Population growth in random environments

1983 ◽  
Vol 45 (4) ◽  
pp. 635-641 ◽  
Author(s):  
Carlos A. Braumann
Keyword(s):  
Population Growth ◽  
Random Environments

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.

THRESHOLD CROSSING PROBABILITIES FOR POPULATION GROWTH MODELS IN RANDOM ENVIRONMENTS

1995 ◽  
Vol 03 (02) ◽  
pp. 505-517 ◽  
Author(s):  
CARLOS A. BRAUMANN
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Animal Cell ◽  
Growth Parameter ◽  
Minimum Size ◽  
Random Environments ◽  
High Threshold ◽  
Demographic Stochasticity ◽  
Threshold Crossing ◽  
Crossing Probabilities

Consider the general population growth model in a random environment dN/dt= (r+σε(t))Nf(N), N(0)=N0>0, where N=N(t) is the (animal, cell, etc.) population size or biomass at time t≥0, r>0 is an intrinsic growth parameter subjected to environmental random fluctuations approximately described by σε(t) (σ>0 noise intensity parameter, ε(t) standard white noise), and f(N) is a well-behaved density-dependence function. Due to demographic stochasticity and Allee effects, a slightly modified model that corrects for inadequacies at small population sizes is also considered. In many applications (wildlife management, environmental impact assessment, pest control, growth of bacterial cultures, tumor or body growth, etc.), one needs the probability of N(t) ever crossing a given threshold during a given time horizon. We consider the cases of a low threshold N1<N0 (for instance, an extinction threshold or a minimum size required for economical, ecological or recreational reasons) and of a high threshold N h >N0 (for instance, a pest’s damaging level). We also obtain other related threshold crossing probabilities of interest. A reference is made to statistical estimation and hypothesis testing.

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.

Population strategies and random environments

1975 ◽  
Vol 53 (2) ◽  
pp. 160-165 ◽  
Author(s):  
Hugh Barclay
Keyword(s):  
Population Growth ◽  
Stochastic Models ◽  
Carrying Capacity ◽  
Death Rate ◽  
Logistic Model ◽  
Birth Rate ◽  
Environmental Variation ◽  
Random Environments ◽  
Probability Of Extinction ◽  
Established Species

It is shown using several models that r and K selection may result from random environmental variation. Probabilities of extinction are derived for both colonizing and well-established species using stochastic models similar to the logistic model, and it is shown that the probability of extinction of a population can be reduced by increasing the birth rate or the carrying capacity or by decreasing the death rate or the effects of the environmental variation on population growth. It is probable that random environmental variation mainly facilitates r selection.

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.

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