Probabilistic Gompertz model of irreversible growth

Area of Science:

• Ecology
• Population Dynamics
• Biometrics

Background:

• Individual size-at-age models, such as the Gompertz model, are crucial for population growth characterization but struggle with parameter variability.
• Size-at-age data is often unavailable, necessitating the use of size-increment data from methods like tag-recapture experiments.
• Existing probabilistic Gompertz models applied to abalone growth data allow for negative growth, which is biologically implausible for structures with irreversible growth.

Purpose of the Study:

• To develop probabilistic Gompertz models that accommodate irreversible growth patterns.
• To resolve the issue of negative growth predictions in size-increment distributions.
• To apply these improved models to abalone growth data.

Main Methods:

• Developed probabilistic Gompertz models by conditioning parameter distributions on size.
• Transformed size-at-age models into size-increment models for data lacking age information.
• Incorporated a growth-limiting biological length scale into the models.

Main Results:

• The developed models successfully prevent negative growth predictions, aligning with irreversible biological processes.
• Conditioning parameter distributions on size allows for accurate modeling of heterogeneous abalone growth data.
• The inclusion of a biological length scale yielded realistic length-increment distributions for abalone.

Conclusions:

• Probabilistic Gompertz models, when conditioned on size, provide a robust framework for analyzing irreversible organism growth.
• These models offer a significant improvement over previous approaches by ensuring biologically realistic growth trajectories.
• The findings have implications for understanding and modeling growth in various biological systems with accumulated structures.