Density Dependent Resource Budget Model for Alternate Bearing

Alternate bearing is the variability of the fruit and nut production with a strongly biennial pattern and is observed in many types of plants. This phenomenon is observed in collective synchrony among trees that are coupled directly and indirectly in orchards and natural forests and is known as masting. This is a yearly phenomenon so discrete time models, coupled nonlinear difference equations, are the appropriate modeling framework, with alternation between local in space dynamics and exchange between locations. The well-known resource budget model, while proposing a mechanism for alternate bearing behavior, can only model the synchronization observed in systems where the trees are coupled through indirect coupling (pollen coupling). We developed a density-dependent resource budget model based on the balance between photosynthesis and reproduction process. We analyzed the model through examination of the bifurcation structure for the uncoupled (local in space) model and numerically for spatially coupled versions. By addressing some of the shortcomings of the well-known resource budget model, our new approach can model the alternate bearing behavior and the synchronization phenomenon observed in trees coupled through direct coupling mechanism (root grafting).