Stage-specificity and the synchronisation of life-cycles to periodic environmental variations

Previous work has shown that life-histories consisting of a contiguous series of stages all with density independent development rates exhibiting the same dependence on time cannot synchronise to a periodic environmental variation. This work also examined models representing both dormancy and quiescence at specific points in the life cycle and showed that both could produce strong synchronising effects. In this paper we examine a very general strategic model of an organism with a two-stage life-cycle each stage having a density independent development rate with a characteristic (periodic) time-dependence. We develop a compact representation of this model in terms of a circle map composed from two simple rotations and the ldquointerphase maprdquo representing the relationship between the physiological times for the two life-history stages. We derive a series of analytic results relating the behaviour of systems whose interphase maps are interrelated and give analytic conditions for a broad class of two-stage circle maps to have a fixed point (that is for the systems they describe to reach the critical life-history stage at the same point in each environmental cycle). Finally we report the results of a numerical investigation of the relationship between the biological characteristics of the development functions and the fine-scale details of the locking behaviour of the systems they define