lecture 7 2009

# lecture 7 2009 - Populations Dynamics II topi pygmy rabbit...

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Populations: Dynamics II topi

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N t+x = N t ( λ ) x How large might our rabbit population be next year under ideal conditions? Nt = 31 λ max = 2.0 pygmy rabbit N t+1 = 31 ( 2 ) 1 = 62
N t+x = N t ( λ ) x How about 5 years from now? Nt = 31 λ max = 2.0 pygmy rabbit N t+ 5 = 31 ( 2 ) 5 = 31 x 32 = 992

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Nt = 31 λ max = 2.0 Population Year 1 0 2 4 3 5 900 500 700 300 100 Exponential population growth (growth without limit)
λ = rate of pop. growth over a fixed interval… …but this isn’t always realistic because pop. growth does not always occur in discrete, annual events. Births and death can be continuous over time. r is a measure of pop. growth that adjusts for continuous growth r = ln λ ..therefore when λ =1, r = 0 λ >1, r > 0 λ <1, r < 0 r = instantaneous rate of growth = individuals produced per individual per small unit of time r max = maximum possible rate of instantaneous growth

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r > 0 population is increasing r = 0 population is stable r < 0 population is decreasing r max maximum possible population growth rate Review r = ln λ ..therefore when λ =1, r = 0 λ >1, r > 0 λ <1, r < 0 r max = maximum possible rate of instantaneous growth
r is the change ( Δ ) in per capita population ( N ) over a tiny change in time ( Δ t ) = Δ N/ Δ t = instantaneous rate of pop. change (growth). Instead of

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lecture 7 2009 - Populations Dynamics II topi pygmy rabbit...

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