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Lec14_2011BILD30

Lec14_2011BILD30 - Lecture 14 Population growth II I...

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Lecture 14: Population growth II I. Geometric and exponential growth II. Logistic growth III. Density dependence IV. Metapopulations
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Four processes make up population growth: Births & deaths Both depend on current population size Immigration & emigration Movement among populations
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Four processes make up population growth: Births & deaths Both depend on current population size Immigration & emigration Movement among populations
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Models that we will consider in this lecture focus on births and deaths only N / t = (b - d) N b, d = per capita birth and death rates X X
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I. Geometric and exponential growth Populations either grow continuously or in discrete time intervals Human populations continuously grow; births (and deaths) occur throughout the year. Many organisms have discrete breeding seasons in which new individuals are added to the population seasonally.
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Modeling geometric population growth N / t = (b - d) N, t is a discrete time interval λ = N t+1 / N t N t+1 = λ N t N(1) = N(0) λ N(2) = N(1) λ = N(0) λ 2 N(3) = N(2) λ = N(0) λ 3 . . . N(t) = N(0) λ t t = is an arbitrary time
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Fifty California Quail were introduced onto Santa Cruz Island in 1950. One year later, there were 70 quail. Assuming this population grew geometrically, how many quail would you expect that there were in 1960? N(t) = N(0) λ t λ = 70/50 = 1.4 N(0) = 50 t = 10 N(10) = 50 (1.4) 10 N(10) = 50 (28.9) = 1445 quail in 1960
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Assuming this population continued to grow geometrically, how many quail would you expect that there were in 2010? N(t) = N(0) λ t λ = 70/50 = 1.4 N(0) = 50 t = 60 N(60) = 50 (1.4) 60 = 2.92854664 X 10 10
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Modeling exponential population growth N / t = (b - d) N, t is instantaneous (b-d) = instantaneous rate of increase = r dN/dt = rN b = instantaneous birth rate (births / [(individuals)(time)]) d = instantaneous death rate (deaths / [(individuals)(time)]) r has the units (individuals / [(individuals)(time)]) r expresses population change on a per capita basis
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r affects how rapidly population size increases; r is constant - not affected by N Modeling exponential population growth
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