[Allometry and the original and modified Janoschek growth function. (author's transl)]

Area of Science:

• Quantitative Biology
• Mathematical Biology
• Growth Modeling

Context:

• The allometry principle describes how biological traits scale with body size.
• Existing growth functions like Bertalanffy and Gompertz are foundational in biological growth studies.
• The Janoschek growth function offers an alternative model for biological growth patterns.

Purpose:

• To adapt and apply the allometry principle to the Janoschek growth function.
• To modify the Janoschek function for non-zero initial growth values.
• To explore implications for growth curves with finite growth times.

Summary:

• The Janoschek growth function is modified to accommodate non-zero initial growth.
• The allometry principle is rigorously applied to this modified function, requiring re-derivation of allometric relationships.
• Integration of a modified increase ansatz results in growth curves exhibiting finite growth duration.
• Approximation methods for calculating inflexion points are presented.
• The study includes comparative examples using recent allometric data.

Impact:

• Provides a novel application of allometry to a different growth model.
• Enhances the flexibility of the Janoschek function for diverse biological scenarios.
• Offers new analytical tools for understanding growth dynamics and scaling.
• Facilitates direct comparison between different growth modeling approaches.