BSC 2011 Lecture Notes - Lecture 28: Carrying Capacity, Doubling Time, Exponential Growth
8 Dec 2016
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The exponential model describes population growth in an idealized environment: abundant resources, no competition. Exponential growth results in a j-shaped curve. If r remains constant, a populatio(cid:374)"s dou(cid:271)li(cid:374)g ti(cid:373)e will also re(cid:373)ai(cid:374) (cid:272)o(cid:374)sta(cid:374)t: tanzania, kenya and somalia have around a 3% growth rate, so they double every 23 years. Exponential growth cannot go on forever: there are limitations to population. A more realistic population model limits growth by incorporating a carry capacity: carrying capacity (k)is the maximum population size that the environment can support. The logistic model incorporates exponential growth and the carrying capacity term: dn/dt = rmaxn[k n)/k, when n = 0,then (k-n)/k = 1, when n = k, then (k-n)/k = 0. As populatio(cid:374)s grow, the a(cid:272)tual (cid:862)r(cid:863) starts to de(cid:272)rease fro(cid:373) rmax. The per capita growth rate for a population at a given point as it grows (called r) is equal to: r = rmax =[(k-n)/k] Logistic growth produces a sigmoid s-shaped curve.
