# Lecture_6_wo_answers - Midterm in one week on Tuesday Will...

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Unformatted text preview: Midterm in one week on Tuesday Will include the material from today’s lecture, but not 10/14 This weeks section reading will be on the exam Make-ups 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: λ = e r Estimate of Population Size = # captured and marked day 1 1 Fraction marked (from 2 nd date) × N N t t λ = d b- + = 1 λ r = b- d rN dt dN = rt t e N N = r = λ ln + + = × dy cx by ax y x d c b a t t N N λ = + 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 long-term 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 density-dependence 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 λ = + 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 λ = + 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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Lecture_6_wo_answers - Midterm in one week on Tuesday Will...

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