Logistic Growth Functions Research Articles

Growth dynamics and yield formation of Cannabis (Cannabis sativa) cultivated in differing growing media under semi-controlled greenhouse conditions

Knowledge on the impact of growing media (GM) composition and management on plant growth and quality parameters in the production of medical cannabis is still scarce. This study compared the most commonly used GM in the cannabis industry, namely rockwool (RW), peat-perlite (PP), and coconut-coir (CC), and their impact on plant growth, CBD yield, assimilate partitioning, and nitrogen (N) uptake of a chemotype III medical cannabis strain in pot cultivation, under GM-specific fertigation schedules. GM were tested in two experiments: i) over the whole cultivation cycle, including a flowering period (FP), and ii) an extended vegetative growth period (VP). In FP, common linear regressions were sufficient to describe the relation between dry inflorescence and CBD yield over growing degree days for all GM. Likewise, the effect of GM was negligible for CBD concentration. Comparisons of height, cumulative side shoot lengths, leaf area index (LAI) and biomass accumulation of leaves, stems and roots were based on parameter comparison of fitted growth functions over growing degree days. In FP, the fitted logistic growth functions indicated, that LAI and biomass accumulation of leaves and stems were impaired in PP when compared with RW and CC. In VP, the same parameters were described by expolinear growth functions, which, except for height, estimated consistently higher growth rates for plants grown in RW. Measured N concentrations in different plant organs were consistently at the upper end or above typical ranges, provided by previous studies. However, N uptake was further improved in RW, except in inflorescences, where this effect was not visible. The effect of GM on assimilate partitioning between vegetative plant organs was marginal but significant. We argue, that the reported differences could be mainly explained by the differences in water-holding capacities and irrigation management between GM.

Renewable resource dynamics: A Web-based classroom experiment

The authors adapted a lab-in-the-field experiment emulating the dynamic extraction of a fishery to create a Web-based classroom experiment. The game includes a multi-player version analogous to an open-access problem and a single-player version analogous to the social planner problem. This game is helpful in introductory microeconomics courses to teach about dominant strategies and the consequences of resource rivalry. In elective courses, the game helps teach bio-economics concepts, including logistic growth functions and optimal extraction paths. Instructions for game deployment and creating the sessions are provided. Conducting the game takes about 20 minutes, and because the game is Web-based, students can access it from their laptops, tablets, or smartphones.

Güneydoğu Karadeniz’de dağılım gösteren kahküllü horozbina balığı Parablennius tentacularis (Brünnich, 1768)’de yaş tahmini ve en uygun büyüme modelinin seçimi

By the study's coverage, 522 individuals of tentacled blenny (Parablennius tentacularis (Brünnich, 1768)), were caught with the bottom trawl operations (commercial fisheries and scientific field surveys) between May 2010 and March 2012 from the southeastern Black Sea. The size distribution range of the sample varied between 4.8-10.8 cm. The difference between sex length (K-S test, Z=3.729, P=0.000) and weight frequency distributions (K-S test, Z=3.605, P=0.000) was found to be statistically significant. The length-weight relationship models were defined as isometric with W = 0.009L3.034 in male individuals and positive allometric with W = 0.006L3.226 in female individuals. Otolith and vertebra samples were compared for the selection of the most accurate hard structure that can be used to determine the age. Otolith was chosen as the most suitable hard structure. The current data set was used to predict the best growth model. For this purpose, the growth parameters were estimated with the widely used von Bertalanffy, Gompertz and Logistic growth functions. Akaike's Information Criterion (AIC), Lmak./L∞ ratio, and R2 criteria were used to select the most accurate growth models established through these functions. Model averaged parameters were calculated with multi-model inference (MMI): L'∞ = 15.091 cm, S.E. (L'∞) = 3.966, K'= 0.232 year-1, S.E. (K') = 0.122.

Maize plant density affects yield, growth and source-sink relationship of crops in maize/peanut intercropping

Abstract Maize (Zea mays L.)/peanut (Arachishypogaea L.) intercropping has been widely practiced in semi-arid regions to reduce wind erosion and improve resource (e.g. water and light) use efficiencies. Knowledge on optimal maize plant density is lacking from perspective of dry matter accumulation among organs in this intercropping system. We quantified the effect of maize plant density on relative yield total (RYT), maize and peanut yields, and maize dry matter of organs (ears, leaves, and stems) in maize/peanut intercropping. Field experiments were conducted in a semi-arid area of China in 2015 and 2016. Three maize plant densities (6, 9 and 12 plants m−2) were tested in maize/peanut intercropping (per unit growing area designed for maize) and sole systems, whereas the plant density of intercropped peanut and sole peanut was fixed as 24 plants m-2. The beta and logistic growth functions were used to quantitatively characterize the dynamics of dry matter allocation among organs in maize. Increasing maize plant density significantly increased maize yield gain, but not increased peanut yield loss, in maize/peanut intercropping. The greatest yield advantage (RYTs of 1.21 in 2015 and 1.13 in 2016) occured in maize/peanut intercropping with maize planted at 9 plants m−2. Increasing plant density increased leaf growth rate, but reduced leaf longevity and dry matter allocation to ears for maize grown in both intercropping and sole systems. But, greater increases in leaf growth rate and leaf longevity for intercropped maize compared with sole maize resulted in a greater increase in dry matter accumulation for maize grown at 9 and 12 plants m−2. Greater increases in ear dry matter accumulation and yield were found for maize grown at 9 plants m−2 due to greater dry matter allocation to ears. We conclude that the different responses to plant density of the source capacity (leaves) and sink strength (ears) for maize in intercropping and sole systems could help optimize maize plant density (9 plants m-2) for greater maize yield gain and yield advantage in maize/peanut intercropping.

Nonlinear models of the dependence of nitrate concentrations on the pumping rate of a water supply system

The aim of this paper is to analyse the influence of a groundwater pumping rate on nitrate concentrations at the Bartolovec wellfield, which is part of a water supply system of the town of Varaždin, Croatia. Over the past 16 years both the pumping rate and nitrate concentrations have increased at the wellfield. The nonlinear models that describe the pumping rate to nitrate concentration levels were developed on the basis of Logistic, Gompertz, and Richards growth functions. For each function, three different types were established regarding the initial lower contamination limit parameter. The conditions that models have to meet were defined and their reliability was established. The models were implemented on the experimental data collected during the period under consideration. The models were validated and mutually compared using Akaike’s Information Criteria (AICc), while the data fitting was estimated by using a coefficient of determination. After the results were obtained by using different models, they were compared to the maximum allowable nitrate concentrations (MAC) in water for human consumption. The dependence of nitrate concentrations on a pumping rate was confirmed and the reliable model for nitrate concentration on pumping rate was created. The model was calibrated and tested on the experimental data. The model exhibits asymptotic behavior and result shows that with the further increase in the pumping rate of groundwater drainage at the Bartolovec wellfield, nitrate concentrations will not exceed the MAC value providing there are no new sources of contamination in the zone of a pollutant influence.

Kinetic modeling of anaerobic carboxylic acid production from swine wastewater

This work aimed to evaluate the potential of anaerobic carboxylic acids (CA) production from swine wastewater (SW), perform modeling studies of the acidogenic process and estimate the kinetic parameters. Tests were carried out in four batch reactors with 250 mL reaction volume, with brewery sludge as inoculum and using chloroform (0.05%, v/v) for methanogenesis inhibition. Hydrolysis was the main limiting step of CA production from SW, once that it took more than twenty days for the particulate COD consumption to stabilize and fourteen days to produce 60% of the acids formed. A yield of 0.33 mg mgCODA−1, corresponding to 0.40 mgCOD mgCODA−1, was obtained. Kinetic models describing logistic growth functions were best suited to simulate CA production.

DEINDUSTRIALIZATION OF SUB-SAHARAN AFRICA

Sub-Saharan African (SSA) countries as a group have been deindustrializing for more than three decades. Logistic growth functions of the share of manufacturing value added in Gross Domestic Product (GDP) provide estimates of the rate at which the manufacturing sector has diffused into each SSA economy. Deindustrializers (industrializers) have negative (positive) manufacturing sector diffusion rates. Sixteen SSA countries experienced significant deindustrialization. Factors associated with deindustrialization trends are identified. Countries with low real per capita incomes and those unable to diversify their manufacturing base, expand production for export, or export sophisticated products more frequently experienced deindustrialization. These countries also had relatively low gross capital formation and educational expenditure shares of GDP. Starting with a small manufacturing base does not appear to constrain the industrialization process. Excessive reliance on minerals production did not encourage deindustrialization. Policies are identified that will help countries avoid deindustrialization.

Dynamic Patterns of Trees Species in Miombo Forest and Management Perspectives for Sustainable Production—Case Study in Huambo Province, Angola

This paper aims to assess important forest parameters, including tree density, diameter at breast height (DBH), and age distribution, investigate the dynamic growth of miombo tree species, and employ this information to design a management framework in miombo forests. The delineation of the management zones was based on unsupervised land cover classification that began with three zones where ground data was collected and increased to five zones. Eighteen circular plots (25.2 m radius) were randomly distributed over the study areas to assess the current situation and potential growth patterns for each species. The patterns of the six most representative tree species of miombo in Angola were described and we used KORFiT 2.4 software to fit data and develop growth curves for at least three miombo species. Growth function fitness was evaluated by root mean squared error (RMSE), coefficient of determination (R2), significance of the parameters (p < 0.05), and Akaike’s information criterion (AIC). The diameter distribution of miombo tree species resembled a typical distribution of uneven-aged forest stands; higher DBH classes had lower abundances of tree species. Logistic and Gompertz growth functions were the best fits for miombo tree species. Brachystegia spiciformis Benth., is suggested as a potential species for timber management in the region because they displayed high growth potential to more quickly reach an assumed minimum DBH of 20 cm. This study concluded that miombo forest stands present an irregular structure in which DBH distribution illustrated only two patterns: many small stems and a bimodal forest structure.

Allee effect induced diversity in evolutionary dynamics

Cyclic dominance is observed in predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations and many other natural systems. Rock-Paper-Scissor(RPS) is a popular game which demonstrates cyclic dominance. In this paper, we investigate replicator dynamics of RPS-game under logistic growth functions with Allee effect. The results obtained are compared with the case of no Allee effect. Due to Allee effect the number of stable attractors increases in a certain parameter region. The obtained result can be interpreted biologically that diversity of an ecological system increases due to Allee effect.

Estimation of Deprivation Level Functions using a Numerical Rating Scale

Evaluating and quantifying human suffering in humanitarian operations offers an innovative and potentially powerful way to assess the performance of humanitarian logistics (HL) and help build optimization models. Previous studies have suggested deprivation cost as a metric and have estimated deprivation cost functions for water using willingness‐to‐pay. Our study proposes deprivation levels, defined as the degree of human suffering caused by lack of access to a good or service, and estimates deprivation level functions using a numerical rating scale. Analyzing data collected from respondents with and without disaster experience, we find that individuals in the latter category estimate deprivation differently from the beneficiaries of disaster relief. Our study demonstrates that deprivation levels can be expressed as logistic growth functions with a typical S‐shape, and that these can be integrated into HL optimization models to better account for human suffering.

Genetic parameters of traits associated with the growth curve in Segureña sheep

This paper studies the genetic importance of growth curve parameters and their relevance as selection criteria in breeding programmes of Segureño sheep. Logistic and Verhulst growth functions were chosen for their best fit to BW/age in this breed; the first showed the best general fit and the second the best individual fit. Live weights of 41 330 individuals from the historical archives of the National Association of Segureña Sheep Breeders were used in the analysis. The progeny of 1464 rams and 27 048 ewes were used to study the genetic and phenotypic parameters of growth curve parameters and derived traits. Reproductive management in the population consists in controlled natural mating inside every herd, with a minimum of 15% of the females fertilized by artificial insemination with fresh semen; with the purpose being the herd genetic connections, all herd genealogies are screened with DNA markers. Estimates of growth curve parameters from birth to 80 days were obtained for each individual and each function by the non-linear regression procedure using IBM SPSS statistics (version 21) with the Levenberg–Marquart estimation method. (Co)variance components and genetic parameters were estimated by using the REML/Animal model methodology. The heritability of mature weight was estimated as 0.41±0.042 and 0.38±0.021 with the logistic and Verhulst models, respectively, and the heritability of other parameters ranged from 0.41 to 0.62 and 0.37 to 0.61, with the models, respectively. A negative genetic correlation between mature weight and rate of maturing was found.

Model Selection for Nondestructive Quantification of Fruit Growth in Pepper

Quantifying fruit growth can be desirable for several purposes (e.g., prediction of fruit yield and size, or for the use in crop simulation models). The goal of this article was to determine the best sigmoid function to describe fruit growth of pepper (Capsicum annuum) from nondestructive fruit growth measurements. The Richards, Gompertz, logistic, and beta growth functions were tested. Fruit growth of sweet pepper was measured nondestructively in an experiment with three different average daily temperatures (18, 21, and 24 °C) and in an experiment with six cultivars with different fruit sizes (20 to 205 g fresh weight). Measurements of fruit length and fruit diameter or circumference were performed twice per week. From these, fruit volume was estimated. A linear relationship related fruit fresh weight to estimated fruit volume, and a Ricker or polynomial function related fruit dry matter content to fruit age. These relations were used to convert estimated fruit volume into fruit fresh and dry weights. As dry weight increased until harvest, fitting the sigmoid function to the dry weight data was less suitable: it would create uncertainty in the estimated asymptote. Therefore, the sigmoid functions were fitted to fresh weight growth of the fruit. The Richards function was the best function in each data set, closely followed by the Gompertz function. The fruit dry weight growth is obtained by multiplication of the sigmoid function and the function relating fruit dry matter content to fruit age.

Total heart volume as a function of clinical and anthropometric parameters in a population of external beam radiation therapy patients

The aim of this paper was to determine anthropometric parameters leading to the least uncertain estimate of heart size when connecting a computational phantom to an external beam radiation therapy (EBRT) patient. From computed tomography images, we segmented the heart and calculated its total volume (THV) in a population of 270 EBRT patients of both sexes, aged 0.7–83 years. Our data were fitted using logistic growth functions. The patient age, height, weight, body mass index and body surface area (BSA) were used as explanatory variables. For both genders, good fits were obtained with both weight (R2 = 0.89 for males and 0.83 for females) and BSA (R2 = 0.90 for males and 0.84 for females). These results demonstrate that, among anthropometric parameters, weight plays an important role in predicting THV. These findings should be taken into account when assigning a computational phantom to a patient.

Age, growth and maturity of the brown stingray (Dasyatis lata) around Oahu, Hawai'i

Baseline data on life-history characteristics of elasmobranchs are often lacking before fisheries exploitation, hindering successful management and conservation of affected species. Age, growth and maturity estimates were determined for the brown stingray, Dasyatis lata, an abundant benthic predator in Hawai’i’s coastal ecosystems, from an unfished population off Oahu, Hawai’i. Age estimates ranged from 0 to 28 years for females and from 0 to 25 years for males. Annual growth-band deposition was verified through marginal increment and centrum edge analysis, as well as recapture of two stingrays marked with oxytetracycline. Multiple growth models were fitted to disk width (DW) and weight-at-age data and evaluated for biological realism and statistical fit. Logistic growth functions best described growth of male and female stingrays, whereas no support was found for von Bertalanffy growth models. Females attained larger sizes (L∞) and exhibited lower growth coefficients (k) than did males. Median size and age at first maturity was estimated to be 104.9 cm DW (15 years) for females and 74.9 cm DW (8.3 years) for males. These life-history characteristics highlight the importance of obtaining baseline data before fisheries are established and indicate that any fishery for brown stingrays should be managed using conservative management strategies.

Growth of captive leatherback turtles, Dermochelys coriacea, with inferences on growth in the wild: Implications for population decline and recovery

Leatherback turtles ( Dermochelys coriacea ) are endangered, and declining population trends suggest that they are vulnerable to becoming extinct in the Pacific Ocean. Population recovery depends on strong conservation measures (e.g., nest protection, reduction of bycatch, and foraging habitat preservation) and on how fast leatherbacks grow and reach maturity, making the latter of grave concern. The research reported here marks the first time that several leatherback turtles have been maintained in captivity for nearly 2 years, from hatchlings (6.31 ± 0.13 cm straight carapace length (SCL) and 46.0 ± 1 g) to juveniles (largest, 72.0 cm SCL and 42.65 kg). Leatherbacks maintained an average growth rate of 31.9 ± 2.8 cm year − 1 in SCL throughout the study period. A length–mass relationship of the form, mass (kg) = 0.000214 ⁎ SCL (cm) 2.86, fitted our data and data from four other captive studies, 11 wild juveniles, and five studies of adult leatherbacks. Von Bertalanffy, Gompertz and logistic growth functions predicted age-at-maturity for leatherbacks of 16.1, 8.7 and 6.8 years, respectively. The accuracy of these age-at-maturity estimates is discussed in the light of skeletochronological studies as well as estimates obtained from conservation and genetic studies. Our data, in combination with data from sightings, suggest that leatherbacks spend their early years (0 to 5 years of age) growing in the warmer waters of the tropical and subtropical seas before entering cooler temperate waters. Information obtained from turtles incidentally captured in fisheries, supplemented with growth curve data, indicates that leatherbacks are vulnerable to entanglement or hooking in various pelagic gear types, such as drift gill nets and longline within 3 years from nest emergence. Consequently, leatherbacks are exposed to threats from marine fisheries for > 80% of their early life before carapace length characteristic of reproductive maturity is attained.

Spatial Management of a Fishery Under Parameter Uncertainty

Spatial management of a fishery under parameter uncertainty is analyzed. The habitat is divided into two areas, and the effort level in the two areas may be different. The migration of biomass between the areas follows a diffusion process; two different specifications are considered. The model features logistic growth and Schaefer production functions. The intrinsic growth rate is treated as uncertain; the uncertainty is symmetric and spatially homogeneous. It is found that the optimal, spatial distribution of effort with respect to expected harvest is neither homogeneous or heterogeneous everywhere, but homogenous for a given subset of the parameter space and heterogeneous elsewhere.

Age and growth characteristics of crimson sea bream Paragyrops edita Tanaka in Beibu Gulf

Age and growth characteristics of crimson sea bream Paragyrops edita Tanaka in Beibu Gulf were studied through bottom trawling and gillnet fleets fishing from July 2006 to December 2007. A total number of 1155 individuals, ranging from 49 to 249 mm in standard length was examined. The age of the fish was determined from sagittal otoliths. One year growth was made up of one translucent and one opaque zone. A maximum likelihood estimation procedure was used to fit the Von Bertalanffy, Logistic and Gompertz growth functions to the length-at-age data. ARSS indicated that there were no significant differences in growth between sexes in the three growth models (P>0.05), and the Von Bertalanffy growth function Lt=292.8{1−exp [−0.167(t+1.116)]} was selected as the most appropriate growth model according to Akaike’s information criterion (AIC).

Comparison of logistic regression and growth function models for the analysis of the incidence of virus infection

A logistic regression model was compared to logistic, Gompertz and log-logistic growth functions for analyzing a set of data describing the incidence of Alfalfa mosaic virus infection in lucerne fields aged from one to five years, and located in three different ecological areas of the Ebro Valley, Northeast Spain. Models were fitted in the form of generalized linear models, and none of them explained well the high variability of the field data, although they were useful to analyze the interdependence among epidemiological factors associated with estimated parameters in the models. The logistic regression model proved more sensitive than classical growth function models to detect significant differences in parameters such as the rate of incidence increase with age of lucerne field or the initial amount of disease, and to detect differences associated to explanatory variables such as the ecological area. Results indicate that logistic regression may be a method well suited to statistical analyses in plant epidemiology.

Mathematical analysis of the cone ERG photopic hill: Clinical applications

Abstract Purpose: With brighter stimuli, the photopic ERG b‐wave increases to a maximal value and then decreases to a plateau, a feature known as the Photopic Hill (PH). Recently, a mathematical model combining a Gaussian (GF) and a Logistic Growth (LGF) functions was developed to fit the PH (Hamilton et al., Vision Research, in press). We examined if this equation could help us sort out selected retinopathies. Methods: We compared PHs (background: 30 cd.m‐2; intensities: ‐0.8 to 2.84 log cd.sec.m‐2) obtained from normals (N=40) and patients (N=20) affected with Congenital Stationary Night Blindness (CSNB), Congenital Postreceptoral Cone Pathway Anomaly (CPCPA) and Retinitis Pigmentosa (RP) with the GL ratio [GL= Gb / (Gb+Vbmax)] were Gb and Vbmax represent the amplitude of the Gaussian and logistic (Vbmax) functions respectively. Results: The normal GL ratio is 0.60 ± 0.08 (mean ± 1SD) compared to ≈1.0 in CSNB (almost pure GF) and 0.32±0.08 in CPCP [reduced GF (p<.05) and normal LF (p>.05)] patients. Six of the 8 RP patients had a GL ratio above 0.5 (mean GL= 0.70 ± 0.19) and 2 below (0.28 and 0.41). Of interest, while in some retinopathies, a decline in Gb and Vbmax occurred with disease progression (longitudinal and transversal comparisons), it did not always modify the GL ratio. Conclusions: Human PH can be dissected into two distinct and concomitant phenomena each represented by its own equation. Altghough the retinal origin of the GF and LGF awaits to be confirmed, use of this mathematical approach appears to add valuable information that will further refine the diagnosis of retinal disorders affecting the photopic (cone) pathway. Supported by CIHR and Réseau Vision.

Modeling doline populations with logistic growth functions

AbstractInitiation and evolution of a large karst depression population consisting of parent and daughter dolines were spatially and temporally modeled using logistic growth functions. Logistic growth models are well suited for analyzing doline population initiation and evolution because they reflect the density‐dependent growth mechanisms present in the evolution of karst depressions. Seven assumptions based upon previous studies were refined into mathematical statements and tested using more than 2000 dolines from a subpopulation of both parent and daughter karst depressions on the Western Highland Rim and Pennyroyal Plain of Tennessee and Kentucky. Logistic growth models quantify the initiation and evolution of doline populations and interface well with recent models describing the evolution of three‐dimensional conduit systems. Logistic growth models should apply to modeling other doline populations in karst terranes with hydraulically efficient, three‐dimensional conduit systems. Copyright © 2006 John Wiley & Sons, Ltd.