Ch. 14 Population Growth and Regulation • • • • • • • • Exponential Population Growth - Fig 14.5 • Exponential Outline Expectations! Doubling time Regulation Density dependent Applications - yield Density independence Human populations Doubling Time Doubling Time - Money • • • • • • • • t2 = [loge2]/r Rule of Thumb for money Doubling time = 70/annual interest rate $1,000 invested at 10% interest • Note r = logeλ • t2 = [loge2]/r • • • • • • • • • 7 years - $2,000 14 years - $4,000 21 years - $8,000 28 years - $16,000 35 years - $32,000 42 years - $64,000 49 years - $128,000 56 years - $256,000 63 years - $512,000 Population Growth Population Growth • Introduce organisms to new habitats • Starlings Fig. 13.17 • Introduce organisms to new habitats • Gypsy Moth t2 = [loge2]/[logeλ] Field vole example - text λ=24 t2 = 0.69/3.18 t2 = 0.22 years (79 days) Smith & Smith 2006 1 Population Growth Population Growth • Introduce organisms to new habitats • Scotts Pine • Introduce organisms to new habitats • Whooping Cranes Molles 2008 Smith & Smith 2006 Regulation Regulation • Introduce organisms to new habitats • Reindeer • Introduce organisms to new habitats • Yeast Smith & Smith 2006 Molles 2008 Regulation • Introduce organisms to new habitats • Paramecium and Barnacles Molles 2008 Molles 2008 2 250 Logistic Growth Curve - Fig. 14.17 • K 200 150 N 100 Logistic Growth 50 0 0 5 10 15 20 Time Exponential Logistic Growth Curve N dN/dt dN/dt • dN/dt = rN(1-N/K) K N • N(t) = Logistic K/(1+e-r(t-i)) Time Time Logistic Growth Curve • N(t) = K/(1+e-r(t-i)) • dN/dt = rN(1-N/K) K • Adjust r N Time 3 • b and d Rate (b or d) Density Dependent Regulation • How can r be adjusted? Rate (b or d) Density Dependent Regulation d b N or ρ Rate (b or d) Density Dependent Predators? N or ρ d Rate d b b K K Density Dependent b Density Dependent N or ρ Food? d N or ρ Density Dependent Regulation - Examples • Insects Fig. 14.19 Rate d b K N or ρ 4 Density Dependent Regulation - Examples Density Dependent Regulation - Examples • Birds Fig. 14.20 • Mammals Fig. 14.21, 22 Density Dependent Regulation - Examples Density Dependent Regulation - Examples • Mammals Fig. 14.21, 22 • Mammals Smith & Smith 2006 Density Dependent Regulation - Examples Density Dependent Regulation - Examples • Performance - tadpoles • Death rate - functional predator response Smith & Smith 2006 Molles 2008 5 Density Dependent Regulation - Examples Density Dependent Regulation - Examples • Death rate - functional predator response • Birds Fig. 14.20 Smith & Smith 2006 Density Dependent Regulation - Examples Density Dependent Regulation - Examples • Plants Fig. 14.23 • Plants Smith & Smith 2006 Density Dependent Regulation - Examples Density Dependent Regulation - Examples • Plants Fig 14.24 • Plants - Self thinning Fig 14.25 6 250 Density Dependent Regulation - Examples • K 200 150 N 100 Logistic Growth 50 0 0 5 10 15 20 Time Activity Space - Figure 9.4 K N 0 5 10 15 20 Time Density Independent Regulation Density Independent Effect • Environmental factors - Fig. 14.13 • Environmental factors • Gibbs and Grant 1989 Smith & Smith 2006 7 Density Independent Effects Density Independent Effects • Environmental factors • Deer • Is this regulation? Human Populations Human Populations • Pearl and Reed - Fig14.19 • Fig 14.1 Rate (b or d) Smith & Smith 2006 d b N or ρ Tuesday • Chapter 15 8