2005, 2005(Special): 833-845. doi: 10.3934/proc.2005.2005.833

Colored coalescent theory


Mathematical Biociences Institute, The Ohio State University, Columbus, OH 43210, United States


Department of Mathematics, University of California, Riverside, Riverside, CA 92521, United States

Received  September 2004 Revised  April 2005 Published  September 2005

We introduce a colored coalescent process which recovers random colored genealogical trees. Here a colored genealogical tree has its vertices colored black or white. Moving backward along the colored genealogical tree, the color of vertices may change only when two vertices coalesce. Explicit computations of the expectation and the cumulative distribution function of the coalescent time are carried out. For example, when $x=1/2$, for a sample of $n$ colored individuals, the expected time for the colored coalescent process to reach a black MRCA or a white MRCA, respectively, is $3-2/n$. On the other hand, the expected time for the colored coalescent process to reach a MRCA, either black or white, is $2-2/n$, which is the same as that for the standard Kingman coalescent process.
Citation: Jianjun Tian, Xiao-Song Lin. Colored coalescent theory. Conference Publications, 2005, 2005 (Special) : 833-845. doi: 10.3934/proc.2005.2005.833

Lluís Alsedà, David Juher, Pere Mumbrú. Minimal dynamics for tree maps. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 511-541. doi: 10.3934/dcds.2008.20.511


Katayun Barmak, Eva Eggeling, Maria Emelianenko, Yekaterina Epshteyn, David Kinderlehrer, Richard Sharp, Shlomo Ta'asan. An entropy based theory of the grain boundary character distribution. Discrete and Continuous Dynamical Systems, 2011, 30 (2) : 427-454. doi: 10.3934/dcds.2011.30.427


Alba Málaga Sabogal, Serge Troubetzkoy. Minimality of the Ehrenfest wind-tree model. Journal of Modern Dynamics, 2016, 10: 209-228. doi: 10.3934/jmd.2016.10.209


Vincent Delecroix. Divergent trajectories in the periodic wind-tree model. Journal of Modern Dynamics, 2013, 7 (1) : 1-29. doi: 10.3934/jmd.2013.7.1


Miaohua Jiang, Qiang Zhang. A coupled map lattice model of tree dispersion. Discrete and Continuous Dynamical Systems - B, 2008, 9 (1) : 83-101. doi: 10.3934/dcdsb.2008.9.83


Frédéric Bernicot, Bertrand Maury, Delphine Salort. A 2-adic approach of the human respiratory tree. Networks and Heterogeneous Media, 2010, 5 (3) : 405-422. doi: 10.3934/nhm.2010.5.405


Wenxiu Gong, Zuoliang Xu. An alternative tree method for calibration of the local volatility. Journal of Industrial and Management Optimization, 2022, 18 (1) : 137-156. doi: 10.3934/jimo.2020146


Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311


Maxim Sølund Kirsebom. Extreme value theory for random walks on homogeneous spaces. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4689-4717. doi: 10.3934/dcds.2014.34.4689


Sheng Zhang, Xiu Yang, Samy Tindel, Guang Lin. Augmented Gaussian random field: Theory and computation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 931-957. doi: 10.3934/dcdss.2021098


Akram Aldroubi, Rocio Diaz Martin, Ivan Medri, Gustavo K. Rohde, Sumati Thareja. The Signed Cumulative Distribution Transform for 1-D signal analysis and classification. Foundations of Data Science, 2022, 4 (1) : 137-163. doi: 10.3934/fods.2022001


Sergei Avdonin, Yuanyuan Zhao. Leaf Peeling method for the wave equation on metric tree graphs. Inverse Problems and Imaging, 2021, 15 (2) : 185-199. doi: 10.3934/ipi.2020060


Sergei Avdonin, Jonathan Bell. Determining a distributed conductance parameter for a neuronal cable model defined on a tree graph. Inverse Problems and Imaging, 2015, 9 (3) : 645-659. doi: 10.3934/ipi.2015.9.645


Rostyslav Kravchenko. The action of finite-state tree automorphisms on Bernoulli measures. Journal of Modern Dynamics, 2010, 4 (3) : 443-451. doi: 10.3934/jmd.2010.4.443


Alberto Bressan, Michele Palladino. Well-posedness of a model for the growth of tree stems and vines. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 2047-2064. doi: 10.3934/dcds.2018083


Reuven Cohen, Mira Gonen, Avishai Wool. Bounding the bias of tree-like sampling in IP topologies. Networks and Heterogeneous Media, 2008, 3 (2) : 323-332. doi: 10.3934/nhm.2008.3.323


Alberto Bressan, Sondre Tesdal Galtung. A 2-dimensional shape optimization problem for tree branches. Networks and Heterogeneous Media, 2021, 16 (1) : 1-29. doi: 10.3934/nhm.2020031


Shahede Omidi, Jafar Fathali. Inverse single facility location problem on a tree with balancing on the distance of server to clients. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1247-1259. doi: 10.3934/jimo.2021017


Klaus Reiner Schenk-Hoppé. Random attractors--general properties, existence and applications to stochastic bifurcation theory. Discrete and Continuous Dynamical Systems, 1998, 4 (1) : 99-130. doi: 10.3934/dcds.1998.4.99


Wenjia Jing, Olivier Pinaud. A backscattering model based on corrector theory of homogenization for the random Helmholtz equation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5377-5407. doi: 10.3934/dcdsb.2019063

 Impact Factor: 


  • PDF downloads (27)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]