Gompertz Growth Model Research Articles

Forecasting and Comparison of Nonlinear Statistical Growth Models for Fish Seed Production in Eastern Coastal States of India

The study was carried out to compare the goodness of fit of three non–linear growth models viz., Monomolecular, Logistic and Gompertz growth models and analysing the instability index among the collected fish seed Production data from the eastern costal states of Indian for the period from 1994–1995 to 2019–2020. The parameters of each model were estimated using Levenberg–Marquardt (LM) iterative method. The ‘independence’ and ‘normality’ of error terms were examined by using ‘Run–test’ and ‘Shapiro–Wilk test’. Among the three models tested, monomolecular model was found as best model to describe variation in fish seed production in all Eastern Costal States of India. The values of CDI for fish seed production were 146.94 %, 79.30 % and 63.41% respectively which revealed that fish seed production had high instability in Odisha, Tamil Nadu and Andhra Pradesh while low instability (14.93 % and 13.13%) in West Bengal and India.

Application of growth models to South African Boer goat castrates and does under feedlot conditions

Mathematical models may aid researchers in describing biological processes, like growth, in animals. This study aimed to collect the body weight data of 18 Boer goat castrates and 20 Boer goat does, from birth until maturity, to model growth and determine growth trends. This is a novel investigation as sufficient information on an age-weight database for these two Boer goat sexes from birth to maturity, is lacking. Using age-weight data, four nonlinear models, namely the Brody, Gompertz, Logistic and Von Bertalanffy growth models, were plotted and evaluated. The model parameters of each growth model were compared for differences between the two sexes. The statistical effectiveness of fit was determined for each model using AIC and RMSE, with R2 also being considered. All models except the Brody model, predicted significantly heavier mature weights for castrates. The Brody model was deemed unfit to describe Boer goat growth as the function severely over-predict weights from birth until maturity for both sexes. The Von Bertalanffy (R2 = 91.3) and Gompertz functions (R2 = 91.3) showed the best fit for Boer goat castrates, while the Gompertz model (R2 = 95.1) showed the best fit for Boer goat does. The Gompertz function is the preferred model to depict Boer goat growth overall, as it accurately characterized growth of both sexes. According to the Gompertz model the age at which the inflection point of the growth curve was reached, did not differ significantly between castrates and does (141.80 days versus 136.31 days). There was also no significant difference in maturation rate between the two sexes.

Age Readings and Assessment in Coastal Batoid Elasmobranchs from Small-Scale Size-Selective Fishery: The Importance of Data Comparability in Multi-Specific Assemblages

The large variation in vertebral shape and calcification observed among elasmobranch species prevents using a single method for enhancing growth bands and reading age. Further, estimating age and growth parameters can be difficult or impractical when samples are incomplete due to the bycatch of a size-selective fishery. Using a single and rapid method, age readings were obtained on the vertebrae of four batoid species, namely 53 individuals of Dasyatis pastinaca, 51 of Raja asterias, 15 of Torpedo marmorata, and 55 specimens of Torpedo torpedo, from the local small-scale trammel net fishery in the coastal waters (5–20 m depth) of the Central Tyrrhenian Sea during 2019–2021. Based on these data, a statistical routine was developed to obtain multiple estimates of age and growth parameters for incomplete samples due to size-selective fishing. The acceptable agreement between and within readers (intra and inter-reader disagreement < 5%) and the rate of increase in vertebral size with body size (differently ranked across species) demonstrated the consistency of the enhancing method. The parameters estimated by the Von Bertalanffy and Gompertz growth models matched the data available in the Mediterranean Sea for the species studied, with D. pastinaca, T. torpedo, and R. asterias showing the lowest (k = 0.05–0.12), intermediate (k = 0.112–0.19), and highest (k = 0.18–0.23) growth rates, respectively, in line with the life history traits of these species. Overall, the method proved effective both in delineating band pairs in vertebrae of different species and in reliably estimating the age and growth parameters of problematic samples due to size-selective fishing. The proposed method supports the collection of comparable demographic data from other areas where similar multi-specific assemblages are bycatch of size-selective fisheries impacting potential nursery areas and other essential habitats for elasmobranchs.

Partial Derivatives of Gompertz, Logistic, and Weibull Non-Linear Growth Models on Confirmed COVID-19 Cases

. The epidemiological picture of COVID-19 is still unknown, and the number of confirmed cases of COVID-19 varies every day. Researchers have studied COVID-19 a lot, and many of them have used statistical models to estimate the growth of the outbreak. Non-linear statistical models can be used to describe growth behavior, as it varies in time. The aim of this research is to analyze, compare, and find the best model from the Gompertz, Logistic, and Weibull non-linear models. Daily cumulative data on confirmed COVID-19 viruses in Indonesia for 2020-2021 will be used in this research. The results obtained by the Logistic model proved to be very effective in describing the COVID-19 epidemic curve and estimating epidemiological parameters. The Logistic Model provides the best results compared to other growth models applied by Gompertz and Weibull. The R-Square of the logistic model is 0.9990, meaning that the model is able to explain or predict 99.90% of the data and 0.10% is explained by other factors. However, this research cannot explain the turning point of the curve, because there are many factors other than the model. One of them is the nature of the virus carrier from one place to another, then the behavior of the carrier who has not fully implemented the health protocol rules.

The effect of gender on growth performance, live weight gain, growth pattern modeling and, survival rate in Turkish native geese of the Kars region

Objective: This study presents a comprehensive investigation into the impact of gender on various aspects of growth performance in Turkish native geese, specifically in the Kars region.
 Materials and Methods: A total of 62 goslings, comprising 25 males and 37 females, were monitored over 12 weeks. The study focused on growth performance, live weight gain, survival rates, and growth pattern modeling.
 Results: The results from the two-way analysis of variance highlighted a statistically significant gender effect on growth performance (P < 0.05), with males consistently exhibiting notably higher live weights during weigh-ins. Significant gender disparities were evident in growth performance both on the hatching day (P < 0.01) and during weeks 6 to 12 (P < 0.05). Remarkably, male geese displayed significantly higher daily live weight gains during weeks 5 to 6 (P < 0.05). Linear regression analyses emphasized gender's influence on live weight gain, with female geese demonstrating an R² value of 0.9044 (P < 0.001) and male geese showing an R² value of 0.8912 (P < 0.001). Gompertz growth models unveiled distinctive growth patterns. In females, an R² value of 0.9300 highlighted their growth trajectory, while males exhibited an R² value of 0.9194. Survival rates after a 12-week period were 81.7% for females and 80.0% for males.
 Conclusion: In conclusion, this meticulous exploration of the impact of gender on growth trajectories underscores the significant role it plays.

A COMPARATIVE ANALYSIS OF GROWTH MODELS ON NIGERIA POPULATION

Growth models have been applied over time to track and forecast changes in variables such as population, body height, biomass, fungal growth, and other aspects of numerous fields of study. This research focuses on modelling the growth of Nigeria’s population from the year 1981 to 2021 and determining the best fit model to represent Nigeria’s population growth (male, female and total). Seven growth models were considered in this research which includes: the linear, the exponential (Malthusian), Logistic (Verhulst), Gompertz, Hyperbolic, Brody and the Von Bertalanffy growth models. The criteria used for comparison of best fitted model were the coefficient of determination (R2), Akaike Information Criterion (AIC), Mean Square Error (MSE), and Bayesian Information Criterion (BIC). The R2 showed that the exponential, the logistic and the Gompertz growth models were all better fits for Nigeria’s population (male, female and total) having the highest R2 (0.999). Further comparison with the MSE, AIC and BIC revealed that the exponential growth model best represented Nigeria’s population growth (male, female and total) having the least MSE, AIC and BIC. Hence the exponential growth model should be considered by researchers in Nigeria population projection.

The Behavioral and Productive Characteristics of Japanese Quails (Coturnix japonica) Exposed to Different Monochromatic Lighting

The purpose of this study is to examine the impact of monochromatic illuminations at wavelengths of white (400–700 nm), green (560 nm), yellow (580 nm), blue (480 nm), and red (660 nm) on the performance and behavioral traits of Japanese quails throughout their fattening period. A total of 300 quails in five lighting experimental groups were housed in their conventional rearing cages. Weekly live weights of quails were measured individually, developmental stability was determined, and behavior and fear tests were performed. The body weight averages of quails exposed to blue, green, and yellow light were determined to be greater than those exposed to white and red light (p < 0.05). In terms of the mature weight parameter and the weight of the inflection point of the Gompertz growth model, the averages of the quails exposed to green and blue monochromatic lighting were higher (p < 0.05). The most negative findings on aggressive behavior were observed in birds exposed to monochromatic yellow and red light. Although the body weight of quails exposed to yellow monochromatic lighting was similar to that of quails exposed to green and blue monochromatic lighting, green and blue monochromatic lighting produced the best results in terms of growth, behavior, and developmental stability characteristics. Consequently, it is believed that consistently using green or blue monochromatic lighting programs when raising Japanese quails may provide economic advantages to the producers.

A computational tumor growth model experience based on molecular dynamics point of view using deep cellular automata

Cancer, as identified by the World Health Organization, stands as the second leading cause of death globally. Its intricate nature makes it challenging to study solely based on biological knowledge, often leading to expensive research endeavors. While tremendous strides have been made in understanding cancer, gaps remain, especially in predicting tumor behavior across various stages. The integration of artificial intelligence in oncology research has accelerated our insights into tumor behavior, right from its genesis to metastasis. Nevertheless, there's a pressing need for a holistic understanding of the interactions between cancer cells, their microenvironment, and their subsequent interplay with the broader body environment. In this landscape, deep learning emerges as a potent tool with its multifaceted applications in diverse scientific challenges. Motivated by this, our study presents a novel approach to modeling cancer tumor growth from a molecular dynamics' perspective, harnessing the capabilities of deep-learning cellular automata. This not only facilitates a microscopic examination of tumor behavior and growth but also delves deeper into its overarching behavioral patterns. Our work primarily focused on evaluating the developed tumor growth model through the proposed network, followed by a rigorous compatibility check with traditional mathematical tumor growth models using R and Matlab software. The outcomes notably aligned with the Gompertz growth model, accentuating the robustness of our approach. Our validated model stands out by offering adaptability to diverse tumor growth datasets, positioning itself as a valuable tool for predictions and further research.

Kinetics of dye decolorization using heterogeneous catalytic system with immobilized Achromobacter xylosoxidans DDB6

Textile effluents containing toxic dyes must be treated effectively before discharge to prevent adverse environmental impacts. Traditional physical and chemical treatment methods are costly and generate secondary pollutants. In contrast, biological treatment is a more suitable, clean, versatile, eco-friendly, and cost-effective technique for treating textile effluent. It is well established that indigenous microbial populations present in effluents can effectively degrade toxic dyes. In this regard, Achromobacter xylosoxidans DDB6 was isolated from the effluent sample to decolorize crystal violet (CV), Coomassie brilliant blue (CBB), and alizarin red (AR) by 67.20%, 28.58%, and 20.41%, respectively. The growth parameters of A. xylosoxidans DDB6 in media supplemented with 100 ppm of various dyes were determined using the modified Gompertz growth model. The immobilized cells in calcium alginate beads showed apparent decolorization rate constant of 0.27, 0.18, and 0.13 h−1 for CV, CBB, and AR, respectively. The immobilized cells in a packed bed reactor with an optimum flow rate of 0.5 mL/min were used to treat 100 ppm of CV with a percentage decolorization of 79.47% after three cycles. Based on the findings, A. xylosoxidans DDB6 could be effectively used for decolorization of various dyes.

From Equations to Insights: Navigating the Canvas of Tumor Growth Dynamics

This report delves into the pivotal role that differential equations play in the modeling of dynamic systems, with a specific emphasis on their utility within the domain to tumor growth modeling. Differential equations furnish a quantitative framework for understanding the complex dynamics inherent in the growth of tumors, thereby empowering the formulation of predictions, possible treatment measures and prolonged prognostic outcomes. In this report we embark upon an exploration of the historical origin of these equations, their associated classifications, features and their extensive deployment in multiple disciplines such as physics, biology, economics and computer science, though the primary emphasis is on the domain of tumor growth. Through the medium of two hypothetical case studies, employing Gompertz and Logistic Growth models, this report vividly illustrates the indispensable role of differential equations in the realm of clinical decision-making, the planning of treatment measures and in building a stable foundation for future endeavors. It concurrently explores the advantages of employing differential equations within the framework of tumor growth modeling, underscoring their mathematical precision, predictive efficacy, quantitative insights and historical success. Nevertheless, the report remains forthright in acknowledging the limitations of these models, particularly their tendency for simplifications, the neglect of spatially distributed information and their disregard for Stochastic Effects.

Ensemble Algorithms to Improve COVID-19 Growth Curve Estimates

In January 2020, the world was taken by surprise as a novel disease, COVID-19, emerged, attributed to the new SARS-CoV-2 virus. Initial cases were reported in China, and the virus rapidly disseminated globally, leading the World Health Organization (WHO) to declare it a pandemic on 11 March 2020. Given the novelty of this pathogen, limited information was available regarding its infection rate and symptoms. Consequently, the necessity of employing mathematical models to enable researchers to describe the progression of the epidemic and make accurate forecasts became evident. This study focuses on the analysis of several dynamic growth models, including the logistics, Gompertz, and Richards growth models, which are commonly employed to depict the spread of infectious diseases. These models are integrated to harness their predictive capabilities, utilizing an ensemble modeling approach. The resulting ensemble algorithm was trained using COVID-19 data from the Brazilian state of Paraíba. The proposed ensemble model approach effectively reduced forecasting errors, showcasing itself as a promising methodology for estimating COVID-19 growth curves, improving data forecasting accuracy, and providing rapid responses in the early stages of the pandemic.

Comparative Study of the Gompertz and Logistic Growth Models on the Prevalence and Fatality of Covid-19 Pandemic in Nigeria

This study models the prevalence and fatality of the Covid-19 pandemic in Nigeria from February 2020 to July 2022. It is a comparative study of two prominent models: The Gompertz and Logistic population growth models. The data for this study was obtained from the website of Our World in Data, OWID (https//www.ourworldindata.org). The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were employed to compare the performance of the models, and the number of iterations before convergence and convergence tolerance for each model was also put into consideration. The study revealed that the Gompertz population growth model provides a better fit compared to the logistic growth in modelling the cumulative covid-19 cases and cumulative covid-19-related deaths in Nigeria. From the models, we obtained important features of the pandemic, such as the growth rate and asymptotes.

Ecological mechanisms of biofilm development in the hybrid sludge-biofilm process: Implications for process start-up and optimization

The hybrid sludge-biofilm processes have been widely applied for the construction or upgradation of biological wastewater treatment process. Ecological mechanisms of biofilm development remain unclear in the hybrid ecosystem, because of the intricate interactive effects between sludge and biofilms. Herein, the establishment principles of biofilms with distinct coexisting sludge amounts were uncovered by varying sludge retention times (SRTs) from 5 to 40 days in the hybrid process. With the increasing of SRTs, biofilm biomass decreased with the increase of suspended sludge, resulting in lower biofilm proportion. As estimated by the Gompertz growth model, the increased sludge amounts (i.e., higher SRTs of 20 and 40 days) prolonged the initial colonization stage and decreased the specific development rate of biofilms when compared to lower sludge amounts with the shorter SRTs (i.e., 5 and 10 days). Null model analysis demonstrated that deterministic homogenous selection could facilitate the colonization and accumulation of biofilms with less coexisting sludge (SRT of 10 days). However, stochastic ecological drift and homogenizing dispersal dominated the colonization and accumulation stages of biofilms with more coexisting sludge (SRT of 20 days), respectively. The ecological networks reflected that positively-related taxa presented taxonomic relatedness, whereas high inconsistency of taxonomic relatedness was observed among aggregate forms or development stages as affected by varied SRTs. The high incidence of intra-taxa co-occurrence patterns suggested that taxa with similar ecological niches could be specifically selected in biofilms when being exposed with less coexisting sludge. This study uncovered ecological mechanisms of biofilm development driven by varying the SRTs of suspended sludge, which would help to propose appropriate strategies for the efficient start-up and optimization of the hybrid sludge-biofilm system.

Discrete-Time Gompertz Model for Adana Breed Pigeons

The mathematical animal growth models in the literature are not in the form of linear models. These growth models in the literature are not in linear form. There are different numerical analysis methods for the estimation of the parameters found in these functions and specific software have been produced to estimate the unknown parameters in these mathematical models and to apply these methods. In these nonlinear mathematical growth models, there may be more than one parameter. For these and other reasons, the number of mathematical numerical operations in estimating parameters is quite high. In this study, the discrete time stochastic Gompertz model (DTSGM) was considered to determine the growth of Adana pigeons. A model is used in which the parameter in the model is estimated by an adaptive Kalman filter (AKF). The aim of this research is to reveal the validity of both the model and the estimation method for Adana breed domestic pigeons. Daily weight measurements of 28 Adana pigeons were considered and estimated using DTSGM and AKF methods in this framework. DTSGM in conjunction with AKF has been shown to provide a convenient analysis tool for modeling daily weight estimates of Adana pigeons.

Lime sludge assisted anaerobic bioreactor landfilling of municipal solid waste for enhanced leachate stabilization and bioenergy yield

Bioreactor landfilling even being advanced technology for enhanced stabilization of municipal solid waste (MSW), often suffers with adverse acidogenic conditions. Such conditions reinforce poor leachate stabilization, and reduced biomethane yield. This work attempts to counter the challenges of adverse MSW landfilling conditions through incorporation of waste alkaline sludge from paper industry. The amendment in anaerobic bioreactor landfilling of MSW was practiced by adding lime sludge (LS) with MSW in three distinct proportions: 20 g LS/kg MSW (LS100), 50 g LS/kg MSW (LS250) and 100 g LS/kg MSW (LS500), keeping LS0 as control. Periodic leachate and biomethane analysis showed benefits of proportionate LS addition. The control reactor often experienced leachate ponding and inhibitory conditions for anaerobic digestion. However, reactor LS250 achieved highest decrease in leachate organic strength removal (76.47 %) and biomethane production (8.315 L) over the period of landfilling. The pH and volatile fatty acids (VFAs) were in coordination with LS proportions. The LS addition beyond 100 g LS/kg MSW (LS500) could decrease the leachate pollution removal and biomethane yield. Finally, the Gompertz growth model showed excellent fit (R2 >0.997) to recorded biomethane. The study expands the scope of utilizing similar sludges for amendment of existing landfilling practices for efficient bioconversion of organic fractions of MSW.

Gomperzt non-linear model for predicting growth performance of commercial broiler chickens

An experiment was conducted to estimate growth parameters for commercial broiler chickens in Indonesia. The data was collected from July 2021 to June 2022. A total of 1,570 samples consisting of four strains of broiler chickens were collected from 74 houses. The samples were daily weighed from 0 to 7 days of age, and they were weekly weighed from 1 to 5 weeks of age. A nonlinear Gompertz growth model was fitted to the observed body weights (BW). The results for five growth parameters were as follows: the asymptotic value (A) of the mature live weight ranged from 3.733 to 5.044 kg; the turning point of growth (B) ranged from 4.499 to 4.561; the value growth rate constant (K) ranged from 0.049 to 0.059 kg/week; Inflection points in ranged from 25.292 – 30.970 days, and 1.373 – 1.855 kg for inflection age (IA) and inflection weight (IW), respectively. The model was an excellent fit for the growth data in the commercial broiler with a low Akaike information criterion (AIC), and high coeffi-cient determination (R2).

The effects of exposure to cold during incubation on developmental stability, fear, growth, and carcass traits in Japanese quails.

The aim of this study was to determine the effects of 6h/day cold (35.0°C) acclimatization between the 9th and 15th days of incubation of Japanese quail embryos on hatchability, livability, chick quality, developmental stability, fear response, live weight, and slaughter-carcass characteristics. Two homologous incubators and a total of 500 hatching eggs were used in the study. Randomly selected half of the eggs were exposed to cold according to the eggshell temperature. The cold acclimation of Japanese quail embryos had no adverse effects on all mentioned traits, except for chick quality. Chicks in the control group had higher Tona scores (99.46) than those exposed to cold (99.00) (P < 0.05). In addition, there were differences among the treatment groups in terms of the parameters of mature weight (β0), instantaneous growth rate (β2), and inflection point coordinates of the Gompertz growth model (P < 0.05 for all). It was found that exposing embryos to cold during the incubation changed the shape of the growth curve. As the development of embryos exposed to cold slows down, a compensatory growth occurs in the early posthatch period. Thus, the growth rate increased in the period before the inflection point of the growth curve.

Modeling of age-dependent natural mortality rates for long-lived fishes based on the Richards model family

Natural mortality rates ( M) are poorly quantified and commonly identified as a key source of uncertainty in fish stock assessments. Increasingly, stock assessments account for size- and age-dependence in M instead of using a constant M for all sizes and ages, as has traditionally been the default assumption. Empirical studies show that M is approximately inversely proportional to body length in fish populations, and this generalization has been used together with a von Bertalanffy growth curve to derive an age-dependent M. Here we extend this approach to the three commonly used growth functions of the Richards family (i.e., Logistic, von Bertalanffy, and Gompertz growth models). These models allow flexible production of various growth curves with a sigmoid shape and an upper asymptote, making them useful for displaying diverse growth curves for various long-lived fishes. The influences of growth parameters on predicted M were investigated, and the outcomes were compared among the three growth models. Age-dependent M for blue sharks ( Prionace glauca) were estimated as an example.

Trends in Area, Production, and Productivity of Coffee in Chikkamagaluru District of Karnataka, India

Coffee is a significant commodity crop worldwide, and Karnataka, an Indian state with coffee-growing regions such as Chikkamagaluru, Kodagu, and Hassan, is a major producer. Chikkamagaluru, also known as the Coffee Land of Karnataka, is the primary location for Arabica coffee production and cultivation of various other spice crops such as areca nut, pepper, cardamom, vanilla, lime, clove, and cinnamon. Despite the importance of coffee production, coffee growers encounter multiple challenges in cultivating and yielding high-quality coffee. Therefore, researchers have explored issues associated with coffee production and yield and suggested feasible solutions. To make informed decisions, it is essential to analyze the productivity and production of the coffee-growing region. This study used 25 years of coffee time series data obtained from the Coffee Board of India, Bengaluru, from 1995-1996 to 2019-2020, to investigate the coffee-growing region's problems. The data was analyzed using linear (linear, cubic) and nonlinear (exponential, logistic, and Gompertz) growth models. The results showed that the cubic model provided the best fit for the Chikkamagaluru district's coffee-growing region. Meanwhile, the linear and Gompertz models were the best fit for coffee output and productivity, respectively. The study revealed a decrease in Chikkamagaluru coffee productivity over the study period, despite an increase in the coffee-growing area.

Airborne inoculum dynamics of Polystigma amygdalinum and progression of almond red leaf blotch disease in Catalonia, NE Spain

AbstractThe dynamics of airborne ascospores and disease progress of red leaf blotch (RLB) of almond, caused by Polystigma amygdalinum, and their correlations with weather variables were studied from 2019 to 2021 in two almond orchards located in Lleida, NE Spain. Airborne ascospores were detected and quantified by real‐time qPCR using species‐specific primers for P. amygdalinum. Ascospores were detected mainly from April to June, with a high variability between the yearly cumulative concentrations. Positive significant correlations were found between the weekly proportion of airborne ascospores and the number of wet and mild days—either combined or separated— accumulated rainfall, number of rainy days, accumulated low temperatures on wet days, and mean and maximum relative humidity. In contrast, several thermal variables (maximum temperature, VPD, and number of warm days) were negatively correlated with ascospore catches. Positive significant correlations were found between the cumulative proportion of ascospores and RLB incidence and severity. Weekly variations in RLB incidence and severity showed significant positive correlations with the number of warm days while negative with the number of mild days. Severity was also positively correlated with several thermal variables (mean, maximum, and minimum temperature, and VPD), and negatively correlated with the number of cold days and wet and mild days. Stronger correlations were generally found with ascospore catches or disease progress when using concurrent weekly weather data. Gompertz, monomolecular, and logistic growth models were evaluated to describe RLB disease progress.