Sufficient sample size to study seed germination
João Paulo Ribeiro-Oliveira A E , Marli A. Ranal B , Denise Garcia de Santana C and Leandro Alves Pereira D
+ Author Affiliations
- Author Affiliations
A Instituto de Ciências Agrárias, Universidade Federal de Uberlândia. Campus Umuarama, Bloco 2E, CEP 38400-902, CP 593, Uberlândia – MG, Brazil.
B Instituto de Biologia, Universidade Federal de Uberlândia. Campus Umuarama, Bloco 2D, CEP 38400-902, CP 593, Uberlândia – MG, Brazil.
C Instituto de Ciências Agrárias, Universidade Federal de Uberlândia. Campus Umuarama, Bloco 4C, CEP 38400-902, CP 593, Uberlândia – MG, Brazil.
D Faculdade de Matemática, Universidade Federal de Uberlândia, Campus Santa Mônica, Bloco 1F, CEP 38400-902, CP 593, Uberlândia – MG, Brazil.
E Corresponding author. Email: ribeirooliveirajp@gmail.com
Australian Journal of Botany 64(4) 295-301 https://doi.org/10.1071/BT15254
Submitted: 7 November 2015 Accepted: 4 May 2016 Published: 7 June 2016
Abstract
Determining the required sample size is still a challenge in biological studies, including work on seed germination estimation. In this context, we studied a mathematical model to calculate sufficient sample size, using seeds of Bowdichia virgilioides Kunth. as a biological model. Coefficients of variation of the germinability (CVG) were calculated to determine the sufficient sample size (nc) to test the germination process. These CVG were subjected to the mathematical model (modified maximum curvature method – MMCM) and sufficient sample size was determined algebraically by the mathematical expression nc = [a2b2(2b + 1)/(b + 2)]1/(2b + 2) where a is the parameter of the model and b is here called the germinability heterogeneity index. Coefficients presented significant adjustment to this model, regardless of the physiological quality of the sample (99.94% ≤ R2 ≤ 99.99%). The nc is the maximum point of inflection of the CVG curve and depends on the physiological quality of the sample. Samples with higher germinability required fewer seeds to reach the nc than those with lower germinability. Thus, considering the variability of the studied material (measured by the CVG), the MMCM allows us to calculate the nc of the germination process. Our results demonstrate that is possible to prepare protocols to test the germination process for any species, with a reduced number of seeds.
Additional keywords: Bowdichia virgilioides, coefficient of variation of the germinability, modified maximum curvature method, forest species, Cerrado.
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