A class of controlled bisexual branching processes with mating depending on the number of progenitor couples

2007 ◽  
Vol 77 (18) ◽  
pp. 1737-1743 ◽  
Author(s):  
Manuel Molina ◽  
Inés M. del Puerto ◽  
Alfonso Ramos
Keyword(s):  
Branching Processes ◽  
Bisexual Branching Processes

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

scholarly journals On the Extinction of a Class of Population-Size-Dependent Bisexual Branching Processes

2005 ◽  
Vol 42 (01) ◽  
pp. 175-184 ◽  
Author(s):  
Yongsheng Xing ◽  
Yongjin Wang
Keyword(s):  
Growth Rate ◽  
Population Size ◽  
Branching Processes ◽  
Suitable Condition ◽  
Size Dependent ◽  
Offspring Distribution ◽  
Bisexual Branching Processes ◽  
The Law ◽  
Mating Unit

In this paper, we study a class of bisexual Galton-Watson branching processes in which the law of offspring distribution is dependent on the population size. Under a suitable condition on the offspring distribution, we prove that the limit of mean growth-rate per mating unit exists. Based on this limit, we give a criterion to identify whether the process admits ultimate extinction with probability one.

Bisexual branching processes with offspring and mating depending on the number of couples in the population

Test ◽  
2007 ◽  
Vol 17 (2) ◽  
pp. 265-281 ◽  
Author(s):  
Manuel Molina ◽  
Christine Jacob ◽  
Alfonso Ramos
Keyword(s):  
Branching Processes ◽  
Bisexual Branching Processes

scholarly journals Bisexual branching processes to model extinction conditions for Y-linked genes

2009 ◽  
Vol 258 (3) ◽  
pp. 478-488 ◽  
Author(s):  
Miguel González ◽  
Rodrigo Martínez ◽  
Manuel Mota
Keyword(s):  
Branching Processes ◽  
Bisexual Branching Processes

scholarly journals On the Extinction of a Class of Population-Size-Dependent Bisexual Branching Processes

2005 ◽  
Vol 42 (1) ◽  
pp. 175-184 ◽  
Author(s):  
Yongsheng Xing ◽  
Yongjin Wang
Keyword(s):  
Growth Rate ◽  
Population Size ◽  
Branching Processes ◽  
Suitable Condition ◽  
Size Dependent ◽  
Offspring Distribution ◽  
Bisexual Branching Processes ◽  
The Law ◽  
Mating Unit

In this paper, we study a class of bisexual Galton-Watson branching processes in which the law of offspring distribution is dependent on the population size. Under a suitable condition on the offspring distribution, we prove that the limit of mean growth-rate per mating unit exists. Based on this limit, we give a criterion to identify whether the process admits ultimate extinction with probability one.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (2) ◽  
pp. 492-505 ◽  
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

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