Photoperiodic time measurement in spider mites

Summary A model has been developed which describes in mathematical terms the incidence of diapause in the spider miteTetranychus urticae under different photoperiodic regimens. The model has been derived from Beck's (1974a, b, 1975, 1976a) Dual System Theory of photoperiodic time measurement, by means of a number of essential alterations and modifications. The spider mite's model is composed of two hour-glass timers, one of which starts at lights-off and measures the length of the night, whereas the other is initiated both by the onset of the first hour-glass timer and by lights-on. This second hour-glass defines the time at which the first hour-glass is read off, the state of the first hour-glass at this particular time being decisive for the developmental alternative (diapause or nondiapause) to be determined. The model may be classified as a form of internal coincidence according to the terminology of Pittendrigh (1972), since it is based on the interaction of two internal systems rather than on the coincidence of light with a particular light-sensitive phase of the timing mechanism, as in the case of external coincidence (cf. Saunders, 1978). Good agreement is attained between diapause incidences predicted by this model and incidences observed in spider mites, both in the diapause induction response curve and in asymmetrical skeleton photoperiods.The authors are grateful to Dr. S.D. Beck for the program printout of the Dual System Theory put at their disposal. It is also a pleasure to thank Miss C. van Ruth and Mr. G. van de Berg for technical assistance, and Mr. H. Bos for drawing the figures. The investigations were supported by a grant to the first author from the Netherlands Organization for the Advancement of Pure Research (ZWO).