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Charnov and Schaefer proposed a simple model to examine whether

# Charnov and Schaefer proposed a simple model to examine whether

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Charnov and Schaefer proposed a simple model to examine whether annuals (species living one year) or perennials (species living more than one year) should be favored. P = number of progeny that survive to reproduce (including the parent in the perennial case), B = number of seeds produced, S 1 = survival during first year of growth, S 2 = survival during subsequent years (subscript a = annual, p = perennial). for the annual: Pa = B a S 1 ; for the perennial: Pp = B p S 1 +S 2 . Now we wont to n=know when is P a > P p (i.e., when is the reproductive output of the annual greater than that of the perennial?) Answer = when B a S 1 > B p S 1 +S 2 . Rearrange to find that the annual habit will be favored when B a - B p > S 2 /S 1 In english this means that for the annual habit to be favored it has to have a reproductive output greater than the perennial by the amount S 2 /S 1 (i.e., the ratio of the "old" survivorship to the "young" survivorship. The result fits well with observations about where annual and perennial plants are found: many desert plants are annuals (low probability of survivorship), perennials common in tropics).
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