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

Masakazu Shimada, Midori Tuda

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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.

Original languageEnglish
Pages (from-to)116-125
Number of pages10
Issue number1
Publication statusPublished - Jan 1 1996
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics

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