Colonies Reaching Completion

Two related quantities that describe a colony that completes its growth are the time (number of generations) taken to reach completion and the colony size at completion. One might expect that a colony that grows for many generations before its growth finally ceases would be much larger than a colony that ceases growth after only a few generations. We examine first the distribution of the number of generations to completion since the derivation of the distribution follows directly from the finite-time recursion of the modified model in Section 3.2. Colony size at completion is covered later.