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The three types of population model studied in this paper. Models of scramble competition increase to a global maximum and then decrease to 0, while models of contest competition are either increasing and bounded or strictly increasing and unbounded. We denote the latter ‘unbounded contest’. Also shown is the line at+1=at. Note that any biologically realistic unbounded contest model will eventually stay below this line, as it would otherwise be capable of unchecked population growth.
