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, S1= survival during first year of growth, S2= survival during subsequent years (subscript a = annual, p = perennial). for the annual: Pa = BaS1; for the perennial: Pp = BpS1+S2. Now we wont to n=know when is Pa> Pp(i.e., when is the reproductive output of the annual greater than that of the perennial?) Answer = when BaS1> BpS1+S2. Rearrange to find that the annual habit will be favored when Ba- Bp> S2/S1 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 S2/S1(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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