scholarly journals Long-time behavior of a size-structured population model with diffusion and delayed birth process

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Dongxue Yan ◽  
Xianlong Fu
Keyword(s):  
Population Model ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Birth Process ◽  
Structured Population Model ◽  
Structured Population ◽  
Long Time

scholarly journals Long-Time Simulation of a Size-Structured Population Model with a Dynamical Resource

2010 ◽  
Vol 5 (6) ◽  
pp. 1-21 ◽  
Author(s):  
L. M. Abia ◽  
O. Angulo ◽  
J. C. López-Marcos ◽  
M. A. López-Marcos
Keyword(s):  
Population Model ◽  
Structured Population Model ◽  
Structured Population ◽  
Time Simulation ◽  
Long Time

Long-Time Behavior of Spatially and Size-Structured Population Dynamics with Delayed Birth Process

2017 ◽  
Vol 27 (03) ◽  
pp. 1750032 ◽  
Author(s):  
Dongxue Yan ◽  
Xianlong Fu
Keyword(s):  
Population Dynamics ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Time Behavior ◽  
Birth Process ◽  
Structured Population ◽  
Population Dynamics Model ◽  
Structured Population Dynamics ◽  
Long Time ◽  
Asynchronous Exponential Growth

This paper is devoted to the study of a spatially and size-structured population dynamics model with delay in the birth process. We investigate some dynamical properties of the equation by using [Formula: see text]-semigroup theory and spectral analysis arguments, through which we obtain some sufficient conditions of asymptotical stability, asynchronous exponential growth at the null equilibrium as well as Hopf bifurcation occurring at the positive steady state of the system. Some examples are presented and simulated to illustrate the obtained results.

scholarly journals Evolution of heterogeneity under constant and variable environments

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257377
Author(s):  
Ryo Oizumi ◽  
Hisashi Inaba
Keyword(s):  
Adaptive Control ◽  
Population Model ◽  
Life Histories ◽  
Structured Population Model ◽  
Variable Environment ◽  
Structured Population ◽  
Variable Environments ◽  
Long Time ◽  
Age Structured ◽  
Hamilton Jacobi Bellman

Various definitions of fitness are essentially based on the number of descendants of an allele or a phenotype after a sufficiently long time. However, these different definitions do not explicate the continuous evolution of life histories. Herein, we focus on the eigenfunction of an age-structured population model as fitness. The function generates an equation, called the Hamilton–Jacobi–Bellman equation, that achieves adaptive control of life history in terms of both the presence and absence of the density effect. Further, we introduce a perturbation method that applies the solution of this equation to the long-term logarithmic growth rate of a stochastic structured population model. We adopt this method to realize the adaptive control of heterogeneity for an optimal foraging problem in a variable environment as the analyzable example. The result indicates that the eigenfunction is involved in adaptive strategies under all the environments listed herein. Thus, we aim to systematize adaptive life histories in the presence of density effects and variable environments using the proposed objective function as a universal fitness candidate.

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