Population Dependent Two-Sex Branching Process with Random Mating and Overlapping Generations

References

[1] K. L. Chung, Markov Chains with Stationary Transition Probabilities, Grundlehren Math. Wiss. 104, Springer, New York, 1967. Search in Google Scholar

[2] S. J. Cornell and V. S. Isham, Ultimate extinction of the promiscuous bisexual Galton–Watson metapopulation, Aust. N. Z. J. Statist. 46 (2004), 87–98. 10.1111/j.1467-842X.2004.00315.xSearch in Google Scholar

[3] D. J. Daley, Extinction conditions for certain bisexual Galton–Watson branching processes, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 9 (1968), 315–322. 10.1007/BF00531755Search in Google Scholar

[4] M. González, R. Martínez and M. Mota, Bisexual branching processes to model extinction conditions for Y-linked genes, J. Theoret. Biol. 258 (2009), no. 3, 478–488. 10.1016/j.jtbi.2008.10.034Search in Google Scholar PubMed

[5] M. González, M. Molina and M. Mota, Limit behaviour for a subcritical bisexual Galton–Watson branching process with immigration, Statist. Probab. Lett. 49 (2000), no. 1, 19–24. 10.1016/S0167-7152(00)00026-2Search in Google Scholar

[6] M. González, M. Molina and M. Mota, On the limit behavior of a supercritical bisexual Galton–Watson branching process with immigration of mating units, Stoch. Anal. Appl. 19 (2001), no. 6, 933–943. 10.1081/SAP-120000755Search in Google Scholar

[7] P. Guttorp, Statistical Inference for Branching Processes, Wiley Ser. Probab. Math. Stat., John Wiley & Sons, New York, 1991. Search in Google Scholar

[8] P. Haccou, P. Jagers and V. A. Vatutin, Branching Processes: Variation, Growth, and Extinction of Populations, Cambridge Studies Adapt. Dyn. 5, Cambridge University, Cambridge, 2005. 10.1017/CBO9780511629136Search in Google Scholar

[9] D. M. Hull, A survey of the literature associated with the bisexual Galton–Watson branching process, Extracta Math. 18 (2003), no. 3, 321–343. Search in Google Scholar

[10] C. Jacob, M. Molina and M. Mota, A general class of population-dependent two-sex processes with random mating, Bernoulli 23 (2017), no. 3, 1737–1758. 10.3150/15-BEJ794Search in Google Scholar

[11] P. Jagers, Branching Processes with Biological Applications, Wiley Ser. Probab. Math. Stat., John Wiley & Sons, London, 1975. Search in Google Scholar

[12] S. Ma and M. Molina, Two-sex branching processes with offspring and mating in a random environment, J. Appl. Probab. 46 (2009), no. 4, 993–1004. 10.1239/jap/1261670684Search in Google Scholar

[13] S. Ma and Y. Xing, The asymptotic properties of supercritical bisexual Galton–Watson branching processes with immigration of mating units, Acta Math. Sci. Ser. B (Engl. Ed.) 26 (2006), no. 4, 603–609. 10.1016/S0252-9602(06)60086-6Search in Google Scholar

[14] S.-X. Ma, Bisexual Galton–Watson branching processes in random environments, Acta Math. Appl. Sin. Engl. Ser. 22 (2006), no. 3, 419–428. 10.1007/s10255-006-0317-4Search in Google Scholar

[15] C. J. Mode, Multitype Branching Processes. Theory and Applications, American Elsevier, New York, 1971. Search in Google Scholar

[16] M. Molina, Two-sex branching process literature, Workshop on Branching Processes and Their Applications, Lect. Notes Stat. Proc. 197, Springer, Berlin (2010), 279–293. 10.1007/978-3-642-11156-3_20Search in Google Scholar

[17] M. Molina, C. Jacob and A. Ramos, Bisexual branching processes with offspring and mating depending on the number of couples in the population, TEST 17 (2008), no. 2, 265–281. 10.1007/s11749-006-0031-9Search in Google Scholar

[18] M. Molina and M. Mota, Population-dependent two-sex branching processes with random mating: Rates of growth, Stoch. Models 35 (2019), no. 3, 252–268. 10.1080/15326349.2019.1618193Search in Google Scholar

[19] M. Molina, M. Mota and A. Ramos, Bisexual Galton–Watson branching process in varying environments, Stoch. Anal. Appl. 21 (2003), no. 6, 1353–1367. 10.1081/SAP-120026110Search in Google Scholar

[20] M. Molina, M. Mota and A. Ramos, Limit behaviour for a supercritical bisexual Galton–Watson branching process with population-size-dependent mating, Stochastic Process. Appl. 112 (2004), no. 2, 309–317. 10.1016/j.spa.2004.02.003Search in Google Scholar

[21] M. Molina, M. Mota and A. Ramos, On L α -convergence ( 1 ≤ α ≤ 2 ) for a bisexual branching process with population-size dependent mating, Bernoulli 12 (2006), no. 3, 457–468. 10.3150/bj/1151525130Search in Google Scholar

[22] M. Molina, M. Mota and A. Ramos, Stochastic modeling in biological populations with sexual reproduction through branching models: Application to Coho salmon populations, Math. Biosci. 258 (2014), 182–188. 10.1016/j.mbs.2014.10.007Search in Google Scholar PubMed

[23] M. Molina, M. Mota and A. Ramos, Estimation of parameters in biological species with several mating and reproduction alternatives, Math. Biosci. 329 (2020), Article ID 108471. 10.1016/j.mbs.2020.108471Search in Google Scholar PubMed

[24] M. Mota, I. del Puerto and A. Ramos, The bisexual branching process with population-size dependent mating as a mathematical model to describe phenomena concerning to inhabit or re-inhabit environments with animal species, Math. Biosci. 206 (2007), no. 1, 120–127. 10.1016/j.mbs.2005.01.007Search in Google Scholar PubMed

[25] S. Pénisson and C. Jacob, Stochastic methodology for the study of an epidemic decay phase, based on a branching model, Int. J. Stoch. Anal. 2012 (2012), Article ID 598701. 10.1155/2012/598701Search in Google Scholar

[26] Y. Xing and Y. Wang, On the extinction of a class of population-size-dependent bisexual branching processes, J. Appl. Probab. 42 (2005), no. 1, 175–184. 10.1239/jap/1110381379Search in Google Scholar