Test modeling of the growth of self-fertilized embryos of Phaseolus vulgaris L. and Phaseolus coccineus L. genotypes

Abstract

Biologists usually rely on modelling tools as well as simulation to try to understand the behaviour of biological phenomena theories. In this research study, we focus on the development and study of mathematical models from environmental problems about genotypes of Phaseolus coccineus L. (NI16 and NI1108) and Phaseolus vulgaris L. (NI637 and X707). Interspecific crosses and histological sections were performed; thereafter, samples were fixed, followed by rinsing and dehydrating in an increasing gradient of ethyl alcohol. After staining procedure, microscope slides of blades were coated with one to three drops of mounting medium DPX (BDH360294H). Analysis of variance (ANOVA I) was conducted, followed by Tukey's test at a significance level of 95%. All statistical analyses were performed using the software MINITAB Release 14. Results reveal divergence of growth rates and thus embryo development between the two species (P. coccineus and P. vulgaris) and between parental and embryos hybrid [P. vulgaris (♀) × P. coccineus]. In this model, a common law of evolution for the different types of embryos was established; it describes the interactions between the length of the embryo, the number of days after pollination and stage of embryo development. Thus, the individualized modeling growth in length of inbred and hybrid embryos margin fluctuations and extrinsic individual responses must be attributed to the plant, which better reflect the embryo development.