Stability analysis of continuous population model involving predation and Allee effect

2009 ◽  
Vol 41 (3) ◽  
pp. 1218-1222 ◽  
Author(s):  
O. Duman ◽  
H. Merdan
Keyword(s):  
Stability Analysis ◽  
Population Model ◽  
Allee Effect ◽  
Continuous Population

A DARWINIAN DYNAMIC MODEL FOR THE EVOLUTION OF POST-REPRODUCTION SURVIVAL

2021 ◽  
pp. 1-18
Author(s):  
J. M. CUSHING ◽  
KATHRYN STEFANKO
Keyword(s):  
Natural Selection ◽  
Dynamic Model ◽  
Discrete Time ◽  
Population Model ◽  
Bifurcation Theory ◽  
Allee Effect ◽  
Phenotypic Trait ◽  
Trade Off ◽  
The Stability ◽  
Low Dimensional

We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role.

scholarly journals Stability analysis of stochastic Ricker population model

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
Natali Hritonenko ◽  
Alexandra Rodkina ◽  
Yuri Yatsenko
Keyword(s):  
Stability Analysis ◽  
Population Model ◽  
Noise Intensity ◽  
Reproduction Rate ◽  
Stochastic Noise ◽  
Population Extinction ◽  
Discrete Population ◽  
Noise Impacts ◽  
Discrete Population Model

A stochastic generalization of the Ricker discrete population model is studied under the assumption that noise impacts the population reproduction rate. The obtained results demonstrate that the demographic-type stochastic noise increases the risk of the population extinction. In particular, the paper establishes conditions on the noise intensity under which the population will extinct even if the corresponding population with no noise survives.

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