Nonlinear Growth Functions Research Articles

Do Distance-Dependent Competition Indices Contribute to Improve Diameter and Total Height Tree Growth Prediction in Juvenile Cork Oak Plantations?

Competition indices may improve tree growth modelling in high-density stands, found often in new cork oak plantations. Distance-dependent competition indices have hardly been considered for juvenile cork oak plantations since existing models were developed for low-density mature stands. This study aims at inspecting the potential of including distance-dependent competition indices into diameter at breast height (d) and total height (h) growth models for Quercus suber L., comparing several distance-dependent and distance-independent competition indices. Annual d and h growth were modelled with linear and non-linear growth functions, formulated as difference equations. Base models were initially fitted considering parameter estimates depending only on site index (S) and/or stand density (N). They were refitted, testing the significance of adding each competition index to the model parameters. Selected models included the best-performing distance-dependent or -independent competition indices as additional predictors. Best base d and h growth models showed a modelling efficiency (ef) of ef = 0.9833 and ef = 0.9900, respectively. Adding a distance-dependent competition index slightly improved growth models, to an ef = 0.9851 for d and ef = 0.9902 for h. Best distance-dependent competition indices slightly overperformed distance-independent ones in diameter growth models. Neither S nor N were included on best fitted models. If inter-tree competition is present in juvenile undebarked cork oak plantations, it does not yet strongly impact individual tree growth, which may diminish the importance of using, at this stage, more complex spatially explicit competition indices on predicting individual tree growth.

Mathematical analysis of a competition model with mutualism

We perform the mathematical analysis of a model describing the interaction of two species in a chemostat, involving competition and mutualism, simultaneously. The model is a five‐dimensional system of differential equations with nonlinear growth functions. We give a comprehensive description of the dynamics of the system by determining analytically the existence and the local stability conditions of all steady‐states, considering a large class of growth rates. We prove that there exists a unique stable coexistence steady‐state and give the conditions under which bistability can occur. We give bifurcation diagrams and operating diagrams showing the rich behavior of the system.

Modelling growth in dairy heifers based on linear body measurements (withers height) using non-linear functions.

This research communication reports a study to model the growth curves for withers height (WH) and body weight (BW) to withers height ratio (BW:WH) using monthly records (from 1 to 24 months of age) for three breeds of dairy heifer (Holstein, Jersey and Brown Swiss). The data sets used were those reported by the Dairy Heifer Evaluation Project of Penn State Extension (USA) between 1991 and 1992. Four growth functions (monomolecular and Michaelis-Menten, both with diminishing returns behaviour, and Schumacher and López, both with asymptotic sigmoidal behaviour) were fitted using the non-linear regression procedure of the SigmaPlot software and the parameters estimated. The models were judged for goodness of fit using adjusted coefficient of determination ($R_{{\rm adj}}^2 $), root mean square error (RMSE), Akaike's information criterion (AIC) and Bayesian information criterion (BIC). Assessing the goodness of fit by $R_{{\rm adj}}^2 $ (>0.99 in all cases) reveals the generally appropriate fit of the models to the data. The non-sigmoidal functions (i.e. Michaelis-Menten and monomolecular) provided the best fits giving the lowest values of RMSE, AIC and BIC. Based on the chosen statistical criteria, the Schumacher and López equations provided acceptable fits to the WH and BW:WH growth curves, but showed points of inflexion at times before birth, indicating that these growth curves are not sigmoidal. In conclusion, evaluation of the different non-linear growth functions used in this study indicated their potential for modelling growth patterns in dairy heifers.

A novel approach for estimating growth and mortality of fish larvae

Abstract Accurate estimates of growth and mortality are needed to understand drivers of production and cohort success. Existing methods for estimating mortality rates, such as catch-curves, require large sample sizes, as they work by grouping individuals into age-bins to determine a frequency distribution. Yet, sampling enough larvae is often not possible at fine scales within the constraints of research projects, due to low density of larvae in pelagic environments. Here, we develop a novel method to simultaneously estimate growth and mortality rates of fish larvae as a continuous function of size using theory of size-structured populations, eliminating the need to group data into age-bins. We compare the effectiveness of our model to existing methods by generating data from a known distribution. This comparison demonstrates that while all models recover correct parameter values under ideal circumstances, our new method performs better than existing methods when sample sizes are low. Additionally, our method can accommodate non-linear growth and mortality functions, while also allowing growth and mortality to vary as functions of environmental co-variates. This increased accuracy and flexibility of our method should improve our ability to relate variability in larval production to environmental fluctuations at finer spatial scales.

The linear and nonlinear growth functions in Cubic Galileon

<p indent=0mm>We introduce the Lagrangian perturbation theory under ΛCDM model, and extend it to the Cubic Galileon (G3) model. We present the second order growth function in G3 model based on the Lagrangian perturbation theory. We find that the effective Newtonian constant in G3 model is almost scale independent. Its value is bigger than that of the ΛCDM model. In the late time dark energy dominated epoch, its value is enhanced by a factor about 2. Based on this, the linear and nonlinear growth functions in the structure formation for G3 model are larger than that of the ΛCDM model. It means G3 model has stronger galaxy clustering effect than ΛCDM model. Besides of this, we find the second order growth function can be separated into spatial and temporal dependent parts. Hence, one only needs to convolve different momentum configurations at the initial stage. This will significantly accelerate the numerical calculation.

Monitoring COVID-19 in Brazil: an application of growth functions to assess the performance of States

A proposal for monitoring and evaluating the performance of Brazilian states against COVID-19 is presented, employing a set of non-linear growth functions. This is necessary given its unprecedented nature in the face of public policies known to Brazilian society in the 21st century. The daily data on the accumulated cases of the 27 Brazilian states were collected on the Ministry of Health of Brazil’s website. As of 17-May-2020, the logistic, Gompertz, and exponential functions, respectively in order, are those that best explain the evolution of COVID-19 in Brazilian states. Moreover, it was identified, through a quadrants system, the States that are being more/less efficient in the short/long term. Thus, it is expected that this monitoring and evaluation framework will allow policy-makers to have a better view of the performance of the actions of Brazilian states in confronting COVID-19 over time.

Nonlinear Height-DBH Model Analysis For Three Tropical Tree Species In Mt. Makiling, Philippines

ABSTRACT Nonlinear growth functions have been commonly used for modeling tree height–diameter at breast height (H-DBH) relationships. The development of a simple yet accurate H-DBH equation to predict the height of individual tree species is a need because using the appropriate model will give precise estimation of the forest inventory resources. In this study, six H-DBH models (CR, EX, KF, ML, SC, and WE) were used to derive and estimate the height of three species in Mt. Makiling, specifically Parashorea malaanonan, Diplodiscus paniculatus, and Celtis luzonica using the DBH as the only predicting variable. The DBH and tree height of the representative trees per species were measured for this study through nondestructive and random sampling. A total of 175 trees represented the P. malaanonan; 178 trees represented D. paniculatus, while 191 trees were measured to represent C. luzonica. Based on the evaluation criteria which include R2, RMSE, Ē, AMD, AIC, and AICw, the performance of the WE model was determined to be the best in predicting the height of P. malaanonan species while the performance of the KL model was the best both for the D. paniculatus, and C. luzonica species.

Nigerian Fulani ecotype chickens : Estimation of growth curve parameters

The study modelled growth curves of Nigerian Fulani ecotype chickens (NFEC) under two production systems with four non-linear growth functions with a view to establishing growth descriptors for NFEC. Two hundred (200) day-old chicks of NFEC were obtained from an established population of NFEC at the Teaching and Research Farm, Obafemi Awolowo University, Ile-Ife, Nigeria. The chickens were separated randomly to intensive and pastured poultry production systems at 12 weeks of age. Data on body weight were taken weekly over a period of 20 weeks. Four non-linear growth functions including Gompertz, Logistic, Bertalanffy and Richard’s models were fitted using the NLIN procedure of SAS® while the best fit model was selected using the goodness-of-fit tests. For all the models, parameter (A), the asymptotic weight, ranged between 1800g and 2417g for male and 1208g and 1550g for female chickens respectively. Parameter (B), the scaling parameter ranged from 0.77 and 19.79. Parameter K, which is the maturity index, ranged between 0.16 and 3.97 for both sexes. The R2 values ranged between 0.9689 and 0.9987 for all the models fitted. Gompertz and Bertalanffy models emerged as the best fit functions. Growth curve parameters of NFEC in the pastured poultry system were not significantly different from those in the intensive system. The growth curve parameters estimated indicates that NFEC growth performance can be improved through effective breeding strategies and improved management practices.

Türkiye 2014-2016 Hayat Tablolarında Doğrusal-olmayan Büyüme Fonksiyonları Uygulaması

In this study, a representation of survivors statistics from TUIK Turkish mortality tables (2014-2016) with non-linear growth functions was investigated by applying advanced statistical methods. Firstly, the Gompertz function was used for this purpose. Gompertz function was specifially developed by Benjamin Gompertz for the analysis of mortality tables. We calculated three functions for both male and female populations and for total population. Successful statistical results were obtained for all groups. Intrinsic contraction rates ranging from 9 to 11% were calculated for the survivors of the three series. Although we have been successful with statistical tests of Gompertz function, Richards logistic growth function didn’t give us satisfactory statistical results when applied this function to survivors series of Turkish mortality table. This was not a suprise because we knew that logistic growth function was already developed by Verhulst mainly for mathematical explanation of increasing population figures not for decreasing population figures . Turkish mortality tables does not include number of dying population by ages. Then we recalculated number of dying population by years from the survivors figures of Turkish mortality tabels. In this case Richards logistic function gave successful statistical results with the number of dying population by years. The intrinsic growth rate was found between 20 and 23% for total population and male and female populations. As result we used Gompertz function successfully for survivors population of mortality table which is a decreasing serie by years and Richards logistic function for number of dying population which is an increasing serie by years. Our priority in the analysis of both functions was to show the calculation and proof power of non-linear growth functions and advanced statistical methods were applied for this reason. Six successful functions were obtained of which three were for the survivors series using the Gompertz function and three were for the number of dying population series using the Richards logistic growth curve.

Nigerian Fulani ecotype chickens - II – Estimation of growth curve parameters

In the study, growth curves of Nigerian Fulani ecotype chickens (NFEC) were modelled under two production systems with four non-linear growth functions with a view to establishing growth descriptors for NFEC. Two hundred, day-old chicks of NFEC were obtained from an established population of NFEC. The chickens were separated randomly to intensive and pastured poultry production systems at 12 weeks of age. Data on body weight were taken weekly over a period of 20 weeks. Four non-linear growth functions including Gompertz, Logistic, Bertalanffy and Richard's models were fitted using the NLIN procedure of SAS while the best fit model was selected using the goodness-of-fit tests. For all the models, parameter (A), the asymptotic weight, ranged between 1800g and 2417g for male and 1208g and 1550g for female chickens respectively. Parameter (B), the scaling parameter ranged from 0.77 and 19.79. Parameter K, which is the maturity index, ranged between 0.16 and 3.97 for both sexes. The R values ranged between 0.9689 and 0.9987 for all the models fitted. Gompertz and Bertalanffy models emerged as the best fit functions. Age and body weight at inflection of NFEC were also predicted by the study. Growth curve parameters of NFEC in the pastured poultry system were not significantly different from those in the intensive system. The growth curve parameters estimated indicates that NFEC growth performance can be improved through effective breeding strategies and improved management practices.

Nonlinear Growth Functions for Body Weight of Thalli Sheep using Bayesian Inference

Nonlinear Growth Functions for Body Weight of Thalli Sheep using Bayesian Inference

Simple hierarchical and general nonlinear growth modeling in sheep

Differential equations and advanced statistical models have been used to predict growth phenomena. In the present study, general nonlinear growth functions such as von Bertalanffy, Gompertz, logistic, and Brody, along with hierarchical modeling were applied to investigate the phenotypic growth pattern of Iranian Lori-Bakhtiari sheep. Growth data from 1410 Lori- Bakhtiari lambs were used in the present study. The results showed that the Brody function outperformed the other three nonlinear growth functions. In addition, including hierarchical growth modeling results allowed the adoption of many random effect structures, suggesting that hierarchical growth modeling has a useful role in growth data modeling. This method provides an estimation of growth parameters based on individual animals, improving individual growth selection. The results suggest this approach for growth modeling. Combining the strength of individual growth modeling with general growth modeling, e.g., von Bertalanffy, Gompertz, logistic, and Brody would be deeply appealing in the future. In this regard, dealing with sheep growth phenomenon using pure mathematical models, i.e. grey system theory models that could be new powerful prediction tools for breeders and experts, has not been done yet. However, running the analysis on large datasets will require significantly higher computational power than is ordinarily available.

Generalized nonlinear height–diameter models for a &amp;lt;i&amp;gt;Cryptomeria fortunei&amp;lt;/i&amp;gt; plantation in the Pingba region of Guizhou Province, China

Abstract. The relationship between height and diameter (H-D) is an important component in forest growth and yield models, and a better understanding of the relationship will improve forest monitoring, management, and biomass estimation. Sixteen nonlinear growth functions were fitted to H-D data for 1261 trees from a Cryptomeria fortunei plantation in the Pingba region of Guizhou Province, China. Of the 1261 trees, 80 % were randomly selected for model calibration, while the remaining trees were reserved for model validation. All models were evaluated and compared by means of multiple-model performance criteria. Although all 16 models showed a good fit to the dataset and each of them accounted for more than 75 % of the total variation in height, a large difference in asymptotic estimates was observed. The Chapman–Richards, Weibull, and Näslund models were recommended for C. fortunei plantations, due to their satisfactory height prediction and biological interpretability.

Nonlinear Growth Models for Modelling Time Series of Groundwater Nitrate Concentrations

In this paper, a novel approach of modelling time series of nitrate concentrations in drinking water by nonlinear growth functions is proposed. An almost constant increase in the average values of nitrate concentrations occurred at the Vinokovscak wellfield in the county of Varaždin, Croatia, in the period between 1998 and 2013. Our hypothesis was that the time series would be well adjusted to the nonlinear growth function with asymptotic properties after smoothing performed by the moving average method. We used a general growth model which does not have asymptotic properties and the logistic, Gompertz and Richards functions which do have asymptotic properties. Last three growth functions were modified based on the knowledge of a constant presence of basic nitrate concentrations in the drinking water before growth. The fit of growth curves to experimental data was assessed using R 2 and Aikake’s information criterion. The modified growth functions gave the best fit to the smoothed time series of nitrate concentrations with R 2 ranging from 0.9960 to 0.9986.

Net Assimilation Rate Determines the Growth Rates of 14 Species of Subtropical Forest Trees.

Growth rates are of fundamental importance for plants, as individual size affects myriad ecological processes. We determined the factors that generate variation in RGR among 14 species of trees and shrubs that are abundant in subtropical Chinese forests. We grew seedlings for two years at four light levels in a shade-house experiment. We monitored the growth of every juvenile plant every two weeks. After one and two years, we destructively harvested individuals and measured their functional traits and gas-exchange rates. After calculating individual biomass trajectories, we estimated relative growth rates using nonlinear growth functions. We decomposed the variance in log(RGR) to evaluate the relationships of RGR with its components: specific leaf area (SLA), net assimilation rate (NAR) and leaf mass ratio (LMR). We found that variation in NAR was the primary determinant of variation in RGR at all light levels, whereas SLA and LMR made smaller contributions. Furthermore, NAR was strongly and positively associated with area-based photosynthetic rate and leaf nitrogen content. Photosynthetic rate and leaf nitrogen concentration can, therefore, be good predictors of growth in woody species.

COMPARING CARCASS END-POINT AND PROFIT MAXIMIZATION DECISION RULES USING DYNAMIC NONLINEAR GROWTH FUNCTIONS

AbstractThis article develops a market timing decision rule for cattle feeders based on profit maximization. We then compare it with the “status quo” strategy of feeding cattle to a targeted carcass end point. We estimate individual nonlinear dynamic growth functions to derive each animal's value of the marginal product in relation to days on feed. Given individual marginal factor costs, our results indicate that the use of a profit maximization rule could have increased average profits by $16.56 to $21.09 per head for the cattle of known age, and $7.67 to $11.32 per head if age was unknown.

A review on fish growth calculation: multiple functions in fish production and their specific application

AbstractModern aquaculture recirculation systems (RASs) are a necessary tool to provide sustainable and continuous aquaculture production with low environmental impact. But, productivity and efficiency of such RAS still have to be optimized to ensure economic viability, putting growth performance into the focus. Growth is often reported as absolute (gain per day), relative (percentage increase in size) or specific growth rate (percentage increase in size per day), based on stocking and harvesting data. These functions describe growth very simplified and are inaccurate because intermediate growth data are not considered. In contrast, nonlinear growth models attempt to provide information of growth across different life stages. On the basis of an empirical RAS data set of 150 all‐female turbot reared in an RAS during a period of 340 days of outgrowth, this paper reviews the most commonly used growth rates (relative, absolute, specific), the thermal‐unit growth coefficient and five nonlinear growth functions (logistic, Gompertz, von Bertalanffy, Kanis and Schnute). Goodness of fit is expressed by R2 and as mean percentage deviation. Nonlinear growth models are also compared by their residual standard error (RSE) and the Akaike information criterion. All processed functions are modelled to illustrate the shape of the generated curve and the possibility of the function to realistically predict growth. Further, the biological meaning of their regression parameters is discussed. This way we can point out differences in nonlinear growth models in contrast to purely descriptive growth rates and the specific advantages, disadvantages and possible applications of each function we review.

Age estimation of Norway spruce using incomplete increment cores: Testing new and improved methods

Information on tree age is often vital for dendrochronological studies, especially when the Regional Curve Standardisation technique is used. Several linear and non-linear methods of tree age estimation using partial increment cores (without the presence of pith) were evaluated and modified to provide more accurate estimations than are currently used. To achieve the objective, core samples from 142 Norway spruce trees (Picea abies [L.] Karst.) were collected from an altitudinal gradient in the Western Carpathians. The samples in which the pith was included were then used for further analyses. Several known age estimation approaches were adjusted to combine the advantages of direct increment- and indirect age-diameter-based methods. Inverse differential forms of non-linear growth functions were tested and proposed as a new advanced approach for age estimation. The results show that most of the modified linear methods achieved a mean square error of less than 10% when the length of the partial core exceeded 90% of the stem radius and less than 20% when the length of the core was at least 60% of the stem radius. Using an appropriate differential form of the non-linear growth functions, a mean square error of less than 20% was reached, even when the core length was shorter than 60% of the radius. The results show that current linear methods for age estimation can only be used if the missing part of the core sample is very short, with only a few rings absent. In the case of a large number of missing rings, a differential form of non-linear functions should preferably be used instead.

A Numerical Method for Estimating the Variance of Age at Maximum Growth Rate in Growth Models

Studies on maturation and body composition mention age at peak height velocity (PHV) as an important measure that could predict adulthood outcome. The age at PHV is often derived from growth models such as the triple logistic fitted to the stature (height) data. Theoretically, for a well-behaved growth function, age at PHV could be obtained by setting the second derivative of the growth function to zero and solving for age. Such a solution obviously depends on the parameters of the growth function. Therefore, the uncertainty in the estimation of age at PHV resulting from the uncertainty in the estimation of the growth model, need to be accounted for in the models in which it is used as a predictor. Explicit expressions for the age at PHV and, consequently the variance of the estimate of the age at PHV, do not exist for some of the commonly used nonlinear growth functions, such as the triple logistic function. Once an estimate of this variance is obtained, it could be incorporated in subsequent modeling either through measurement error models or by using the inverse variances as weights. A numerical method for estimating the variance is implemented. The accuracy of this method is demonstrated through comparisons in models where explicit solution for the variance exists. The method of estimating the variance is illustrated by applying to growth data from the Fels study and subsequently used as weights in modeling two adulthood outcomes from the same study.

Nonlinear growth functions for modeling tree height–diameter relationships for Gmelina arborea (Roxb.) in south-west Nigeria

Tree height–diameter relationship can be used as an important input component in forest growth and yield models, and description of stand dynamics. Five nonlinear growth functions were fitted to tree height–diameter data of a 21-year-old Gmelina arborea plantation in Ibadan, Nigeria. The data consisted of three sets obtained in 2004, 2008 and 2011 for total tree height and diameter at breast height (DBH). According to the model statistics, the five growth functions fitted the data equally well, but resulted in different asymptote estimates. Modified exponential fit was observed to give the best fit for the three data sets based on least square error, coefficient of determination and significance. The predicted values follow the same nonlinear pattern and formed close to the line of best fit without much outlier. The result of this study revealed that the ability of DBH in determining height is not strong enough based on the model's goodness of fit and the model's ability for predictive purposes. Hence, more variables such as age, crown area and soil fertility were recommended to be incorporated in future prediction of the tree height in the study area.