Parameter identifiability and model selection for sigmoid population growth models

Sigmoid growth models, such as the logistic and Gompertz growth models, are widely used to study various population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and precise parameter estimation are critical if these models are to be used to make useful inferences about underlying ecological mechanisms. However, the question of parameter identifiability for these models -- whether a data set contains sufficient information to give unique or sufficiently precise parameter estimates for the given model -- is often overlooked; We use a profile-likelihood approach to systematically explore practical parameter identifiability using data describing the re-growth of hard coral cover on a coral reef after some ecological disturbance. The relationship between parameter identifiability and checks of model misspecification is also explored. We work with three standard choices of sigmoid growth models, namely the logistic, Gompertz, and Richards' growth models; We find that the logistic growth model does not suffer identifiability issues for the type of data we consider whereas the Gompertz and Richards' models encounter practical non-identifiability issues, even with relatively-extensive data where we observe the full shape of the sigmoid growth curve. Identifiability issues with the Gompertz model lead us to consider a further model calibration exercise in which we fix the initial density to its observed value, neglecting its uncertainty. This is a common practice, but the results of this exercise suggest that parameter estimates and fundamental statistical assumptions are extremely sensitive under these conditions; Different sigmoid growth models are used within subdisciplines within the biology and ecology literature without necessarily considering whether parameters are identifiable or checking statistical assumptions underlying model family adequacy. Standard practices that do not consider parameter identifiability can lead to unreliable or imprecise parameter estimates and hence potentially misleading interpretations of the underlying mechanisms of interest. While tools in this work focus on three standard sigmoid growth models and one particular data set, our theoretical developments are applicable to any sigmoid growth model and any relevant data set. MATLAB implementations of all software available on GitHub.

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Age estimation and the best growth model selection of the tentacled blenny Parablennius tentacularis (Brünnich, 1768) in the southeastern Black Sea

Ege Journal of Fisheries and Aquatic Sciences ◽

10.12714/egejfas.38.2.13 ◽

2021 ◽

Vol 38 (2) ◽

pp. 229-236

Author(s):

Ayşe Van ◽

Aysun Gümüş ◽

Melek Özpiçak ◽

Serdar Süer

Keyword(s):

Growth Model ◽

Black Sea ◽

Growth Parameters ◽

Growth Models ◽

Information Criterion ◽

Current Data ◽

Logistic Growth ◽

Data Set ◽

Frequency Distributions ◽

Selection Of

By the study's coverage, 522 individuals of tentacled blenny (Parablennius tentacularis (Brünnich, 1768)), were caught with the bottom trawl operations (commercial fisheries and scientific field surveys) between May 2010 and March 2012 from the southeastern Black Sea. The size distribution range of the sample varied between 4.8-10.8 cm. The difference between sex length (K-S test, Z=3.729, P=0.000) and weight frequency distributions (K-S test, Z=3.605, P=0.000) was found to be statistically significant. The length-weight relationship models were defined as isometric with W = 0.009L3.034 in male individuals and positive allometric with W = 0.006L3.226 in female individuals. Otolith and vertebra samples were compared for the selection of the most accurate hard structure that can be used to determine the age. Otolith was chosen as the most suitable hard structure. The current data set was used to predict the best growth model. For this purpose, the growth parameters were estimated with the widely used von Bertalanffy, Gompertz and Logistic growth functions. Akaike's Information Criterion (AIC), Lmak./L∞ ratio, and R2 criteria were used to select the most accurate growth models established through these functions. Model averaged parameters were calculated with multi-model inference (MMI): L'∞ = 15.091 cm, S.E. (L'∞) = 3.966, K'= 0.232 year-1, S.E. (K') = 0.122.

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Predictive Monitoring of Shake Flask Cultures with Online Estimated Growth Models

Bioengineering ◽

10.3390/bioengineering8110177 ◽

2021 ◽

Vol 8 (11) ◽

pp. 177

Author(s):

Barbara Pretzner ◽

Rüdiger W. Maschke ◽

Claudia Haiderer ◽

Gernot T. John ◽

Christoph Herwig ◽

...

Keyword(s):

Growth Model ◽

Shake Flask ◽

Growth Models ◽

Early Stage ◽

Growth Dynamics ◽

Growth Conditions ◽

Logistic Growth ◽

Model Parameters ◽

Time Varying ◽

Strain Characterization

Simplicity renders shake flasks ideal for strain selection and substrate optimization in biotechnology. Uncertainty during initial experiments may, however, cause adverse growth conditions and mislead conclusions. Using growth models for online predictions of future biomass (BM) and the arrival of critical events like low dissolved oxygen (DO) levels or when to harvest is hence important to optimize protocols. Established knowledge that unfavorable metabolites of growing microorganisms interfere with the substrate suggests that growth dynamics and, as a consequence, the growth model parameters may vary in the course of an experiment. Predictive monitoring of shake flask cultures will therefore benefit from estimating growth model parameters in an online and adaptive manner. This paper evaluates a newly developed particle filter (PF) which is specifically tailored to the requirements of biotechnological shake flask experiments. By combining stationary accuracy with fast adaptation to change the proposed PF estimates time-varying growth model parameters from iteratively measured BM and DO sensor signals in an optimal manner. Such proposition of inferring time varying parameters of Gompertz and Logistic growth models is to our best knowledge novel and here for the first time assessed for predictive monitoring of Escherichia. coli (E. coli) shake flask experiments. Assessments that mimic real-time predictions of BM and DO levels under previously untested growth conditions demonstrate the efficacy of the approach. After allowing for an initialization phase where the PF learns appropriate model parameters, we obtain accurate predictions of future BM and DO levels and important temporal characteristics like when to harvest. Statically parameterized growth models that represent the dynamics of a specific setting will in general provide poor characterizations of the dynamics when we change strain or substrate. The proposed approach is thus an important innovation for scientists working on strain characterization and substrate optimization as providing accurate forecasts will improve reproducibility and efficiency in early-stage bioprocess development.

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Parameter identifiability and model selection for sigmoid population growth models

Journal of Theoretical Biology ◽

10.1016/j.jtbi.2021.110998 ◽

2021 ◽

pp. 110998

Author(s):

Matthew J Simpson ◽

Alexander P Browning ◽

David J Warne ◽

Oliver J Maclaren ◽

Ruth E Baker

Keyword(s):

Model Selection ◽

Population Growth ◽

Growth Models ◽

Parameter Identifiability ◽

Selection For ◽

Population Growth Models

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The poststagnation stage for mature tourism areas

Tourism Economics ◽

10.5367/te.2015.0533 ◽

2016 ◽

Vol 23 (2) ◽

pp. 387-402 ◽

Cited By ~ 6

Author(s):

Isabel P. Albaladejo ◽

María Pilar Martínez-García

Keyword(s):

Life Cycle ◽

Growth Model ◽

Logistic Model ◽

Temporal Evolution ◽

Growth Models ◽

Life Cycles ◽

Logistic Growth ◽

Tourism Sector ◽

Passenger Flows ◽

Logistic Growth Model

The tourism area life cycle (TALC) model of Butler explains the temporal evolution of a tourism resort. Lundtorp and Wanhill find that the logistic growth model represents the first phases of the TALC model. However, since the logistic model assumes a fixed tourism market ceiling, it fails to explain the poststagnation stage, where rejuvenation, decline, or any other intermediate possibility may arise. Taking into account the data of passenger flows to Bornholm from 1912 to 2001 collected by Lundtorp and Wanhill, the authors find that the superposition of several logistic growth models fits better with these data. Then they propose a multilogistic growth model, where investment or innovation in the tourism sector boosts the addition of new logistic curves which superpose the old ones. The continuous birth and superposition of these new life cycles is not free; it requires the purposive effort of entrepreneurs and governments seeking new markets and the improvement of infrastructures.

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Trends in Growth Modeling in Fisheries Science

Fishes ◽

10.3390/fishes6010001 ◽

2021 ◽

Vol 6 (1) ◽

pp. 1

Author(s):

Shane A. Flinn ◽

Stephen R. Midway

Keyword(s):

Model Selection ◽

Growth Model ◽

Growth Models ◽

Growth Modeling ◽

Age And Growth ◽

Von Bertalanffy ◽

Fisheries Science ◽

Growth Studies ◽

Stock Assessments ◽

Von Bertalanffy Growth Model

Growth models estimate life history parameters (e.g., growth rates and asymptotic size) that are used in the management of fisheries stocks. Traditionally in fisheries science, it was common to fit one growth model—the von Bertalanffy growth model—to size-at-age data. However, in recent years, fisheries science has seen an increase in the number of growth models available and the evaluation of multiple growth models for a given species or study. We reviewed n = 196 peer-reviewed age and growth studies and n = 50 NOAA (National Oceanic and Atmospheric Administration) regional stock assessments to examine trends in the use of growth models and model selection in fisheries over time. Our results indicate that the total number of age and growth studies increased annually since 1988 with a slight proportional increase in the use of multi-model frameworks. Information theoretic approaches are replacing goodness-of-fit and a priori model selection in fisheries studies; however, this trend is not reflected in NOAA stock assessments, which almost exclusively rely on the von Bertalanffy growth model. Covariates such as system (e.g., marine or fresh), location of study, diet, family, maximum age, and range of age data used in model fitting did not contribute to which model was ultimately the best fitting, suggesting that there are no large-scale patterns of specific growth models being applied to species with common life histories or other attributes. Given the importance and ubiquity of growth modeling to fisheries science, a historical and contemporary understanding of the practice is critical to evaluate improvements that have been made and future challenges.

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Dynamic growth models for continuous cover multi-species forestry in Iranian Caspian forests

Journal of Forest Science ◽

10.17221/32/2017-jfs ◽

2017 ◽

Vol 63 (No. 11) ◽

pp. 519-529 ◽

Cited By ~ 1

Author(s):

Limaei Soleiman Mohammadi ◽

Lohmander Peter ◽

Olsson Leif

Keyword(s):

Growth Model ◽

Growth Models ◽

Function Analysis ◽

Basal Area ◽

Tree Height ◽

Logistic Growth ◽

Planning Problem ◽

General Function ◽

Adaptive Optimization ◽

Forest Modelling

This study concerns some of the relevant topics of the Iranian Caspian forestry planning problem, in particular the first central components in this modelling process, such as forest modelling, forest statistics and growth function estimations. The required data was collected from Iranian Caspian forests. To do so, 201 sample plots were determined and the parameters such as number of trees, tree diameter at breast height and tree height were measured at each sample plot. Three sample plots at different 3 elevations were chosen to measure the tree increment. Data has been used to estimate a modified logistic growth model and a model that describes the growth of the basal area of individual trees as a function of basal area. General function analysis has been applied in combination with regression analysis. The results are interpreted from ecological perspectives. Furthermore, a dynamic multi-species growth model theory is developed and analysed with respect to dynamic behaviour, equilibria, convergence and stability. Logistic growth models have been found applicable for continuous cover forest management optimization. Optimization of management decisions in a changing and not perfectly predictable world should always be based on adaptive optimization.

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Logistic growth models of China pinks, cultivated on seven substrates, as a function of degree days

Ciência Rural ◽

10.1590/0103-8478cr20150839 ◽

2016 ◽

Vol 46 (11) ◽

pp. 1924-1931

Author(s):

Marília Milani ◽

Sidinei José Lopes ◽

Rogério Antônio Bellé ◽

Fernanda Alice Antonello Londero Backes

Keyword(s):

Growth Model ◽

Rice Husk ◽

Rice Husk Ash ◽

Growth Models ◽

Growth Period ◽

Leaf Number ◽

Logistic Growth ◽

Maximum Height ◽

Degree Days ◽

Logistic Growth Model

ABSTRACT: The objective of this study was to characterize the height (H) and leaf number (LN) of China pinks, grown in seven substrates, as a function of degree days, using the logistic growth model. H and LN were measured from 56 plants per substrate, for 392 plants in total. Plants that were grown on substrates formed of 50% soil with 50% rice husk ash (50% S + 50% RH) and 80% rice husk ash with 20% worm castings (80% RH + 20% W) had the longest vegetative growth period (74d), corresponding to 1317.9ºCd. The logistic growth model, adjusted for H, showed differences in the estimation of maximum expected height (α) between the substrates, with values between 10.47cm for 50% S + 50% RH and 35.75cm for Mecplant(r). When α was estimated as LN, variation was also observed between the different substrates, from approximately 30 leaves on plants growing on 50% S + 50% RH to 34 leaves on the plants growing on the substrate formed of 80% RH + 20% W. Growth of China pinks can be characterized using H or LN in the logistic growth model as a function of degree days, being the provided plants adequately fertilized. The best substrates in terms of maximum height and leaf number were 80% soil + 20% worm castings and Mecplant(r). However, users must recalibrate the model with the estimated parameters before applying it to different growing conditions.

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A Logistic Growth Model for Software Reliability Estimation Considering Uncertain Factors

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539321500327 ◽

2021 ◽

pp. 2150032

Author(s):

Md. Asraful Haque ◽

Nesar Ahmad

Keyword(s):

Growth Model ◽

Software Reliability ◽

Growth Models ◽

Reliability Estimation ◽

Logistic Growth ◽

Systematic Analysis ◽

Software Reliability Growth ◽

Logistic Growth Model ◽

Operational Phase ◽

Special Parameter

Software reliability growth models (SRGMs) are widely used to estimate software reliability by analyzing failure dataset throughout the testing process. A large number of SRGMs have been proposed on a regular basis by researchers since the 1970s. They are represented with a set of assumptions and a set of parameters. One major problem in SRGMs is that the uncertainties surrounding the assumptions and parameters are generally not taken into account by most of them. Therefore, sometimes, the predicted reliability on testing phase significantly varies in actual operational phase. This paper presents a logistic growth model that incorporates a special parameter to consider the effects of all possible uncertainties. A systematic analysis is carried out to identify the major uncertain factors and their impacts on the fault detection rate. The applicability of the model is shown by validating it on two different real datasets that are commonly used in various studies. The comparisons with nine established models in terms of mean square error (MSE), variance, predictive-ratio risk (PRR), [Formula: see text]and AIC have been presented.

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Pitting the Gumbel and logistic growth models against one another to model COVID-19 spread

10.1101/2020.05.24.20111633 ◽

2020 ◽

Author(s):

Keunyoung Yoo ◽

Mohammad Arashi ◽

Andriette Bekker

Keyword(s):

United States ◽

Growth Model ◽

Growth Curve ◽

United States Of America ◽

Growth Models ◽

The United States ◽

Growth Curve Modeling ◽

Data Driven ◽

Logistic Growth ◽

Curve Modeling

AbstractIn this paper, we investigate briefly the appropriateness of the widely used logistic growth curve modeling with focus on COVID-19 spread, from a data-driven perspective. Specifically, we suggest the Gumbel growth model for behaviour of COVID-19 cases in European countries in addition to the United States of America (US), for better detecting the growth and prediction. We provide a suitable fit and predict the growth of cases for some selected countries as illustration. Our contribution will stimulate the correct growth spread modeling for this pandemic outbreak.

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