Biol 201 - Notes - 3.27.2009

# Biol 201 - Notes - 3.27.2009 - Population Growth Geometric...

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Population Growth 3.27.2009 Geometric Growth - Non-overlapping generations - Each individual only lives for a single time period (only one reproductive opportunity) - N1 = N0 + B – D - N1 = N0 + bN0 – dN0 - N1 = bN0 = RoN0 = N0( λ ) in the case of non-overlapping generations, since d = 1 - N2 = N1 = (N0 ) λ λ λ - Nt = N0 λ t - This rate of increase cannot go on indefinitely; resources will become more scarce Exponential Growth - Continuous growth (overlapping generations; more than one reproductive opportunity) - N1 = N0 + bN0 – dN0 - N 1 – N 0 = N = bN Δ 0 – dN 0 = (b – d)N 0 b – d = r - N = rN Δ 0 - dN/dt = r max N differential equation - (1/N)(dN/dt) = r max intrinsic - N t = N 0 e rmax t rmax = per capita rate of increase, intrinsic rate of increase - Higher rmax makes steeper acceleration of growth - Examples of exponential growth: o Whooping cranes between 1940 and 2005 Still low, but has gone up a lot in 60 years - Fictional example: o Brown rats originally from china, invasive species now found everywhere but Antarctica

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Biol 201 - Notes - 3.27.2009 - Population Growth Geometric...

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