Lecture 3

Lecture 3 - Dynamics of Metapopulation Models H 1.0 0.8 0.6...

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Dynamics of Metapopulation Models 1.0 0.8 0.6 0.4 0.2 0.0 There is an equilibrium fraction of occupied patches The fraction of occupied patches is less than one H
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Population Density Habitat Suitability x All go into A A and B are chosen equally y A, B, and C are chosen equally z Prediction: Organisms perform equally well in good and poor habitats in the field. Organisms choose inferior habitats because their fitness is the same as in superior habitats after accounting for competition. H Ideal Free Distribution
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Population size now is 10 plants Each plant produces 6 new plants in a year, but does this continuously throughout the year No plants die How many plants will you have in one year? You know:
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Population size now is 10 plants Each plant produces 6 new plants in a year, but does this continuously throughout the year No plants die You know: 60 new plants over the year, plus the ten that began year = 70
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4000 plants!
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Lecture Three Outline- “Geometric and Exponential Population Growth” I. Discrete time models of population growth A. Annual plant populations B. Longer lived organisms C. Assumptions II. Continuous time models of population growth A. Instantaneous birth and death rates B. Differential equation models III. Measuring population size H
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Fall Winter Spring Summer Life Cycle of California Annual Plants
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Single seed Year 1, 1 individual germinates Produces and disperses seeds Parent dies
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Single seed Year 1, 1 individual Year 2, 4 individuals Year 3, 16 individuals
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Model of Geometric Growth number next year = the multiplicative × number this year rate of increase H
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Geometric Growth number next year = the multiplicative × number this year rate of increase N is the number or density (number / area) of individuals in the population t is time Difference Equation (phrased with respect to t , t +1) = multiplicative growth rate of the population over one year H
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H
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Model of Geometric Growth Lambda is the ratio of population sizes between consecutive years (regardless of the population size)
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H
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H
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If λ > 1, the population grows if λ < 1, the population shrinks If λ = 1, the population stays the same λ ranges from 0 to infinity H
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We can directly calculate the population size at any time t : the initial population size H
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H
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Die in winter and young are produced in the spring
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Lecture 3 - Dynamics of Metapopulation Models H 1.0 0.8 0.6...

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