An optimal branching migration process

1975 ◽  
Vol 12 (3) ◽  
pp. 569-573 ◽  
Author(s):  
S. D. Durham
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Branching Processes ◽  
The Other ◽  
Random Fluctuation ◽  
Random Environments ◽  
Migration Process ◽  
Fixed Rate ◽  
One Dimensional ◽  
Optimal Population

We consider a population distributed over two habitats as represented by two separate one-dimensional branching processes with random environments. The presence of random fluctuation in reproduction rates in both habitats implies the possibility that neither habitat is universally superior to the other for all times and that a maximal population size is to be achieved by having population members present in both habitats. We show that optimal population growth occurs when migration between habitats occurs at a fixed rate which can be found from the environmentally determined reproduction variables of the separate habitats. The optimal processes are themselves two-type branching processes with random environments.

An optimal branching migration process

1975 ◽  
Vol 12 (03) ◽  
pp. 569-573 ◽  
Author(s):  
S. D. Durham
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Branching Processes ◽  
The Other ◽  
Random Fluctuation ◽  
Random Environments ◽  
Migration Process ◽  
Fixed Rate ◽  
One Dimensional ◽  
Optimal Population

We consider a population distributed over two habitats as represented by two separate one-dimensional branching processes with random environments. The presence of random fluctuation in reproduction rates in both habitats implies the possibility that neither habitat is universally superior to the other for all times and that a maximal population size is to be achieved by having population members present in both habitats. We show that optimal population growth occurs when migration between habitats occurs at a fixed rate which can be found from the environmentally determined reproduction variables of the separate habitats. The optimal processes are themselves two-type branching processes with random environments.

scholarly journals Ethnic Immigration Policy Implementation (1992- 2009)

2013 ◽  
pp. 109-117
Author(s):  
Shugatai Amangul
Keyword(s):  
National Identity ◽  
Population Growth ◽  
Policy Implementation ◽  
Population Size ◽  
International Migration ◽  
Immigration Policy ◽  
International Affairs ◽  
Migration Process ◽  
Economic Stability ◽  
Positive Effect

After Kazakhstan declared its independence, it became a large perform­er in the worldwide international migration process. The attraction of social and economic stability (with an increase in the level of liv­ing standard), stable ethno-demographic and population growth, no nationalist struggles as well as positive geopolitical situations, have lead to a huge flow of immigrants to Kazakhstan in the years since independence. In this study, I have suggested that results of the ethnic immigration policy include strengthening the national identity, creating a positive effect on the ethno-demographic outcomes, and increasing the number of the population size over the last nineteen years. DOI: http://dx.doi.org/10.5564/mjia.v0i17.87 Mongolian Journal of International Affairs, No.17 2012: 109-117

Asymptotic behaviour of population-size-dependent branching processes in Markovian random environments

1999 ◽  
Vol 36 (2) ◽  
pp. 611-619 ◽  
Author(s):  
Han-Xing Wang ◽  
Dafan Fang
Keyword(s):  
Asymptotic Behaviour ◽  
Population Size ◽  
Branching Process ◽  
Branching Processes ◽  
Random Environments ◽  
Real Numbers ◽  
Size Dependent ◽  
Recurrent Markov Chain ◽  
The Mean ◽  
Positive Recurrent

A population-size-dependent branching process {Zn} is considered where the population's evolution is controlled by a Markovian environment process {ξn}. For this model, let mk,θ and be the mean and the variance respectively of the offspring distribution when the population size is k and a environment θ is given. Let B = {ω : Zn(ω) = 0 for some n} and q = P(B). The asymptotic behaviour of limnZn and is studied in the case where supθ|mk,θ − mθ| → 0 for some real numbers {mθ} such that infθmθ > 1. When the environmental sequence {ξn} is a irreducible positive recurrent Markov chain (particularly, when its state space is finite), certain extinction (q = 1) and non-certain extinction (q < 1) are studied.

Branching processes in near-critical random environments

2004 ◽  
Vol 41 (A) ◽  
pp. 17-23
Author(s):  
Peter Jagers ◽  
Fima Klebaner
Keyword(s):  
Polymerase Chain Reaction ◽  
Population Size ◽  
Linear Growth ◽  
Branching Processes ◽  
Random Environments ◽  
Chain Reaction ◽  
Polymerase Chain

Branching processes are studied in random environments that are influenced by the population size and approach criticality as the population gets large. Results are applied to the polymerase chain reaction (PCR), which is empirically known to exhibit first exponential and then linear growth of molecule numbers.

Branching processes in near-critical random environments

2004 ◽  
Vol 41 (A) ◽  
pp. 17-23 ◽  
Author(s):  
Peter Jagers ◽  
Fima Klebaner
Keyword(s):  
Polymerase Chain Reaction ◽  
Population Size ◽  
Linear Growth ◽  
Branching Processes ◽  
Random Environments ◽  
Chain Reaction ◽  
Polymerase Chain

Branching processes are studied in random environments that are influenced by the population size and approach criticality as the population gets large. Results are applied to the polymerase chain reaction (PCR), which is empirically known to exhibit first exponential and then linear growth of molecule numbers.

Extinction of population-size-dependent branching processes in random environments

1999 ◽  
Vol 36 (1) ◽  
pp. 146-154 ◽  
Author(s):  
Han-xing Wang
Keyword(s):  
Population Size ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Random Environments ◽  
Size Dependent ◽  
Branching Model

We generalize a population-size-dependent branching process to a more general branching model called the population-size-dependent branching process in random environments. For the model where {Zn}n≥0 is associated with the stationary environment ξ− = {ξn}n≥0, let B = {ω : Zn(ω) = for some n}, and q(ξ−) = P(B | ξ−, Z0 = 1). The result is that P(q(̅ξ) = 1) is either 1 or 0, and sufficient conditions for certain extinction (i.e. P(q(ξ−) = 1) = 1) and for non-certain extinction (i.e. P(q(ξ−) < 1) = 1) are obtained for the model.

Asymptotic behaviour of population-size-dependent branching processes in Markovian random environments

1999 ◽  
Vol 36 (02) ◽  
pp. 611-619 ◽  
Author(s):  
Han-Xing Wang ◽  
Dafan Fang
Keyword(s):  
Asymptotic Behaviour ◽  
Population Size ◽  
Branching Process ◽  
Branching Processes ◽  
Random Environments ◽  
Real Numbers ◽  
Size Dependent ◽  
Recurrent Markov Chain ◽  
The Mean ◽  
Positive Recurrent

A population-size-dependent branching process {Z n } is considered where the population's evolution is controlled by a Markovian environment process {ξ n }. For this model, let m k,θ and be the mean and the variance respectively of the offspring distribution when the population size is k and a environment θ is given. Let B = {ω : Z n (ω) = 0 for some n} and q = P(B). The asymptotic behaviour of lim n Z n and is studied in the case where supθ|m k,θ − m θ| → 0 for some real numbers {m θ} such that infθ m θ &gt; 1. When the environmental sequence {ξ n } is a irreducible positive recurrent Markov chain (particularly, when its state space is finite), certain extinction (q = 1) and non-certain extinction (q &lt; 1) are studied.

scholarly journals Phenotypic diversity and population growth in a fluctuating environment

2011 ◽  
Vol 43 (02) ◽  
pp. 375-398 ◽  
Author(s):  
Clément Dombry ◽  
Christian Mazza ◽  
Vincent Bansaye
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Environmental Changes ◽  
Phenotypic Diversity ◽  
Branching Processes ◽  
Optimal Strategies ◽  
Exact Expression ◽  
Random Environments ◽  
Lyapounov Exponent ◽  
Net Growth Rate

Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring distribution of some organism having trait t ∈ in environment e ∈ ε is given by some (fixed) distribution ϒ t,e on ℕ. Then, the phenotypes are attributed using a distribution (strategy) π t,e on the trait space . We look for the optimal strategy π t,e , t ∈ , e ∈ ε, maximizing the net growth rate or Lyapounov exponent, and characterize the set of optimal strategies. This is considered for various models of interest in biology: hereditary versus nonhereditary strategies and strategies involving or not involving a sensing mechanism. Our main results are obtained in the setting of nonhereditary strategies: thanks to a reduction to simple branching processes in a random environment, we derive an exact expression for the net growth rate and a characterization of optimal strategies. We also focus on typical genealogies, that is, we consider the problem of finding the typical lineage of a randomly chosen organism.

Extinction of population-size-dependent branching processes in random environments

1999 ◽  
Vol 36 (01) ◽  
pp. 146-154 ◽  
Author(s):  
Han-xing Wang
Keyword(s):  
Population Size ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Random Environments ◽  
Size Dependent ◽  
Branching Model

We generalize a population-size-dependent branching process to a more general branching model called the population-size-dependent branching process in random environments. For the model where {Z n } n≥0 is associated with the stationary environment ξ− = {ξ n } n≥0, let B = {ω : Z n (ω) = for some n}, and q(ξ−) = P(B | ξ−, Z 0 = 1). The result is that P(q(̅ξ) = 1) is either 1 or 0, and sufficient conditions for certain extinction (i.e. P(q(ξ−) = 1) = 1) and for non-certain extinction (i.e. P(q(ξ−) &lt; 1) = 1) are obtained for the model.

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