Understanding the Alternate Bearing Phenomenon: Resource Budget Model

TL;DR

This paper analyzes the resource budget model for plant energy resources to understand the ecological alternate bearing phenomenon, revealing complex chaotic dynamics, effects of parameters, and implications for real-world fruit crop yield patterns.

Contribution

It provides a detailed study of the resource budget model's chaotic behavior and its relevance to ecological alternate bearing, including effects of noise and parameter variations.

Findings

Chaotic bands in the model explain alternate bearing patterns.

Parameter variations influence the stability of yield cycles.

Noise impacts the predictability of the model's outcomes.

Abstract

We consider here the resource budget model of plant energy resources, which characterizes the ecological alternate bearing phenomenon in fruit crops, in which high and low yields occur in alternate years. The resource budget model is a tent-type map, which we study in detail. An infinite number of chaotic bands are observed in this map, which are separated by periodic unstable fixed points. These $m$ bands chaotic attractors become m/2 bands when the period-m unstable fixed points simultaneously collide with the chaotic bands. The distance between two sets of coexisting chaotic bands that are separated by a period-1 unstable fixed point is discussed. We explore the effects of varying a range of parameters of the model. The presented results explain the characteristic behavior of the alternate bearing estimated from the real field data. Effect of noise are also explored. The significance of these results to ecological perspectives of the alternate bearing phenomenon are highlighted.