Ch. 18. Biological applications of branching processes

Handbook of Statistics

Volumn 21, Issue , 2003, Pages 693-773

  Pakes, Anthony G ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649656117     PISSN: 01697161     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0169-7161(03)21020-8     Document Type: Review

References (330)

1. Abraham R., and L. M. Branching properties of Brownian paths and trees. Exposition Math. 16 (1998) 59-73
2. Afanas'ev V.I. On the nonextinction probability of a subcritical branching process in random environment. Manuscript Dept. VINITI No. 1 (1979) 794-799
3. Alexandersson M. Branching Processes and Cell Populations (1999), Matematiskt Centrum, New York
4. Allen E.J., Harris J.M., and Allen L.J.S. Presistence-time models for use in viability analysis. J. Theor. Biol. 155 (1992) 33-53
5. Alsmeyer G., and Rösler U. The bisexual Galton-Watson process with promiscuous mating: extinction probabilities in the supercritical case. Ann. Appl. Probab. 6 (1996) 922-939
6. Alsmeyer G., and Rösler U. Asexual versus promiscuous bisexual Galton-Watson processes: the extinction probability ratio. Ann. Appl. Probab. 12 (2002) 125-142
7. Alsmeyer G., and Rösler U. The Martin entrance boundary of the Galton-Watson process. Report 13/02-S (2002), Universität Münster, Göteborg
8. Anderson W.J. Continuous-Time Markov Chains (1991), Springer-Verlag, New York
9. Andersson M. The asymptotic final size distribution of multitype chain-binomial epidemic processes. Adv. Appl. Probab. 31 (1999) 220-234
10. Arino O., Kimmel M., and Webb G.F. Mathematical modeling of the loss of telomere sequences. J. Theor. Biol. 177 (1995) 45-57
11. Asmussen S. On some two-sex population models. Ann. Probab. 8 (1980) 727-744
12. Asmussen S., and Hering H. Branching Processes (1983), Birkhäuser, New York
13. Assaf D., Goldstein L., and Samuel-Cahn E. An unexpected connection between branching processes and optimal stopping. J. Appl. Probab. 37 (2000) 613-626
14. Athreya K.B. Rates of decay for the survival probability of a mutant gene. J. Math. Biol. 30 (1992) 577-581
15. In: Athreya K.B., and Jagers P. (Eds). Classical and Modern Branching Processes (1997), Springer-Verlag, Boston
16. Athreya K.B., and Karlin S. Limit theorems for the split times of branching processes. J. Math. Mech. 17 (1967) 257-277
17. Athreya K., and Ney P.E. Branching Processes (1972), Springer-Verlag, New York
18. Bailey N.T.J. The Mathematical Theory of Infections Diseases and its Applications. 2nd ed (1975), Charles Griffin, Berlin
19. Ball F. Deterministic and stochastic epidemics with several kinds of susceptibles. Adv. Appl. Probab. 17 (1985) 1-22
20. Ball F. Coupling methods in epidemic theory. In: Mollison D. (Ed). Epidemic Models: Their Structure and Relation to Data (1995), Cambridge University Press, London 34-52
21. Ball F. The threshold behaviour of stochastic epidemics among a population divided into households. In: Heyde C.C., Prohorov Yu.V., Pyke R., and Rachev S.T. (Eds). Athens Conference on Applied Probability and Time Series Vol. I: Applied Probability (1996), Springer, Cambridge 253-266
22. Ball F. The threshold behaviour of stochastic epidemics. In: Arino O., Axelrod D., and Kimmel M. (Eds). Advances in Mathematical Population Dynamics (1997), World Scientific, New York 407-424
23. Ball F. Stochastic and deterministic models for SIS epidemics among a population partitioned into households. Math. Biosci. 156 (1999) 41-67
24. Ball F., and Clancy D. The final size and severity of a generalized stochastic multitype epidemic model. Adv. Appl. Probab. 25 (1993) 721-736
25. Ball F., and Clancy D. The final outcome of an epidemic model with several different types of infective in a large population. J. Appl. Probab. 32 (1995) 579-590
26. Ball F., and Donnelly P. Branching process approximation of epidemic models. Theory Probab. Appl. 34 (1990) 119-121
27. Ball F., and Donnelly P. Strong approximations for epidemic models. Stochastic Process. Appl. 55 (1995) 1-21
28. Ball F., and Lyne O.D. Stochastic multi-type SIR epidemics among a population partitioned into households. Adv. Appl. Probab. 33 (2001) 99-123
29. Ball F., and Nsell I. The shape of the size distribution of an epidemic in a finite population. Math. Biosci. 123 (1994) 167-181
30. Ball F., and O'Neill P. Strong convergence of stochastic epidemics. Adv. Appl. Probab. 26 (1994) 629-655
31. Ball F., Mollison D., and Scalia-Tomba G. Epidemics with two levels of mixing. Ann. Appl. Probab. 7 (1997) 46-89
32. Barbour A.D. Threshold phenomena in epidemic theory. In: Kelly F.P. (Ed). Probability, Statistics and Optimization (1994), Wiley, Singapore 101-116
33. Barbour A.D., and Kafetzaki M. A host parasite model yielding heterogeneous parasite loads. J. Math. Biol. 31 (1993) 157-176
34. Barnett S.A. The Science of Life (1998), Allen & Unwin, St Leonards, Chichester
35. Bartlett M.S. An Introduction to Stochastic Processes. 3rd ed. (1978), Cambridge University Press, Australia
36. Bartoszyński R. Branching processes and models of epidemics. Dissertations Math LXI (1969) 1-48
37. Becker N.G. Analysis of Infectious Disease Data (1989), Chapman & Hall, Cambridge
38. Becker N.G., and Marschner I. The effect of heterogencity on the spread of disease. In: Gabriel J.-P., Lefrèvre C., and Picard P. (Eds). Stochastic Processes in Epidemic Theory (1990), Springer-Verlag, London 90-103
39. Bennies J., and Kersting G. A random walk approach to Galton-Watson trees. J. Theor. Probab. 13 (2000) 777-803
40. Biggins J.D. How fast does a general branching random walk spread?. In: Athreya K.B., and Jagers P. (Eds). Classical and Modern Branching Processes (1997), Springer-Verlag, New York 19-39
41. Bingham N.H., Goldie C.M., and Teugels J.L. Regular Variation (1987), Cambridge University Press, New York
42. Boiko R.V. A limit theorem for branching random processes with variable mode (critical case). Ukrainian Math. J. 29 (1977) 68-73
43. Boiko R.V. A supercritical branching process with variable mode. Ukrainian Math. J. 32 (1980) 118-122
44. Born E. A point process model with stochastic intensities for a branching population of two dependent types. Adv. Appl. Probab. 30 (1998) 723-739
45. Boucher K., Zorin A., Yakovlev A.Y., Mayer-Proschel M., and Noble M. An alternative stochastic model of generation of oligodendrocytes in cell culture. J. Math. Biol. 43 (2001) 22-36
46. Brillinger D.R. Some aspects of modern population mathematics. Canad. J. Statist. 9 (1981) 173-194
47. Brockwell P.J., Gani J., and Resnick S. Birth, immigration and catastrophe processes. Adv. Appl. Probab. 14 (1982) 709-731
48. Brook D. Bounds for moment generating functions and for extinction probabilities. J. Appl. Probab. 3 (1966) 171-178
49. Bru B., Jongmans, and Seneta E. I. J. Bienaymé: Family information and proof of the criticality theorem. Int. Statist. Rev. 60 (1992) 177-183
50. Bruss F.T. A note on the extinction criteria for bisexual Galton-Watson processes. J. Appl. Probab. 21 (1984) 915-919
51. Burkey T.V. Extinction in nature reserves: the effect of fragmentation and the importance of migration between reserve fragments. Oikos 55 (1989) 75-81
52. Butler S.M. The early and final states of an epidemic in a large heterogeneous population with a small initial number of infectives. Adv. Appl. Probab. 26 (1994) 671-689
53. Cavalli-Sforza L.L., and Feldman M.W. Cultural Transmission and Evolution: A Quantitative Approach (1981), Princeton University Press, Cambridge
54. Chauvin B., and Rouault A. KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees. Probab. Theory Related Fields 80 (1988) 299-314
55. Chauvin B., and Rouault A. A stochastic simulation for solving scalar reaction-diffusion equations. Adv. Appl. Probab. 22 (1990) 88-100
56. In: Chauvin B., Cohen S., and Rouault A. (Eds). Trees: Workshop in Versailles, June 14-16, 1995 (1996), Birkhäuser, Princeton
57. Consul P.C. Evolution of surnames. Int. Statist. Rev. 59 (1991) 271-278
58. Hachette, Paris, §36. Cournot A.A. De l'Origine et des Limites de la Correspondance entre l'Algebre et la Géométrie. 1989 (1847), Réédition, Basel
59. Crump K.S., and Gillespie J.H. The dispersion of a neutral allele considered as a branching process. J. Appl. Probab. 13 (1976) 208-218
60. Daley D.J. Extinction conditions for certain bisexual Galton-Watson branching process. Z. Wahrsceinlichkeitsth 9 (1968) 315-322
61. Daley D.J. Extinction probabilities in branching processes: a note on Holgate and Lakhani's paper. Bull. Math. Biophys. 31 (1969) 35-37
62. Daley D.J., and Gani J. Epidemic Modelling (1999), Cambridge University Press, Vrin, Paris
63. Daley D.J., Hull D.M., and Taylor J.M. Bisexual Galton-Watson branching processes with superadditive mating functions. J. Appl. Probab. 23 (1986) 585-600
64. Dawson D.A. Measure-valued Markov processes. In: Hennequin P.L. (Ed). Ecole d'Eté de Probabilités de Saint-Flour XXI - 1991. Lecture Notes in Math. Vol. 1541 (1993), Springer-Verlag, Cambridge 1-260
65. Demetrius L., Schuster P., and Sigmund K. Polynucleotide evolution and branching processes. Bull. Math. Biol. 47 (1985) 239-262
66. Devroye L. Branching processes and their applications in the analysis of tree structures and tree algorithms. In: Habib M., et al. (Ed). Probability Methods for Algorithmic Discrete Mathematics (1998), Springer, Berlin 249-314
67. Diamond J. The island dilemma: lessons of modern biogeographic studies for the design of natural reserves. Biol. Conserv. 7 (1975) 129-146
68. Dion J.-P. Statistical Inference for Discrete Time Branching Processes. Lecture Notes, 7th International Summer School on Probability and Mathematical Statistics (1991), Varna, Berlin
69. Dobzhansky T., Ayala F.J., Stebbins G.L., and Valentine J.W. Evolution (1977), W. H. Freeman & Co., Bulgaria
70. Donnelly P. Comment. Statist. Sci. 6 (1991) 277-279
71. D'Souza J.C., and Hambly B.M. On the survival probability of a branching process in a random environment. Adv. Appl. Probab. 29 (1997) 38-55
72. Durrett R. Probability Models for DNA Sequence Evolution (2002), Springer, San Francisco
73. Dynkin E.B. An Introduction to Branching Measure-Valued Processes (1994), Amer. Math. Soc., New York
74. Eshel I. On the survival probability of a slightly advantageous mutant gene with a general distribution of progeny - a branching process model. J. Math. Biol. 12 (1981) 355-362
75. Eshel I. On the survival probability of a slightly advantageous gene in a multitype population: a multidimensional branching process model. J. Math. Biol. 19 (1984) 201-209
76. Etheridge A.M. An Introduction to Superprocesses. University Lecture Series Vol. 20 (2000), Amer. Math. Soc., Providence, RI
77. Ethier S.N., and Kurtz T.G. Markov Processes (1986), Wiley, Providence, RI
78. Ewens W.J. Some applications of multi-type branching processes in population genetics. J. Roy. Statist. Soc. B 30 (1968) 164-175
79. Ewens W.J. Population Genetics (1969), Methuen & Co., New York
80. Ewens W.J. Mathematical Population Genetics (1979), Springer-Verlag, London
81. Fahady K.S., Quine M.P., and Vere-Jones D. Heavy traffic approximations for the Galton-Watson process. Adv. Appl. Probab. 3 (1971) 282-300
82. Falahati A. Two-sex branching populations. Dissertation, Dept. Math. Statistics (1999), Chalmers Univ. Tech., Berlin
83. Farrington C., and Grant A.D. The distribution of time to extinction in subcritical branching processes: applications to outbreaks of infectious disease. J. Appl. Probab. 36 (1999) 771-779
84. Ferrari P.A., Kesten H., and Martínez S. R-positivity, quasi-stationary distributions and ratio limit theorems for a class of probabilistic automata. Ann. Appl. Probab. 6 (1996) 577-616
85. Finkelstein M., and Tucker H.G. A law of small numbers for a mutation process. Math. Biosci. 95 (1989) 85-98
86. Finkelstein M., Tucker H.G., and Veeh J.A. The limit distribution of the number of rare mutants. J. Appl. Probab. 27 (1990) 239-250
87. Fisher R.A. On the dominance ratio. Proc. Roy. Soc. Edinburgh 42 (1922) 321-341
88. Fisher R.A. The distribution of gene ratios for rare mutations. Proc. Roy. Soc. Edinburgh 50 (1930) 205-220
89. Fisher R.A. The advance of advantageous genes. Ann. Eugenics 7 (1937) 355-369
90. Fisher R.A. The Genetical Theory of Natural Selection. 2nd ed. (1958), Dover Publications, Götebors, Sweden
91. Foley P. Extinction models for local populations. In: Hanski I.A., and Gilpin M.E. (Eds). Metapopulation Biology: Ecology, Genetics and Evolution (1997), Academic Press, New York 215-246
92. Fox W.R., and Lasker G.W. The distribution of surname frequencies. Int. Statist. Rev. 51 (1983) 81-87
93. In: Gabriel J.-P., Lefevre C., and Picard P. (Eds). Stochastic Processes in Epidemic Theory (1990), Springer-Verlag, San Diego
94. Gabriel W., and Bürger R. Survival of small populations under demographic stochasticity. Theor. Popn. Biol. 41 (1992) 44-71
95. Gale J.S. Theoretical Population Genetics (1990), Unwin Hyman, New York
96. Gale J.S., and Lawrence M.J. The decay of variability. In: Holden J.H.W., and Williams J.T. (Eds). Crop Genetic Resources: Conservation & Evaluation (1984), Allen & Unwin, London 77-101
97. Galton F., and Watson H.W. On the probability of the extinction of families. J. Roy. Anthropol. Inst. 4 (1874) 138-144
98. Gawel B., and Kimmel M. The iterated Galton-Watson process. J. Appl. Probab. 33 (1996) 949-959
99. Geiger J. Elementary new proofs of classical limit theorems for Galton-Watson processes. J. Appl. Probab. 36 (1999) 301-309
100. Geiger J. Poisson point process limits in size-biased Galton-Watson trees. Electronic J. Probab. 5 (2000) 1-12
101. Gillespie J.H. The Causes of Molecular Evolution (1991), Oxford University Press, London
102. Gladstien K., and Lange K. Number of people and number of generations affected by a single deleterious mutation. Theor. Pop. Biol. 14 (1978) 313-321
103. Gladstien K., and Lange K. Equilibrium distributions for deleterious genes in large stationary populations. Theor. Pop. Biol. 14 (1978) 322-328
104. Goel N.S., and Richter-Dyn N. Stochastic Models in Biology (1974), Academic Press, New York
105. González M., and Molina M. On the limit behaviour of a superadditive bisexual Galton-Watson branching process. J. Appl. Probab. 33 (1996) 960-967
106. 2-convergence of a superadditive bisexual Galton-Watson branching process. J. Appl. Probab. 34 (1997) 575-582
107. Goodman D. Consideration of stochastic demography in the design and management of biological reserves. Nat. Res. Modelling 1 (1987) 205-234
108. Goodman D. The demography of chance extinction. In: Soulé M.E. (Ed). Viable Populations for Conservation (1987), Cambridge University Press, New York 11-34
109. Goodman L.A. How to minimize or maximize the probabilities of extinction in a Galton-Watson process and in some related multiplicative population processes. Ann. Math. Statist. 39 (1968) 1700-1710
110. Gosselin F. Extinction in a simple source/sink system: application of new mathematical results. Acta Oecologica 17 (1996) 563-584
111. Gosselin F. Asymptotic behaviour of some discrete-time Markov chains conditional on non-extinction. Part I: Theory. Rapport #98-04 (1998), Inst. Recherche Agronomique, New York 1-54
112. Gosselin F. Asymptotic behaviour of some discrete-time Markov chains conditional on non-extinction. Part II: Applications. Rapport #98-05 (1988), Inst. Recherche Agronomique, Montpellier 1-39
113. Gosselin F. Asymptotic behaviour of absorbing Markov chains conditional on nonabsorption for applications in conservation biology. Ann. Appl. Probab. 11 (2001) 261-284
114. Gosselin F., and Lebreton J.-D. The potential of branching processes as a modeling tool for conservation biology. In: Ferson S. (Ed). Quantitative Methods for Conservation Biology (1997), Springer-Verlag, Montpellier
115. In: Gottlieb K. (Ed). Human Biology Vol. 55 (1983) 209-408
116. Grey D.R. Minimisation of extinction probabilities in reproducing populations. Theor. Pop. Biol. 18 (1980) 430-445
117. Grey D.R., and Lu Z. The asymptotic behaviour of extinction probability in the Smith-Wilkinson branching process. Adv. Appl. Probab. 25 (1993) 263-289
118. Grey D.R., Hutson V., and Szathmáry E. A re-examination of the stochastic corrector model. Proc. Roy. Soc. London B 262 (1995) 29-35
119. Griffiths D.A. Multivariate birth-and-death processes as approximations to epidemic processes. J. Appl. Probab. 10 (1973) 15-26
120. Griffiths R.C., and Pakes A.G. An infinite-alleles version of the simple branching process. Adv. Appl. Probab. 20 (1988) 489-524
121. Grimmett G. Percolation (1989), Springer-Verlag, Berlin
122. Gupta S.C., Srivastava O.P., and Singh M. Branching processes with emigration - a genetic model. Math. Biosci. 111 (1992) 159-168
123. Guttorp P. Statistical Inference for Branching Processes (1991), Wiley, Berlin
124. Guttorp P. Three papers on the history of branching processes. Int. Statist. Rev. 63 (1995) 233-245
125. Haccou P., and Iwasa Y. Establishment probability in fluctuating environments: a branching process model. Theor. Pop. Biol. 50 (1996) 254-280
126. Haigh J., and Maynard Smith J. Population size and protein variation in man. Genet. Res. Camb. 19 (1972) 73-89
127. Haldane J.B.S. A mathematical theory of natural and artificial selection, Part V: Selection and mutation. Proc. Cambridge Philos. Soc. 23 (1927) 838-844
128. Haldane J.B.S. The rate of spontaneous mutation of a human gene. J. Genet. 23 (1935) 317-326
129. Haldane J.B.S. The equilibrium between mutation and random extinction. Ann. Eugen. 9 (1939) 400-405
130. Haldane J.B.S. The Causes of Evolution. In: Egbert G. Jr. L. (Ed). With a new Introduction and Afterword (1990), Princeton University Press, New York
131. Hanin L.G. Iterated birth and death process as a model of radiation cell survival. Math. Biosci. 169 (2001) 89-107
132. Harnevo L.E., and Agur Z. The dynamics of gene amplification described as a multitype compartmental model and as a branching process. Math. Biosci. 103 (1991) 115-138
133. Harris S.C. Travelling-waves for the FKPP equation via probabilistic arguments. Proc. Roy. Soc. Edinburgh A 129 (1999) 503-517
134. Harris T.E. Some mathematical models for branching processes. In: Neyman J. (Ed). Second Symposium on Probability and Statistics (1951), University of California Press, Princeton 305-328
135. Harris T.E. The Theory of Branching Processes (1963), Springer-Verlag, Berkeley
136. Helland I.S. Minimal conditions for weak convergence to a diffusion process on the line. Ann. Probab. 9 (1981) 429-452
137. Heyde C.C. On an explanation for the characteristic clutch size of some bird species. Adv. Appl. Probab. 10 (1978) 723-725
138. Heyde C.C. On assessing the potential severity of an outbreak of a rare disease: a Bayesian approach. Austral. J. Statist. 21 (1979) 282-292
139. In: Heyde C.C. (Ed). Branching Processes: Proceedings of the First World Congress (1995), Springer-Verlag, Berlin
140. Heyde C.C., and Schuh H.-J. Uniform bounding of probability generating functions and the evolution of reproduction rates in birds. J. Appl. Probab. 15 (1978) 243-250
141. Heyde C.C., and Seneta E. I. J. Bienaymé: Statistical Theory Anticipated (1977), Springer-Verlag, New York
142. Hofbauer J., and Sigmund K. The Theory of Evolution and Dynamical Systems (1988), Cambridge University Press, New York
143. Högnäs G. On the quasi-stationary distribution of a stochastic Ricker model. Stochastic Process. Appl. 70 (1997) 243-263
144. Holgate P. A mathematical study of the founder principle of evolutionary genetics. J. Appl. Probab. 3 (1966) 115-128
145. Holgate P.A. Divergent population processes and mammal outbreaks. J. Appl. Probab. 4 (1967) 1-8
146. Holgate P. Population survival and life history phenomena. J. Theor. Biol. 14 (1967) 1-10
147. Holgate P., and Lakhani K.H. Effect of offspring distribution on population survival. Bull. Math. Biophys. 29 (1967) 831-839
148. Höpfner R. On some classes of population-size-dependent Galton-Watson processes. J. Appl. Probab. 22 (1985) 25-36
149. Höpfner R. A note on the probability of extinction in a class of population-size-dependent Galton-Watson processes. J. Appl. Probab. 22 (1985) 920-925
150. Hoppe F.M. Asymptotic rates of growth of the extinction probability of a mutant gene. J. Math. Biol. 30 (1992) 547-566
151. Hoppe F.M. The survival probability of a mutant in a multidimensional population. J. Math. Biol. 30 (1992) 567-575
152. Hull D.M. Conditions for extinction in those bisexual Galton-Watson branching processes governed by superadditive mating functions. J. Appl. Probab. 19 (1982) 847-850
153. Hull D.M. A necessary condition for extinction in certain bisexual Galton-Watson branching processes. J. Appl. Probab. 21 (1984) 414-418
154. Hull D.M. How many mating units are needed to have a positive probability of survival?. Math. Magazine 66 (1993) 28-33
155. Hull D.M. A reconsideration of Galton's problem (Using a two-sex population). Theor. Pop. Biol. 54 (1998) 105-116
156. Hull D.M. A reconsideration of Lotka's extinction probability using bisexual branching processes. J. Appl. Probab. 38 (2001) 776-780
157. Islam M.N. A stochastic model for surname evolution. Biom. J. 37 (1995) 119-126
158. Ismail M.E.H., Masson D.R., Letassier J., and Valent G. Birth and death processes and orthogonal polynomials. In: Nevai P. (Ed). Orthogonal Polynomials (1990), Kluwer Academic Publishers,, Cambridge 229-255
159. Jacquez J.A. A note on chain binomial models of epidemic spread: what is wrong with the Reed-Frost formulation?. Math. Biosci. 87 (1987) 73-82
160. Jagers P. Branching Processes with Biological Applications (1975), Wiley, Dordrecht, The Netherlands
161. Jagers P. The growth and stabilization of populations. Statist. Sci. 6 (1991) 269-283
162. Jagers P. Branching processes as population dynamics. Bernoulli 1 (1995) 191-200
163. Jagers P. Branching processes with dependent but homogeneous growth. Ann. Appl. Probab. 9 (1999) 1160-1174
164. Jagers P., Nerman O., and Ziab T. When did Joe's great ... grandfather live? or: On the time scale of evolution. In: Basawa I.V., and Taylor R.L. (Eds). Selected Proceedings of the Sheffield Symposium on Applied Probability. IMS Lecture Notes Monograph Ser. Vol. 18 (1991) 118-126
165. Johnson N.L., Kotz S., and Kemp A.W. Univariate Discrete Distributions. 2nd ed (1992), Wiley, Hayward, CA
166. Kämmerle K. The extinction probability of descendents in bisexual models of fixed population size. J. Appl. Probab. 28 (1991) 489-502
167. Kaplan N. A continuous time branching model with random environments. Adv. Appl. Probab. 5 (1973) 37-54
168. Karlin S., and Kaplan N. Criteria for extinction of certain population growth processes with interacting types. Adv. Appl. Probab. 5 (1973) 183-199
169. Karlin S., and Tavaré S. Detecting particular genotypes in populations under nonrandom mating. Math. Biosci. 59 (1982) 57-75
170. Keiding N. Lecture Notes on the Stochastic Population Model (1973), Institute of Mathematical Statistics, New York
171. Keiding N. Extinction and exponential growth in random environments. Theor. Pop. Biol. 8 (1975) 49-63
172. Kendall D.G. Branching processes since 1873. J. London Math. Soc. 41 (1966) 385-406
173. Kendall D.G. The genealogy of genealogy: branching processes before (and after) 1873. Bull. London Math. Soc. 7 (1975) 225-253
174. Kersting G. Some properties of stochastic difference equations. In: Tautu P. (Ed). Stochastic Modelling in Biology (1990), World Scientific, Univ. of Copenhagen 328-339
175. Kesten H. Quadratic transformations: a model for population growth. Adv. Appl. Probab. 2 (1970) 1-82
176. Kesten H. Quadratic transformations: a model for population growth. Adv. Appl. Probab. 2 (1970) 179-228
177. Keyfitz N. Introduction to the Mathematics of Population (1968), Addison-Wesley, Singapore
178. Keyfitz N., and Tyree A. Computerization of the branching process. Behav. Sci. 12 (1967) 329-336
179. Kijima M. Markov Processes for Stochastic Modelling (1997), Chapman & Hall, Reading, MA
180. Kimmel M. Quasistationarity in a branching model of division-within-division. In: Athreya K.B., and Jagers P. (Eds). Classical and Modern Branching Processes (1997), Springer-Verlag, London 157-164
181. Kimmel M., and Axelrod D.E. Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenecity. Genetics 125 (1990) 633-644
182. Kimmel M., and Axelrod D.E. Branching Processes in Biology (2002), Springer, New York
183. Kimmel M., Axelrod D.E., and Wahl G.M. A branching process model of gene amplification following chromosome breakage. Mutation Res. 276 (1992) 225-239
184. Kimmel M., and Stivers D.N. Time-continuous branching random walk models of unstable gene amplification. Bull. Math. Biol. 56 (1994) 337-357
185. Klebaner F.C. Geometric rate of growth in population-size-dependent branching processes. J. Appl. Probab. 21 (1984) 40-49
186. Klebaner F.C. On population-size-dependent branching processes. Adv. Appl. Probab. 16 (1984) 30-55
187. Klebaner F.C. A limit theorem for population-size-dependent branching processes. J. Appl. Probab. 22 (1985) 48-57
188. Klebaner F.C. Population and density dependent branching processes. In: Athreya K.B., and Jagers P. (Eds). Classical and Modern Branching Processes (1997), Springer-Verlag, New York 165-169
189. Klebaner F.C., and Zeitouni O. The exit problem for a class of density-dependent branching processes. Ann. Appl. Probab. 4 (1994) 1188-1205
190. Klebaner F.C., Lazar J., and Zeitouni O. On the quasi-stationary distribution for some randomly perturbed transformations on an interval. Ann. Appl. Probab. 8 (1998) 300-315
191. Kojima K.-I., and Kellerher T.M. Survival of mutant genes. Amer. Naturalist 96 (1962) 329-346
192. Kojima K.-I., and Schaffer H.E. Accumulation of epistatic gene complexes. Evolution 18 (1964) 127-129
193. Krawczak M., Reiss J., Schmidtke J., and Rösler U. Polymerase chain reaction: replication errors and reliability of gene diagnosis. Nucl. Acids Res. 17 (1989) 2197-2201
194. Kurtz T.G. Diffusion approximations for branching processes. In: Joffe A., and Ney P.E. (Eds). Branching Processes (1978), Marcel Dekker, Inc., New York 269-292
195. Kyriakidis E.G. A Markov decision algorithm for optimal pest control through uniform catastrophes. Europ. J. Oper. Res. 64 (1993) 38-44
196. Lande R. Genetics and demography in biological conservation. Science 241 (1988) 1455-1460
197. Lange K. Minimum extinction probability for surnames and favourable mutations. Math. Biosci. 54 (1981) 71-78
198. Lange K. Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform. Biometrics 38 (1982) 79-86
199. Lange K., and Fan R.Z. Branching process models for mutant genes in nonstationary populations. Theor. Pop. Biol. 51 (1997) 118-133
200. Lange K., and Gladstein K. Further characterization of the long-run population distribution of a deleterious gene. Theor. Pop. Biol. 18 (1980) 31-43
201. Lange K., Gladstein K., and Zatz M. Effects of reproductive compensation and genetic drift in X-linked lethals. Am. J. Hum. Genet. 30 (1978) 180-189
202. Lasker G.W. Surnames and Genetic Structure (1985), Cambridge University Press, New York
203. Lebreton J.-D. Application of discrete time branching processes to bird population dynamics modelling. Anais 10a Conferênca Internacional de Biometria (1982), Empraba, New York 115-133
204. Lebreton J.-D., and Clobert J. Bird population dynamics, management and conservation: the role of mathematical modelling. In: Perrins C.M., Lebreton J.-D., and Hirons G.J.M. (Eds). Bird Population Studies (1991), Oxford University Press, Brasilia 105-125
205. Lee C. The density of the extinction probability of a time homogeneous linear birth and death process under the influence of randomly occurring disasters. Math. Biosci. 164 (2000) 93-102
206. Lefevre C., and Picard Ph. On the formulation of discrete-time epidemic models. Math. Biosci. 95 (1989) 27-35
207. Lefèvre C., and Picard Ph. Collective epidemic processes: a general modelling approach to the final outcome of SIR infectious diseases. In: Mollison D. (Ed). Epidemic Models: Their Structure and Relation to Data (1995), Cambridge University Press, Oxford 53-70
208. Le Gall J.-F. Spatial Branching Processes, Random Snakes and Partial Differential Equations (1999), Birkhäuser, Cambridge
209. Leigh E.G. Population fluctuations, community stability, and environmental variability. In: Cody M.L., and Diamond J.M. (Eds). Ecology and Evolution of Communities (1975), Belknap Press, Basel 51-73
210. Leigh E.G. The average lifetime of a population in a varying environment. J. Theor. Biol. 90 (1981) 213-239
211. Lewontin R.C., and Cohen D. On population growth in a randomly varying environment. Proc. Nat. Acad. Sci. 62 (1969) 1056-1060
212. Li F.H.F., Neel J.V., and Rothman E.D. A second study of the survival of a neutral mutant in a simulated amerindian population. Amer. Naturalist 112 (1978) 83-96
213. Liggett T.M. Stochastic Interacting Systems: Contact, Voter, and Exclusion Processes (1999), Springer-Verlag, Cambridge, MA
214. Lipow C. A branching process model with size dependence. Adv. Appl. Probab. 5 (1977) 14-24
215. Lipow C. Limiting diffusions for population-size dependent branching processes. J. Appl. Probab. 14 (1977) 14-24
216. Lipow C. Behaviour of limiting diffusions for density-dependent branching processes. In: Jäger W., Rost H., and Tautu P. (Eds). Biological Growth and Spread (1980), Springer-Verlag, Berlin 130-137
217. Liu Q. On the survival probability of a branching process in a random environment. Ann. Inst. H. Poincaré 32 (1996) 1-10
218. López-Mimbela J.A., and Wakolbinger A. Which critically branching populations persist?. In: Athreya K.B., and Jagers P. (Eds). Classical and Modern Branching Processes (1997), Springer-Verlag, Berlin 203-216
219. Lotka A. The extinction of families, I. J. Washington Acad. Sci. 21 (1931) 377-380
220. Lotka A. The extinction of families, II. J. Washington Acad. Sci. 21 (1931) 453-459
221. Ludwig D. Final size distributions for epidemics. Math. Biosci. 23 (1975) 33-46
222. Ludwig D. The distribution of population survival times. Amer. Naturalist 147 (1996) 506-526
223. McArthur R.H., and Wilson E.O. The Theory of Island Biogeography (1967), Princeton University Press, New York
224. Mahmoud H.M. Evolution of Random Search Trees (1992), Wiley, Princeton, NJ
225. Macken C.A., and Perelson A.S. Branching Processes Applied to Cell Surface Aggregation Phenomena (1985), Springer-Verlag, New York
226. Macken C.A., and Perelson A.S. Stem Cell Proliferation and Differentiation: A Multitype Branching Process Model (1989), Springer-Verlag, Berlin
227. Marschner I.D. The effect of preferential mixing on the growth of an epidemic. Math. Biosci. 109 (1992) 39-67
228. McKean H.P. Application of Brownian motion to the equation of Kolmogorov-Petrovski-Piscounov. Comm. Pure Appl. Math. 28 (1975) 323-331
229. McKean H.P. Application of Brownian motion to the equation of Kolmogorov-Petrovski-Piscounov. Comm. Pure Appl. Math. 29 (1975) 553-554
230. McKenzie A., and Steel M. Distributions of cherries for two models of trees. Math. Biosci. 164 (2000) 81-92
231. Mode C.J. On the probability a line becomes extinct before a favourable mutation appears. Bull. Math. Biophys. 29 (1967) 343-348
232. Mode C.J. Multitype Branching Processes (1971), Elsevier, Berlin
233. Mode C.J., and Jacobson M.E. A study of the impact of environmental stochasticity on extinction probabilities by Monte Carlo integration. Math. Biosci. 83 (1987) 103-125
234. Mode C.J., and Jacobson M.E. On estimating critical population size for an endangered species in the presence of environmental stochasticity. Math. Biosci. 85 (1987) 185-209
235. Mode C.J., and Root T. Projecting age-structured populations in a random environment. Math. Biosi. 88 (1988) 223-245
236. Möhle M. Forward and backward processes in bisexual models with fixed population sizes. J. Appl. Probab. 31 (1994) 309-332
237. In: Molison D. (Ed). Epidemic Models: Their Structure and Relation to Data (1995), Cambridge University Press, New York
238. Moody M.E. A branching process model for the evolution of transposable elements. J. Math. Biol. 26 (1988) 347-357
239. Moran P.A.P. The Statistical Processes of Evolutionary Theory (1962), Oxford University Press, Cambridge
240. Mountford M.D. The significance of clutch size. In: Bartlett M.S., and Hiorns R.W. (Eds). The Mathematical Theory of the Dynamics of Biological Populations (1973), Academic Press, Oxford 315-323
241. Mountford M.D. Population regulation, density dependence, and heterogencity. J. Animal Ecol. 57 (1988) 845-858
242. Müller J., Kretzschmar M., and Dietz K. Contact tracing in stochastic and deterministic epidemic models. Math. Biosci. 164 (2000) 39-64
243. Murray J.D. Mathematical Biology (1989), Springer-Verlag, London
244. Nadkarni U.G. On some discrete models in branching processes. J. Indian Soc. Agric. Statist. 16 (1964) 72-82
245. Nadkarni U.G. Generating function of modified branching process. J. Indian Soc. Agric. Statist. 23 (1971) 67-76
246. Narayan P. On bounds for probability generating functions. Austral. J. Statist. 23 (1981) 80-90
247. Nåsell I. The threshold concept in stochastic epidemic and endemic models. In: Mollison D. (Ed). Epidemic Models: Their Structure and Relation to Data (1995), Cambridge University Press, Berlin 71-83
248. Nei M. Extinction time of deleterious mutant genes in large populations. Theor. Pop. Biol. 2 (1971) 419-425
249. Nei M. Total number of individuals affected by a single deleterious mutation in large populations. Theor. Pop. Biol. 2 (1971) 426-430
250. Ohta T., and Kojima K.-I. Survival probabilities of new inversions in large populations. Biometrics 24 (1968) 501-516
251. Olofsson P. Mathematical modeling of telomere shortening: an overview. Archives of Control Sci. 9 XLV (1999) 133-141
252. Olofsson P. A branching process model of telomere shortening. Comm. Statist. Stochastic Models 16 (2000) 167-177
253. Olofsson P., and Kimmel M. Stochastic models of telomere shortening. Math. Biosci. 158 (1999) 75-92
254. Olofsson P., Schwalb O., Chakraborty R., and Kimmel M. An application of a general branching processes in the study of the genetics of aging. J. Theor. Biol. 213 (2001) 547-557
255. O'Neill P. Epidemic models featuring behaviour change. Adv. Appl. Probab. 27 (1995) 960-979
256. O'Neill P. An epidemic model with removal-dependent infection rate. Ann. Appl. Probab. 7 (1997) 90-109
257. O'Neill P.D. On a branching model of division-within-division. IMA J. Math. Biol. Medicine 16 (1999) 395-405
258. Pakes A.G. The Galton-Watson process with killing. Math. Biosci. 69 (1984) 171-188
259. Pakes A.G. The Markov branching-catastrophe process. Stochastic Process. Appl. 23 (1986) 1-33
260. Pakes A.G. Limit theorems for the population size of a birth and death process allowing catastrophes. J. Math. Biol. 25 (1987) 307-325
261. Pakes A.G. The Markov branching process with density-independent catastrophes I. Behaviour of extinction probabilities. Math. Proc. Cambridge Philos. Soc. 103 (1988) 351-366
262. Pakes A.G. An infinite alleles version of the Markov branching process. J. Austral. Math. Soc. Ser. A 46 (1989) 146-170
263. Pakes A.G. Asymptotic results for the extinction time of Markov branching processes allowing emigration, I. Random walk decrements. Adv. Appl. Probab. 21 (1989) 243-269
264. Pakes A.G. Limit theorems for the numbers of rare mutants: a branching process model. Adv. Appl. Probab. 24 (1992) 778-794
265. Pakes A.G. Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state. Adv. Appl. Probab. 27 (1995) 120-145
266. Pakes A.G. A hitting time for Lévy processes, with applications to dams and branching processes. Ann. Faculté des Sciences de Toulouse V (1996) 521-544
267. Pakes A.G. A limit theorem for the maxima of the para-critical simple branching process. Adv. Appl. Probab. 30 (1998) 740-756
268. Pakes A.G. Revisiting conditional limit theorems for the mortal simple branching process. Bernoulli 5 (1999) 969-998
269. Pakes A.G., and Speed T.P. Lagrange distributions and their limit theorems. SIAM J. Appl. Math. 32 (1977) 71-87
270. Parthasarathy P.R., and Lenin R.B. On the exact transient solution of finite birth and death processes with specific quadratic rates. Math. Scientist 22 (1997) 92-105
271. Pettigrew H.M., and Weiss G.H. Epidemics with carriers: the large population approximation. J. Appl. Probab. 4 (1967) 257-263
272. Piau D. Processus de branchement en champ moyan et réaction PCR. Adv. Appl. Probab. 33 (2001) 391-403
273. Picard Ph. Sur les modèles stochastiques logistiques en démographie. Ann. Inst. H. Poincaré II (1965) 151-172
274. Pierre-Loti-Viaud D. Large deviations for random perturbations of discrete time dynamical systems. Bull. Sci. Math. 117 (1993) 333-355
275. Pimm S.L. The Balance of Nature? (1991), Univ. Chicago Press, Cambridge
276. Pitman J. Enumeration of trees and forests related to branching processes and random walks. In: Aldous D., and Propp J. (Eds). Microsurveys in Discrete Probability (1998), American Mathematical Society, Chicago 163-180
277. Pollak E. On the survival of a gene in a subdivided population. J. Appl. Probab. 3 (1966) 142-155
278. Pollak E. Some effects of fluctuating offspring distributions on the survival of a gene. Biometrika 53 (1966) 391-396
279. Pollak E. On three methods for estimating mutation rates indirectly. Am. J. Hum. Genet. 38 (1986) 209-227
280. Pollak E. Survival probabilities for some multitype branching processes in genetics. J. Math. Biol. 30 (1992) 583-596
281. Pollak E. The effective population size of some age-structured populations. Math. Biosci. 168 (2000) 39-56
282. Pollard J.H. Mathematical Models for the Growth of Human Populations (1973), Cambridge University Press, Providence, RI
283. Pollett P.K. On a model for interference between searching insect parasites. J. Austral. Math. Soc. Ser. B 32 (1990) 133-150
284. Pommerenke Ch. On the stationary measures of critical branching processes. Z. Wahrscheinlichkeitsth. 55 (1981) 305-312
285. Pötscher B.M. Moments and order statistics of extinction times in multitype branching processes and their relation to random selection models. Bull. Math. Biol. 47 (1985) 263-272
286. Primack R.B. Essentials of Conservation Biology (1993), Sinauer Associates Inc., Cambridge
287. Rahimov I. Random Sums and Branching Stochastic Processes (1995), Springer-Verlag, Sunderland, MA
288. Raup D.M. The role of chance in Evolution. In: Godfrey L.R. (Ed). What Darwin Began: Modern Darwinian and Non-Darwinian Perspectives on Evolution (1985), Allyn and Bacon, New York 94-112
289. Raup D.M., Gould S.J., Schopf T.J.M., and Simberloff D.S. Stochastic models of phylogeny and the evolution of diversity. J. Geol. 81 (1973) 525-542
290. Reinhard I. The quantitative behaviour of some slowly growing population-dependent Markov branching processes. In: Tautu P. (Ed). Stochastic Modelling in Biology (1990), World Scientific, Singapore 267-277
291. Révész P. Random Walks of Infinitely Many Particles (1994), World Scientific, Singapore
292. Rittgen W. Diffusion limits of population-dependent Markov branching processes. In: Tautu P. (Ed). Stochastic Modelling in Biology (1990), World Scientific, Singapore 278-292
293. Rosenzweig M.L. Species Diversity in Space and Time (1995), Cambridge University Press, Singapore
294. Sankaranarayanan G. Branching Processes and its Estimation Theory (1989), Wiley Eastern Ltd., Cambridge
295. Sawyer S. Branching diffusion processes in population genetics. Adv. Appl. Probab. 8 (1976) 659-689
296. Sawyer S. Comment: the geographical structure of populations. Statist. Sci. 6 (1991) 280-281
297. Sawyer S., and Fleischman J. Maximum geographic range of a mutant allele considered as a subtype of a Brownian branching random field. Proc. Natl. Acad. Sci. USA 76 (1979) 872-875
298. Schaffer H.E. Survival of mutant genes as a branching process. In: Kojima K.-I. (Ed). Mathematical Topics in Population Genetics (1970), Springer-Verlag, New Delhi 317-336
299. Schuster P., and Sigmund K. Self-organization of biological macromolecules and evolutionary stable strategies. In: Haken H. (Ed). Dynamics of Synergetic Systems (1980), Springer-Verlag, Berlin 156-169
300. Schuster P., and Sigmund K. Random selection - a simple model based on linear birth and death processes. Bull. Math. Biol. 46 (1984) 11-17
301. Schuster P., and Sigmund K. Random selection and the neutral theory - sources of stochasticity in replication. In: Schuster P. (Ed). Stochastic Phenomena and Chaotic Behaviour in Complex Systems (1984), Springer-Verlag, Berlin 186-207
302. Seneta E. Round the historical work on Bienaymé. Austral. J. Statist. 21 (1979) 209-220
303. Senate E. I. J. Bienaymé [1786-1878]: criticality, inequality, and internationalization. Int. Statist. Rev. 66 (1998) 291-301
304. Seneta E., and Tavaré S. A note on some models using the branching process with immigration stopped at zero. J. Appl. Probab. 20 (1983) 11-18
305. Sevast'yanov B.A. Theory of branching processes. Progress in Mathematics 7 (1970) 1-51
306. Sevast'yanov B.A. Verzweigungsprozesse (1974), Akademie-Verlag, Berlin
307. Shafer C.F. Nature Reserves (1990), Smithsonian Institute Press, Berlin
308. Shaffer M.L. Minimum population sizes for species conservation. BioScience 31 (1981) 131-134
309. Shaffer M.L., and Sampson F.B. Population size and extinction: a note on determining critical population size. Amer. Naturalist 125 (1985) 144-152
310. Simberloff D., and Abele L. Island biogeographic theory and conservation practice: strategy and limitations. Science 191 (1976) 1032
311. Skellam J.G. The probability distribution of gene-differences in relation to selection, mutation, and random extinction. Proc. Cambridge Philos. Soc. 45 (1949) 364-367
312. Steffensen J.F. Deux problèmes du calcul des probabilités. Ann. H. Poincaré 3 (1932) 319-344
313. Sun F., and Waterman M.S. Whole genome amplification and branching processes. Adv. Appl. Probab. 29 (1997) 629-688
314. Taib Z. Branching Processes and Neutral Evolution. Lecture Notes in Biomathematics Vol. 93 (1992), Springer-Verlag, Washington DC
315. Vatutin V.A. The asymptotic probability of the first degeneration for branching processes with immigration. Theory Probab. Appl. XIX (1974) 25-34
316. Vatutin V.A., and Zubkov A.M. Branching processes I. J. Soviet Math. 39 (1987) 2431-2475
317. Vatutin V.A., and Zubkov A.M. Branching Processes II. J. Soviet Math. 67 (1993) 3407-3485
318. von Bahr B. Threshold limit theorems for some epidemic processes. Adv. Appl. Probab. 12 (1980) 319-349
319. Wakolbinger A. Limits of spatial branching populations (with discussion). Bernoulli 1 (1995) 171-189
320. Watterson G.A. On a recent paper by Cook and Nassar. Biometrics 29 (1973) 595-600
321. Wang F.J.S. Gaussian approximation of some closed stochastic epidemic models. J. Appl. Probab. 14 (1977) 221-231
322. Wang H.-X. Extinction of population-size-dependent branching processes in random environments. J. Appl. Probab. 36 (1999) 146-154
323. Whittle P. The outcome of a stochastic epidemic - a note on Bailey's paper. Biometrika 42 (1955) 571-579
324. Wick D., and Self S.G. Early HIV infection in vivo: branching-process model for studying timing of immune responses and drug therapy. Math. Biosci. 165 (2000) 115-134
325. Williamson M. Island Populations (1981), Oxford University Press, Berlin
326. Wissel C., and Stöcker. Extinction of populations by random influences. Theor. Pop. Biol. 39 (1991) 315-328
327. Yakovlev A.Yu., and Yanev N. Transient Processes in Cell Proliferation Kinetics (1989), Springer-Verlag, Oxford
328. Yasuda N., Cavalli-Sforza L.L., Skolnick M., and Moroni A. The evolution of surnames: an analysis of their distribution and extinction. Theor. Pop. Biol. 5 (1974) 123-142
329. Zheng Q. Progress of a half century in the study of the Luria-Delbrück distribution. Math. Biosci. 162 (1999) 1-32
330. Zhivotovsky L.A., and Feldman M.W. On the probability of loss of new mutations in the presence of linkage disequilibrium. J. Math. Biol. 31 (1993) 177-188