Unformatted text preview: a volume of about 5 cubic meters! Darwin: After 500 yrs there would be 15 million elephants
(more like 16,000)… not such a great mathematician, but:!
After 2500 yrs, there would be 73 x 1018 elephants!
Which would occupy 1/3 of the volume of the Earth!
(actual population size currently around 500,000)!
so, something is limiting Density dependent regulation: per individual
birth and death rates depend on density!
!
As density increases:!
#Per individual birth rate decreases!
#Per individual death rate increases! carrying capacity (K) is the maximum population
size that can be supported by available resources
or physical space! What causes birth and death rates to change with
increasing density?!
Resource depletion (energy limitation):!
Decreases per individual birth rates (fecundity)!
Decreased individual growth (fewer offspring)!
Increased death rate due to starvation! Waste product accumulation!
Space limitation!
Predators!
#intraspeciﬁc (cannibalism)!
#interspeciﬁc (predation or disease)!
Dispersal or emigration! Growth rate decelerates as
K is approached and
popuation stabilizes at K!
Maximum growth
rate is reached! Paramecium in lab culture dishes shows logistic growth… why?
What limits population growth of Paramecium in the lab?! Growth starts
nearly exponential! Logistic population growth: including density dependence!
dN/dt = rN [1(N/K)]!
Exponential growth! *K = carrying capacity! Fraction of K remaining! In words: population growth equals the amount expected
under exponential growth multiplied by what percent of
the carrying capacity is left [understand this!]!
If N is very close to K, then population growth will be slow!
! How do we get this type of growth?! If N is very small...
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 Spring '13

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