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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 …