Biomass-Based Leaf Curvilinear Model for Rapeseed (Brassica napus L.)

Leaf is one of the most important photosynthetic organs of rapeseed (Brassica napus L.). To quantify relationships between the leaf curve and the corresponding leaf biomass for rapeseed on main stem, this paper presents a biomass-based leaf curvilinear model for rapeseed. Various model variables, including leaf length, bowstring length, tangential angle, and bowstring angle, were parameterized based on data derived from the field experiments with varieties, fertilizer, and transplanting densities during 2011 to 2012, and 2012 to 2013 growing seasons. And then we analysed the biological significance of curvilinear equation for straight leaves, constructed the straight leaf probabilistic model on main stem, quantified the relationship between leaf curvature and the corresponding leaf biomass, and constructed the leaf curvilinear model based on the assumption and verification of the curvilinear equation form for curving leaf. The probability of straight leaf can be quantified with piecewise function according to the different trend in the normalized leaf ranks ((0, 0.4], and (0.4, 1]). The leaf curvature decreased with the increasing of leaf biomass, and can be described with reciprocal function. The curve of straight leaf and the curving leaf can be simulated by linear equation and the quadratic function, respectively. Our models were validated with the independent dataset from the field experiment, and the results indicated that the model could effectively predict the straight leaf probability and leaf curvature, which would be useful for linking the rapeseed growth model with the rapeseed morphological model, and set the stage for the development of functional-structural rapeseed models.