Lectures6-7_4pp

717 base of natural log or ln r intrinsic rate of

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Unformatted text preview: e = 2.717 (base of natural log, or ln)! r = intrinsic rate of increase! t = time! 400 200 0 ! r r r r r ! ! -200 = = = = = !! !! 0.1 0.2 0.3 -0.3 0 ! !! ! ! ! ! ! ! ! ! ! ! ! 0 1 2 3 4 5 6 ! 7 time 8 9 10 11 Small changes in r make a big difference! ! ! !! !! 800 700 600 500 400 300 200 100 0 -100 ! ! dN/dt = rN Intuitively, a population increases in size when its birth rate exceeds its death rate: b > d or when r is positive;! r = 0 when b = d! r > 0 when b > d! r < 0 when b < d! Population Size lets call this r, the intrinsic growth rate of the population! Nt = N0 ert! ! This is a continuous time expression: works if organisms reproduce continuously (overlapping generations) ! b-d = (birth rate - death rate) = the instantaneous rate of increase! dN/dt = rN (as time --> 0) !! N0 =50, r = 0.1 N0 = 5 r = 0.5 ! !! ! !! ! ! ! ! ! ! ! ! ! ! ! 0 1 2 3 4 5 6 ! 7 time 8 9 10 11 The influence of N0 vs. r on population growth! Doubling time: time required for population size to double! Nt = N0 2 ert! Nt = N0 ert! Under what conditions is density independent population growth possible?! N0 = N0 ert! 2 = ert! Ln (2) =rt! Tdouble = ln(2) / r! (increasing r decreases doubling time)! r = 0.001: Tdouble = 693 time units! r = 0.01: Tdouble = 69.3 time units! r = 0.05: Tdouble = 13.8 time units! Can populations increase forever w ithout limit?! Limits to population size! Darwin s Elephant calculation ! (similar to the prelab 3 calculations):! 1.  Elephants live about 90 years ! 2.  Elephants become sexually mature and can reproduce at about age 30! 3.  Thus, an elephant has a reproductive lifetime of about 60 years! 4.  A pair of elephants produce about 6 offspring in their lifetimes.! 5.  An elephant has...
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