| Citation: |
Xue-yang Yu, Si-yuan Ye, 2020. The universal applicability of logistic curve in simulating ecosystem carbon dynamic, China Geology, 3, 292-298. doi: 10.31035/cg2020029
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The universal applicability of logistic curve in simulating ecosystem carbon dynamic
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Abstract
As an S-shaped curve, the logistic curve has both high and low limit, which provides advantages in modelling the influences of environmental factors on biogeological processes. However, although the logistic curve and its transformations have drawn much attention in theoretical modelling, it is often used as a classification method to determine a true or false condition, and is less often applied in simulating the real data set. Starting from the basic theory of the logistic curve, with observed data sets, this paper explored the new application scenarios such as modelling the time series of environmental factors, modelling the influence of environmental factors on biogeological processes and modelling the theoretical curve in ecology area. By comparing the performance of traditional model and the logistic model, the results indicated that logistic modelling worked as well as traditional equations. Under certain conditions, such as modelling the influence of temperature on ecosystem respiration, the logistic model is more realistic than the widely applied Lloyd-Taylor formulation under extreme conditions. These cases confirmed that the logistic curve was capable of simulating nonlinear influences of multiple factors on biogeological processes such as carbon dynamic.
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References
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Xue-yang Yu, Si-yuan Ye, 2020. The universal applicability of logistic curve in simulating ecosystem carbon dynamic, China Geology, 3, 292-298. doi: 10.31035/cg2020029
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Figure 1.
Basic shape and transformation of logistic curve. a–the basic form of logistic curve. The curve has both high and low limitation, with symmetric center of (x0, 0.5×L). Parameter k determined the steepness of the S-shaped curve and the product of k and the length of increasing interval (s) is approximately 13.8135. b–the basic form of logistic curve with a given parameter set (L=1, x0=0, k=1). c–curve transformation by adding a constant c to basic logistic curve with given parameter set (L=1, x0=0, k=1, c=−1). d–curve transformation by adding two basic logistic curves together with parameter sets (f1: L=1, x0=4, k=1) and (f2: L=−1, x0=10, k=1).
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Figure 2.
The application examples of logistic curve when simulating the variation of environmental variables. The black points represented the observed data and the blue curve indicated the simulated results. a–simulating seasonal variation of LAI using logistic curve. b–simulating diurnal variation of air temperature change with logistic curve. The performance of each fitting was described in Table 1.
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Figure 3.
The comparison of NEE fitting as well as ER fitting using logistic curve and traditional equations. a–modelling the correlations between PPFD and NEE using different modelling equations (the Michaelis-Menten equation and the Logistic form equation). b–modelling the correlations between soil temperature at 5 cm and ER using different modelling equations (the Lloyd-Taylor equation and the Logistic form equation).
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Figure 4.
The application of logistic curve in modelling the combination effect of plant basal diameter (D) and plant height (H) on fresh aboveground biomass (AGB).