Density dependent Resource Budget Model for alternate bearing.

Area of Science:

• Ecology
• Mathematical Biology
• Plant Physiology

Background:

• Alternate bearing, a biennial yield pattern, affects many plant species.
• Existing models like the Resource Budget Model simplify resource dynamics and reproduction.
• A more nuanced model is needed to capture the complexities of plant yield variability.

Purpose of the Study:

• To introduce a novel mathematical model for alternate bearing behavior in plants.
• To incorporate finite resource reservoir capacity and non-zero low yields into the model.
• To investigate the model's behavior with environmental stochasticity and coupled tree systems.

Main Methods:

• Developed a new model based on resource accumulation and reproduction balance.
• Included a finite resource reservoir capacity using a density-dependent accumulation function.
• Incorporated environmental stochasticity with uncorrelated noise terms.
• Analyzed a system of two directly coupled trees.

Main Results:

• The individual tree model exhibits a stable two-cycle solution, suitable for pronounced alternate bearing.
• The model successfully incorporates finite resource capacity and low non-zero yields.
• Coupled tree simulations reveal stable in-phase period-2 solutions, unlike previous models.
• Environmental stochasticity was integrated into nutrient accumulation and reproduction parameters.

Conclusions:

• The new model provides a more realistic representation of alternate bearing in plants.
• It offers insights into the mechanisms driving biennial yield patterns.
• The model's ability to predict in-phase synchrony in coupled trees suggests potential for explaining larger-scale spatial synchrony.