Sigmoid growth curves, a new approach to study the dynamics of the epicotyl emergence of oak

Autorzy

• Joanna Ukalska Warsaw University of Life Sciences, Institute of Forest Sciences, Department of Forest Management Planning, Dendrometry and Forest Economics, Laboratory of Dendrometry and Forest Productivity, Nowoursynowska 159, 02-776 Warsaw, Poland
  e-mail: joanna_ukalska@sggw.pl
• Szymon Jastrzębowski Forest Research Institute, Department of Sylviculture and Forest Tree Genetics, Braci Leśnej 3, Sękocin Stary, 05-090 Raszyn, Poland

Abstract

Three of the most frequently used sigmoidal growth curves from the Richards family are the logistic model, Gompertz model and Richards model. They are used in the analysis of organismal growth over time in many disciplines/studies and were proposed in many parameterisations. Choosing the right parameterisation is not easy. The correct parameterisation of the model should take into account such parameters that are useful to describe the analysed growth phenomenon and are biologically relevant without additional calculations. In addition, each parameter of the model only affects one shape characteristic of each growth curve, which makes it possible to determine standard errors and confidence intervals using statistical software.
Growth curves in germination dynamics studies should provide information on topics such as the length of the lag in onset of germination, the maximum germination rate and, when it occurs, the time at which 50% of seeds will germinate and the final germination proportion. In this article, we present three parameterisations of the logistic, Gompertz and Richards models and indicate two parameterisations for each model, corresponding to the abovementioned issues. Our proposition is parameterisation by taking into account the maximum absolute growth rate. Parameterisations indicated as useful for germination dynamics are characterised by the fact that each parameter has the same meaning in every model, so its estimates can be compared directly amongst the models. We also discussed the goodness-of-fit measures for nonlinear models and in particular measures of nonlinear behaviour of a model’s individual parameters as well as overall measures of nonlinearity.
All described models were used to study the dynamics of the epicotyl emergence of pedunculate oak. After checking the close-to-linear behaviour of the studied model parameters and by taking into account the criteria of model selection (AICc of each growth curve and the residual variance [RV]), the best model describing the dynamics of epicotyl appearance of pedunculate oak was the Richards curve.

Keywords

• cumulative germination
• Gompertz model
• growth curves
• logistic model
• nonlinear regression
• Richards model
• Pedunculate oak