scholarly journals A One-Sex Population Dynamics Model with Discrete Set of Offsprings and Child Care

2008 ◽  
Vol 13 (4) ◽  
pp. 525-552
Author(s):  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Child Care ◽  
Maternal Care ◽  
Deterministic Model ◽  
Large Time Behavior ◽  
Reproductive Age ◽  
Time Behavior ◽  
Care Groups ◽  
Population Dynamics Model ◽  
Long Time

We present a one-sex age-structured population dynamics deterministic model with a discrete set of offsprings, child care, environmental pressure, and spatial migration. All individuals have pre-reproductive, reproductive, and post-reproductive age intervals. Individuals of reproductive age are divided into fertile single and taking child care groups. All individuals of pre-reproductive age are divided into young (under maternal care) and juvenile (offspring who can live without maternal care) classes. It is assumed that all young offsprings move together with their mother and that after the death of mother all her young offsprings are killed. The model consists of integro-partial differential equations subject to the conditions of the integral type. Number of these equations depends on a biologically possible maximal newborns number of the same generation produced by an individual. The existence and uniqueness theorem is proved, separable solutions are studied, and the long time behavior is examined for the solution with general type of initial distributions in the case of non-dispersing population. Separable and more general (nonseparable) solutions, their large time behavior, and steady-state solutions are studied for the population with spatial dispersal, too.

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.

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

scholarly journals A random effects population dynamics model based on proportions-at-age and removal data for estimating total mortality

2012 ◽  
Vol 69 (11) ◽  
pp. 1881-1893 ◽  
Author(s):  
Verena M. Trenkel ◽  
Mark V. Bravington ◽  
Pascal Lorance
Keyword(s):  
Population Dynamics ◽  
Random Effects ◽  
Fixed Effects ◽  
Random Effect ◽  
Total Mortality ◽  
Estimation Bias ◽  
Effective Sample Size ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Study Parameter

Catch curves are widely used to estimate total mortality for exploited marine populations. The usual population dynamics model assumes constant recruitment across years and constant total mortality. We extend this to include annual recruitment and annual total mortality. Recruitment is treated as an uncorrelated random effect, while total mortality is modelled by a random walk. Data requirements are minimal as only proportions-at-age and total catches are needed. We obtain the effective sample size for aggregated proportion-at-age data based on fitting Dirichlet-multinomial distributions to the raw sampling data. Parameter estimation is carried out by approximate likelihood. We use simulations to study parameter estimability and estimation bias of four model versions, including models treating mortality as fixed effects and misspecified models. All model versions were, in general, estimable, though for certain parameter values or replicate runs they were not. Relative estimation bias of final year total mortalities and depletion rates were lower for the proposed random effects model compared with the fixed effects version for total mortality. The model is demonstrated for the case of blue ling (Molva dypterygia) to the west of the British Isles for the period 1988 to 2011.

A microbial treatment population dynamics optimization approach

2021 ◽  
pp. 1-15
Author(s):  
Jinding Gao
Keyword(s):  
Population Dynamics ◽  
Information Exchange ◽  
Information Diffusion ◽  
Optimization Problems ◽  
Microbial Control ◽  
Function Optimization ◽  
Optimization Approach ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Number Of Individuals

In order to solve some function optimization problems, Population Dynamics Optimization Algorithm under Microbial Control in Contaminated Environment (PDO-MCCE) is proposed by adopting a population dynamics model with microbial treatment in a polluted environment. In this algorithm, individuals are automatically divided into normal populations and mutant populations. The number of individuals in each category is automatically calculated and adjusted according to the population dynamics model, it solves the problem of artificially determining the number of individuals. There are 7 operators in the algorithm, they realize the information exchange between individuals the information exchange within and between populations, the information diffusion of strong individuals and the transmission of environmental information are realized to individuals, the number of individuals are increased or decreased to ensure that the algorithm has global convergence. The periodic increase of the number of individuals in the mutant population can greatly increase the probability of the search jumping out of the local optimal solution trap. In the iterative calculation, the algorithm only deals with 3/500∼1/10 of the number of individual features at a time, the time complexity is reduced greatly. In order to assess the scalability, efficiency and robustness of the proposed algorithm, the experiments have been carried out on realistic, synthetic and random benchmarks with different dimensions. The test case shows that the PDO-MCCE algorithm has better performance and is suitable for solving some optimization problems with higher dimensions.

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