scholarly journals Optimal Sampling Regimes for Estimating Population Dynamics

Stats ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 291-307
Author(s):  
Rebecca E. Atanga ◽  
Edward L. Boone ◽  
Ryad A. Ghanam ◽  
Ben Stewart-Koster
Keyword(s):  
Population Growth ◽  
Monte Carlo Sampling ◽  
Optimal Designs ◽  
Logistic Growth ◽  
Model Parameters ◽  
Optimal Sampling ◽  
Ecological Data ◽  
Time Frequency ◽  
Regular Time ◽  
Expensive Process

Ecologists are interested in modeling the population growth of species in various ecosystems. Specifically, logistic growth arises as a common model for population growth. Studying such growth can assist environmental managers in making better decisions when collecting data. Traditionally, ecological data is recorded on a regular time frequency and is very well-documented. However, sampling can be an expensive process due to available resources, money and time. Limiting sampling makes it challenging to properly track the growth of a population. Thus, this design study proposes an approach to sampling based on the dynamics associated with logistic growth. The proposed method is demonstrated via a simulation study across various theoretical scenarios to evaluate its performance in identifying optimal designs that best estimate the curves. Markov Chain Monte Carlo sampling techniques are implemented to predict the probability of the model parameters using Bayesian inference. The intention of this study is to demonstrate a method that can minimize the amount of time ecologists spend in the field, while maximizing the information provided by the data.

Optimal Design of Biaxial Tests for Structural Material Characterization of Flat Tissues

1996 ◽  
Vol 118 (1) ◽  
pp. 41-47 ◽  
Author(s):  
Y. Lanir ◽  
O. Lichtenstein ◽  
O. Imanuel
Keyword(s):  
Optimal Design ◽  
Material Characterization ◽  
Structural Model ◽  
Optimal Designs ◽  
Model Parameters ◽  
Optimal Sampling ◽  
Material Symmetry ◽  
Wide Range ◽  
Biaxial Tests

A rational methodology is developed for optimal design of biaxial stretch tests intended for estimating material parameters of flat tissues. It is applied to a structural model with a variety of constitutive equations and test protocols, and for a wide range of parameter levels. The results show nearly identical optimal designs under all circumstances. Optimality is obtained with two uniaxial stretch tests at mutually normal directions inclined by 22.5 deg to the axes of material symmetry. Protocols which include additional equibiaxial tests provide superior estimation with lower variance of estimates. Tests performed at angles 0, 45, and 90 deg to the axes of material symmetry provide unreliable estimates. The optimal sampling is variable and depends on the protocols and model parameters. In conclusion, the results indicate that biaxial tests can be improved over presently common procedures and show that this conclusion applies for a variety of circumstances.

scholarly journals Simulation of non-stationary stochastic ground motions based on recent Italian earthquakes

2021 ◽  
Author(s):  
Fabio Sabetta ◽  
Antonio Pugliese ◽  
Gabriele Fiorentino ◽  
Giovanni Lanzano ◽  
Lucia Luzi
Keyword(s):  
Ground Motion ◽  
Ground Motions ◽  
Strong Motion ◽  
Stochastic Simulations ◽  
Model Parameters ◽  
Motion Model ◽  
Arias Intensity ◽  
Time Frequency ◽  
Ground Motion Model ◽  
Ground Motion Records

AbstractThis work presents an up-to-date model for the simulation of non-stationary ground motions, including several novelties compared to the original study of Sabetta and Pugliese (Bull Seism Soc Am 86:337–352, 1996). The selection of the input motion in the framework of earthquake engineering has become progressively more important with the growing use of nonlinear dynamic analyses. Regardless of the increasing availability of large strong motion databases, ground motion records are not always available for a given earthquake scenario and site condition, requiring the adoption of simulated time series. Among the different techniques for the generation of ground motion records, we focused on the methods based on stochastic simulations, considering the time- frequency decomposition of the seismic ground motion. We updated the non-stationary stochastic model initially developed in Sabetta and Pugliese (Bull Seism Soc Am 86:337–352, 1996) and later modified by Pousse et al. (Bull Seism Soc Am 96:2103–2117, 2006) and Laurendeau et al. (Nonstationary stochastic simulation of strong ground-motion time histories: application to the Japanese database. 15 WCEE Lisbon, 2012). The model is based on the S-transform that implicitly considers both the amplitude and frequency modulation. The four model parameters required for the simulation are: Arias intensity, significant duration, central frequency, and frequency bandwidth. They were obtained from an empirical ground motion model calibrated using the accelerometric records included in the updated Italian strong-motion database ITACA. The simulated accelerograms show a good match with the ground motion model prediction of several amplitude and frequency measures, such as Arias intensity, peak acceleration, peak velocity, Fourier spectra, and response spectra.

Hysteretic Poisson INGARCH model for integer-valued time series

2017 ◽  
Vol 17 (6) ◽  
pp. 401-422 ◽  
Author(s):  
Buu-Chau Truong ◽  
Cathy WS Chen ◽  
Songsak Sriboonchitta
Keyword(s):  
Time Series ◽  
Model Comparison ◽  
Monte Carlo Sampling ◽  
Information Criteria ◽  
Model Parameters ◽  
Modelling Framework ◽  
South Wales ◽  
Proposed Model ◽  
Over Dispersion ◽  
Ingarch Model

This study proposes a new model for integer-valued time series—the hysteretic Poisson integer-valued generalized autoregressive conditionally heteroskedastic (INGARCH) model—which has an integrated hysteresis zone in the switching mechanism of the conditional expectation. Our modelling framework provides a parsimonious representation of the salient features of integer-valued time series, such as discreteness, over-dispersion, asymmetry and structural change. We adopt Bayesian methods with a Markov chain Monte Carlo sampling scheme to estimate model parameters and utilize the Bayesian information criteria for model comparison. We then apply the proposed model to five real time series of criminal incidents recorded by the New South Wales Police Force in Australia. Simulation results and empirical analysis highlight the better performance of hysteresis in modelling the integer-valued time series.

Optimized blood sampling protocols and sequential design of kinetic experiments

1981 ◽  
Vol 240 (5) ◽  
pp. R259-R265 ◽  
Author(s):  
J. J. DiStefano
Keyword(s):  
Endocrine System ◽  
Primary Objective ◽  
Blood Sampling ◽  
Optimal Designs ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reverse T3 ◽  
Model Parameter ◽  
Maximum Accuracy ◽  
Sampling Protocols

Design of optimal blood sampling protocols for kinetic experiments is discussed and evaluated, with the aid of several examples--including an endocrine system case study. The criterion of optimality is maximum accuracy of kinetic model parameter estimates. A simple example illustrates why a sequential experiment approach is required; optimal designs depend on the true model parameter values, knowledge of which is usually a primary objective of the experiment, as well as the structure of the model and the measurement error (e.g., assay) variance. The methodology is evaluated from the results of a series of experiments designed to quantify the dynamics of distribution and metabolism of three iodothyronines, T3, T4, and reverse-T3. This analysis indicates that 1) the sequential optimal experiment approach can be effective and efficient in the laboratory, 2) it works in the presence of reasonably controlled biological variation, producing sufficiently robust sampling protocols, and 3) optimal designs can be highly efficient designs in practice, requiring for maximum accuracy a number of blood samples equal to the number of independently adjustable model parameters, no more or less.

scholarly journals The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

2018 ◽  
Author(s):  
Emanuel A. Fronhofer ◽  
Lynn Govaert ◽  
Mary I. O’Connor ◽  
Sebastian J. Schreiber ◽  
Florian Altermatt
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Population Level ◽  
Logistic Growth ◽  
Population Densities ◽  
Density Regulation ◽  
Logistic Growth Model ◽  
Regulation Functions ◽  
Consumer Resource ◽  
Population Growth Models

AbstractThe logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated.Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer-resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density-regulation functions are usually non-linear and may exhibit convex or both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.Importantly, we show how population-level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. As a solution, we propose simple and general relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer-resource systems.Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time-series from microbial food chains to fit population growth models and validate theoretical predictions.Our results show that density-regulation functions need to be chosen carefully as their shapes will depend on the study system’s biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

scholarly journals Psi-Caputo Logistic Population Growth Model

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muath Awadalla ◽  
Yves Yannick Yameni Noupoue ◽  
Kinda Abu Asbeh
Keyword(s):  
Population Growth ◽  
Fractional Derivative ◽  
Carrying Capacity ◽  
Chinese Population ◽  
Logistic Model ◽  
Logistic Equation ◽  
Logistic Growth ◽  
Growth Equation ◽  
Uniqueness Of The Solution ◽  
Better Than

This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α  = 1.6455.

Density-Dependent Population Growth

2020 ◽  
pp. 29-46
Author(s):  
Michael J. Fogarty ◽  
Jeremy S. Collie
Keyword(s):  
Population Density ◽  
Population Growth ◽  
Density Dependence ◽  
Multiple Equilibria ◽  
Dynamical Behavior ◽  
Logistic Growth ◽  
Density Dependent ◽  
Per Capita ◽  
Discrete Time Models ◽  
Complex Dynamical Behavior

The observation that no population can grow indefinitely and that most populations persist on ecological timescales implies that mechanisms of population regulation exist. Feedback mechanisms include competition for limited resources, cannibalism, and predation rates that vary with density. Density dependence occurs when per capita birth or death rates depend on population density. Density dependence is compensatory when the population growth rate decreases with population density and depensatory when it increases. The logistic model incorporates density dependence as a simple linear function. A population exhibiting logistic growth will reach a stable population size. Non-linear density-dependent terms can give rise to multiple equilibria. With discrete time models or time delays in density-dependent regulation, the approach to equilibrium may not be smooth—complex dynamical behavior is possible. Density-dependent feedback processes can compensate, up to a point, for natural and anthropogenic disturbances; beyond this point a population will collapse.

scholarly journals Testing parallelism for the four-parameter logistic model with D-optimal design

2020 ◽  
Vol 15 (3) ◽  
pp. 273-284
Author(s):  
Lin Ying ◽  
Hyun Seung Won
Keyword(s):  
Optimal Design ◽  
Logistic Model ◽  
Test Preparation ◽  
Test Sample ◽  
Optimal Designs ◽  
Model Parameters ◽  
Reference Standard ◽  
Response Curves ◽  
Classical Design ◽  
Intersection Union Test

In order to determine the potency of the test preparation relative to the standard preparation, it is often important to test parallelism between a pair of dose-response curves of reference standard and test sample. Optimal designs are known to be more powerful in testing parallelism as compared to classical designs. In this study, D-optimal design was implemented to study the parallelism and compare+ its performance with a classical design. We modified D-optimal design to test the parallelism in the four-parameter logistic (4PL) model using Intersection-Union Test (IUT). IUT method is appropriate when the null hypothesis is expressed as a union of sets, and by using this method complicated tests involving several parameters are easily constructed. Since D-optimal design minimizes the variances of model parameters, it can bring more power to the IUT test. A simulation study will be presented to compare the empirical properties of the two different designs.

scholarly journals Planning of experiments for a nonautonomous ornstein-uhlenbeck process

2012 ◽  
Vol 51 (1) ◽  
pp. 101-113 ◽  
Author(s):  
Vladimír Lacko
Keyword(s):  
Sampling Design ◽  
Information Matrix ◽  
Mean Reversion ◽  
Time Dependent ◽  
Optimal Designs ◽  
Optimal Sampling ◽  
Uhlenbeck Process ◽  
Optimal Sampling Design ◽  
Ornstein Uhlenbeck Process ◽  
Planning Of Experiments

ABSTRACT We study exact optimal designs for processes governed by mean- -reversion stochastic differential equations with a time dependent volatility and known mean-reversion speed. It turns out that any mean-reversion It¯o process has a product covariance structure.We prove the existence of a nondegenerate optimal sampling design for the parameter estimation and derive the information matrix corresponding to the observation of the full path. The results are demonstrated on a process with exponential volatility.

Parametric uncertainty quantification in the Rothermel model with randomised quasi-Monte Carlo methods

2015 ◽  
Vol 24 (3) ◽  
pp. 307 ◽  
Author(s):  
Yaning Liu ◽  
Edwin Jimenez ◽  
M. Yousuff Hussaini ◽  
Giray Ökten ◽  
Scott Goodrick
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Monte Carlo Methods ◽  
Wildland Fire ◽  
Parametric Uncertainty ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Quasi Monte Carlo ◽  
Control Variate ◽  
Fuel Model

Rothermel's wildland surface fire model is a popular model used in wildland fire management. The original model has a large number of parameters, making uncertainty quantification challenging. In this paper, we use variance-based global sensitivity analysis to reduce the number of model parameters, and apply randomised quasi-Monte Carlo methods to quantify parametric uncertainties for the reduced model. The Monte Carlo estimator used in these calculations is based on a control variate approach applied to the sensitivity derivative enhanced sampling. The chaparral fuel model, selected from Rothermel's 11 original fuel models, is studied as an example. We obtain numerical results that improve the crude Monte Carlo sampling by factors as high as three orders of magnitude.

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