Comparison between modified exponential model and common models of light-response curve

doi:10.3724/SP.J.1258.2012.01277

Abstract

Abstract:

Aims Our primary aim was to compare the differences and accuracies of light-response curves between C₃ and C₄ plants as described by five light-response curve models: modified exponential (a new model), rectangular hyperbola, modified rectangular hyperbola , non-rectangular hyperbola and exponential. Methods Light-response curves of Xizang hulless barley (Hordeum vulgare), grain sorghum (Sorghum bicolor), amaranth (Amarantus mangestbus) and Pinellia ternate were measured by a portable photosynthetic gas analysis system with a LED radiation source (LI-6400). The collected data were used to fit and test the five light-response curve models, and photosynthetic parameters, such as light saturation point and maximum net photosynthetic rate, were compared with the measured values. Important findings The results show that the light-response curves of the four plants described by the modified exponential and modified rectangular hyperbola models are better than the rectangular hyperbola, non-rectangular hyperbola and exponential models, especially when light intensity is beyond the light saturation point. The results also indicate that the modified exponential and modified rectangular hyperbola models also describe the light-response curves characteristics of C₄ plants, although the two models were established based on C₃plants. Therefore, these two models provide a reference for the application of light-response curve models in plants with different photosynthetic pathways including C₃ and C₄.

Key words: light response curves, light saturation point, maximum net photosynthetic rate, modified exponential model

CHEN Wei-Ying, CHEN Zhen-Yong, LUO Fu-Yan, PENG Zheng-Song, YU Mao-Qun. Comparison between modified exponential model and common models of light-response curve[J]. Chin J Plant Ecol, 2012, 36(12): 1277-1285.

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URL: https://www.plant-ecology.com/EN/10.3724/SP.J.1258.2012.01277

https://www.plant-ecology.com/EN/Y2012/V36/I12/1277

Figures/Tables 3

References 27

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材料 Material	模型 Model	拟合值的MSE Fitted MSE	拟合值的MAE Fitted MAE	预测值的MSE Test MSE	预测值的MAE Test MAE
高粱 Sorghum bicolor	指数改进模型 Modified exponential model	0.092	0.239	0.070	0.239
	直角双曲线修正模型 Modified rectangular hyperbola model	0.159	0.320	0.112	0.295
	直角双曲线模型 Rectangular hyperbola model	0.329	0.476	0.363	0.527
	非直角双曲线模型 Nonrectangular hyperbola model	0.052	0.192	0.217	0.383
	指数模型 Exponential model	0.098	0.243	0.065	0.204
苋 Amaranthus tricolor	指数改进模型 Modified exponential model	0.043	0.186	0.119	0.272
	直角双曲线修正模型 Modified rectangular hyperbola model	0.049	0.186	0.208	0.357
	直角双曲线模型 Rectangular hyperbola model	0.325	0.458	1.113	0.757
	非直角双曲线模型 Nonrectangular hyperbola model	0.194	0.363	0.217	0.409
	指数模型 Exponential model	0.053	0.215	0.235	0.320
半夏 Pinellia ternata	指数改进模型 Modified exponential model	0.116	0.288	0.404	0.308
	直角双曲线修正模型 Modified rectangular hyperbola model	0.042	0.160	0.190	0.235
	直角双曲线模型 Rectangular hyperbola model	0.494	0.569	1.569	0.912
	非直角双曲线模型 Nonrectangular hyperbola model	0.261	0.402	1.026	0.628
	指数模型 Exponential model	0.210	0.295	0.919	0.514
大麦‘藏青320’ Hordeum vulgare ‘zangqing320’	指数改进模型 Modified exponential model	0.070	0.237	0.250	0.307
	直角双曲线修正模型 Modified rectangular hyperbola model	0.023	0.122	0.107	0.214
	直角双曲线模型 Rectangular hyperbola model	0.548	0.643	1.490	0.778
	非直角双曲线模型 Nonrectangular hyperbola model	0.192	0.324	0.855	0.626
	指数模型 Exponential model	0.114	0.224	0.586	0.453

材料 Material	模型 Model	拟合值的MSE Fitted MSE	拟合值的MAE Fitted MAE	预测值的MSE Test MSE	预测值的MAE Test MAE
高粱 Sorghum bicolor	指数改进模型 Modified exponential model	0.092	0.239	0.070	0.239
	直角双曲线修正模型 Modified rectangular hyperbola model	0.159	0.320	0.112	0.295
	直角双曲线模型 Rectangular hyperbola model	0.329	0.476	0.363	0.527
	非直角双曲线模型 Nonrectangular hyperbola model	0.052	0.192	0.217	0.383
	指数模型 Exponential model	0.098	0.243	0.065	0.204
苋 Amaranthus tricolor	指数改进模型 Modified exponential model	0.043	0.186	0.119	0.272
	直角双曲线修正模型 Modified rectangular hyperbola model	0.049	0.186	0.208	0.357
	直角双曲线模型 Rectangular hyperbola model	0.325	0.458	1.113	0.757
	非直角双曲线模型 Nonrectangular hyperbola model	0.194	0.363	0.217	0.409
	指数模型 Exponential model	0.053	0.215	0.235	0.320
半夏 Pinellia ternata	指数改进模型 Modified exponential model	0.116	0.288	0.404	0.308
	直角双曲线修正模型 Modified rectangular hyperbola model	0.042	0.160	0.190	0.235
	直角双曲线模型 Rectangular hyperbola model	0.494	0.569	1.569	0.912
	非直角双曲线模型 Nonrectangular hyperbola model	0.261	0.402	1.026	0.628
	指数模型 Exponential model	0.210	0.295	0.919	0.514
大麦‘藏青320’ Hordeum vulgare ‘zangqing320’	指数改进模型 Modified exponential model	0.070	0.237	0.250	0.307
	直角双曲线修正模型 Modified rectangular hyperbola model	0.023	0.122	0.107	0.214
	直角双曲线模型 Rectangular hyperbola model	0.548	0.643	1.490	0.778
	非直角双曲线模型 Nonrectangular hyperbola model	0.192	0.324	0.855	0.626
	指数模型 Exponential model	0.114	0.224	0.586	0.453

材料 Material	模型 Model	LCP	LSP	P_max	R_dark	φ₀	θ
高粱 Sorghum bicolor	观测值 Measured value	40-50	2 200	19.362	1.616	-	-
	指数改进模型 Modified exponential model	42.815	1 952	16.944	1.911	0.047	-
	直角双曲线修正模型 Modified rectangular hyperbola model	41.033	2 071	18.873	1.981	0.051	-
	直角双曲线模型 Rectangular hyperbola model	40.600	-	26.028	2.347	0.064	-
	非直角双曲线模型 Nonrectangular hyperbola model	41.398	-	22.043	1.585	0.039	0.776
	指数模型 Exponential model	41.438	-	20.892	1.835	0.046	-
苋 Amaranthus tricolor	观测值 Measured value	80-100	2 200	39.618	5.626	-	-
	指数改进模型 Modified exponential model	95.385	2 295	40.720	5.390	0.060	-
	直角双曲线修正模型 Modified rectangular hyperbola model	94.607	2 574	40.099	5.484	0.062	-
	直角双曲线模型 Rectangular hyperbola model	90.161	-	65.378	6.135	0.075	-
	非直角双曲线模型 Nonrectangular hyperbola model	97.738	-	50.000	4.719	0.049	0.809
	指数模型 Exponential model	94.924	-	48.382	5.502	0.062	-
半夏 Pinellia ternata	观测值 Measured value	0-20	1 200	11.762	0.630	-	-
	指数改进模型 Modified exponential model	8.012	967	11.619	0.422	0.054	-
	直角双曲线修正模型 Modified rectangular hyperbola model	9.839	1 122	11.729	0.610	0.064	-
	直角双曲线模型 Rectangular hyperbola model	11.167	-	13.424	0.987	0.095	-
	非直角双曲线模型 Nonrectangular hyperbola model	8.680	-	11.822	0.392	0.045	0.906
	指数模型 Exponential model	10.910	-	11.882	0.651	0.061	-
大麦‘藏青320’ Hordeum vulgare ‘zangqing320’	观测值 Measured value	20-40	1 600	19.953	1.399	-	-
	指数改进模型 Modified exponential model	21.611	1 577	19.601	1.150	0.055	-
	直角双曲线修正模型 Modified rectangular hyperbola model	23.327	1 580	19.743	1.386	0.062	-
	直角双曲线模型 Rectangular hyperbola model	25.536	-	25.439	2.061	0.088	-
	非直角双曲线模型 Nonrectangular hyperbola model	23.828	-	22.182	1.237	0.053	0.768
	指数模型 Exponential model	23.897	-	21.083	1.381	0.060	-

材料 Material	模型 Model	LCP	LSP	P_max	R_dark	φ₀	θ
高粱 Sorghum bicolor	观测值 Measured value	40-50	2 200	19.362	1.616	-	-
	指数改进模型 Modified exponential model	42.815	1 952	16.944	1.911	0.047	-
	直角双曲线修正模型 Modified rectangular hyperbola model	41.033	2 071	18.873	1.981	0.051	-
	直角双曲线模型 Rectangular hyperbola model	40.600	-	26.028	2.347	0.064	-
	非直角双曲线模型 Nonrectangular hyperbola model	41.398	-	22.043	1.585	0.039	0.776
	指数模型 Exponential model	41.438	-	20.892	1.835	0.046	-
苋 Amaranthus tricolor	观测值 Measured value	80-100	2 200	39.618	5.626	-	-
	指数改进模型 Modified exponential model	95.385	2 295	40.720	5.390	0.060	-
	直角双曲线修正模型 Modified rectangular hyperbola model	94.607	2 574	40.099	5.484	0.062	-
	直角双曲线模型 Rectangular hyperbola model	90.161	-	65.378	6.135	0.075	-
	非直角双曲线模型 Nonrectangular hyperbola model	97.738	-	50.000	4.719	0.049	0.809
	指数模型 Exponential model	94.924	-	48.382	5.502	0.062	-
半夏 Pinellia ternata	观测值 Measured value	0-20	1 200	11.762	0.630	-	-
	指数改进模型 Modified exponential model	8.012	967	11.619	0.422	0.054	-
	直角双曲线修正模型 Modified rectangular hyperbola model	9.839	1 122	11.729	0.610	0.064	-
	直角双曲线模型 Rectangular hyperbola model	11.167	-	13.424	0.987	0.095	-
	非直角双曲线模型 Nonrectangular hyperbola model	8.680	-	11.822	0.392	0.045	0.906
	指数模型 Exponential model	10.910	-	11.882	0.651	0.061	-
大麦‘藏青320’ Hordeum vulgare ‘zangqing320’	观测值 Measured value	20-40	1 600	19.953	1.399	-	-
	指数改进模型 Modified exponential model	21.611	1 577	19.601	1.150	0.055	-
	直角双曲线修正模型 Modified rectangular hyperbola model	23.327	1 580	19.743	1.386	0.062	-
	直角双曲线模型 Rectangular hyperbola model	25.536	-	25.439	2.061	0.088	-
	非直角双曲线模型 Nonrectangular hyperbola model	23.828	-	22.182	1.237	0.053	0.768
	指数模型 Exponential model	23.897	-	21.083	1.381	0.060	-

[1]	LUO Fu-Yan,CHEN Wei-Ying,CHEN Zhen-Yong. Applicability of modified exponential model in photosynthetic-CO₂ response curve of barley [J]. Chin J Plant Ecol, 2013, 37(7): 650-655.
[2]	YE Zi-Piao, YU Qiang. COMPARISON OF NEW AND SEVERAL CLASSICAL MODELS OF PHOTOSYNTHESIS IN RESPONSE TO IRRADIANCE [J]. Chin J Plant Ecol, 2008, 32(6): 1356-1361.