Gompertz Nonlinear Model Research Articles

Bayesian analysis of the growth of pears in the cultivate Shinseiki using non-linear models

The pear of the Pyrus genus is the third most consumed fruit in Brazil, however, internal production is low and most demand is obtained through imports. Brazil has favorable conditions for its cultivation and one of its main economic sectors is agriculture, being responsible for generating a large number of jobs and income for the country. In this sense, studies related to this fruit can provide information and encourage its production. Using non-linear models, it is possible to identify growth patterns such as fruit length and diameter, which can help determine the ideal harvest point. Therefore, the goal of this article was to compare the Logistic and Gompertz non-linear models in describing the growth curves in diameter and length of the Asian pear tree using the Bayesian approach. The results indicated the Logistic model as the best to describe these two variables and provided asymptotic averages of 70.0607 and 79.706 for length and diameter, respectively.

Predicting height growth in bean plants using non-linear and polynomial models

Brazil has stood out worldwide as one of the main producers and consumers of beans, which makes their cultivation important for the economic and social development of the country. As the bean plant has a short growth cycle, its modeling is essential for optimizing management plans for this crop. This modeling can be performed by linear and non-linear models, but the latter have stood out for providing more information to the researcher, mainly due to the practical interpretation of their parameters. In this sense, in the R statistical software, the third-degree linear polynomial model and the Logistic and Gompertz non-linear models were adjusted to height data, in centimeters, in relation to time, in days after emergence, totaling 11 observations. As criteria to assess the quality of the fit, the adjusted coefficient of determination, the corrected Akaike information criterion and the residual standard deviation were used. The logistic model best fitted the data.

Adjusting the growth curve of sugarcane varieties using nonlinear models

ABSTRACT: Assessing sugarcane (Saccharum spp.) stalk growth helps to adequately manage the phenological stages of the crop. The aim of this study was to describe the height-growth curve of four sugarcane varieties (RB92579, RB93509, RB931530 and SP79-1011), in irrigated plant-cane and ratoon cane plantations, using the Logistic and Gompertz nonlinear models, while considering all deviations from assumptions. The model parameters were estimated based on the least squares method using the Gauss-Newton algorithm. To select the most suitable model, nonlinear measures, adjusted coefficient of determination (R2 adj), residual standard deviation (RSD), and corrected Akaike information criterion (AICc) were used. Based on the best models, stalk height growth rates and crop phenological stages were determined using critical points. All tests were performed in the free software environment for statistical computing and graphics, R. In general, the Logistic and Gompertz models without AR(1) better described the plant-cane and ratoon cane stalk height, respectively. All varieties showed early growth, and the RB92579 variety presented higher rates in both cycles.

Comparison of polynomial and nonlinear models on description of pepper growth

Pepper (Capsicum sp.) is important for the Brazilian agribusiness, serving as raw material for the food, pharmaceutical and cosmetic industries. The adequate evaluation of its plants growth may help in understanding the causes of crops yield variation, with it being able to be studied by regression models, which help to adequate the management with the different phenological phases. This study aimed to compare the fit of linear Polynomial model and the Logistic and Gompertz nonlinear models in the description of pepper plants growth from the Doce cultivar. Estimates were obtained by the Gauss-Newton method, with the quality of fitted models compared by graphical analysis and evaluators: adjusted coefficient of determination (R2 adj), Residual Standard Deviation (RSD) and the corrected Akaike Information Criterion (AICc). Residues were normal, independent and homocedastic at 5% level of significance. All models properly described the height of the Doce cultivar. The Logistic model was the most adequate according to the fitting evaluators, having higher value of R2 adj, and lower RSD and AICc values.

<b>Parameterization effects in nonlinear models to describe growth curves

Various parameterizations of nonlinear models are common in the literature.In addition to complicating the understanding of these models, these parameterizations affect the nonlinearity measures and subsequently the inferences about the parameters. Bates and Watts (1980) quantified model nonlinearity using the geometric concept of curvature. Here we aimed to evaluate the three most common parameterizations of the Logistic and Gompertz nonlinear models with a focus on their nonlinearity and how this might affect inferences, and to establish relations between the parameters under the various expressions of the models. All parameterizations were adjusted to the growth data from pequi fruit. The intrinsic and parametric curvature described by Bates and Watts were calculated for each parameter. The choice of parameterization affects the nonlinearity measures, thus influencing the reliability and inferences about the estimated parameters. The most used methodologies presented the highest distance from linearity, showing the importance of analyzing these measures in any growth curve study. We propose that the parameterization in which the estimate of B is the abscissa of the inflection point should be used because of the lower deviations from linearity and direct biological interpretation for all parameters.

Fitting nonlinear autoregressive models to describe coffee seed germination

Cumulative germination of coffee has a longitudinal behavior mathematically characterized by a sigmoidal model. In the seed germination evaluation, the study of the germination curve may contribute to better understanding of this process. The aim of this study was to evaluate the goodness of fit of Logistic and Gompertz models, with independent and first-order autoregressive errors structure, AR (1), in the description of coffee (Coffea arabica L.) line Catuai vermelho IAC 99 germination, at five different potential germination. The data used were from an experiment conducted in 2011 at the Seed Analysis Laboratory of the Federal University of Lavras. The Logistic and Gompertz nonlinear models were appropriately adjusted to the percentage germination data. The Gompertz model with first-order autoregressive errors structure was the best to describe the germination process

Methane production and hydrolysis kinetics in the anaerobic degradation of wastewater screenings

Anaerobic biodegradability and hydrolysis rates of wastewater screenings were determined using the biochemical methane potential test at 37 °C. The extent and rate of screenings conversion to methane of this complex and particulate substrate were investigated and since two stages of hydrolysis were identified, corresponding to the different types of materials in screenings, a linear and non-linear model was used. No accumulation of intermediary products was observed and so it was possible to use the methane production rate and a linear model to estimate the hydrolysis rate in the first phase of hydrolysis. The measured values of 0.061-0.127 d(-1) are in the range reported for other comparable organic wastes. It was also observed that the inoculum-to-substrate ratio has a large impact on methane production rate of screenings. The difference in biodegradation rates from the materials in screenings and the overall hydrolysis could be represented by the modified Gompertz non-linear model which was able to describe the methane production rate of screenings with a high confidence. Screenings were found to have 52% biodegradability on average and this shows the potential for volatile solids destruction. A two-stage process with an improved hydrolysis rate is proposed to ensure that the full potential of the material is exploited.

Egg production forecasting: Determining efficient modeling approaches

Several mathematical or statistical and artificial intelligence models were developed to compare egg production forecasts in commercial layers. Initial data for these models were collected from a comparative layer trial on commercial strains conducted at the Poultry Research Farms, Auburn University. Simulated data were produced to represent new scenarios by using means and SD of egg production of the 22 commercial strains. From the simulated data, random examples were generated for neural network training and testing for the weekly egg production prediction from wk 22 to 36. Three neural network architectures-back-propagation-3, Ward-5, and the general regression neural network-were compared for their efficiency to forecast egg production, along with other traditional models. The general regression neural network gave the best-fitting line, which almost overlapped with the commercial egg production data, with an R(2) of 0.71. The general regression neural network-predicted curve was compared with original egg production data, the average curves of white-shelled and brown-shelled strains, linear regression predictions, and the Gompertz nonlinear model. The general regression neural network was superior in all these comparisons and may be the model of choice if the initial overprediction is managed efficiently. In general, neural network models are efficient, are easy to use, require fewer data, and are practical under farm management conditions to forecast egg production.

Behavior of Enterobacter amnigenus and Salmonella typhimurium in Crottin goat's cheese: Influence of fluctuating storage temperature

The fully integrated cold chain is an important part in the implementation of Hazard Analysis and Critical Control Points procedures by food industry. The aim of this work was to determine the behavior of Enterobacter amnigenus (ATCC 33072 and an isolated cheese strain: LAM 200) and Salmonella typhimurium in Crottin goat's cheese during chill storage and when the cold chain is broken during different time intervals. The inoculated samples were stored in sterile bags at 5 °C for 5 days and were later divided into three groups, each with its own treatment: (A) reference (Ref) at 5 °C for a maximum period of 40 days; (B) kept along 8 h at 25 °C and then taken to 5 °C till the end of the experiment; (C) kept along 24 h at 25 °C and then taken to 5 °C till the end of the experiment. The behavior of the three strains with time in Ref experiments was analyzed with the modified Gompertz nonlinear model. In Ref treatment E. amnigenus LAM 200 did not show a lag phase but grew steadily up to K 8.1 log cfu/g; E. amnigenus ATCC 33072 did show a lag phase (7.35 days), after which it grew up to K 7.68 log cfu/g. S. typhimurium population decreased rapidly during the first 5 days. After that a second inactivation kinetics phase was observed. The behavior of E. amnigenus LAM 200 was not affected by the break in the cold chain. It seems that the cells could adapt to the stresses and fluctuating conditions. On the other hand, E. amnigenus ATCC 33072 suffered a behavior modification, as cells needed some time to acclimatize to the new conditions. The evolution of Salmonella in B treatment closely resembled Ref treatment. On the other hand in the cheese kept along 24 h at 25 °C it showed an increase of 2.4 log units after the break in the cold chain; probably as a consequence of the reparation of higher cellular numbers. It is very important factories regard GMP in order to avoid any kind of contamination, as only controlling the temperature would not be a preventive enough measure to ensure the shelf life and safety of the products.

Organ Weights and Growth Profiles in Bottlenose Dolphins (<I>Tursiops truncatus</I>) from the Northwestern Gulf of Mexico

Systematic necropsies were performed on 63 bottlenose dolphins (Tursiops truncatus), and data on organ mass, standard body length (SBL), body mass (BM), gender, sexual maturity, and age were measured and/or estimated. Animals were extremely fresh and recovered from along the Texas and Louisiana coastline in the northwestern Gulf of Mexico. Organ reference tables were established for this species to facilitate comparisons with other bottlenose dolphins and to provide a baseline for other cetacean species. Organs examined included lungs, adrenal glands, kidneys, testes, ovaries, heart, liver, pancreas, brain, pituitary, thyroid, thymus, and spleen. Individuals were separated into three size classes: 225 cm, based on SBL to further facilitate comparisons. Growth rates of length and mass were described using Gompertz nonlinear models as a function of gender. No sexual dimorphism was identified in BM or organ weights, and SBL was only significantly larger for older mature males. SBL and BM were strongly correlated with age when all animals were included in analyses, although this is not an accurate predictor of age, especially in older individuals. Organ weights were significantly correlated with both SBL (except thymus and spleen) and BM (except left ovary, spleen, and thymus). Age was significantly correlated with all organ weights (except thymus, thyroid, and ovaries). There were no significant differences in the weight of any paired organs (adrenal glands, kidneys, lungs, ovaries, testes), and all were significantly correlated with BM. These data on organ weights of bottlenose dolphins, when interpreted with SBL, BM, and age, are significant tools for pathologists and veterinarians interpreting animal health status.

Genetic trends in the expected progeny difference of the asymptotic weight of Nelore females

There are few studies on weight covering the full life cycle of Zebu cattle, and there is no entire growth description or mean growth pattern for animals belonging to this breed. In order to provide such data, 1,158 Nelore females born between 1985 and 1995 were weighed 14,563 times from birth to full growth maturity, in ten herds spread over seven Brazilian states. The Von Bertalanffy, Brody, logistic and Gompertz non-linear models were used to obtain the asymptotic weights (A) and the maturation rates (K). The (co)variance and breeding value components for A and K were obtained by using the multiple trait derivative free restricted maximum likelihood method under the animal model. Genetic trends were calculated in function of the mean expected progeny differences (EPD) for the trait (A or K) divided by the number of animals according to their year of birth. The genetic trends of the expected progeny difference with reference to the date of birth of the cows were, on average, -6.5g y-1 for A and 2.0g y-1 for K, close to zero as confirmed by the low (0.0023 to 0.003) coefficient of regression values. The curve parameters are recommended as a selection criterion to reach precocity and avoid adult weight increase in the female herd.

Increase and Patterns of Spread of Citrus Tristeza Virus Infections in Costa Rica and the Dominican Republic in the Presence of the Brown Citrus Aphid, Toxoptera citricida

ABSTRACT Citrus tristeza virus (CTV) was monitored for 4 years by monoclonal antibody probes via enzyme-linked immunosorbent assay in four citrus orchards in northern Costa Rica and four orchards in the Dominican Republic following the introduction of the brown citrus aphid, Toxoptera citricida. The Gompertz nonlinear model was selected as the most appropriate in most cases to describe temporal increase of CTV. Ordinary runs analysis for association of CTV-positive trees failed to show a spatial relationship of virus status among immediately adjacent trees within or across rows. The beta-binomial index of dispersion for various quadrat sizes suggested aggregations of CTV-positive trees for all plots within the quadrat sizes tested. Spatial autocorrelation analysis of proximity patterns suggested that aggregation often existed among quadrats of various sizes up to four lag distances; however, significant lag positions discontinuous from the main proximity pattern were rare. Some asymmetry was also detected for some spatial autocorrelation proximity patterns. These results were interpreted to mean that, although CTV-positive trees did not often influence immediately adjacent trees, virus transmission was common within a local area of influence that extended two to eight trees in all directions. Where asymmetry was indicated, this area of influence was somewhat elliptical. The spatial and temporal analyses gave some insight into possible underlying processes of CTV spread in the presence of T. citricida and suggested CTV spread was predominantly to trees within a local area. Patterns of longer-distance spread were not detected within the confines of the plot sizes tested. Longer-distance spread probably exists, but may well be of a complexity beyond the detection ability of the spatial analysis methods employed, or perhaps is on a scale larger than the dimensions of the plots studied.

Wilt Avoidance in St. Augustinegrass Germplasm

St. Augustinegrass [Stenotaphrum secundatum (Walt.) Kuntze] is less drought-resistant than other C4 grasses and frequently requires irrigation in lawns. The objectives of this study were to search for St. Augustinegrass germplasm having little wilting and to determine if minimal wilting under drought is associated with reduced canopy loss. St. Augustinegrass cultivars and breeding lines, representing polyploids (2n = 27 to 32) and diploids (2n = 18), were grown in sand soil and exposed to irrigation suspensions during seasonal droughts in three experiments. In the first experiment, during brief (3 to 14 day) irrigation suspensions, wilted area over 3 years was significantly less for polyploids (6% of canopy) than for diploids (23%). In the second experiment, during a permanent irrigation suspension, frequency of wilt was highest for diploids (57%), least for African polyploids (27%), and intermediate (53%) for other polyploids. When rain resumed after 41 days of drought, allowing refoliation, canopy loss was 51%, 4%, and 47% for diploids, African polyploids, and other polyploids, respectively. In the third experiment, during a permanent irrigation suspension, wilted area was 33% for `Jade,' a diploid, which was more (P ≤ 0.05) than for the polyploid `FX-10,' with a wilted area of 20%. `Floratam' and `Bitterblue' were intermediate in wilted area, 28% and 25%, respectively. When rain resumed after 18 days of drought, canopy loss was 58% and 56% for `Jade' and `Bitterblue,' respectively, which was more than for `Floratam' and `FX-10,' 11% and 6%. Following permanent irrigation suspensions, canopy loss was closely associated with wilting, r2 = 0.88 and 0.94 by the Gompertz nonlinear model. Because the sand soil had low water-holding capacity, the wet subsoil and shallow (1.35 m deep) water table may have been a source of water. Wilt-avoidant St. Augustinegrass may help reduce turfgrass water use.

Selection Criteria for Drought-resistance Breeding in Turfgrass

Cumulative evapotranspiration (ETcum) patterns of 10 commercially available cool-season turfgrass species and cultivars were evaluated under progressive water stress in the semi-field conditions using a gravimetric mass balance method in three studies. At the end of water stress, the cultivars were visually scored for green appearance on a 0 (no green) to 10 (100% green) scale. A Gompertz nonlinear model gave a best fit to ETcum vs. days adjusted for pan evaporation variation. Two of the ETcum attributes (ti, the time during which the rate change in ET is zero, and ETmax, the maximum ET rate) estimated from the Gompertz model appeared to reflect efficient water-use attributes in the turfgrass. Among the physiological screening techniques studied, electrolyte leakage, relative water content, and the difference between canopy and air temperature appeared to separate cultivars by drought resistance and water use efficiency (WUE). These physiological attributes were also relatively easy to measure and had high correlations with color score and WUE. Biplot display is a graphical technique in which the interrelationships between the cultivars and water-use attributes can be displayed together. Based on ti, ETmax, color score, and physiological attributes, `Wabash' and `Bristol' Kentucky bluegrass (Poa pratensis L.), `Aurora' hard fescue (Festuca ovina var. duriuscula L. Koch.), and `FRT-30149' fine fescue (F. rubra L.) were identified as cultivars with higher WUE.

Comparing Turfgrass Cumulative Evapotranspiration Curves

Twenty-five commercially available turfgrass cultivars were evaluated for cumulative evapotranspiration (ETcum) attributes under progressive water stress for 0 to 21 and 0 to 24 days using the gravimetric mass balance method in two greenhouse studies. At the end of the water-stress treatment, the cultivars were scored visually for their green appearance on a 0 (no green) to 10 (100% green) scale. The Gompertz nonlinear model gave a best fit to ETcum vs. days adjusted for pan evaporation variation in the greenhouse compared with monomolecular and logistic nonlinear regression models. Two ETcum attributes—maximum evapotranspiration rates (ETmax) and inflection time (ti) (the time when the change in ET becomes zero)—were estimated for each cultivar using the Gompertz model. Based on final ETcum, ETmax, ti, and greenness score, `Bristol', `Challenger', and `Wabash' Kentucky bluegrass (Poa pratensis L.); `Shademaster' creeping fescue (Festuca rubra L.); `FRT-30149' fine fescue (F. rubra L.); and `Aurora' hard fescue (F. ovina var. duriuscula L. Koch.) were identified as low water-use cultivars.