A First Order Piece-Wise Linear Differential Equation Explains Alternate Bearing In Perennial Plants

The phenomenon of Alternate Bearing observed in polycarpic plants has long been a problem of interest for ecologists and biologists due to its cascading ecological and socio-economical effects. The discrete Resource Budget Model (RBM) with tent-map equations was the first mathematical attempt to model the underlying physical mechanism behind the phenomenon. In this work, the presence of resource budgeting of photosynthate in plants confirmed by past experimental studies was modeled as a continuous process and an ordinary, first-order, and piece-wise linear differential equation was derived in compliance with the discrete model. This led to the emergence of additional parameters that introduced an evolutionary window to understand the onset of flowering and fruiting phenophases of different plant species. The new parameters were dependent on the plant’s internal reproductive clock evolutionarily set by the regional duration of favorable weather conditions and defined the duration of flowering and fruiting phenophases of the species. This could not be explained by the discrete model. The continuous model also allowed for different annual onset times of flowering phenophase for different species.Modifications to RBM have been made in the literature to address problems related to alternate-bearing in individual trees and masting in a coupled population of trees but those models do not address the storage of photosynthate as a continuous process as done in this work. The incorporation of coupling between plants in the continuous RBM to explain the problem of masting is the subject of our future studies.