Branching Processes and Neutral Evolution (Lecture Notes in Biomathematics) - Softcover

Ziad Taib

Softcover

ISBN 10: 0387555293 ISBN 13: 9780387555294

Publisher: Springer Nature, 1992

Synopsis

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.

Edition details

• Publisher: Springer Nature
• Publication date: 1992
• Language: English
• ISBN 10: 0387555293
• ISBN 13: 9780387555294
• Binding: Paperback
• Number of pages: 112
• Editor: Simon A. Levin