Nonlinear Models for Plant Height of Rye Cultivars at Sowing Times

Jéssica Andiara Kleinpaul,Daniela Lixinski Silveira,Cirineu Tolfo Bandeira,Alberto Cargnelutti Filho,Ismael Mario Marcio Neu,Andréia Procedi

doi:10.5539/jas.v10n12p157

Abstract

Adjusting nonlinear Gompertz and Logistic models will help in the understanding of the growth pattern of the rye crop and also in the height response of the plant, when planted in different environmental conditions. The the aims of this study were to adjust the nonlinear Gompertz and Logistic models for plant height and indicate the one that best describes growth of two rye cultivars in five sowing times. Ten uniformity trials were conducted with the rye crop in the 2016 harvest. In each trial, ten randomly selected plants were evaluated from the first expanded leaf weekly. In each plant height was measured. The adjustment of the Gompertz and Logistic models as a function of the accumulated thermal sum was performed with the average plant height at each evaluation. The parameters a, b, and c were estimated for each model. The confidence interval for each parameter and the inflection points, maximum acceleration, maximum deceleration and asymptotic deceleration were calculated. The quality of fit of the models was verified by the coefficient of determination, Akaike&#39;s information criterion and residual standard deviation. Intrinsic non-linearity and non-linearity of the parameter effect were quantified. Both models describe satisfactorily the plant height. The model that best describes the growth of rye cultivars is Logistic.

Highlights

Rye (Secale cereale L.) is a winter cereal from the family Poaceae
The cultivar BRS Progresso presented its maximum plant height values in times 2 and 3, while the Temprano cultivar has shown its maximum values in times 3 and 4 (Table 1)
Comparing the cultivars by the method of confidence interval overlap, the results have shown the same pattern between the estimates of the parameters of the Gompertz and Logistic models (Table 3)

Summary

Introduction

Rye (Secale cereale L.) is a winter cereal from the family Poaceae. The crop is efficient both as soil cover and grain production. In Brazil, the rye cultivated area is 3.6 thousand hectares, with a grain productivity of 2,222 kg ha-1 (CONAB, 2017), being a potential alternative for crop rotation during winter. It stands out by its hardiness and for playing an important role as cover plant (Doneda et al, 2012). Mathematical models are, basically, a simplified description of a mathematical system, elaborated to better understand the functioning of a real system In this way, the nonlinear models describe growth curves that enable the interpretation of the processes involved in plant growth, since their parameters allow practical interpretation (Sorato, Prado, & Morais, 2014)

Objectives

Methods

Results