Geometric and Logistic Growth
Geometric and Logistic Growth WFS 446
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This 2 page Class Notes was uploaded by Dani on Friday January 30, 2015. The Class Notes belongs to WFS 446 at Pennsylvania State University taught by David Miller in Spring2015. Since its upload, it has received 63 views. For similar materials see Population Dynamics in Wildlife Studies at Pennsylvania State University.
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Date Created: 01/30/15
Average rate of increase 0 LnNTNo1 r Ex NT 500 N0 100 T 34 o r 0473 O Tdouble ExponentialGeometric Equations 0 Other applications I Banks and finance interest calculated using exponential equation I Physics halflife of a radioactive isotope Plotting abundance O Exponential curves on a natural scale I Linear on a log scale 0 Stable flat line 0 Decline negative slope 0 Increase positive slope I LnNT lnNo rT 0 r constant 0 lnNo intercept Plotting GeometricExponential Growth 0 O O O Abundance versus time Lnabundance versus time Change in abundance versus abundance Per capita growth rate versus abundance BIDE and Geometric growth 0 O O 0 Delta N BD For geometric or exponential growth B and D are proportional to N Bt bNt and Dt dNt I b and d are constants per capita birth and death rates Nt1 N bNt dNt 9 1bdNt I R bd 39 Nt NtR Nt1 I A 1bd 1R I deltaN NtR Nt1 If birth rate greater than death rate increasing population Negative Density Dependence 12615 12815 0 Population growth rate decreases as abundance increases 0 Carrying capacity abundance where we expect population growth to be stable 0 Denoted using K o K is I Abundance where birth rate equals death rate I Abundance where A1 or r0 o Equilibrium value population abundance will tend to move towards the carrying capacity I If NgtK the population will decrease I If NltK the population will increase 0 Logistic equations continuous o dNdt roN 1 NK o NT K1IltNo No e T 0 When does population size increase fastest 0 Max population change when NK2
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