Population Ecology ; 36.6 Pgs Population Growth Rates Objective: I can use mathematical formulas and graphs to describe how populations grow in different scenarios.

Population Ecology Changes in population Changes in population Increases by Increases by Births Births Immigration Immigration Decreases by Decreases by Deaths Deaths Emigration Emigration All 4 affect size… All 4 affect size… Size vs. Density Size vs. Density Dispersion Patterns Dispersion Patterns Clumped, Uniform, Random Clumped, Uniform, Random

Survivorship Value # of survivors = population - # of deaths # of survivors = population - # of deaths s = # of survivors ÷ original population s = # of survivors ÷ original population Life Tables & Survivorship Curves Life Tables & Survivorship Curves Type I Type I Most young survive Most young survive Old die (care for young) Old die (care for young) K-selected organisms  K-selected organisms  Type II Type II In between… In between… Type III Type III Most young die off Most young die off Old live (no care for young) Old live (no care for young) r-selected organisms  r-selected organisms  Evolved in more stable environments Pop. growth is steady and slower Larger bodies, few young (cared for) Evolved in unstable environments Pop. growth is rapid and chaotic Smaller bodies, many young (no care)

Population Growth Variables N = population size B = # of births D = # of deaths dN/dt = change in population in given time (population growth rate): treat as 1 variable Per capita means… by average individual Per capita means… by average individual b = per capita birth rate…so, b = B/N d = per capita death rate…so, d = D/N r = per capita growth rate (individual growth rate) …so, r = b – d …but also r = dN/dt = B - D dNdt N = Does N = B – D…? What if N = 1000, B = 50 and D = 25… ∆N∆N∆t∆t∆N∆N∆t∆t = Your book uses G for dN/dt

Population Growth Formulas dN/dt = B-D b = B/N d = D/N r = b - d r = dN/dt / N (messy)  rN = THINK ABOUT IT… rN = B –D which leads to THINK ABOUT IT… rN = B –D which leads to r = (B – D) / N formulas are interrlated! When r is positive / 0 / negative, then… When r is positive / 0 / negative, then… population increases/constant/decreases r max = maximum per capita growth rate r max = maximum per capita growth rate There are 2 different population growths 1) Exponential Growth 2) Logistic Growth dNdt

Exponential Growth Growing at an increasing rate of growth Growing at an increasing rate of growth When r is max (r max )  r stays constant… When r is max (r max )  r stays constant… Happens under ideal conditions Happens under ideal conditions Results in a J-shaped curve Results in a J-shaped curve dN/dt increases dN/dt increases each generation dN/dt = 100 dN/dt = 200 dN/dt = 400 dN/dt = 1600 r r dN/dt dN/dt = 3200

Logistic Growth Growth with a maximum limit Growth with a maximum limit Called carrying capacity (K) Called carrying capacity (K) Limiting factors prevent exponential grow Limiting factors prevent exponential grow Results in an S-shaped curve Results in an S-shaped curve dN/dt increases, but levels off, then decreases dN/dt increases, but levels off, then decreases S-shape curve dN/dt = 100 dN/dt = 500 dN/dt = 100 dN/dt = “0” dN/dt = 500

Exponential Growth Unlimited Resources or Limited Resources? Unlimited Resources or Limited Resources? Expect the population to… Expect the population to… Go up and higher (never down or levels off) Go up and higher (never down or levels off) Expect the change in population (dN/dt) to… Expect the change in population (dN/dt) to… Increase with each generation Increase with each generation Unlimited Resources or Limited Resources? Unlimited Resources or Limited Resources? Expect the population to… Expect the population to… – Go up to a carrying capacity and level off… Expect the change in population (dN/dt) to… Expect the change in population (dN/dt) to… – Increase at beginning (as small pop gets bigger), – then level off to a linear growth rate (before K), – then decrease down to 0 (as get close to K) Logistic Growth

Comparison of Formulas Have a starting population of 10 organisms r = 2 and K (for logistic) = 100 Exponential Growth Logistic Growth Formula 1 st Generation 10dN/dt = 2 * 10 = 20 10dN/dt = 18 2 nd Generation 30dN/dt = 2 * 30 = 60 28dN/dt = rd Generation 90dN/dt = 2 * 90 = dN/dt = th Generation 270dN/dt = 2 * 270 = dN/dt = th Generation 810dN/dt = dN/dt = th Gen

Population Dynamics Interactions of different population affecting each other’s growth (bust & boom) Interactions of different population affecting each other’s growth (bust & boom)