. Bulletin. Science; Natural history; Natural history. MONARCH BUTTERFLY 13. TIME (hours) Fig. 5. Effect of functional day length and population density on mating frequency, when frequency of males equals frequency of females in the population (h = 0). Frequency of unmated individuals (qt = Pt) versus time during any specified day is depicted (unmated male frequency equals unmated female frequency). Results are given for values of aN,, from 10' to 10"* (curves 1 to -4). Percent unmated individuals asymptotically approaches zero. Higher densities accelerate decline in frequency of un- mate
. Bulletin. Science; Natural history; Natural history. MONARCH BUTTERFLY 13. TIME (hours) Fig. 5. Effect of functional day length and population density on mating frequency, when frequency of males equals frequency of females in the population (h = 0). Frequency of unmated individuals (qt = Pt) versus time during any specified day is depicted (unmated male frequency equals unmated female frequency). Results are given for values of aN,, from 10' to 10"* (curves 1 to -4). Percent unmated individuals asymptotically approaches zero. Higher densities accelerate decline in frequency of un- mated individuals (from Wells et al. 1990). on cumulative mating frequencies observed by Zalucki and Sasuki 1987). Statis- tically, less than (using 11 matings), or (using 12 matings), of the males would exceed those limits if it were energetically possible. Thus, male mating behavior in overwinter aggregations does not appear to be significantly influenced by energy limitations. The model predicts that, at least in overwintering butterflies, egg fertilization dependency on mating order (, first, last, each) would not select for altered male behavior. Prior to the spring mating frenzy, environmental conditions are generally too cool for in-flight activity and mating, although oligopause is not complete. Occasional warm winter days would be too short to substantially in- crease the rate of gamete maturation, and days would still have a short photo- period; both would inhibit mating. After aggregation dispersal, the probability of mating is very low because but- terfly density is low and mating success is a second order kinetic function. This is true even if females are still receptive. Finally, during the spring mating frenzy males energetically are capable of mating every day that they can catch a female. Thus, by mating every day a male would maximize its fecundity during the spring mating period (Wells et al. 1990). In fact, some data now exist which suggest tha
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