Dissecting external effects on logistic-based growth: equations, analytical solutions and applications

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.