Population growth II: branching processes

1995 ◽  
pp. 204-218
Author(s):  
Henry C. Tuckwell
Keyword(s):  
Population Growth ◽  
Branching Processes

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.

Branching Processes and Population Growth

1994 ◽  
pp. 437-483
Author(s):  
Howard M. Taylor ◽  
Samuel Karlin
Keyword(s):  
Population Growth ◽  
Branching Processes

scholarly journals Phenotypic diversity and population growth in a fluctuating environment

2011 ◽  
Vol 43 (2) ◽  
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 ϒt,e on ℕ. Then, the phenotypes are attributed using a distribution (strategy) πt,e on the trait space . We look for the optimal strategy πt,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.

Branching Processes and Population Growth

1984 ◽  
pp. 305-340
Author(s):  
Howard M. Taylor ◽  
Samuel Karlin
Keyword(s):  
Population Growth ◽  
Branching Processes

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.

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.

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.

Ultrastructure of myoepithelial cell in parotid gland

1988 ◽  
Vol 46 ◽  
pp. 342-343
Author(s):  
C. N. Sun
Keyword(s):  
Parotid Gland ◽  
Osmium Tetroxide ◽  
Individual Cell ◽  
Branching Processes ◽  
Muscle Cells ◽  
Myoepithelial Cells ◽  
Uranyl Acetate ◽  
Thin Sections ◽  
Gland Carcinoma ◽  
Parotid Gland Carcinoma

Myoepithelial cells have been observed in the prostate, harderian, apocrine, exocrine sweat and mammary glands. Such cells and their numerous branching processes form basket-like structures around the glandular acini. Their shapes are quite different from structures seen either in spindleshaped smooth muscle cells or skeletal muscle cells. These myoepithelial cells lie on the epithelial side of the basement membrane in the glands. This presentation describes the ultrastructure of such myoepithelial cells which have been found also in the parotid gland carcinoma from a 45-year old patient.Specimens were cut into small pieces about 1 mm3 and immediately fixed in 4 percent glutaraldehyde in phosphate buffer for two hours, then post-fixed in 1 percent buffered osmium tetroxide for 1 hour. After dehydration, tissues were embedded in Epon 812. Thin sections were stained with uranyl acetate and lead citrate. Ultrastructurally, the pattern of each individual cell showed wide variations.

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