Three-dimensional Dynamic Growth and Yield Simulation of Daylily Plants Based on Source-Sink Relationships

doi:10.12133/j.smartag.SA202310011

Abstract

Abstract:

Objective The daylily, a resilient perennial belonging to the lily family, is widely cultivated across diverse regions of China. This plant boasts a rich nutritional profile, containing significant amounts of protein, carbohydrates, fats, vitamins, and a variety of amino acids, making it a vegetable that is both nourishing and visually appealing. It is often affectionately termed the 'wealth flower' by farmers, due to its high market value and profitability as a crop. Given its economic importance, boosting its yield is a crucial objective. However, current research into daylily cultivation is limited, particularly in the realm of three-dimensional dynamic growth simulation of daylily plants. This study presents an innovative three-dimensional dynamic growth and yield simulation model for daylily plants, grounded in the understanding of the plant's source-sink relationship and harnessing the power of three-dimensional modeling techniques from the functional-structural plant model (FSPM) platform. The simulation model provides a technological foundation for improved cultivation management, growth dynamics prediction, and the design of plant variety types in daylily crops, thereby enhancing agricultural practices and economic returns. Methods This study utilized the open-source GroIMP software platform to simulate and visualize three-dimensional scenes. With Datong daylily, the primary cultivated variety of daylily in the Datong area, as the research subject, a field experiment of daylily was conducted from March to September 2022, which covered the growth season of daylily. Through actual cultivation experiment measurements, morphological data and leaf photosynthetic physiological parameters of daylily leaves, flower stems, flower buds, and other organs were collected. The FSPM platform's three-dimensional modeling technology was employed to establish the Cloud Cover-based solar radiation models (CSRMs) and the Farquhar, von Camerer, and Berry model (FvCB model) suitable for daylily. Moreover, based on the source-sink relationship of daylily, the carbon allocation model of daylily photosynthetic products was developed. By using the β growth function, the growth simulation model of daylily organs was constructed, and the daily morphological data of daylily during the growth period were calculated, achieving the three-dimensional dynamic growth and yield simulation of daylily plants. Finally, the model was validated with measured data. Results and Discussions The coefficient of determination (R²) between the measured and simulated outdoor surface solar radiation was found to be 0.87, accompanied by a Root Mean Squared Error (RMSE) of 28.52 W/m². For the simulated model of each organ of the daylily plant, the R² of the measured against the predicted values ranged from 0.896 to 0.984, with an RMSE varying between 1.4 and 17.7 cm. The R² of the average flower bud yield simulation was 0.880, accompanied by an RMSE of 0.5 g. The overall F-value spanned from 82.244 to 1 168.533, while the Sig. value was consistently below the 0.05 significance level, suggesting a robust fit and statistical significance for the aforementioned models. Subsequently, a thorough examination of the light interaction, temperature influences, and photosynthetic attributes of daylily leaves throughout their growth cycle was carried out. The findings revealed that leaf nutrition growth played a pivotal role in the early phase of daylily's growth, followed by the contribution of leaf and flower stem nutrition in the middle stage, and finally the growth of daylily flower buds, which is the crucial period for yield formation, in the later stages. Analyzing the photosynthetic traits of daylily leaves comprehensively, it was observed that the photosynthetic rate was relatively low in the early spring as the new leaves were initially emerging and reached a plateau during the summer. Considering real-world climate conditions, the actual net photosynthetic rate was marginally lower than the rate verified under optimal conditions, with the simulated net assimilation rate typically ranging from 2 to 4 μmol CO₂/m²·s. Conclusions The appropriate timing, mode of planting, and plant type structure are vital to securing high and consistent yields of daylily. A three-dimensional dynamic growth simulation of daylily plants offers an inclusive representation of their growth and development, morphological structures, and yield formation, spanning from their response to the external environment through germination and growth to the final plant type structure. The three-dimensional dynamic growth model of daylily plants developed in this study can faithfully articulate the growth laws and morphological traits of daylily plants across the three primary growth stages. This model not only illustrates the three-dimensional dynamic growth of daylily plants but also effectively mimics the yield data of daylily flower buds. The simulation outcomes concur with actual conditions, demonstrating a high level of reliability. Consequently, the model exhibits an exemplary simulation effect, providing a comprehensive depiction of the development and transformation of daylily crops. This model serves as an invaluable tool for visualizing plant type design, cultivation management, growth prediction, and other facets of daylily crop research, effectively addressing the demands of precision agriculture.

Key words: Daylily citrina Baroni, source-sink relationship, photosynthesis model, morphological model, three-dimensional dynamic growth simulation, yield simulation

ZHANG Yue, LI Weijia, HAN Zhiping, ZHANG Kun, LIU Jiawen, HENKE Michael. Three-dimensional Dynamic Growth and Yield Simulation of Daylily Plants Based on Source-Sink Relationships[J]. Smart Agriculture, doi: 10.12133/j.smartag.SA202310011.

Figures/Tables 14

Fig. 1

Table 1

Fig. 2

Table 2

Equations of the modules for energy balance， photosynthesis （FvCB model）， stomatal conductance （BWB model） in the plant functional-structural model of daylily and nomenclature

模型类型	公式	描述
叶片能量平衡模型	$T L = T a + R a b s - ε σ T a 4 - λ g v D / P a c p g h + g r + λ [d e s (T a) / d T P a] g v$ （6）	叶片温度 $T L$ 的能量平衡方程
	$g r = 4 ε σ T L 3 C p$ （7）	叶片辐射电导
	$g h = g b × 0.135 / 0.147$ （8）	用于叶片传热计算的叶边界层电导
	$g v = 0.5 × g s g b g s + g b$ （9）	叶片边界层电导
	$e s T = 0.611 e x p (17.502 T 240.97 + T)$ （10）	在T ℃下的叶饱和蒸气压
	$e = 2 g V e s (T L) - e a P a$ （11）	叶片蒸腾速率
光合作用模型（FvCB模型）	$A = V c - 0.5 V 0 - R d = m i n A c, A j, A p - R d$ （12）	净光合速率
	$A c = V c m a x C c - Γ * C c + K c (1 + O / K o)$ （13）	Rubisco限制条件下光合速率
	$A j = J (C i - Γ ) 4 (C i + 2 Γ )$ （14）	RuBP再生限制条件下光合速率
	$θ J 2 - I 2 + J m a x J + I 2 J m a x = 0$ （15）	电子传输速率的光依赖性
	$I 2 = I (1 - f) (1 - δ) / 2$ （16）	光系统II对PAR的吸收
	$A p = 3 P u$ （17）	TPU限制条件下光合速率
	$K T = k 25 e x p E a (T L - 25) 298 R T L + 273$ （18）	Arrhenius函数； $K c, K o, R d, V c m a x$ 的温度依赖性
	$J m a x =$ $J m 25 e x p T p - 25 E a R T p + 273 298 1 + e x p S 298 - H R 298 1 + e x p S T p + 273 - H R (T p + 273)$ （19）	$J m a x$ 的温度依赖性
	$Γ * = 36.9 + 1.88 T p - 25 + 0.036 (T p - 25) 2$ （20）	$Γ *$ 的温度依赖性
	$f ξ = d 0 1 - e x p - d 1 ξ e x p (- d 2 ξ)$ （21）	$J m a x, V c m a x$ 和 $P u$ 的叶龄依赖性
	$C i = C a - A (1 g b + 1 g s) P a$ （22）	胞间CO₂浓度
	$C c = C i - A g m P a$ （23）	叶绿体内CO₂浓度
	$g m = e x p (c - ∆ H a R T k) 1 + e x p (∆ S × T k - ∆ H d R T)$ （24）	叶肉细胞对于CO₂的电导
气孔导度模型（BWB模型）	$g s = b + m A h s (C s / P a)$ （25）	气孔导度
	$Γ = R d K c (1 + O / K o) + V c m a x Γ * V c m a x - R d$ （26）	CO₂补偿点，考虑呼吸作用（R_d ）
	$C s = C a - A g b P a$ （27）	叶片表面CO₂分压
	$g b = 0.147 u / d$ （Gr/Re² >1）（28） $g b = 0.055 ∙ (T p - T a d) 14$ （Gr/Re² <1）（29） $d = 0.72 w$ （30）	水蒸气的边界层电导
	$a h h s 2 + b h h s + c h = 0$ 其中 $a h = (g 1 A) / C s b h = g 0 + g b - (g 1 A / C s) c h = - R H g b - g 0$ （31）	$将 h s 和 g s$ 与扩散方程相结合得到的二次方程

Table 2

Table 3

Symbol specification of the modules for energy balance， photosynthesis， stomatal conductance in the plant functional-structural model of daylily and nomenclature

符号类型	符号	含义及单位
光合作用	$Γ$	存在R_d 时的CO₂补偿点［μbar］
	$Γ *$	无R_d 时的CO₂补偿点［μbar］
	$ξ$	以展开后的天数计算的叶龄［day］
	$θ$	电子传递对PAR的响应曲率［0.7，-］
	$δ$	叶反射率加上透射率［0.15，-］
	$A$	叶片净光合速率［μmol/m²·s］
	$A c$	Rubisco限制的CO₂同化率［μmol/m²·s］
	$A j$	电子传输限制的CO₂同化率［μmol/m²·s ］
	$A m a x$	环境条件下光饱和CO₂同化速率［CO₂］［μmol/m²·s］
	$A p$	磷酸丙糖再利用受限的CO₂同化率［μmol/m²·s］
	$C a$	空气CO₂分压
	$C i$	细胞间CO₂分压［μbar］
	$d 0$	叶龄效应的比例因子［1.296，-］
	$d 1$	叶龄效应生长的经验系数［0.146 8，-］
	$d 2$	叶龄效应下降斜率的经验系数［0.010 3，-］
	$E a$	活化能［kJ mol^-1］
	$f$	光谱校正因子［0.15，-］
	$H$	$J m a x$ 温度依赖性的曲率参数［219.4 kJ mol^-1］
	$I$	入射PAR ［μmol photons/m²·s］
	$J$	光合电子传递速率［μmol electrons/m²·s］
	$J m 25$	25 °C 时电子传输的潜在速率［36.8 μmol/m²·s］
	$K c 25$	CO₂的Rubisco-Michaelis-Menten常数［267 μbar］
	$K o 25$	25 °C时O₂的Rubisco-Michaelis-Menten常数［164 mbar］
	O	氧分压［205 mbar ］
	$P u 25$	25 °C时磷酸丙糖利用率［10.35 μmol/m²·s］
	R	通用气体常数［8.314 J/mol·K ^［31］］
	$R d 25$	25 °C时光照条件下的线粒体呼吸作用［0.0089V_cmax25 ］
	S	电子传输温度响应参数［704.2 J/mol·K］
	$V c$	羧化率［μmol/m²·s］
	$V c m 25$	25 °C时的光合Rubisco潜力［92.07 μmol/m²·s］
	$V o$	氧合率［μmol/m²·s］
温度相关的变量	E	每个过程的活化能
	$J m a x$	最大电子传输速率［μmol/m²·s］
	$K c$	CO₂的Rubisco-Michaelis-Menten常数［μmol/m²·s］ E_Kc 80 990
	$K o$	O₂的Rubisco-Michaelis-Menten常数［μmol/m²·s］ E_Ko 36 000
	$P u$	磷酸丙糖利用率［μmol/m²·s］ E_Pu 47 140.1
	$R d$	光下的线粒体呼吸速率［μmol/m²·s］ E_Rd 46 390
	$V c m a x$	Rubisco羧化的最大速率［μmol/m²·s］ E_Vcmax 65 330
气孔导度模型	b	光补偿点时BWB模型对水汽的最小气孔导度［0.096 0 mol/m²·s］
	$C a$	环境CO₂分压［μbar］
	$C s$	叶面CO₂分压［μbar］
	$g b$	边界层对水蒸气的电导［mol/m²·s］
	$g s$	气孔对水蒸气的导度［mol/m²·s］
	$g h$	用于传热的叶片边界层传导率［mol/m²·s］
	$g v$	叶边界层电导［］
	$h s$	叶面相对湿度［］
	m	BWB模型中g_s 对A、C_s 和h_s 敏感度的经验系数［10.055，-］
能量平衡方程	$ε$	叶片热发射率［0.97］
	$σ$	斯特藩-玻尔兹曼常数［ $5.67 × 10 - 8 W / m 2 · K 4$ ］
	$λ$	25 ℃时的潜热［44.0 kJ/mol］
	$c p$	空气的比热容［29.3 J/mol·℃］
	D	环境空气的水蒸气压差［kPa］
	$D s$	叶片表面的水蒸气压差［kPa］
	E	单位叶面积的蒸腾速率［mol/m²·s］
	$e a$	单位投影叶面积的蒸腾速率［kPa］
	$e s$	叶片表面的水蒸气压力［kPa］
	$g h$	边界层单位表面叶面积的热传导率［mol/m²·s］
	$g r$	单位表面叶面积的辐射传导率［mol/m²·s］
	$g v$	单位表面叶面积的总水蒸气传导率［mol/m²·s］
	$P a$	大气压力［kPa］
	$R a b s$	单位表面叶面积吸收的长波和短波辐射能量［W/m²］
	$T a$	周围空气温度［℃］

Table 3

Fig. 3

Fig. 4

Fig.5

Fig.6

Fig.7

Fig.8

Table 3

Fig. 9

Fig.10

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形态指标（生长最终值）	最大值	最小值	极差	平均值	标准差
叶片长度（1~13叶位）/cm	70.30、84.10、98.20、102.40、109.80、112.70、120.80、122.20、124.10、130.90、132.30、134.20、136.40	45.80、54.20、66.30、71.70、77.90、80.20、81.80、88.00、92.20、94.50、99.30、101.40、102.90	24.50、29.90、31.90、30.70、31.90、32.50、39.00、34.20、31.90、36.40、33.00、32.80、33.50	55.35、64.45、76.85、82.25、90.25、94.63、98.20、104.83、106.28、115.43、120.20、126.38、127.66	8.90、11.53、12.46、10.26、11.90、10.84、14.01、10.20、10.52、12.20、9.83、10.38
叶片宽度/mm	29.44	16.32	13.12	24.61	2.19
花蕾长度/mm	153	91	62	127	1.27
花蕾直径/mm	13.07	8.11	4.96	10.42	1.08
花蕾鲜重/g	6.17	1.92	4.25	3.79	0.84
薹蕾数/（蕾/薹）	59	18	41	40.1	11.48
花葶高度/cm	133.90	86.50	47.40	118.57	16.12
花葶鲜重/g	45.47	25.02	20.45	38.48	7.14

类别	R ²	RMSE	F	Sig.
叶位1	0.984	0.028	304.046	1.14×10^-5
叶位2	0.943	0.064	82.244	2.73×10^-4
叶位3	0.980	0.057	344.191	3.28×10^-7
叶位4	0.938	0.083	106.812	1.72×10^-5
叶位5	0.916	0.142	109.306	1.06×10^-6
叶位6	0.938	0.111	166.137	5.56×10^-8
叶位7	0.919	0.177	158.659	5.01×10^-9
叶位8	0.896	0.144	138.523	2.72×10^-9
叶位9	0.934	0.111	270.099	1.09×10^-12
叶位10	0.920	0.123	230.845	1.9×10^-12
叶位11	0.951	0.123	508.713	1.35×10^-18
叶位12	0.909	0.147	278.480	4.41×10^-16
叶位13	0.926	0.129	426.891	7.99×10^-21
花葶长	0.972	0.088	1 168.533	6.49×10^-28
平均花蕾长	0.914	0.014	211.946	9.72×10^-12
平均花蕾鲜重	0.880	0.511	146.685	1.15×10^-10