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Days 13-14 Applied population dyn

Days 13-14 Applied population dyn - Just an outline NOT all...

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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 0 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 0 0 2 λ λλ N N N = = change in population size from year 0 to year t: N t = N 0 λ t = geometric growth example: N 0 = 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
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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 0 = also can calculate r directly from pop growth data take log of both sides: t N N r so rt N N t t 0 0 ln ln ln ln - = + = and comparison: Growth constant pop size Exponential (r) Geometric ( λ ) Decreasing < 0 0 – 1 Constant 0 1 Increasing > 0 > 1 0 100 200 300 400 500 600 700 0 1 2 3 4 5 t N doubling time - a commonly reported measure that comes from this: N t = 2N 0 (= 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 =
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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 boom-bust growth (many inverts, fish) d) current human population growth 3
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Just an outline – NOT all you need to know example: Ring-necked 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 . 0 ) 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? (2) populations tend to fluctuate, rather than remain stable – why? - changes in climate, food availability - variability in death and reproduction - affected by longevity – longer lived spp fluctuate less - affected by repro output – less output, less fluctuation - pop dyn of predators, prey, diseases 4
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Just an outline – NOT all you need to know Alernative growth model: density-dependent population regulation Logistic population growth – caused by negative feedback Limits to growth exist; related to population size - = K N rN dt dN 1 =
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