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Dissecting external effects on logistic-based growth: equations, analytical solutions and applications
1The Horticulture and Food Research Institute of New Zealand Limited, Palmerston North Research Centre, Tennent Drive, Private Bag 11030, Palmerston North, 4474, New Zealand. Email.
Functional Plant Biology : FPB
|July 22, 2020
Summary
This study introduces a new dynamical system to model organ growth, considering both genetic and environmental factors. The model helps understand how resources and development impact final size and growth duration.
Area of Science:
- Plant Biology
- Mathematical Modeling
- Ecology
Background:
- Organ growth is influenced by genetics, resource competition, and environmental conditions.
- Existing models for logistic growth under resource limitation have limitations.
Purpose of the Study:
- To propose a novel dynamical system for modeling logistic growth with dual control (genetic and environmental).
- To offer a simpler and more broadly applicable alternative to existing models.
Main Methods:
- Defined a dynamical system with state variables: size (s) and developmental age (α).
- Incorporated potential relative growth rate as a function of α to represent intrinsic properties.
- Dissected external effects into components altering growth duration and final size.
Main Results:
- The model successfully separates effects on growth duration from effects on final size.
- The formulation allows for analyzing the relationship between developmental age and time.
- The system provides a new trajectory for size over developmental age, s(α).
Conclusions:
- The proposed dynamical system offers a simplified approach to modeling organ growth under dual control.
- This model has broader applications in ecology and comparative studies of genotypes and environmental responses.
- It provides a valuable tool for understanding complex growth dynamics in plants.
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