Search results for "Gompertz function"

Improving risk assessments in conservation ecology

2019

Conservation efforts and management decisions on the living environment of our planet often rely on the results from statistical models. Yet, these models are imperfect and quantification of risk associated with the estimate of management-relevant quantities becomes crucial in providing robust advice. Here we demonstrate that estimates of risk themselves could be substantially biased but by combining data fitting with an extensive simulation–estimation procedure, one can back-calculate the correct values. We apply the method to 627 time series of population abundance across four taxa using the Gompertz state-space model as an example. We find that the risk of large bias in population status…

Laser speckle imaging for early detection of microbial colony forming units

2021

In this study, an optical contactless laser speckle imaging technique for the early identification of bacterial colony-forming units was tested. The aim of this work is to compare the laser speckle imaging method for the early assessment of microbial activity with standard visual inspection under white light illumination. In presented research, the growth of Vibrio natriegens bacterial colonies on the solid medium was observed and analyzed. Both – visual examination under white light illumination and laser speckle correlation analysis were performed. Based on various experiments and comparisons with the theoretical Gompertz model, colony radius growth curves were obtained. It was shown that…

Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters

2020

[EN] In spite of its simple formulation via a nonlinear differential equation, the Gompertz model has been widely applied to describe the dynamics of biological and biophysical parts of complex systems (growth of living organisms, number of bacteria, volume of infected cells, etc.). Its parameters or coefficients and the initial condition represent biological quantities (usually, rates and number of individual/particles, respectively) whose nature is random rather than deterministic. In this paper, we present a complete uncertainty quantification analysis of the randomized Gomperz model via the computation of an explicit expression to the first probability density function of its solution s…

Logistic Growth Described by Birth-Death and Diffusion Processes

2019

We consider the logistic growth model and analyze its relevant properties, such as the limits, the monotony, the concavity, the inflection point, the maximum specific growth rate, the lag time, and the threshold crossing time problem. We also perform a comparison with other growth models, such as the Gompertz, Korf, and modified Korf models. Moreover, we focus on some stochastic counterparts of the logistic model. First, we study a time-inhomogeneous linear birth-death process whose conditional mean satisfies an equation of the same form of the logistic one. We also find a sufficient and necessary condition in order to have a logistic mean even in the presence of an absorbing endpoint. Then…

Pressure inactivation kinetics of Enterobacter sakazakii in infant formula milk

2007

Survival curves of Enterobacter sakazakii inactivated by high hydrostatic pressure were obtained at four pressure levels (250, 300, 350, and 400 MPa), at temperatures below 30 degrees C, in buffered peptone water (BPW; 0.3%, wt/vol) and infant formula milk (IFM; 16%, wt/vol). A linear model and four nonlinear models (Weibull, log-logistic, modified Gompertz, and Baranyi) were fitted to the data, and the performances of the models were compared. The linear regression model for the survival curves in BPW and IFM at 250 MPa has fitted regression coefficient (R2) values of 0.940 to 0.700, respectively, and root mean square errors (RMSEs) of 0.770 to 0.370. For the other pressure levels, the lin…

Susceptibility and resistance to ethanol in Saccharomyces strains isolated from wild and fermentative environments

2010

11 pages, 3 figures, 3 tables.-- Article first published online: 8 SEP 2010

Modeling the isothermal inactivation curves of Listeria innocua CECT 910 in a vegetable beverage under low-temperature treatments and different pH le…

2015

Thermal inactivation kinetics of Listeria innocua CECT 910 inoculated in a vegetable beverage at three pH conditions (4.25, 4.75, and 5.20), four levels of temperature (50, 55, 60, 65℃), and different treatment times (0–75 min) were obtained. Survival curves did not follow a log-linear relationship and consequently were fitted to various mathematical models: Weibull, Geeraerd, Cerf with shoulder, and the modified Gompertz equation. Results indicated that the best model for the treatment conditions was the modified Gompertz equation, which provides the best goodness-of-fit and the lowest Akaike information criterion value. Sensitivity analysis indicated that the most influential factors affe…

A new model for germination of fungi.

2010

Abstract The objective of this study was to design a germination model dedicated to fungi. The percentage of germinated spores, P(%), depended on the maximum percentage of germination P max (%), the germination time, τ (h) and a design parameter, d (-) according to : P = P max 1 − 1 1 + t τ d . The model was capable to fit satisfactorily either apparent symmetric and asymmetric shapes of germination curves. The accuracy of τ determined by using the logistic or the present model was at least twice that obtained by the Gompertz equation. In contrast to the logistic model, the new model is by essence asymmetric. Therefore, its use is consistent with skewed distributions of the individual germi…

2013

Information on aging, maturation, and growth is important for understanding life histories of organisms. In extinct dinosaurs, such information can be derived from the histological growth record preserved in the mid-shaft cortex of long bones. Here, we construct growth models to estimate ages at death, ages at sexual maturity, ages at which individuals were fully-grown, and maximum growth rates from the growth record preserved in long bones of six sauropod dinosaur individuals (one indeterminate mamenchisaurid, two Apatosaurus sp., two indeterminate diplodocids, and one Camarasaurus sp.) and one basal sauropodomorph dinosaur individual (Plateosaurus engelhardti). Using these estimates, we e…

Mould germination: data treatment and modelling.

2006

Abstract The objectives of this study were i/ to examine germination data sets over a range of environmental conditions (water activity, temperature) for eight food spoilage moulds, ii/ to compare the ability of the Gompertz equation and logistic function to fit the experimental plots, iii/ to simulate germination by assessing various distributions of the latent period for germination amongst a population of spores. Data sets (percentage germination, P (%), versus time, t) of Aspergillus carbonarius, Aspergillus ochraceus, Fusarium verticillioides, Fusarium proliferatum, Gibberella zeae, Mucor racemosus, Penicillium chrysogenum and Penicillium verrucosum were analysed. No correlation, or re…