ECOL 3505H Lecture Notes - Lecture 4: Exponential Growth, Natural Disaster, Growth Factor
24 Aug 2016
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Exponential growth dn/dt = rn n(t) = n(0)ert. If growth factor ( ) or growth rate (r) is constant, exponential growth results. Discrete time population dynamics can be recast in continuous time (i. e. ln = r) How is the per capita growth rate influenced by n? (1/n)dn/dt= r. *per capita growth rate is constant, independent of population size. Amount of resources, carrying capacity, birth and death rate, immigration and emigration. Bottom up energy and biomass available from lower trophic levels dn/dt = rn r= births + immigrations deaths emigrations = (b+i) (d+e) Density dependent factor (disease and famine) dn/dt = rn -rn2/k. Population growth rate must decrease as n grows. N vs per capita growth rate x intersect = k. Multiple per capita growth rate with population size to achieve overall population growth rate (upside: to show that maximum growth rate is at k/2. Not really we"ve passed carrying capacities predicted by researchers.
