메뉴 건너뛰기




Volumn 16, Issue 4, 2006, Pages 2195-2214

The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance

Author keywords

Airy distribution; Catalan trees; Central limit theorem; Contraction method; Random phylogenetic trees; Shape statistics; Yule process

Indexed keywords


EID: 33846885862     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051606000000547     Document Type: Article
Times cited : (76)

References (38)
  • 1
    • 0036963179 scopus 로고    scopus 로고
    • Power of eight tree shape statistics to detect nonrandom diversification: A comparison by simulation of two models of cladogenesis
    • AGAPOW, P.-M. and PURVIS, A. (2002). Power of eight tree shape statistics to detect nonrandom diversification: A comparison by simulation of two models of cladogenesis. Systematic Biology 51 866-872.
    • (2002) Systematic Biology , vol.51 , pp. 866-872
    • AGAPOW, P.-M.1    PURVIS, A.2
  • 2
    • 33846851879 scopus 로고    scopus 로고
    • ALDOUS, D. J. (1991a). The continuum random tree II: An overview. In Stochastic Analysis (N. T. Barlow and N. H. Bingham, eds.) 23-70. Cambridge Univ. Press. MR1166406
    • ALDOUS, D. J. (1991a). The continuum random tree II: An overview. In Stochastic Analysis (N. T. Barlow and N. H. Bingham, eds.) 23-70. Cambridge Univ. Press. MR1166406
  • 3
    • 0001324627 scopus 로고
    • Asymptotic fringe distributions for general families of random trees
    • MR1102319
    • ALDOUS, D. J. (1991b). Asymptotic fringe distributions for general families of random trees. Ann. Appl. Probab. 1 228-266. MR1102319
    • (1991) Ann. Appl. Probab , vol.1 , pp. 228-266
    • ALDOUS, D.J.1
  • 4
    • 33846860124 scopus 로고    scopus 로고
    • ALDOUS, D. J. (1996). Probability distributions on cladograms. In Random Discrete Structures (D. Aldous and R. Pemantle, eds.) 1-18. Springer, Berlin. MR1395604
    • ALDOUS, D. J. (1996). Probability distributions on cladograms. In Random Discrete Structures (D. Aldous and R. Pemantle, eds.) 1-18. Springer, Berlin. MR1395604
  • 5
    • 0002717710 scopus 로고    scopus 로고
    • Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today
    • MR1838600
    • ALDOUS, D. J. (2001). Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. Statist. Sci. 16 23-34. MR1838600
    • (2001) Statist. Sci , vol.16 , pp. 23-34
    • ALDOUS, D.J.1
  • 6
    • 19544368505 scopus 로고    scopus 로고
    • On statistical tests of phylogeny imbalance: The Sackin and other indices revisited
    • MR2146473
    • BLUM, M. G. B. and FRANÇOIS, O. (2005). On statistical tests of phylogeny imbalance: The Sackin and other indices revisited. Math. Biosci. 195 141-153. MR2146473
    • (2005) Math. Biosci , vol.195 , pp. 141-153
    • BLUM, M.G.B.1    FRANÇOIS, O.2
  • 7
    • 33750245951 scopus 로고    scopus 로고
    • Which random processes describe the Tree-of-Life? A large-scale study of phylogenetic tree imbalance
    • BLUM, M. G. B. and FRANÇOIS, O. (2006). Which random processes describe the Tree-of-Life? A large-scale study of phylogenetic tree imbalance. Systematic Biology 55 685-691.
    • (2006) Systematic Biology , vol.55 , pp. 685-691
    • BLUM, M.G.B.1    FRANÇOIS, O.2
  • 8
    • 0036959868 scopus 로고    scopus 로고
    • Whole-tree methods for detecting differential diversification rates
    • CHAN, K. M. A. and MOORE, B. R. (2002). Whole-tree methods for detecting differential diversification rates. Systematic Biology 51 855-865.
    • (2002) Systematic Biology , vol.51 , pp. 855-865
    • CHAN, K.M.A.1    MOORE, B.R.2
  • 9
    • 0002168111 scopus 로고
    • Review of phylogenetics: The theory and practice of phylogenetic systematics
    • COLLESS, D. H. (1982). Review of phylogenetics: The theory and practice of phylogenetic systematics. Systematic Zoology 31 100-104.
    • (1982) Systematic Zoology , vol.31 , pp. 100-104
    • COLLESS, D.H.1
  • 10
    • 0003809032 scopus 로고
    • Reprinted by Penguin Books, London, UK
    • DARWIN, C. (1859). The Origin of Species. Reprinted by Penguin Books, London, UK.
    • (1859) The Origin of Species
    • DARWIN, C.1
  • 11
    • 0030304083 scopus 로고    scopus 로고
    • On the distribution for binary search trees under the random permutation model
    • MR1368848
    • FILL, J. A. (1996). On the distribution for binary search trees under the random permutation model. Random Structures Algorithms 8 1-25. MR1368848
    • (1996) Random Structures Algorithms , vol.8 , pp. 1-25
    • FILL, J.A.1
  • 12
    • 5144220595 scopus 로고    scopus 로고
    • Limiting distributions for additive functionals on Catalan trees
    • MR2094243
    • FILL, J. A. and KAPUR, N. (2004). Limiting distributions for additive functionals on Catalan trees. Theoret. Comput. Sci. 326 69-102. MR2094243
    • (2004) Theoret. Comput. Sci , vol.326 , pp. 69-102
    • FILL, J.A.1    KAPUR, N.2
  • 13
    • 0001463608 scopus 로고    scopus 로고
    • Analytic variations on the Airy distribution
    • MR1855255
    • FLAJOLET, P. and LOUCHARD, G. (2001). Analytic variations on the Airy distribution. Algorithmica 31 361-377. MR1855255
    • (2001) Algorithmica , vol.31 , pp. 361-377
    • FLAJOLET, P.1    LOUCHARD, G.2
  • 14
    • 33846876864 scopus 로고    scopus 로고
    • Probabilities on cladogram: Introduction to the alpha model
    • FORD, D. J. (2005). Probabilities on cladogram: Introduction to the alpha model. Arxiv preprint math-0511246.
    • (2005) Arxiv preprint math-0511246
    • FORD, D.J.1
  • 15
    • 0001996348 scopus 로고
    • The probabilities of rooted tree-shapes generated by random bifurcation
    • MR0282451
    • HARDING, E. F. (1971). The probabilities of rooted tree-shapes generated by random bifurcation. Adv. in Appl. Probab. 3 44-77. MR0282451
    • (1971) Adv. in Appl. Probab , vol.3 , pp. 44-77
    • HARDING, E.F.1
  • 16
    • 33846893981 scopus 로고
    • Quicksort
    • MR0142216
    • HOARE, C. A. R. (1962). Quicksort. Comput. J. 5 10-15. MR0142216
    • (1962) Comput. J , vol.5 , pp. 10-15
    • HOARE, C.A.R.1
  • 17
    • 0036766889 scopus 로고    scopus 로고
    • Phase change of limit laws in the quicksort recurrence under varying toll functions
    • MR1954876
    • HWANO, H.-K. and NEININGER, R. (2002). Phase change of limit laws in the quicksort recurrence under varying toll functions. SIAM J. Comput. 31 1687-1722. MR1954876
    • (2002) SIAM J. Comput , vol.31 , pp. 1687-1722
    • HWANO, H.-K.1    NEININGER, R.2
  • 18
    • 0038095487 scopus 로고    scopus 로고
    • The Wiener index of simply generated random trees
    • MR1980963
    • JANSON, S. (2003). The Wiener index of simply generated random trees. Random Structures Algorithms 22 337-358. MR1980963
    • (2003) Random Structures Algorithms , vol.22 , pp. 337-358
    • JANSON, S.1
  • 20
    • 0001337578 scopus 로고
    • Searching for evolutionary patterns in the shape of a phylogenetic tree
    • KIRKPATRICK, M. and SLATKIN, M. (1993). Searching for evolutionary patterns in the shape of a phylogenetic tree. Evolution 47 1171-1181.
    • (1993) Evolution , vol.47 , pp. 1171-1181
    • KIRKPATRICK, M.1    SLATKIN, M.2
  • 21
    • 33846889223 scopus 로고    scopus 로고
    • KNUTH, D. E. (1973). The Art of Computer Programming 3. Sorting and Searching. Addison-Wesley, Reading, MA. MR0378456
    • KNUTH, D. E. (1973). The Art of Computer Programming 3. Sorting and Searching. Addison-Wesley, Reading, MA. MR0378456
  • 22
    • 33846878855 scopus 로고    scopus 로고
    • MAHMOUD, H. (1992). Evolution of Random Search Trees. Wiley, New York. MR1140708
    • MAHMOUD, H. (1992). Evolution of Random Search Trees. Wiley, New York. MR1140708
  • 23
    • 10044266639 scopus 로고    scopus 로고
    • MARTINEZ, C., PANHOLZER, A. and PRODINGER, H. (1998). The number of descendants and ascendants in random search trees. Electron. J. Combin. 5. MR1615346
    • MARTINEZ, C., PANHOLZER, A. and PRODINGER, H. (1998). The number of descendants and ascendants in random search trees. Electron. J. Combin. 5. MR1615346
  • 24
    • 0035084255 scopus 로고    scopus 로고
    • Properties of phylogenetic trees generated by Yule-type speciation models
    • MR1818785
    • MCKENZIE, A. and STEEL, M. (2001). Properties of phylogenetic trees generated by Yule-type speciation models. Math. Biosci. 170 91-112. MR1818785
    • (2001) Math. Biosci , vol.170 , pp. 91-112
    • MCKENZIE, A.1    STEEL, M.2
  • 25
    • 0002638760 scopus 로고    scopus 로고
    • Inferring evolutionary process from phylogenetic tree shape
    • MOOERS, A. and HEARD, S. B. (1997). Inferring evolutionary process from phylogenetic tree shape. Quarterly Review Biology 72 31-54.
    • (1997) Quarterly Review Biology , vol.72 , pp. 31-54
    • MOOERS, A.1    HEARD, S.B.2
  • 26
    • 0035539864 scopus 로고    scopus 로고
    • On a multivariate contraction method for random recursive structures with applications to quicksort
    • MR1871564
    • NEININGER, R. (2001). On a multivariate contraction method for random recursive structures with applications to quicksort. Random Structures Algorithms 19 498-524. MR1871564
    • (2001) Random Structures Algorithms , vol.19 , pp. 498-524
    • NEININGER, R.1
  • 27
    • 0036026970 scopus 로고    scopus 로고
    • The Wiener index of random trees
    • MR1940122
    • NEININGER, R. (2002). The Wiener index of random trees. Combin. Probab. Comput. 11 587-597. MR1940122
    • (2002) Combin. Probab. Comput , vol.11 , pp. 587-597
    • NEININGER, R.1
  • 28
    • 0036346960 scopus 로고    scopus 로고
    • Evaluating phylogenetic tree shape: Two modifications to Fusco and Cronk's method
    • PURVIS, A., KATZOURAKIS, A. and AGAPOW, P. M. (2002). Evaluating phylogenetic tree shape: Two modifications to Fusco and Cronk's method. J. Theor. Biol. 214 99-103.
    • (2002) J. Theor. Biol , vol.214 , pp. 99-103
    • PURVIS, A.1    KATZOURAKIS, A.2    AGAPOW, P.M.3
  • 29
    • 0001131997 scopus 로고
    • Probability metrics and recursive algorithms
    • MR1341885
    • RACHEV, S. T. and RÜSCHENDORF, L. (1995). Probability metrics and recursive algorithms. Adv. in Appl. Probab. 27 770-799. MR1341885
    • (1995) Adv. in Appl. Probab , vol.27 , pp. 770-799
    • RACHEV, S.T.1    RÜSCHENDORF, L.2
  • 30
    • 0000555301 scopus 로고
    • Central moments and probability distribution of Colless' coefficient of tree imbalance
    • ROGERS, J. S. (1994). Central moments and probability distribution of Colless' coefficient of tree imbalance. Evolution 48 2026-2036.
    • (1994) Evolution , vol.48 , pp. 2026-2036
    • ROGERS, J.S.1
  • 31
    • 0030336191 scopus 로고    scopus 로고
    • Central moments and probability distributions of three measures of phylogenetic tree imbalance
    • ROGERS, J. S. (1996). Central moments and probability distributions of three measures of phylogenetic tree imbalance. Systematic Biology 45 99-110.
    • (1996) Systematic Biology , vol.45 , pp. 99-110
    • ROGERS, J.S.1
  • 32
    • 0002731988 scopus 로고
    • A limit theorem for Quicksort
    • MR1104413
    • RÖSLER, U. (1991). A limit theorem for "Quicksort. " Theor. Inform. Appl. 25 85-100. MR1104413
    • (1991) Theor. Inform. Appl , vol.25 , pp. 85-100
    • RÖSLER, U.1
  • 33
    • 33645523017 scopus 로고    scopus 로고
    • Survey of multivariate aspects of the contraction method
    • MR2247515
    • RÜSCHENDORF, L. and NEININGER, R. (2006). Survey of multivariate aspects of the contraction method. Discrete Math. Theor. Comput. Sci. 8 31-56. MR2247515
    • (2006) Discrete Math. Theor. Comput. Sci , vol.8 , pp. 31-56
    • RÜSCHENDORF, L.1    NEININGER, R.2
  • 34
    • 84959788094 scopus 로고
    • Good" and "bad" phenograms
    • SACKIN, M. J. (1972). "Good" and "bad" phenograms. Systematic Zoology 21 225-226.
    • (1972) Systematic Zoology , vol.21 , pp. 225-226
    • SACKIN, M.J.1
  • 37
    • 0000703623 scopus 로고
    • A Bernoulli excursion and its various applications
    • MR1122875
    • TAKACS, L. (1991). A Bernoulli excursion and its various applications. Adv. in Appl. Probab. 23 557-585. MR1122875
    • (1991) Adv. in Appl. Probab , vol.23 , pp. 557-585
    • TAKACS, L.1
  • 38
    • 33846865940 scopus 로고    scopus 로고
    • YULE, G. U. (1924). A mathematical theory of evolution, based on the conclusions of Dr J. C. Willis. Philos. Trans. Roy. Soc. London Ser. B 213 21-87.
    • YULE, G. U. (1924). A mathematical theory of evolution, based on the conclusions of Dr J. C. Willis. Philos. Trans. Roy. Soc. London Ser. B 213 21-87.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.