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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) ! bd = (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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 Spring '13

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