Modified Maximum Curvature Method Research Articles

A test on methods for Mc estimation and spatial-temporal distribution of b-value in the eastern Tibetan Plateau

Seismic b-value is one of the most important parameters for seismological research and seismic hazards assessment, while the accuracy of the b-value largely depended on the completeness of seismic catalog. This article compares eight methods for estimating the minimum magnitude of completeness (Mc). The results indicate that the modified maximum curvature method (MMAXC), exhibits greater stability and accuracy, closely approximating the standard Mc obtained from the synthetic seismic catalogs. We then calculate the b-value using the instrumental seismic catalog from 2000–2023 in the eastern Tibetan Plateau. The results indicate that the five major earthquakes occur in regions with lower b-value. In addition, the temporal evolution of b-value before and after major earthquakes exhibits a common trend of decreasing before earthquakes, and increasing after earthquakes, which may reflect the stress accumulation and release during earthquakes. Combining the results of maximum shear strain rate and b-value, we identify five regions characterized by low b-value and high shear strain rate, indicating a higher potential seismic hazard in the future.

Optimal plot size in lettuce seed germination experiments

Lettuce in works under controlled conditions is widely used in experiments with a direct focus on the species itself, or as an indicator species used in allelopathy works. But despite its frequent use, there is no support in the literature for using a single plot size and, therefore, there are works from the use of 5 to 100 seeds per experimental plot. It is understood that the works have been developed using different experimental precisions. The low experimental precision caused by a smaller-than-optimal plot size can lead to a high residual value in the analysis of variance and consequent difficulties in detecting statistical difference between treatments. On the other hand, the use of a high number of seeds per plot can lead to unnecessary expenditure and does not contribute to improving experimental precision. The objective of this work was to determine the optimal plot size in seed germination experiments under controlled conditions. The modified maximum curvature method according to Meier and Lessman was used. After the subsequent analysis, the high variations between different sizes and the factors that can be interfered because of this were observed, and the optimal plot size was defined as six seeds for the biogerminative test of lettuce by petri dishes of 10 cm in diameter.

Morpho-Agronomic Characterization, Sample Size, and Plot Size for the Evaluation of Capsicum chinense Genotypes

The Amazon is a center of diversity for Capsicum chinense Jacq., with wide genetic and morphological variability, but little exploration has been performed there to facilitate their improvement. This study aimed to characterize and evaluate C. chinense genotypes for the development of cultivars by determining the optimal size of the experimental plot and the minimum sample size to ensure a precise estimation of yield. A total of 23 genotypes were evaluated, and in multivariate analyses, the plants were characterized by 21 morphological descriptors and eight quantitative traits related to biometry and yield. The recommended sample size for fruit evaluation was defined based on simulations with subsample resampling and evaluation of the semi-amplitudes of the confidence interval of the mean estimate. The optimal plot size was estimated by the modified maximum curvature method. The similarity coefficients among the genotypes ranged from 0.54 to 0.93, indicating that the established clusters contained important information for future crosses. According to the sample size methodologies, 25 to 40 fruits should be sampled for valid evaluations of biometric traits. Experiments with five to eight plants per plot are recommended to test progenies of the species, ensuring good experimental precision combined with high selection accuracy for yield traits.

Determining the minimum size of experimental plot for evaluating field parameters for Arabica coffee

The coffee production chain has great socio-economic importance in Brazil, generating foreign exchange with great job-generating capacity. The Brazilian coffee production is circa 2.863 k tons and coffee research has contributed to the development of new technologies in order to increase yield. However, the size of plots used for coffee experiments has been variable and mostly based on the empirical researcher's experience. Therefore, this research was carried out aiming to determine the optimal size of experimental plots to evaluate field growing parameters of Arabica coffee. The modified maximum curvature model and the comparison of variances were the methods used. It is concluded that 2, 3, 3, and 6 plants per useful experimental plot of Arabica coffee are enough to evaluate the field growing parameters plant height, plant canopy diameter, vigor, and wet mass, respectively by the method of modified maximum curvature. Two plants per experimental plot were required when using the variance comparison method to the parameters plant height, and plant canopy diameter, and 4 plants were enough to the parameters vigor and wet mass. In general, four useful plants per experimental plot were enough using the variance comparison method and six useful plants when using the modified maximum curvature method.

Optimal plot size for experimentation of common beans (Phaseolus vulgaris L.) in the northern region of Minas Gerais, Brazil

The objective was to evaluate the minimum size of experimental plots for the common bean (Phaseolus vulgaris L.) using the modified maximum curvature method. The experiment consisted of a uniformity trial with the cultivar BRSFC-402 sown at a spacing of 0.5 m between plant rows and 10 plants per meter within the row. 20 central rows measuring 20 m in length were considered for measurements, totaling 4,000 plants on an area of 200 m2. Final bean stand (FS), mean number of pods per plant (NPP), mean number of grain per pod (NGP), mean 100-grain weight (M100), and grain yield (kg ha-1) were evaluated. At evaluations, each row with 10 plants was considered a basic unit (0.5 m2), amounting to 400 basic units whose dimensions were combined into 14 plot shapes. The methods of relative information and modified maximum curvature were used to obtain the best shape and the most appropriate plot size, respectively, for experimental evaluation with common bean. Using these methods, and considering that the optimum plot should enable an efficient evaluation of all evaluated characteristics, the appropriate plot size was five UB (25 plants) in the format with five rows x one UB per row. Highlights Support for experimental evaluation of common beans under edaphoclimatic conditions in the northern region of Minas Gerais Experimental plots with five basic units ensure maximum precision for joint evaluation of the main phenotypic descriptors of common beans. The characteristics mass of 100 grains and productivity were associated with the smallest and the largest plot sizes, respectively.

ESTIMATION OF THE OPTIMUM SIZE OF PLOTS FOR SOYBEAN RADIOMETER EXPERIMENTS

The lack of error of experimental planning in agricultural field studies can result in rework, causing the waste of financial resources. The determination of the optimal size of the experimental plot for carrying out the treatments can minimize these problems. The objective of this paper was to estimate the optimal plot size for measuring reflectance in soybeans, without treatment, using the modified maximum curvature method and the maximum distance method. Reflectance readings were taken in the soybean crop with the aid of the GreenSeeker® equipment, in basic experimental units of 0.45 m², in an area of 7 lines and 8 meters in length. The data were collected in three phenological stages of soy (R4, R5.5 and R6), obtaining 63 simulations of experimental area in each stage. Based on the results, it is recommended to use plots of 7.20 m², with grouping of 4 lines of 4 m in length.

Sampling representativeness of soil carbon and physiological parameters of marandu palisadegrass in a tropical silvopastoral system

The sampling methods for soil and plant evaluation in integrated production systems need to be refined for their use in experiments. This study purposed a sampling representativeness model to evaluate soil carbon and physiological parameters of marandu palisadegrass intercropped with double rows of eucalyptus in a silvopastoral system in southeastern Brazil. Four transects were delimited within the silvopastoral system and the soil was sampled at 0-5, 5-10, and 10- 20 cm depths to evaluate two parameters of soil organic matter: total organic carbon (TOC) and soil microbial carbon (Cmic). We also evaluated three physiological parameters of marandu palisadegrass: stomatal conductance, transpiration rate, and photosynthetic rate. The sampling strategy was evaluated by the Hatheway and Modified Maximum Curvature (MMC) methods. We found that cultivation of the alley with forage grass and double rows of eucalyptus must be considered to ensure sampling representativeness in a silvopastoral system, once TOC and Cmic and physiological parameters showed variation within the integrated production system. The MMC method could be useful to evaluate silvopastoral systems for experiments and characterization of agricultural areas, as 11 soil samples are representative to evaluate Cmic and TOC, and 13 samples are enough to evaluate the physiological parameters in marandu palisadegrass. The Hatheway method could be applied to experiments that need higher accuracy with a reduction in the minimum difference to be detected between the treatments and a consequent increase in the number of samples to be collected.

Calculation of the ideal plot size for experiments using eucalyptus

An adequate experimental planning depends on several factors, such as homogeneity of the area and experimental unity, number of repetition and plot size. The adoption of an ideal plot size reduces the experimental error and, consequently, maximizes the information obtained in an experiment. Thus, the aim of the present study was to calculate the optimal plot size of eucalyptus culture in a greenhouse, in order to optimize labor and costs in the cultivation process of this economically important culture. To calculate the optimal plot size, several simulations were performed using the modified maximum curvature method. Throughout the experimental period, clonal seedlings of the Eurograndis hybrid were used and evaluated for height (H), stem diameter at the base (DB), chlorophyll content in old leaves (Chlor V) and new leaves (Chlor N) at 30, 60, 90 and 120 days after seedling transplantation. After 120 days, the seedlings were collected to determine the dry mass of the aerial part (DMAP) and the root system (DMRS). Results indicated that the optimal recommended plot size for eucalyptus, in a greenhouse, were 6 plants per plot.

Size of plots for experiments with cactus pear cv. Gigante

ABSTRACT The definition of experimental plot size is an essential tool to ensure precision in statistical analysis in experiments. The objective of this study was to estimate the plot size for the cactus pear cv. Gigante using the Modified Maximum Curvature Method, under the semi-arid conditions of Northeastern Brazil. The uniformity test was conducted at the Federal Institute of Bahia, Guanambi Campus, Bahia state, Brazil, during the agricultural period from 2009 to 2011. The spatial arrangement was composed of ten rows with 50 plants each, whose evaluated area was formed by the eight central rows with 48 plants per row, making 384 plants and area of 153.60 m2. The following variables were evaluated: plant height; length, width and thickness of cladode; number of cladodes; total area of cladodes; cladode area and green mass yield in the third production cycle. In the evaluations, each plant was considered as a basic experimental unit (BEU), with an area of 0.4 m2, comprising 384 basic units (BU), whose adjacent ones were combined to form 15 pre-established plot sizes with rectangular shapes and in rows. The characteristics total area of cladodes and green mass yield require larger plot sizes to be evaluated with greater experimental accuracy. For experimental evaluation of cactus pear cv. Gigante, plot size should be eight plants in the direction of the crop row.

Optimal size of experimental plots of papaya trees using a modified maximum curvature method

ABSTRACT: This study aimed to evaluate the optimum plot size for the papaya crop by using the modified maximum curvature method under soil and climatic conditions of the Recôncavo Baiano. The experiment comprised a uniformity test using the CNPMF-L78 strain developed by Embrapa Mandioca and Fruticultura, planted at a spacing of 3 m x 2 m, with 16 central rows and 22 plants per row, totaling 352 plants and an area of 2,112 m2. The following parameters were evaluated: plant height and diameter; height of insertion of the first fruits; precocity; number of commercial fruits per plant; productivity; length, diameter, weight, firmness, internal cavity diameter, pulp thickness, and soluble fruit solids. Each plant was considered as a basic unit, with an area of 6 m2, thus making up 352 basic units whose adjacent units were combined to form 11 pre-established parcel arrangements with rectangular and row formats. The optimal plot size is seven plants perpendicular to the crop rows, that is, seven rows with one plant in each row, corresponding to the area of 42 m2, considering spacing of 3 m between rows and 2 m between papaya plants in the soil and climatic conditions of the Recôncavo Baiano.

Estimation of optimum experimental plot size for taro culture

ABSTRACT: Taro is a tropical tuberous vegetable that produces cormels of high nutritional and energetic value. In recent years, its cultivation has expanded, creating the need for more research. However, the experimental plot size interferes directly with the precision of the experiment.Literature describes several methods for establishing the optimum experimental plot size. The objective of the current research was to estimate the optimal experimental plot size for taro culture, utilizing the Modified Maximum Curvature Method. The field experiment was conducted in the vegetable garden of the Departamentode Fitotecnia of Universidade Federal de Viçosa, from September 2011 to June 2012, with Japanese taro. Twenty-two rows with 20 plants each were planted, at 1.0×0.3 m spacing, considering the 20 central rows with 18 plants each as useful area, totaling 360 plants. Each plant corresponded to a basic unit (BU). Once the possible clusters were made, 23 different plot sizes were formed. At harvest, the fresh mass characteristics of large, medium, and marketable cormels were evaluated. The optimum plot sizes were: 8.77 BU for marketable cormels; 14.75 BU for large cormels, and 13.37 BU for medium cormels. Among the plot sizes estimated in this study, the aim was to improve precision of experiments performed with taro, plots formed by 15 BU that corresponded to a 4.5 m2 area are recommended.

Estimation of the optimal plot size and number of replications in a field pepper crop experiment with varying irrigation depths and application frequencies

Abstract The precision of an agronomic field trial, or its ability to detect true treatment effects, can be improved by using both plots of suitable size and an appropriate number of replicates. The objective of this work was to determine the optimal size and number of replications of the experimental plots, by examining differences in plant height, stem diameter and number of fruits per plant, of a bell pepper (Capsicum annuum L.) crop that was irrigated with different water heights and frequencies of application. Five treatments were compared: T0, control with no irrigation; T1, water depth 50% of crop evapotranspiration (ETc) and daily frequency; T2, water depth 100% of ETc and daily frequency; T3, water depth 50% of ETc and frequency every two days; and T4, water depth 100% of ETc and frequency every two days. In the experimental plots, 4 m wide × 12 m long (48 m2), a total of 120 bell pepper (cultivar ‘Impacto’) plants were arranged in four rows. Plants in each row were irrigated with a drip irrigation system with drippers placed between them 0.2 m apart and having a flow rate of 0.8 L h−1. The growth rates of the pepper crop and the number of fruits per standing plant were lower in the treatment without irrigation than in the irrigated treatments. Among the irrigated treatments, daily irrigation provided higher growth rates when the lowest depth of water was applied. In the plants irrigated every two days the highest growth rates were observed in those that received the largest water depth. The number of fruits per standing plant was greater in the daily irrigated plants than in those irrigated every two days, regardless of the amount of the water applied. The optimal plot size was determined by the modified maximum curvature method (MMC) and the linear model with plateau effect (LPR). For each of the three variables, the criterion followed to establish the optimal plot size was to choose the largest one, regardless of whether the method used in its determination was MMC or LPR. The size of the experimental plot was always smaller in the case of treatments with irrigation than in the treatment without irrigation, as well as for the crop variables exhibiting lower variability. Therefore, the optimal sizes of the experimental plots for the plant stem height and diameter, and for the number of fruits per plant was estimated at 3.2 m2 (8 plants); 3.6 m2 (9 plants); and 10.8 m2 (27 plants), respectively. Regardless of the experimental design, complete randomized or complete randomized block, the number of replications of the experimental plots was conditioned by the variability of the three variables. Thus, 10 replicates were required to detect between the five irrigation treatments differences of 10% in the mean value of plants height, 5 replicates in the case of the stem diameter of the plants and 15 replicates for the number of fruits per plant.

Sample size and water dynamics on germinating diaspores: the first step for physiological and molecular studies on the germination process

Water dynamics on germinating diaspores is normally used as a chronological marker in molecular biology and physiological studies focusing on germination. However, there is no protocol to analyze this process, which may undermine all results generated. In this context, we determined the sufficient sample size to study water dynamics on germinating diaspores by means of a modified maximum curvature method (MMCM). As a biological model, we used diaspores from agricultural species with different physiological qualities. These diaspores were put in contact with distilled water and were analyzed regarding mass, every hour, until embryo protrusion. Data collected in the last observation were used to measure the sufficient sample size. Here, we show that (i) MMCM is an adequate method to measure the variability of water dynamics on germinating diaspores; (ii) the b coefficient can be used to infer the homogeneity of water dynamics on diaspores of different species as a function of the increase in sample size; (iii) in general, to study this process in an easier, safer and standardized way, seven diaspores are needed and (iv) water dynamics on germinating diaspores estimated by weighted mass demonstrated to be a very stable process which depends more on the species than on the physiological quality. We also discussed why the sample size and water dynamics on germinating diaspores should be the first step for protocols on physiological and molecular aspects of the germination process.

English

An experimental error can lead to rework and, consequently, to the loss of financial and human resources. One way to reduce this problem is the estimation of the optimum size of experimental plot to carry out the treatments. The objective of this study was to estimate the optimal size of plots for reflectance measurements in beans by the modified maximum curvature method and the maximum distance method. Reflectance readings were made on bean plants with the aid of the GreenSeeker® equipment, obtaining basic units of 0.45 m² in an area of lines 6 and 8 m in length, performing 46 combinations of experimental area. X0 was determined using the modified maximum curvature and the maximum distance method. To increase the R², the calculations have been redone using 20 combinations of experimental area. By adopting the bigest obtained area, it was concluded that the optimum size of an experimental plot for works with reflectance in beans is 5.40 m² and the combination that presents the best distribution is 2 lines totalling 6 m long. Key words: Reflectance, experimental error, modified maximum curvature, maximum distance.

Plateau regression reveals that eight plants per accession are representative for Jatropha germplasm bank

The aim of this study was to estimate the minimum number of perennial Jatropha trees per accession that gives an accurate assessment of available genetic diversity within an accession. Thus, methodologies based on non-linear regression were tested (with linear-plateau response, quadratic-plateau response, and modified maximum curvature) involving ​​grain yield and one hundred seed weight. The germplasm bank used in the experiment had 160 accessions, and 10 plants represented each accession initially. From this, resampling was performed ranging from 2 to 10 plants per line. After resampling, four million analyzes of variance were done for estimating the coefficient of variation, variance within accessions, genetic variance, phenotypic variance, and heritability. Confidence interval was calculated for each parameter. Once it presented acceptable accuracy, heritability was the parameter used for calculating the minimum number of plants between plots, and it was efficient. The modified maximum curvature method estimated less than one plant per accession, which was inefficient in estimating the number of plants to represent the accession. The methods of regression with linear response estimated between 5 and 6 plants, and quadratic-plateau estimated eight plants per accession as minimum number, being R2 superior to 80%. Therefore, eight is the minimum number of plants to represent an accession of Jatropha for maintenance and expansion of germplasm bank.

Tamanho mínimo de parcela para avaliação de caracteres de raiz em cenoura

A estimação do número ideal de plantas para a avaliação de populações de cenoura é importante para que se possa reduzir o erro experimental e, com isso, maximizar a precisão das informações obtidas em um experimento, além de contribuir sobremaneira para a redução de recursos financeiros empregados na pesquisa. O objetivo do trabalho foi estimar o número mínimo de plantas por parcela para avaliação de caracteres de raiz em ensaios de populações de cenoura utilizando os métodos de máxima curvatura modificado e da estabilização da média e variância genética. Os experimentos foram desenvolvidos em três locais no verão de 2004: Brasília (DF); São Gotardo (MG) e Lapão (BA), utilizando o delineamento em blocos casualisados com quatro repetições e parcelas com 2 m². Aos 90 dias após o plantio, 15 plantas competitivas em cada uma de nove populações foram colhidas e avaliadas para massa da raiz, comprimento de raiz, comprimento do ombro verde da raiz, formato de ponta da raiz, formato de ombro da raiz, diâmetro da raiz, diâmetro do xilema da raiz, relação diâmetro do xilema / diâmetro da raiz e as variáveis de cor L* a* b* para os tecidos xilema e floema. Os procedimentos de reamostragem com simulação de subamostras e o método da curvatura máxima modificado foram utilizados para estimar o número mínimo de plantas para representar cada parcela. Os valores constatados em ambos os procedimentos comprovam que uma amostra de 13 plantas por parcela é suficiente para garantir uma adequada avaliação de populações de cenoura para o conjunto de caracteres estudados.

Estimativas de tamanho de parcelas para avaliação de descritores fenotípicos em bananeira

O objetivo deste trabalho foi estimar o tamanho adequado de parcelas experimentais, para avaliação de descritores fenotípicos em bananeira, a partir de um ensaio de uniformidade com a cultivar Tropical, no espaçamento de 3x2 m, em área útil com nove fileiras de 40 plantas. Foram avaliados: altura da planta; perímetro do pseudocaule; número de filhos emitidos e número de folhas vivas, no florescimento e na colheita; peso do cacho e das pencas; número de pencas e de frutos; peso da segunda penca; e peso, comprimento e diâmetro do fruto, em dois ciclos de produção. As plantas, consideradas unidades básicas, foram combinadas para formar diferentes tamanhos de parcelas. Os dados foram submetidos à análise de variância em modelo hierárquico. O tamanho da parcela foi estimado pelos métodos da máxima curvatura, máxima curvatura modificado e comparação de variâncias. Determinaram-se o índice de heterogeneidade do solo e a diferença detectável entre médias de tratamentos. A variabilidade aumentou entre os ciclos, com reflexos nos tamanhos de parcela, que variaram com o método utilizado, a variável avaliada e o ciclo de produção. O método da máxima curvatura modificado apresenta estimativas mais ajustadas. Parcelas com seis unidades básicas (36 m²) são apropriadas para avaliar, com precisão, os descritores fenotípicos em bananeira.

Plot size and experimental unit relationship in exploratory experiments

Quality of field experiments data dependent upon adequate experimental design. This study investigated the relationship between the size of the basic unit for exploratory experiments and the optimum plot size, and the experiment precision with potato crop. Tuber yield of 24 rows, 144 mounds, were used to arrange experimental units of one, two, three, four, six, eight and 12 mounds. Tuber yield data of different mounds were used to arrange plot sizes with different numbers of basic units. The model CV(x)=A/X B was adjusted, in which CV(x) was the coefficient of variation among plots with different numbers of basic units. Optimum plot size was estimated with the modified maximum curvature method of the function CV(x)=A/X B, allowing completely random design. Experimental precision was estimated though the Hatheway method for different experimental arrangements. Based upon the modification of the maximum curvature method, for a fixed total experimental area, experimental unit size of potato initial experiments affects optimum plot size estimations with the same experimental precision and variable number of treatments.

Estimation of optimum plot sizes in field experiments with annatto

The objective of this study was to estimate the optimum plots size for experiments with annatto. The uniformity assay consisted of 12 rows with 12 plants in each row. The variety Bico de Pato was used, planted in 5 x 4 m spacing and evaluated at 5 years of age. Three methods were used: maximum curvature, modified maximum curvature and the comparison of variances. The plot size estimate varied according to the methodology used and the characteristic analyzed. The adequate plot size was found to be 107.2 m² (5 plants) using the modified maximum curvature method, which resulted in more precise estimates , taking into consideration that the ideal plot should facilitate the efficient evaluation of all characteristics analyzed in this experiment.