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Lecture 13 Density Dependence
Calculating doubling time of a population that is exhibiting exponential growth:
solution: N
t
= N
o
e
rt
let 2N
o
= N
t
2N
o
= N
o
e
rt
2 = e
rt
Continuous:
ln2 = lne
rt
ln2 = rtlne
(lne = 1)
ln2 = rt
t = ln2/r
doesn’t matter what population size is, doubling time is same
t = 0.7/r
Discrete:
t = 0.7/lnλ
Review assumptions of geometric/exponential growth
Discrete growth = N
t
= N
o
λ
t
Continuous growth = N
t
= N
o
e
rt
Assumptions:
1. pop. is “closed” – there is no immigration or emigration
2. birth and death rates (and therefore λ and r) are constant
 unlimited resources
 no environmental stoichasticity
 no predators
3.
all individuals are identical
4. no time lags
Incorporate random noise
 exponential growth and environmental stoichasticity
N
t
= N
o
e
rt
N
t
= N
o
e
rt
average population size, average r
σ
2
Nt
= N
o
e
e
2rt
(e
σ2rt
1)
variants increase over time
can predict mean pop size but variance increases over time and becomes harder to
predict over
time
spread (variances) increases over time
pop size
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View Full Document N
t
time
Arim et al 2006
 density dependent population growth: the per capita growth rate is affected by the
density or
size of the population
nonlog
non
log
N
(1/N)dN/dt
time
N
N
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 Winter '08
 R.Howard
 Biology

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