Eco%204_Pop%20Growth%20and%20Regulation

Eco%204_Pop%20Growth%20and%20Regulation - Population Growth...

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Unformatted text preview: Population Growth Ecology, Lecture 4: Population Growth & Regulation Basic terms: ∆N = (B + I) – (D + E) Population growth models and exponential growth ∆N = (B – D) Density-dependent effects and logistic growth ∆N/∆t = (B – D) Allee effects Predator-prey dynamics Births Deaths Population Size Emigration Immigration 1 Life Table 2 Reproductive Table 3 4 Population Growth Population Growth Basic terms: Per capita rate of increase (r) = b – d If r = 0, zero population growth (ZPG) If r > 0, the population is growing If r < 0 the population is declining Basic terms: Per capita birth rate (b) Per capita death rate (d) B=bN D=dN ∆N/∆t = bN – dN ∆N/∆t = bN – dN ∆N/∆t = N (b–d) ∆N/∆t = rN 5 6 Exponential Growth Exponential Growth From fixed interval to instantaneous Population size (N) ∆N/∆t = r N dN/dt = rinst N dN/dt = rmax N dN/dt = r N 2,000 Population size (N) 1,500 dN = rN dt 1,000 500 Number of generations 0 0 5 10 Number of generations 15 7 8 Human population growth 6 5 4 3 2 The Plague 1 # individuals (billions) 7 0 -8000 -4000 -3000 -2000 -1000 0 1000 2000 Year 9 10 Elephants in Kruger Park, South Africa 2,000 dN 1.0N = dt Population size (N) Elephant population (N) 8,000 6,000 4,000 2,000 0 1900 Effect of r on growth 1,500 dN 0.5N = dt 1,000 500 0 1920 1940 1960 0 5 10 15 Number of generations Year 11 12 Regulation (density dependent) Effect of competition on number of offspring Effect of competition on seed production Song sparrow (Melospiza melodia) Plaintain (Plantago major) % of juveniles with lambs 13 100 14 Density dependent forces Soay sheep of Hirta Island 80 60 Territoriality Toxicity of waste Parasites 40 Predation 20 0 200 300 400 500 600 Population size (N) 15 16 Logistic Growth Allee Effects Limited resources and carrying capacity (K) K = maximum population size that an environment can sustain standard (negative) density dependence r=b–d dN/dt = rN dN K–N = rN K dt positive effect Population size (N) K = carrying capacity negative effect Berec et al. 2006 TREE 22(4): 185–191 Number of generations 17 18 2,000 Population size (N) Population size (N) Logistic Growth Model K = carrying capacity dN K–N =r N K dt dN = 1.0N dt 1,500 1,000 dN 1.0 N dt = 500 1,500–N 1,500 0 Number of generations 0 5 10 15 Number of generations 19 20 Logistic growth in laboratory ecosystems: Overshooting (time lag) in Daphnia Number of Daphnia / 50 mL # of Paramecium / mL Beetles, crustaceans, yeast, paramecia, prokaryotes... 1,000 800 600 400 200 0 0 5 10 15 180 150 120 90 60 30 0 0 20 40 60 80 100 120 140 160 Time (days) Time (days) 21 22 ...
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This note was uploaded on 09/16/2010 for the course BIO 1B taught by Professor Carlson,mischel,power during the Fall '07 term at University of California, Berkeley.

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