Nonoverlapping generations Geometric Growth

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SUMMARY
Nonoverlapping generations (Geometric
Growth) Nt1 R0Nt pop size after one
generation average number of offspring produced
per lifetime x pop size at present NtN0?t numb
er at some time t number at some initial time 0
x average number of offspring left by an
individual during one time interval, to the power
of the number of time intervals. geometric rate
of increase (?) ?Nt1 /Nt
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SUMMARY Generation Time T(? xlxmx)/R0
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Overlapping Generations r (per capita rate of
increase) rather than ? (geometric rate of
increase).   r (per capita rate of increase)
the change in population size per individual per
unit time.   r is equivelent to b-d, so when
deaths exceed births, r is negative and the
population declines. rlt0 pop decreases, rgt0
pop increases.  
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Overlapping Generations We can calculate r if we
know Ro and generation time T (average interval
between birth of mothers and birth of
daughters)   r (ln Ro) / T, so r is derived
from the life table.
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Overlapping Generations r (ln Ro) / T For
turtle example r(ln 0.601) / 10.6
-.5092/10.6 -0.05   Where ln is the natural
log.
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r per capita rate of increase - the actual or
realized change in population size per individual
per unit time. rmax intrinsic rate of increase
maximum rate of increase in the absence of
limiting factors.
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ASSUMPTIONS OF EXPONENTIAL GROWTH EQ. (dN/dt
rmaxN) No immigration or emigration Constant
birth and death rates, thus resources are not
limiting No genetic structure (all ind have
same birth and death rates) No age or size
structure (all ind have same birth and death
rates). Continuous growth with not time lags.
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Summary
For Geometric Populations (nonoverlapping
generations) Population size after one
generation Nt1 R0Nt Population size as some
future time Nt1Nt?t For Exponential
Populations (overlapping generations) Number
added to population dN/dt rmaxN Population
size as some future time NtN0ermaxt
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• In a rapidly expanding, continuously breeding
  population of human lice (no resource
  limitations), r was calculated to be 0.111 per
  day. What is the rate of increase of a
  population of 100 lice?

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• In a rapidly expanding, continuously breeding
  population of human lice (no resource
  limitations), r was calculated to be 0.111 per
  day. What is the rate of increase of a
  population of 100 lice?
• dN/dtrN.111x10011.1/day

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• 2. The text describes population trajectories
  for Lithuania and Rwanda. The current population
  of Lithuania is 4 million and the intrinsic rate
  of increase is .001. Estimate the population
  size 20 years into the future, assuming
  exponential growth. Do a similar calculation for
  Rwanda (N7.5 million, r.018)

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• The text describes population trajectories for
  Lithuania and Rwanda. The current population of
  Lithuania is 4 million and the intrinsic rate of
  increase is .001. Estimate the population size
  20 years into the future, assuming exponential
  growth. Do a similar calculation for Rwanda
  (N7.5 million, r.018)
• NtNert, N204e(.001x20)4e(.02)4 x 1.024.08
  million
• NtNert, N207.5e(.018x20)7.5e(.36)7.5 x
  1.4310.75 million