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Keywords:

  • additive Poisson autoregression;
  • competition and cannibalism;
  • ecological dimension;
  • nonlinear dynamics;
  • periodic fluctuations;
  • stage-structured model;
  • stochastic limit cycle;
  • time series analysis

1.  Laboratory populations of the Indian meal moth [Plodia interpunctella (Hübner) (Lepidoptera: Pyralidae)], undergo sustained periodic fluctuations in abundance. The period is just longer than the generation time. The fluctuations are accentuated in the presence of the P. interpunctella granulosis virus (PiGV).

2.  Time series spanning 8–10 generations from three replicate populations of the virus-free (VF) system and three from the virus-infected (VI) system are investigated using nonparametric autoregressive time series models.

3.  The dynamics are concluded to correspond to a third order process consistent with interactions in a three-dimensional stage-structured model for both systems. The functionally different interactive stages are believed to be the egg stage (preyed upon by larvae), small larvae (competing for resources and cannibalized by large larvae) and large larvae (competing for resources).

4.  The virus is seen as a modulator of the host vital rates more than an independent agent in a trophic host–pathogen interaction. The virus increases developmental time and decreases fecundity of the moths.

5.  A significantly nonlinear additive autoregressive model of order 3 appears to give a parsimonious description of the series.

6.  The demographic (birth and death) nature of the stochasticity inherent in the system is explicitly incorporated in the statistical model for the time series by assuming an overdispersed Poisson process. The variability around the skeleton is found to conform closely to this assumption. The demographic nature of the stochasticity cannot be fully understood on the basis of Gaussian (least-squares) models on transformed (variance-stabilized) data.

7.  Significant density dependencies are found at a 1-week lag, a 2- to 3-week lag and at a 6- to 7-week lag. These are argued to be the signatures of within-stage competition, between-stage interactions and reproduction, respectively. Negative and statistically significant density dependence is apparent for the first two of these. No significant negative density dependence is apparent in the lag corresponding to reproduction.

8.  The fluctuations in both the VF and VI system appear to represent limit cycles or weakly dampened cycles clothed by Poisson demographic stochasticity.

9.  The enhanced cycles of the VI system are demonstrated to be consistent with a situation where the functional forms for the interactions are nearly the same as for the VF, but with delay structure shifted by just less than a week.