Speed Determinacy of Traveling Waves to a Stream-Population Model with Allee Effect

2020 ◽  
Vol 80 (4) ◽  
pp. 1820-1840
Author(s):  
Zhe Huang ◽  
Chunhua Ou
Keyword(s):  
Traveling Waves ◽  
Population Model ◽  
Allee Effect

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.

Bifurcation Analysis of the γ-Ricker Population Model Using the Lambert W Function

2020 ◽  
Vol 30 (07) ◽  
pp. 2050108 ◽  
Author(s):  
J. Leonel Rocha ◽  
Abdel-Kaddous Taha
Keyword(s):  
Population Model ◽  
Allee Effect ◽  
Pitchfork Bifurcation ◽  
Big Bang ◽  
Lambert W Function ◽  
Dynamical Study ◽  
Existence And Stability ◽  
Fixed Point Equation ◽  
Bifurcation Structures ◽  
Global And Local

In this work, we present the dynamical study and the bifurcation structures of the [Formula: see text]-Ricker population model. Resorting to the Lambert [Formula: see text] function, the analytical solutions of the positive fixed point equation for the [Formula: see text]-Ricker population model are explicitly presented and conditions for the existence and stability of these fixed points are established. The main focus of this work is the definition and characterization of the Allee effect bifurcation for the [Formula: see text]-Ricker population model, which is not a pitchfork bifurcation. Consequently, we prove that the phenomenon of Allee effect for the [Formula: see text]-Ricker population model is associated with the asymptotic behavior of the Lambert [Formula: see text] function in a neighborhood of zero. The theoretical results describe the global and local bifurcations of the [Formula: see text]-Ricker population model, using the Lambert [Formula: see text] function in the presence and absence of the Allee effect. The Allee effect, snapback repeller and big bang bifurcations are investigated in the parameters space considered. Numerical studies are included.

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