Application of compound interest laws in biology: Reunification of existing models to develop seed bank dynamics model of annual plants

Reunification of widely-usedclassic models in ecology is a very important step for the field to grow. In this study, classic models based on compound interest law, which exists in many natural phenomena, were reunified, and a seed bank dynamics model of annual plants was developed. We found an intrinsic relationship between the compound interest of unit period and density dependence, and the relationship was interpreted using evolutionary stability strategies of a single seed. Based on the relationship, a seed bank dynamic model of annual plants was constructed, and compound interest of the unit period and discrete-time dynamic processes, by which a new density-dependence based on the benefit balance of storage and investment (defined as the compound interest law) was derived. Our model not only can be used to reunify the three classic models (Cohen's, Goldberg's, and Fulmer's) but can also support different levels of density dependence in the seed bank dynamics of annual plants. Our study has shown that the compound interest law interprets seed bank dynamics more clearly than the traditional power law, not only because there are close relationships between the compound interest law and the power laws in numerical simulations but also because the compound interest law can be directly interpreted by the evolutionary stability theory. Our study provides new insight into the bet hedging theory and the life-history evolution of plants with seed banks by adding a compound interest term to the fitness function of annual plants. We suggest that if the interest rate of delaying growth can be defined by compensating for delayed growth, compound interest of the unit period will play an important role in biology and ecology. (C) 2014 The Authors. Published by Elsevier B.V. All rights reserved.