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Fitting leaf area data to nonlinear sigmoidal growth curves

Author Affiliations

  • 1Ecophysiology Laboratory, Department of Functional Plant Biology, Kumaon University, Almora Campus, Almora, Uttrakhand, India

Int. Res. J. Environment Sci., Volume 11, Issue (1), Pages 9-17, January,22 (2022)


Three of the most commonly used sigmoidal growth curves from Richard family which are applied in plant growth simulation modelling are the Logistic, Richard and Gompertz curves. These mathematical functions are suitable to study the sigmoidal pattern of determinate growth. Logistic and Gompertz models have 3 parameters while Richard function has one additional parameter to describe growth kinetics. Both Richard and Gompertz function are flexible enough in describing asymmetrical sigmoidal patterns while logistic function describes symmetrical sigmoidal growth and because of this, all discussed modelscan be used to predict leaf growth dynamics. Leaf area data was collected from one semi-deciduous species (Shorea robusta Gaertn. f.; Family Dipterocarpaceae) and one deciduous species (Adina cordifolia Hook. f. ex. Brandis; Family Rubiaceae)growing naturally in terai region at the foot hills of central Kumaon Himalaya to explain the fitting performance of some nonlinear asymptotic models to leaf data. Leaf area expansion was considered a function of time, y=f(x). Growth curves in explaining leaf area dynamics provides insight on the following logical questions which are: length of lag phase, maximum growth rate, when it occurs, the time at which 50% of leaf area growth is completed and finally the upper limit (value) of leaf area growth. For model fitting performance four comparison criteria were used. Coefficient of Determination (R2), Sum of Squared Error (SSE), Root Mean Square Error (RMSE) and Mean Relative Error (MRE). All the three models fitted well to leaf area data from two species. In both the data sets, Richard curve behaved much more like a logistic curve (δ close to 1), than Gompertz curve. Results indicated that nonlinear sigmoidal fitting is much reliable in explaining leaf growth variations over time as compared to other model forms.


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