A critical branching process model for biodiversity

Advances in Applied Probability

Volumn 37, Issue 4, 2005, Pages 1094-1115

  Aldous, David ^a   Popovic, Lea ^b,c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

^c Department of Molecular Biology and Genetics   (United States)

Author keywords

Biodiversity; Brownian excursion; Contour process; Critical branching process; Genealogy; Local weak convergence; Phylogenetic tree; Point process

Indexed keywords

APPROXIMATION THEORY; BROWNIAN MOVEMENT; MATHEMATICAL MODELS; MATHEMATICAL TECHNIQUES; RANDOM PROCESSES; TIME SERIES ANALYSIS;

BROWNIAN EXCURSION; CONTOUR PROCESS; CRITICAL BRANCHING PROCESS; GENEALOGY; LOCAL WEAK CONVERGENCE; PHYLOGENETIC TREE; POINT PROCESS;

BIODIVERSITY;

EID: 31944437577     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1134587755     Document Type: Article

References (19)

1. Aldous, D. J. (1991). Asymptotic fringe distributions for general families of random trees. Ann. Appl. Prob. 1, 228-266.
2. Aldous, D. J. (1993). The continuum random tree. III. Ann. Prob. 21, 248-289.
3. Aldous, D. J. and Steele, J. M. (2004). The objective method: probabilistic combinatorial optimization and local weak convergence. In Probability on Discrete Structures (Encyclopaedia Math. Sci. 110), ed. H. Kesten, Springer, Berlin, pp. 1-72.
4. Dembo, A. and Zeitouni, O. (1992). Large Deviations and Applications, 2nd edn. Jones and Bartlett, Boston, MA.
5. Duquesne, T. and Le Gall, J.-F. (2002). Random trees, Lévy processes and spatial branching processes. Astérisque 281, vi+147.
6. Ewens, W. J. (1979). Mathematical Population Genetics. Springer, Berlin.
7. Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. I, 3rd edn. John Wiley, New York.
8. Geiger, J. (2000). Poisson point processes in size-biased Galton-Watson trees. Electron. J. Prob. 5, 12pp.
9. Hey, J. (1992). Using phylogenetic trees to study speciation and extinction. Evolution 46, 627-640.
10. Krikun, M., Popovic, L. and Aldous, D. J. (2005). Stochastic models for phylogenetic trees on higher order taxa. In preparation.
11. Le Gall, J.-F. (1989). Marches aléatoires, mouvement brownien et processus de branchement. In Séminaire de Probabilités XXIII (Lecture Notes Math. 1372), Springer, Berlin, pp. 258-274.
12. Möhle, M. (2000). Ancestral processes in population genetics. J. Theoret. Biol. 204, 629-638.
13. Nee, S., May, R. M. and Harvey, P. H. (1994). The reconstructed evolutionary process. Philos. Trans. R. Soc. London B 344, 305-311.
14. Neveu, J. and Pitman, J. (1989). Renewal property of the extrema and tree property of a one-dimensional Brownian motion. In Séminaire de Probabilités XXIII (Lecture Notes Math. 1372), Springer, Berlin, pp. 239-247.
15. Page, R. D. M. and Holmes, E. C. (1998). Molecular Evolution: A Phylogenetic Approach. Blackwell Science, Oxford.
16. Pitman, J. (2002). Combinatorial stochastic processes. Tech. Rep. 621, Department of Statistics, University of California, Berkeley.
17. Popovic, L. (2004). Asymptotic genealogy of a critical branching process. Ann. Appl. Prob. 14, 2120-2148.
18. Wollenberg, K., Arnold, J. ad Avise, J. C. (1996). Recognizing the forest for the trees: testing temporal patterns of cladogenesis using a null model of stochastic diversification. Molec. Biol. Evol. 13, 833-849.
19. Yule, G. U. (1924). A mathematical theory of evolution, based on the conclusions of Dr J. C. Willis. Philos. Trans. R. Soc. London B 213, 21-87.