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Unformatted text preview: Just an outline – NOT all you need to know Population growth: the basics: population size changes over time: N t+1 = N t + births  deaths + immigrants  emigrants to start with, we will be dealing with closed populations (no migration) → per capita pop growth rate = # individuals in 1 year, divided by # in previous year: 1 = t t N N λ → change in population size from year 0 to year 1: λ 1 N N = → change in population size from year 1 to year 2: λ 1 2 N N = → change in population size from year 0 to year 2: 2 2 λ λλ N N N = = → change in population size from year 0 to year t: N t = N λ t = geometric growth example: N = 100, N 1 = 160 → λ = 1.6 → keep constant λ for t = 15 → N 15 = 100 * 1.6 15 = 115,000 can express as continuous growth rate rather than discrete (by generation) o easier to compare growth rates between populations 1 Just an outline – NOT all you need to know substitute e r for λ t r = intrinsic rate of increase; b – d exponential growth rt t e N N = → also can calculate r directly from pop growth data → take log of both sides: t N N r so rt N N t t ln ln ln ln = + = and comparison: Growth constant ∆ pop size Exponential (r) Geometric ( λ ) Decreasing < 0 0 – 1 Constant 1 Increasing > 0 > 1 100 200 300 400 500 600 700 1 2 3 4 5 t N doubling time  a commonly reported measure that comes from this: • N t = 2N (= doubled size) 2 Plotting: λ =e rt geometric is discrete: λ = 1.6 exponential is continuous: r = 0.47 (Draw really close together) rN dt dN = Just an outline – NOT all you need to know • from the previous equation, then 2 = e rt (or 2 = λ t ) take log of both sides and divide by r => double t r = ) 2 ln( r Population doubles in: .01 (= 1% growth rate) 69 years .02 (2%) 35 .03 (3%) 23 .04 (4%) 17 exponential (geometric) growth rates observed under certain conditions a) early in a species invasion of a new area b) population growth after a population crash c) species with boombust growth (many inverts, fish) d) current human population growth 3 Just an outline – NOT all you need to know example: Ringnecked pheasants 2 males, 6 females introduced to Protection Island, Washington (1937) 5 yrs later – 1,325 λ = 2.8 example: European rabbits 12 pairs introduced to ranch in Australia (1859) 6 yrs later – 20,000 killed in 1 year; pop estimated > 60,000 λ = 4.7 max λ s, ideal settings, in lab: field vole = 24 o doubling time = days yrs 79 22 . ) ln( ) 2 ln( = = λ flour beetles = 10 billion (10 10 ) Daphnia (water flea) = 10 30 if r > 0, and time goes on, population size rises to infinity – according to this model (1) obviously cannot go on indefinitely – why not?...
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 Spring '08
 REED
 Demography, Conservation Biology, Population Ecology, World population, population size

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