.21, 1924.

S. Karlin and H. Taylor, A first course in stochastic processes, 1975.

M. E. Newman, Power laws, pareto distributions and zipf's law. Contemporary physics, vol.46, p.323, 2005.

A. S. Novozhilov, G. P. Karev, and E. V. Koonin, Biological applications of the theory of birth-and-death processes, Briefings in bioinformatics, vol.7, p.70, 2006.

I. Yanai, C. J. Camacho, and C. Delisi, Predictions of gene family distributions in microbial genomes: evolution by gene duplication and modification, Physical Review Letters, vol.85, p.2641, 2000.

W. J. Reed and B. D. Hughes, A model explaining the size distribution of gene and protein families, Mathematical biosciences, vol.189, p.97, 2004.

Y. Tambovtsev and C. Martindale, Phoneme frequencies follow a yule distribution, SKASE Journal of Theoretical Linguistics, vol.4, p.1, 2007.

D. M. Raup, Mathematical models of cladogenesis, Paleobiology, vol.11, p.42, 1985.

D. J. Aldous, Stochastic models and descriptive statistics for phylogenetic trees, from yule to today, Statistical Science, p.23, 2001.

S. Nee, R. M. May, and P. H. Harvey, The reconstructed evolutionary process, Philosophical Transactions of the Royal Society of London Series B: Biological Sciences, vol.344, p.305, 1994.

, (tjT)dt. In this plot T = 1, ? = 11, ? = 5, ? = 0.01, t = 1.5 and dt = 0.00001. Circles denote the results of numerical simulation and dots were obtained using the analytic formulas (25) for zero value and (39) for non-zero values. Note the gap between zero and non-zero probabilities due to small bin size

, Statistical Properties of Yule Trees PLOS ONE, 2015.

S. Nee, E. C. Holmes, R. M. May, and P. H. Harvey, Extinction rates can be estimated from molecular phylogenies, Philosophical Transactions of the Royal Society of London Series B: Biological Sciences, vol.344, p.77, 1994.

D. G. Kendall, Stochastic processes and population growth, Journal of the Royal Statistical Society Series B (Methodological), vol.11, p.230, 1949.

P. H. Harvey, R. M. May, and S. Nee, Phylogenies without fossils, p.523, 1994.

A. Mckenzie and M. Steel, Distributions of cherries for two models of trees, Mathematical biosciences, vol.164, p.81, 2000.

M. Steel and A. Mckenzie, Properties of phylogenetic trees generated by yule-type speciation models, Mathematical biosciences, vol.170, p.91, 2001.

N. A. Rosenberg, The mean and variance of the numbers of r-pronged nodes and r-caterpillars in yule-generated genealogical trees, Annals of Combinatorics, vol.10, p.129, 2006.

W. H. Mulder, Probability distributions of ancestries and genealogical distances on stochastically generated rooted binary trees, Journal of theoretical biology, vol.280, p.139, 2011.

M. Steel and A. Mooers, The expected length of pendant and interior edges of a yule tree, Applied Mathematics Letters, vol.23, p.1315, 2010.

A. Mooers, O. Gascuel, T. Stadler, H. Li, and M. Steel, Branch lengths on birth-death trees and the expected loss of phylogenetic diversity, Systematic biology, vol.61, p.195, 2012.
URL : https://hal.archives-ouvertes.fr/lirmm-00715445

S. Kumar, Molecular clocks: four decades of evolution, Nature Reviews Genetics, vol.6, p.654, 2005.

M. Slatkin and R. R. Hudson, Pairwise comparisons of mitochondrial dna sequences in stable and exponentially growing populations, Genetics, vol.129, p.555, 1991.

C. Mora, D. P. Tittensor, S. Adl, A. G. Simpson, and B. Worm, How many species are there on earth and in the ocean?, PLoS biology, vol.9, p.1001127, 2011.

S. L. Pimm, G. J. Russell, J. L. Gittleman, and T. M. Brooks, The future of biodiversity, p.347, 1995.

S. Hohna, T. Stadler, F. Ronquist, and T. Britton, Inferring speciation and extinction rates under different sampling schemes, Molecular biology and evolution, vol.28, p.2577, 2011.

D. G. Kendall, On some modes of population growth leading to ra fisher's logarithmic series distribution, Biometrika, p.6, 1948.

F. Massip, M. Sheinman, S. Schbath, and P. F. Arndt, How Evolution of Genomes Is Reflected in Exact DNA Sequence Match Statistic, Mol. Biol. Evol, vol.32, issue.2, p.524, 2015.

T. Stadler, On incomplete sampling under birth-death models and connections to the samplingbased coalescent, Journal of Theoretical Biology, vol.261, p.58, 2009.

W. Jetz, G. Thomas, J. Joy, K. Hartmann, and A. Mooers, The global diversity of birds in space and time, Nature, vol.491, p.444, 2012.

P. W. Holland and R. E. Welsch, Robust regression using iteratively reweighted least-squares, Communications in Statistics-Theory and Methods, vol.6, p.813, 1977.

R. Bouckaert, J. Heled, D. Kuhnert, T. Vaughan, and C. H. Wu, Beast 2: a software platform for bayesian evolutionary analysis, PLoS computational biology, vol.10, p.1003537, 2014.

F. Ronquist and J. P. Huelsenbeck, Mrbayes 3: Bayesian phylogenetic inference under mixed models, Bioinformatics, vol.19, p.1572, 2003.