Ecological Research (1992) 7, 55-62 Optimal seasonal timing of univoltine and bivoltine insects YOH IWASA, ATSUSHIYAMAUCHI AND SHINJI NOZOE Department of Biology, Faculty of Science, Kyushu University, Fukuoka, 812Japan This study examines the optimal seasonal timing of the life cycle for univoltine and bivoltine insects, assuming that resource availability has a peak in the middle of a year and is symmetric around it. Results show that if the growth rate increases in proportion to the bodyweight, bivoltine life cannot be optimal. If the growth rate is a power function of the bodyweight with a power smaller than unity, a symmetric bivoltine solution can be the optimal provided that the resource availability has a plateau in the middle of the season. If the resource availability has a sharp peak, the optimal pattern is an asymmetric bivoltine solution in which the larval periods of two generations differ in length. The bivoltine life cycle is more likely to be superior to the univoltine one if: growth is fast, suitable growing season is long, biomass loss during nonlarval stages is small, and egg size is small. Key words: asymmetric bivoltinism; bivoltine insect; optimal phenology; seasonal environment; univoltine insect. INTRODUCTION Insects in temperate regions have diverse seasonal adaptation (Kidokoro & Masaki 1978; Masaki 1980; Furunishi & Masaki 1982; Tauber et al. 1986; Sota 1987). For example, the variation in the number of generations in a year is often observed among closely related species and even within the same species. Sota (1988) examined the condition for the evolution of univoltine and bivoltine life history by density-dependent natural selection. Even if the number of generations per year is the same, the timing of life history events may vary. For example, eight univoltine oak-feeding butter- flies, studied by Shapiro (1975), differ in the seasonal timing of adult or egg periods, and also in the overwintering stage. However, larval feeding period of all the species were constrained to match with environmental food availability. A previous paper (Iwasa 1991) has discussed the stable timing, in terms of evolution, of feeding stage of univoltine insects when resource avail- ability changes seasonally. If resource competition Accepted 1 November 1991. among feeding larvae reduces their growth rate, the evolutionary stable population includes a mixture of individuals differing in the seasonal timing. In addition, the degree of asynchrony is larger for pupation date than for hatching date. In this paper, the optimal phenotype was analysed with respect to the timing of hatching and pupation within a year and to the number of generations per year. The pattern of life history to evolve is the one that maximizes the fitness by choosing hatching and pupation dates for a given resource availability curve that changes seasonally. Underlying this argument is the assumption that the population size is regulated through the density-dependent processes in nonlarval periods, such as overwintering mortality, and that these processes are independent of the timing of larval periods. Thus the phenotype realizing the greatest success during the summer months would be the one realized at the evolutionary endpoint. Since the frequency dependence of natural selection is neglected, there is a single phenotype that is to evolve in this modelling setup, unlike in Iwasa (1991; further discussion on this point will be given later).