Selection Of Growth Models Research Articles

Software Reliability Growth Model Selection by using VIKOR Method Based on q-Rung Orthopair Fuzzy Entropy and Divergence Measures

Software Reliability Growth Model Selection by using VIKOR Method Based on q-Rung Orthopair Fuzzy Entropy and Divergence Measures

Dynamic Model Selection and Optimal Batch Design for Polyhydroxyalkanoate (PHA) Production by Cupriavidus necator.

Mathematical modelling of microbial polyhydroxyalkanoates (PHAs) production is essential to develop optimal bioprocess design. Though the use of mathematical models in PHA production has increased over the years, the selection of kinetics and model identification strategies from experimental data remains largely heuristic. In this study, PHA production from Cupriavidus necator utilizing sucrose and urea was modelled using a parametric discretization approach. Product formation kinetics and relevant parameters were established from urea-free experimental sets, followed by the selection of growth models from a batch containing both sucrose and urea. Logistic growth and Luedeking-Piret model for PHA production was selected based on regression coefficient (R2: 0.941), adjusted R2 (0.930) and AICc values (-42.764). Model fitness was further assessed through cross-validation, confidence interval and sensitivity analysis of the parameters. Model-based optimal batch startup policy, incorporating multi-objective desirability, suggests an accumulation of 2.030g l-1 of PHA at the end of 120h. The modelling framework applied in this study can be used not only to avoid over-parameterization and identifiability issues but can also be adopted to design optimal batch startup policies.

Quantitative microbiological risk assessment of traditional food of animal origin produced in short supply chains in Poland.

Polish raw-milk cheeses produced in short supply chains may pose a threat to consumer safety due to pathogen presence. Listeria monocytogenes is a bacterium of great importance for the food safety of refrigerated RTE foods due to its ability to grow at refrigeration temperatures. During the EU-FORA fellowship, a stochastic risk assessment was designed and executed to estimate the risk for consumers from L. monocytogenes in these products. The aim was to develop a probabilistic QMRA model that would incorporate the variability and uncertainty of the model's inputs such as prevalence, initial concentration levels, product intrinsic factors, domestic storage temperature and consumer behaviour. The project involved data collection and analysis, growth model selection, mathematical modelling and Monte Carlo analysis in R programming language. Microbiological and physicochemical testing were carried out throughout the year on two types of cheeses in combination with a domestic refrigerator temperature survey and accompanying consumption questionnaire. Collected data were fitted to probability distributions using R. The appropriate growth model for the pathogen was selected based on an inoculation study performed on one of the raw-milk cheeses and the chosen mathematical model was written into the R script developed for the QMRA. The dose-response model used the ingested dose calculated from the modelled concentration of L. monocytogenes at the time of consumption and the single serving size from the questionnaire to estimate the probability of illness. The final risk was expressed as probability of listeriosis for Polish consumers per serving of raw-milk cheese.

Study on the Spatial Structure and City Form Construction of River Valley-Type Cities in the Context of Artificial Intelligence—A Case Study of Northwest China

This paper uses Northwest China as an example to present an in-depth study and analysis of river valley cities’ spatial structure and city form in the context of artificial intelligence. The paper focuses on alleviating the “core-edge” spatial structure locking effect, achieving the “industry-space” scale effect and cooperation, solving the problem of endogenous dynamics to promote regional and urban development, and promoting various main functional areas based on the derivation discussion and spatial growth model selection. The study focuses on the exploration of paths to alleviate the “core-edge” spatial structure’s locking effect, realize the scale effect and cooperation ability of “industry-space,” solve the problem of endogenous power to promote regional and urban development, and promote the new urbanization path of different main functional areas based on the discussion and spatial growth mode selection. We measure the evolution characteristics of industrial and spatial elements and the level of intersystem synergistic development to address the spatial growth and industrial transformation of the northwest region urban agglomeration in the special development period, discover the defects of the northwest China urban agglomeration’s spatial growth, and select the appropriate spatial growth model in the foreseeable spatial and temporal scope. The new city spatial form in the northwest region, which strengthens regional characteristics, is the spatial form combined with the new city plan form in two dimensions. This paper investigates the relationship between regional characteristics and urban spatial carriers by developing spatial planning design ideas and methods that reflect the regional characteristics of new cities in the northwest region, in order to improve the spatial quality of new cities in the northwest region and their sense of belonging to the city, provide a new spatial expansion idea for small cities in river valleys in the Qinling Mountains of southern Shaanxi, and enrich the spatial quality of new cities in the northwest region.

APPROXIMATION OF GROWTH INDICATORS AND ANALYSIS OF INDIVIDUAL GROWTH CURVES BY LINEAR DIMENSIONS OF TUBULAR BONES IN CHICKENS OF MEAT PRODUCTION DIRECTION DURING POSTNATAL PERIOD OF ONTOGENESIS

Medical and biological sciences, including morphology, now require the introduction of the latest information technologies and mathematical methods to process the obtained and accumulated research results. To study the growth dynamics of body weight in domestic birds, classical growth models, Gompertz, were used for the purpose of quantitative description of the growth processes in biological objects, in particular for the growth and development of birds – Von Bertalanffy, Richards, and hyperbolastic models. The research material was tubular bones of the thoracic (humerus, ulna, and radius) and pelvic (femur, tibia, and tarsometatarsus) limbs in birds of meat production (broiler chickens and laying hens from the parent broiler flock of Cobb-500 strain) of different age groups during the postnatal period of ontogenesis. An appropriate regression analysis of experimental data based on known growth models was performed to solve the goal of obtaining growth curves and identifying special points (extremes, inflections, etc.), to build a picture of the overall development of the body as a whole and individual bones of the extremities. The most biologically suitable growth models for describing the growth dynamics of the body as a whole and individual studied bones were determined. The absence of a unified growth model of linear parameters of different tubular bones in meat producing chickens during the postnatal period of ontogenesis was established. This implies the need for a clear selection of growth models taking into account age, species, breed, keeping and feeding conditions of domestic birds. The growth model that best describes the body weight dynamics of broiler chickens is the hyperbolastic growth model of the H3 type, and in laying hens from the parent broiler flock – the Brody growth model.

Multi-Model Approach on Growth Estimation and Association With Life History Trait for Elasmobranchs

Age and growth information is essential for stock assessment of fish, and growth model selection may influence the accuracy of stock assessment and subsequent fishery management decision making. Previous descriptions of the age and growth of elasmobranchs relied mainly on the von Bertalanffy growth model (VBGM). However, it has been noted that sharks, skates and rays exhibit significant variety in size, shape, and life history traits. Given this variation, the VBGM may not necessarily provide the best fit for all elasmobranchs. This study attempts to improve the growth estimates by using multi-model approach to test four growth models—the VBGM, the two-parameter VBGM, the Robertson (Logistic) and the Gompertz models to fit observed or simulated length-at-age data for 38 species (44 cases) of elasmobranchs. The best-fit growth model was selected based on the bias corrected Akaike’s Information Criterion (AICc), the AICc difference, the AICc weight, the Bayesian Information Criterion (BIC), and the Leave-one-out cross-validation (LOOCV). The VBGM and two-parameter VBGM provide the best fit for species with slow growth and extended longevity (L∞ > 100 cm TL, 0.02 < k < 0.25 yr–1), such as pelagic sharks. For fast-growing small sharks (L∞ < 100 cm TL, kr or kg > 0.2 yr–1) in deep waters and for small-sized demersal skates/rays, the Robertson and the Gompertz models provide the best fit. The best-fit growth models for small sharks in shallow waters are the two-parameter VBGM and the Robertson model. Although it was found that the best-fit growth models for elasmobranchs were associated with their life history trait, exceptions were also noted. Therefore, a multi-model approach incorporating with the best-fit model selected for each group in this study was recommended in growth estimation for elasmobranchs.

Modeling growth on the cannonball jellyfish Stomolophus meleagris based on a multi-model inference approach

Worldwide catches of cannonball jellyfish Stomolophus meleagris (Cnidaria: Scyphozoa) have increased during the last years; nevertheless, this species still lacks updated biological knowledge for its management. This research proposes that the individual growth pattern for jellyfish can be estimated in the absence of age readings through cohort follow-up over time and by multi-model inference approach (MMI). Length data were obtained during 2010–2011 in Gulf of California to obtain cohort information using a multinomial analysis and then assign age; growth model selection was based on MMI. Three cohorts were identified and the von Bertalanffy model suitably described their growth. The species has an accelerated growth with a short life cycle; cohorts one and two reached their asymptotic length, and the third one barely reached the length-at-first sexual maturity. Growth variations among cohorts could be explained by their different biological strategies where the first two prioritized asymptotic length and the third one reproduction length. The three cohorts shared a common goal for medusoid phase, which was sexual reproduction. This information could be used for estimating harvest rates or assessing their capacity for redoubling as an invasive population in coastal ecosystems. The proposed methodology may be applied in other jellyfish species around the world.

Abstract 4613: Mathematical modeling of tumor growth in mouse models

Abstract A variety of tumor models are used in preclinical oncology drug discovery, including patient-derived xenografts (PDXs), cell line-derived xenografts (CDXs), and syngeneic homografts. Tumors in mouse models exhibit heterogeneous growth patterns with or without drug treatment, which is further complicated by measurement errors. Mathematical modeling of tumor growth helps us better understand such patterns and analyze drug efficacy in transplanted tumor models. Many mathematical models have been proposed to describe tumor growth curves, each with certain assumptions and equations, suitable for specific situations or data sets1-5. It is yet unknown which models are best in fitting the growth curves for a large collection of mouse models. In this study, we systematically evaluated a set of mathematical models including exponential models, logistic and Gompertz model, biphasic models, dynamic carrying capacity model, and power law model on more than 50,000 tumor growth datasets collected from in vivo efficacy studies in PDXs, CDXs and syngeneic models. A set of metrics were used to evaluate the goodness of fit, including Akaike Information Criterion (AIC), root mean square error (RMSE), coefficient of determination, mean absolute relative error, etc. We also proposed a new composite metric to combine many criteria for easy selection of growth models. Our results show that tumor growth patterns are less complex under vehicle treatment, and different mathematical models have relatively small difference in modeling the growth curves. Tumor growth patterns are more diverse under drug treatment. Tumors may shrink or completely remit, though some may grow in the first days after inoculation before drug effect takes place. Still some tumors stop growing or even shrink before drug resistance develops and resume fast growing. Therefore, different mathematical models are needed to describe the different patterns. Finally, we present summary statistics to give an overall picture on the applicability of the mathematical models, and suggest statistical models for subsequent analysis for drug efficacy evaluation and biomarker discovery. Citation Format: Chao Zhang, Xiaoqian Jiang, Sheng Guo, Qixiang Li. Mathematical modeling of tumor growth in mouse models [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 4613.

The influence of sample distribution on growth model output for a highly-exploited marine fish, the Gulf Corvina (Cynoscion othonopterus).

Estimating the growth of fishes is critical to understanding their life history and conducting fisheries assessments. It is imperative to sufficiently sample each size and age class of fishes to construct models that accurately reflect biological growth patterns, but this may be a challenging endeavor for highly-exploited species in which older fish are rare. Here, we use the Gulf Corvina (Cynoscion othonopterus), a vulnerable marine fish that has been persistently overfished for two decades, as a model species to compare the performance of several growth models. We fit the von Bertalanffy, Gompertz, logistic, Schnute, and Schnute–Richards growth models to length-at-age data by nonlinear least squares regression and used simple indicators to reveal biased data and ensure our results were biologically feasible. We then explored the consequences of selecting a biased growth model with a per-recruit model that estimated female spawning-stock-biomass-per-recruit and yield-per-recruit. Based on statistics alone, we found that the Schnute–Richards model described our data best. However, it was evident that our data were biased by a bimodal distribution of samples and underrepresentation of large, old individuals, and we found the Schnute–Richards model output to be biologically implausible. By simulating an equal distribution of samples across all age classes, we found that sample distribution distinctly influenced model output for all growth models tested. Consequently, we determined that the growth pattern of the Gulf Corvina was best described by the von Bertalanffy growth model, which was the most robust to biased data, comparable across studies, and statistically comparable to the Schnute–Richards model. Growth model selection had important consequences for assessment, as the per-recruit model employing the Schnute–Richards model fit to raw data predicted the stock to be in a much healthier state than per-recruit models employing other growth models. Our results serve as a reminder of the importance of complete sampling of all size and age classes when possible and transparent identification of biased data when complete sampling is not possible.

Novel metrics for growth model selection

BackgroundLiterature surrounding the statistical modeling of childhood growth data involves a diverse set of potential models from which investigators can choose. However, the lack of a comprehensive framework for comparing non-nested models leads to difficulty in assessing model performance. This paper proposes a framework for comparing non-nested growth models using novel metrics of predictive accuracy based on modifications of the mean squared error criteria.MethodsThree metrics were created: normalized, age-adjusted, and weighted mean squared error (MSE). Predictive performance metrics were used to compare linear mixed effects models and functional regression models. Prediction accuracy was assessed by partitioning the observed data into training and test datasets. This partitioning was constructed to assess prediction accuracy for backward (i.e., early growth), forward (i.e., late growth), in-range, and on new-individuals. Analyses were done with height measurements from 215 Peruvian children with data spanning from near birth to 2 years of age.ResultsFunctional models outperformed linear mixed effects models in all scenarios tested. In particular, prediction errors for functional concurrent regression (FCR) and functional principal component analysis models were approximately 6% lower when compared to linear mixed effects models. When we weighted subject-specific MSEs according to subject-specific growth rates during infancy, we found that FCR was the best performer in all scenarios.ConclusionWith this novel approach, we can quantitatively compare non-nested models and weight subgroups of interest to select the best performing growth model for a particular application or problem at hand.

Implications of Growth Model Selection on the Associations of Fetal and Infant Growth with Later Childhood Outcomes

Implications of Growth Model Selection on the Associations of Fetal and Infant Growth with Later Childhood Outcomes

AIC-Based Selection of Growth Models: The Case of Piglets from Organic Farming

The selection and comparison of different growth models for describing weight gain of piglets raised in organic farming is investigated by using the Akaike’s Information Criterion (AIC). In total, 49,699 data points of 5188 piglets recorded between 2007 and 2013 were considered. From the day of birth, up to 40 days (i.e. until weaning) the model of von Bertalanffy was favored by the AIC. This model is with 60.32% more likely to truly reflect reality than any other of the analyzed models. Up to 105 days, the two-linear model was favored by the AIC (probability 99.75%). The intersection point of the two-linear model was calculated by 53.8 days, which fitted well to the actual change in the food situations.

Growth model selection for the jumbo squid Dosidicus gigas from the Gulf of California, Mexico

We analyzed mantle length and age data of the whole ontogenic cycle of the jumbo squid Dosidicus gigas in the Gulf of California, Mexico, to describe its growth pattern. Several individual growth models that included asymptotic and non-asymptotic patterns were fitted to the data, and Akaike’s information criterion and multimodel inference were used to identify the model that best fit the data. The length-at-age data were divided into males and females (recruits and adults) for analysis separately and then combined to assess the overall growth pattern. The Schnute general model (ρ≠0, η≠0, where ρis the constant relative rate of the relative growth rate, ηis the incremental relative rate of the relative growth rate) was the function that best described the growth of females, males and both sexes of D. gigas together. For females, the Akaike difference and Akaike weight were 0 and 0.91, respectively; for males, the Akaike difference was also 0, but the Akaike weight was 0.39, showing that alternative growth models could explain the individual growth; these growth models were the Gompertz (L0, length at time zero), Gompertz (L∞, asymptotic length) and Schnute (ρ≠0, η = 0) models. We estimated the age and mantle length at which the growth rate changes for both sexes, estimating an age of 162.36 d (separately, 167.51 d for females and 158.98 d for males), and a length of 299.52mm for the growth inflection point (separately, 312.84 mm for females and 292.86 mm for males). Once D. gigas reaches this point, the species exhibits more gradual growth until reaching an asymptotic mantle length of 859.45 mm (for females, 904.80 mm, and for males, 828.49 mm). A comparison of the growth patterns of D. gigas reported in the Eastern Pacific indicated nonasymptotic growth of this species in the Humboldt Current and Costa Rica Dome; in contrast, asymptotic growth was identified for the western coast of Baja California and Gulf of California. The reason for this difference is unclear, and this issue will be a topic of future studies.

Application of Growth Models to Human Computer Interaction (hci) Research Literature

The study explores the applicability of three models namely exponential model, logistic model and power model on HCI research literature of world and top twenty nations, as reflected in Science Citation Index-Expanded for a period of 25 years, from 1987 to 2011. The criteria for selection of growth models are based on two growth rate functions suggested by Egghe and Rao. This methodology is found satisfactory, except for data series where there is no clear trend observed in second growth rate function. The analysis suggests that growth of all the 21 data set is explained by both logistic growth model and exponential growth model equally well. Although, power growth model is indicated for four data sets, by the two growth rate function methodology, it was logistic or exponential model found fit to explain growth of those data sets as well. Therefore, results in this study emphasises the need to undertake more such studies on the time series data on publications growth of various fields to test the utility of two growth rate functions methodology.

Growth Models for Fisheries: The Effect of Unbalanced Sampling Error On Model Selection, Parameter Estimation, and Biological Predictions

Field studies that attempt to estimate the mean growth rates of individuals in a population usually yield unbalanced data and various forms of sampling error. If these data are a poor representation of a population, then the estimates of growth rates may also be unrepresentative of the population. We present an assessment of the performance and uncertainty in 4 growth models—the von Bertalanffy, Gompertz, inverse logistic, and Schnute models—fitted to data with various scenarios of sampling error. The performance of each model was determined by comparing highest likelihoods outcomes to known case outcomes. A Monte Carlo simulation framework was used to generate data consisting of 8 typical scenarios of sampling error common in tag-recapture data. Each growth model was evaluated according to 2 metrics: the error rate (i.e., a metric for model uncertainty) and the prediction error (i.e., the accuracy of biological predictions such as age). Results indicate that an inadequate size range in the data (i.e., a lack of juvenile size classes) would often lead to a high error rate. When negative growth increment data are included, the K parameter of the von Bertalanffy model increased, and the L∞ decreased. The inverse logistic model sometimes produced absurd parameter estimates but nevertheless generated the lowest prediction errors. A high prediction error can potentially have far more serious implications to fishery stock assessments than is currently appreciated. Given widespread use of the von Bertalanffy and Gompertz models, selected solely on the basis of model selection criteria, it is clear that greater care and scrutiny are warranted in the selection of growth models in the presence of sampling error.

Gear selectivity and sample size effects on growth curve selection in shark age and growth studies

The effects of gear selectivity and sample size on growth model selection for shark length-at-age data was investigated using simulated data sets for dusky ( Carcharhinus obscurus) and Atlantic sharpnose ( Rhizoprionodon terraenovae) sharks. Simulated data sets were generated using four different individual growth functions (von Bertalanffy, Gompertz, logistic and Schnute) with five different sample sizes and seven different sampling gear selectivity functions. Five growth models were fit to each data set and the Akaike information criterion (AIC) and AIC weights used to evaluate which fit best to the data. The accuracy of each of the fitting models was also determined and compared with estimates derived from AIC multi-model inference (MMI). The results demonstrated that no one growth model outperformed all other models in all situations, with the two-parameter von Bertalanffy model being selected most often by AIC. There were clear differences between the fitting models that were ranked the highest based on AIC selection or AIC weights and those based on models accuracy of length and growth parameter estimates. In most situations, the two-parameter von Bertalanffy model provided the least accuracy in parameter recovery, while the Schnute model was the most accurate individual model in most situations. The AIC MMI approach improved estimation accuracy over most individual models, except at very low sample sizes. These simulation results suggest that sample sizes of 200 are required to consistently achieve good accuracy for growth parameters, and that sampling gear selectivity has clear effects on which growth models fit best to the data. The use of the AIC MMI approach is recommended, as it provides the most robust estimates of growth parameters.

Comparison and selection of growth models using the Schnute model

Forestmodellers have long faced the problem of selecting an appropriate mathematical model to describe tree ontogenetic or size-shape empirical relationships for tree species. A common practice is to develop many models (or a model pool) that include different functional forms, and then to select the most appropriate one for a given data set. However, this process may impose subjective restrictions on the functional form. In this process, little attention is paid to the features (e.g. asymptote and inflection point rather than asymptote and nonasymptote) of different functional forms, and to the intrinsic curve of a given data set. In order to find a better way of comparing and selecting the growth models, this paper describes and analyses the characteristics of the Schnute model. This model has both flexibility and versatility that have not been used in forestry. In this study, the Schnute model was applied to different data sets of selected forest species to determine their functional forms. The results indicate that the model shows some desirable properties for the examined data sets, and allows for discerning the different intrinsic curve shapes such as sigmoid, concave and other curve shapes. Since no suitable functional form for a given data set is usually known prior to the comparison of candidate models, it is recommended that the Schnute model be used as the first step to determine an appropriate functional form of the data set under investigation in order to avoid using a functional form a priori.

A COMPARATIVE ASSESSMENT OF GROWTH CURVES AS ESTIMATORS OF MALE AND FEMALE ONTOGENY INORYZOMYS ALBIGULARIS

We analyzed growth of the sigmodontine rodent Oryzomys albigularis under laboratory conditions, fitting data to growth models, to test the null hypothesis that no differences exist between sexes. We propose a biologic criterion for growth-model selection, under the assumption that the curve should show critical stages of the organism's postnatal development and growth. Following this approach, growth of O. albigularis best fits a logistic curve. Our results show that, although males and females grow at the same rate, the final size is significantly different, being slightly dimorphic. These results, together with behavioral observations of the animals in the laboratory, support the hypothesis of a monogamic mating system for this species.

Growth of world and Indian physics literature

The paper deals with the nature of growth models currently used in the literature for modeling the growth of publications. It introduces briefly three growth models and explores the applicability of these models in the growth of world and Indian physics literature. The analysis suggests that the growth of Indian physics literature follows a logistic model, while the growth of world physics literature is explained by a combination of logistic and power models. The criteria for selection of growth models based on the new growth rate functions suggested by Egghe and Ravichandra Rao are given. The methodology suggested by Egghe and Ravichandra Rao is shown to work satisfactorily, except for longer time series growth data, when we may have to restore to data splitting approach, if suggested by the plots of new growth rate functions. This approach helped us to use a combination of two growth models instead of one, to explain the growth of world physics literature.

Perspectives on the relationship between otolith growth and the conversion of isotope activity ratios to fish ages

Ageing of fish otoliths using radiometric methods is now becoming widely accepted. Using this methodology, one has the choice of extracting otolith cores or modeling otolith mass growth. Modeling otolith growth forgoes the difficult work of extracting cores, but one is left with the nearly equally daunting task of selecting and validating an otolith growth model and deriving the corresponding decay equations. We note that the mathematical aspects of this problem appear to have been satisfactorily resolved. However, problems of interpretation remain, and it is not clear whether practitioners fully appreciate the sensitivity of their results to growth model selection and interpretation. We note that the two-stage linear growth model appears to be generally misapplied in the literature. Also, we present evidence that the process of using otolith growth curves estimated from annular ring counts to validate the method of counting annular rings can constitute circular reasoning. Although tedious work, extracting otolith cores seems the most valid way to avoid some serious problems in radiometric age determination work.