Parameter Identification and Estimation For Stage–Structured Population Models

Abstract A stage-structured population model with unknown parameters is considered. Our purpose is to study the identifiability of the model and to develop a parameter estimation procedure. First, we analyze whether the parameter vector can or cannot uniquely be determined with the knowledge of the input-output behavior of the model. Second, we analyze how the information in the experimental data is translated into the parameters of the model. Furthermore, we propose a process to improve the recursive values of the parameters when successive observation data are considered. The structure of the state matrix leads to an analysis of the inverse of a sum of rank-one matrices.

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On the Interplay between Cannibalism and Harvest in Stage-Structured Population Models

Journal of Marine Biology ◽

10.1155/2015/580520 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Arild Wikan

Keyword(s):

Parameter Space ◽

Population Model ◽

Stable Equilibrium ◽

Structured Population Model ◽

Structured Population Models ◽

Structured Population ◽

Nonstationary Dynamics ◽

Mature Part ◽

Harvest Pressure

By use of a nonlinear stage-structured population model the role of cannibalism and the combined role of cannibalism and harvest have been explored. Regarding the model, we prove that in most parts of parameter space it is permanent. We also show that the transfer from stability to nonstationary dynamics always occurs when the unique stable equilibrium undergoes a supercritical Neimark-Sacker (Hopf) bifurcation. Moreover, the dynamic consequences of catch depend not only on which part of the population (immature or mature) is exposed to increased harvest pressure but also on which part of the immature population (newborns, older immature individuals) suffers from cannibalism. Indeed, if only newborns are exposed to cannibalism an enlargement of harvest pressure on the mature part of the population may act in a stabilizing fashion. On the other hand, whenever the whole immature population is exposed to cannibalism there are parts in parameter space where increased harvest on the mature population acts in a destabilizing fashion.

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Resonance in physiologically structured population models

10.1101/2021.01.18.427157 ◽

2021 ◽

Author(s):

Kevin Gross ◽

André M. de Roos

Keyword(s):

Transfer Function ◽

Frequency Spectrum ◽

Natural Populations ◽

Environmental Variation ◽

Population Models ◽

Time Model ◽

Structured Population Model ◽

Structured Population Models ◽

Structured Population ◽

Physiologically Structured Population Models

AbstractEcologists have long sought to understand how the dynamics of natural populations are affected by the environmental variation those populations experience. A transfer function is a useful tool for this purpose, as it uses linearization theory to show the frequency spectrum of the fluctuations in a population’s abundance relates to the frequency spectrum of environmental variation. Here, we show how to derive and to compute the transfer function for a continuous-time model of populations that are structured by a continuous individual-level state variable such as size. To illustrate, we derive, compute, and analyze the transfer function for a size-structured population model of stony corals with open recruitment, parameterized for a common Indo-Pacific coral species complex. This analysis identifies a sharp, multi-decade resonance driven by space competition between existing coral colonies and incoming recruits. The resonant frequency is most strongly determined by the rate at which colonies grow, and the potential for resonant oscillations is greatest when colony growth is only weakly density-dependent. While these resonant oscillations are unlikely to be predominant dynamical features of degraded reefs, they suggest the dynamical possibilities for marine invertebrates in more pristine waters. The size-structured model that we analyze is a leading example of a broader class of physiologically structured population models, and the methods we present should apply to a wide variety of models in this class.

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THE REALIZATION OF THE ITERATIVE METHOD OF THE LEAST SQUARES FOR THE ESTIMATION OF STATIC OBJECT PARAMETERS IN MATLAB ENVIRONMENT

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY SERIES MANAGEMENT COMPUTER SCIENCE AND INFORMATICS ◽

10.24143/2072-9502-2017-1-28-36 ◽

2017 ◽

pp. 28-36

Author(s):

Galina Vasil’evna Troshina ◽

Alexander Aleksandrovich Voevoda

Keyword(s):

Parameter Estimation ◽

Iterative Method ◽

Least Squares ◽

Input Signal ◽

Layer Structure ◽

Estimation Procedure ◽

Parameter Estimation Procedure ◽

Noise Simulation ◽

Static Object ◽

Object Parameters

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.

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