Harvesting Policies with Stepwise Effort and Logistic Growth in a Random Environment

2020 ◽  
pp. 95-110
Author(s):  
Nuno M. Brites ◽  
Carlos A. Braumann
Keyword(s):  
Random Environment ◽  
Logistic Growth

Driven periodic structures in random environment

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-85-Pr10-87
Author(s):  
V. M. Vinokur
Keyword(s):  
Random Environment ◽  
Periodic Structures

Driven elastic system in a random environment

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-69-Pr10-71 ◽  
Author(s):  
P. Chauve ◽  
T. Giamarchi ◽  
P. Le Doussal
Keyword(s):  
Random Environment ◽  
Elastic System

The Effects of Environmental Autocorrelations on the Progress of Selection in a Random Environment

1978 ◽  
Vol 112 (987) ◽  
pp. 897-909 ◽  
Author(s):  
John H. Gillespie ◽  
Harry A. Guess
Keyword(s):  
Random Environment

scholarly journals The Probability of Fixation in Populations of Changing Size

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 723-733 ◽  
Author(s):  
Sarah P Otto ◽  
Michael C Whitlock
Keyword(s):  
Diffusion Equation ◽  
Adaptive Evolution ◽  
Process Model ◽  
Branching Process ◽  
Approximate Solutions ◽  
Logistic Growth ◽  
Beneficial Mutations ◽  
Demographic Models ◽  
Deleterious Alleles ◽  
Probability Of Fixation

The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.

scholarly journals The influence of density in population dynamics with strong and weak Allee effect

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kamrun Nahar Keya ◽  
Md. Kamrujjaman ◽  
Md. Shafiqul Islam
Keyword(s):  
Population Dynamics ◽  
Allee Effect ◽  
Global Bifurcation ◽  
Reaction Diffusion ◽  
Logistic Growth ◽  
Allee Effects ◽  
Reaction Diffusion Model ◽  
Positive Steady States ◽  
The Stability ◽  
The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

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