Dissecting external effects on logistic-based growth: equations, analytical solutions and applications
Alla N. SeleznyovaA The Horticulture and Food Research Institute of New Zealand Limited, Palmerston North Research Centre, Tennent Drive, Private Bag 11030, Palmerston North, 4474, New Zealand. Email: aseleznyova@hortresearch.co.nz
This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.
Functional Plant Biology 35(10) 811-822 https://doi.org/10.1071/FP08078
Submitted: 14 March 2008 Accepted: 22 September 2008 Published: 11 November 2008
Abstract
Characteristic growth patterns of individual organs are, to a large extent, determined by genetic factors, but can also be affected by intra-plant competition for resources and by environmental conditions. The current study proposes a dynamical system for modelling this dual control for logistic-based growth. The state of the system is defined by two state variables: size (s), and developmental age (α). The intrinsic properties of the system are represented by the potential relative growth rate as a function of α. This formulation allows dissection of the external effects on the system dynamics into two components: one that changes the duration of growth without affecting the final size and one that affects the final size without much effect on the duration. The former component determines the relationship between α and time, while the latter determines the effect on the system trajectory, s(α). The presented dynamical system is simpler and has a wider range of potential applications than the system proposed by Thornley and France (2005) for modelling logistic growth under resource limitation. The current approach can be also useful in ecology and in comparative studies of different genotypes and their responses to environmental conditions.
Additional keywords: developmental age, leaf growth, logistic function, modelling, relative growth rate, resource limitation, θ-logistic.
Acknowledgements
This study was supported by New Zealand Foundation for Science Research and Technology, contract C06X0202.
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