. Bulletin. Science; Natural history; Natural history. 10 SOUTHERN CALIFORNIA ACADEMY OF SCIENCES 140 120 100 (xio'). 100 TIME (years) Fig. 4. Monte Carlo simulations of monarch aggregation population size. Number of individuals (N) in an aggregation verses time wth multiple mating (•) and without multiple mating (o) are presented. Life expectancies of overwintering monarchs are based on Figure 3. First appearance of milkweed each year (u = 140 cr = 10) and summer population fitness as it relates to population growth rate {o^'-. tim = 1. o-^, = ) were variables, normally distributed and ind


. Bulletin. Science; Natural history; Natural history. 10 SOUTHERN CALIFORNIA ACADEMY OF SCIENCES 140 120 100 (xio'). 100 TIME (years) Fig. 4. Monte Carlo simulations of monarch aggregation population size. Number of individuals (N) in an aggregation verses time wth multiple mating (•) and without multiple mating (o) are presented. Life expectancies of overwintering monarchs are based on Figure 3. First appearance of milkweed each year (u = 140 cr = 10) and summer population fitness as it relates to population growth rate {o^'-. tim = 1. o-^, = ) were variables, normally distributed and independent. Summer population growih was based on the Pearl-Verhulst logistic model (Pielou 1977) with carrying capacity 100,000,000 and 5 generations per summer. The probability' of last summer generation butterflies reaching the overwinter aggregation is Without multiple mating monarch populations decline to the point where extinction is likelv. by selection in the female population. Under conditions where food is abundant for nectivores, energ\' transfer from males to females is not an important factor for female sundval (Svard and Wiklund 1988); correspondingly, monarchs need not aggregate under these conditions (, Hawaii: Etchegaray and Nishida 1975; Australia: Smithers 1977). Studies based on Australian monarch butterflies show that females move from milkweed patch to milkw-eed patch after dispersal from overwinter aggregations, rather than remaining at a single patch (Zalucki and Kitching 1982, 1984). This behavior leads to discover}' of oviposition sites by a female as a linear function of time; thus oviposition rate is a constant. Expected total eggs oviposited by an ovenAintering female throughout its life is then predictable, based upon milkweed first appearance. When variable time of spring milkweed first appearance is also considered, Monte Carlo simulations using this model of population dynamics have demonstrated fWells et al. 1992) that, without


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