Delayed density dependence and oscillatory population dynamics in overlapping-generation systems of a seed beetle Callosobruchus chinensis: matrix population model

Abstract

Long-term experimental systems with overlapping generations using a seed beetle, Callosobruchus chinensis, were maintained by providing 5 g of azuki beans (Vigna angularis) in two different renewal intervals: either 7 days or 10 days. The 7-day-renewal system (system 1) showed oscillatory dynamics with a constant periodic cycle of ca. 7 weeks. More stable population dynamics were seen in the 10-day-interval system (system 2). Short-term experiments showed that survivorship of adults increased with higher adult density, and that the survival rate of adults up to the age of 7 days was much higher than up to 10 days of age. In addition, the per capita production of hatched eggs by females which had survived for 7 days increased with increasing density experienced by the females. Females aged 10 days rarely laid eggs which hatched. We constructed a matrix population model based on either 1 week for system 1 or 10 days for system 2. The model included five stages in system 1: the hatched egg, the final instar larva, the pupa, the young adult and the old adult. Four stages were incorporated in the model for system 2: the young instar larva, the pupa, the young adult, and the old adult. Logistic-difference equations were applied to formulate both overcompensatory density dependence in the hatched-egg production by adults and undercompensatory response in the larval development up to the pupa. The survivorship of young adults to the old stage and the per capita hatched-egg productivity of the old females followed a linear regression against the young adult density. Inside-bean processes were adjusted to be equivalent in the two models, irrespective of the resource renewal intervals. The model predicted that system 1 would oscillate for a long time but that system 2 would rapidly converge to the equilibrium point. Multiplicative effects of both the delayed density dependence through interstage restraint effects and the overcompensatory density dependence in hatched-egg production generated various dynamic patterns ranging from a quickly disappearing damped oscillation to stable limit cycles in system 1. The relationship between resource renewal cycles and delayed density dependence was discussed based on these simulations.