The derivation of this equation is not shown here for brevity. If we recursively write out this equation we obtain:

Then is simply that is one less recursive function of , i.e.

Then by plugging Eq.17 into Eq.16 we obtain:

which is much more handy for calculating the probability of extinction than the previous form, . This relation is useful if we realize that the probability of extinction is identical to the probability generation function when * s=0*. This is because , where is the probability that the total number of people of the * n*-th generation is equal to zero. Thus the linkage between the probability of extinction and the probability generation function is:

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