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Unformatted text preview: Midterm in one week on Tuesday Will include the material from todays lecture, but not 10/14 This weeks section reading will be on the exam Makeups will only be granted for those with medical or family emergencies. Review session will be announced on Thursday Sample questions on the website. DSP students NEED a proctor. Please let DSP know today so they can provide one. No calculators H Equations you should understand and memorize: = e r Estimate of Population Size = # captured and marked day 1 1 Fraction marked (from 2 nd date) N N t t = d b + = 1 r = b d rN dt dN = rt t e N N = r = ln + + = dy cx by ax y x d c b a t t N N = + 1 mp p cp dt dp = ) 1 ( H c m p = 1 * mp d p cp dt dp = ) 1 ( d c m p = 1 * What is the size of the cod population that should be maintained to maximize the longterm yield of fishery? Lecture 6 Outline Density Dependence I. Density dependence in population growth II. Population regulation III. r versus K selection IV. Instability in discrete time models with densitydependence H Causes of variability (stochasticity) in population growth rates Environmental Stochasticity variability in demographic rates driven by variability in environmental conditions. (i.e. the finches example, rainfall, temperature, etc.) Demographic Stochasticity variability in vital rates caused by the finite nature of births and deaths H 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 Time Observed Death Rate 10 100 1000 Demographic Stochasticity H Demographic stochasticity only adds variation in vital rates in small populations What does adding variability to a growth rate do to the long term average growth rate? H What does adding variability to a growth rate do to the long term average growth rate? 3 2 3 4 3 2 3 4 3 4 3 2 Yearly growth rates (lambda): Constant Variable 3 2 3 4 3 2 3 4 3 4 H What does adding variability to a growth rate do to the long term average growth rate? 3 2 3 4 3 2 3 4 3 4 3 2 Yearly growth rates (lambda): Constant Variable 3 2 3 4 3 2 3 4 3 4 100000 200000 300000 400000 500000 600000 1 2 3 4 5 6 7 8 9 10 11 12 13 Years Population Size t t N N = + 1 H Constant Variable What does adding variability to a growth rate reduce the long term average growth rate? 3 2 3 4 3 2 3 4 3 4 3 2 Yearly growth rates (lambda): Constant Variable 3 2 3 4 3 2 3 4 3 4 Growth is a multiplicative process The product of a series of numbers depends not just on their average value, but also their variability. Adding variability reduces the product. t t N N = + 1 4 3 3 2 Average of sides 3 3 3 Area 5 8 9 1 5 The less variability in the sides, the greater their product, even if they have the same mean Another multiplicative process: H What does adding variability to a growth rate do to the long term average growth rate?...
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 Spring '08
 NISBET

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