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Branching Processes and Neutral Evolution : Results and Problems in Cell Differentiation - Ziad Taib

Branching Processes and Neutral Evolution

Results and Problems in Cell Differentiation

By: Ziad Taib

Paperback ISBN: 9783540555292
Number Of Pages: 112

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This monograph sets out to apply the current knowledge of single-type branching processes to a particular area of mathematical genetics: neutral evolution. It can also serve as an introductory text to branching processes seen as a methodology that can be used in various problems in populationdynamics. The work will be of interest to applied probabilists, researchers in branching processes, researchers in evolution theory and population geneticists. The reader is assumed to befamiliar with some of the concepts of probability theory, but no particular background in branching processes or evolution theory is required. The introduction of the book is accessible to a large audience.

0. Introduction.- 0.1. The general branching process.- 0.2. The neutral theory.- 0.3. The results.- 1. The Construction of the Process.- 1.1. The basic probability space.- 1.2. Processes counted with random characteristics.- 1.3. Special cases.- 1.4. Decompositions.- 1.5. General assumptions.- 2. Labelled Branching Processes.- 2.1. Labelled branching populations.- 2.2. The fate of the ancestral label.- 3. The Number of Distinct Labels.- 3.1. The total number of labels.- 3.2. The number of present labels.- 3.3. A Bellman-Harris application.- 3.4. The lattice case.- 4. The Label Process.- 4.1. The embedded label process.- 4.2. The oldest labels.- 4.3. The most frequent labels.- 5. The Limiting Stable Case.- 5.1. The stable pedigree space.- 5.2. The stable pedigree measure.- 5.3. Sampling among living individuals.- 6. The Process of Mutant Ancestors.- 6.1. The age of the label of an RSI.- 6.2. A renewal process.- 7. A Measure of Relatedness.- 7.1. The mean size of a label.- 7.2. The distribution of the size of a label.- 7.3. The probability of identity by descent.- 8. Infinite Sites Labels.- 8.1. The mean size.- 8.2. Another measure of relatedness.- 9. Related Individuals.- 9.1. Genealogical distances.- 9.2. Distances between relatives.- 10. Embeddings in Branching Processes.- 10.1. Trees and general branching processes.- 10.2. The branching property.- 10.3. Generalized individuals.- 11. Extensions.- 11.1. Other sampling schemes.- 11.2. Further developments.- Appendices.- A. Basic convergence theorems.- B. The lattice case.- A List of Symbols and Conventions.- References.

ISBN: 9783540555292
ISBN-10: 3540555293
Series: Results and Problems in Cell Differentiation
Audience: General
Format: Paperback
Language: English
Number Of Pages: 112
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 25.4 x 17.78  x 0.66
Weight (kg): 0.23