Lecture 17 Notes

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12 Apr 2012
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Lecture 17: Human Population Ecology
Slide 2
Human impact is a function of population and consumption (affluence and
oAffluence the consumption that humans are imposing on natural
oTechnology efficiency with which that affluence is gained
Slide 4
Exponential growth model can’t be sustained forever, it may fit this model for
a while, but not indefinitely
oThis model will hold for any population that has constant birth and death
oIf rates are constant and if (birth rate + immigration) > (death rate +
emigration), population growth is density-dependent and exponential
oExponential growth if r>0
oFor any population that grows and the parameters stay constant, they will
grow faster and faster
dN/dt = rN; solved as Nt = N0ert
Slide 6
The simplest model of density-dependent regulation is the logistic model
oDensity-dependent growth rates are not constant but vary with the
number of individuals in the population
Logistic growth sigmoid growth, asymptotic approach to carrying capacity
oPopulation starts with exponential growth but flattens out at K
oThe breaking term [(K-N)/K] shows how resources are being exhausted
Slide 7
The data from Allee from before 1949 best fit the sigmoid curve
They reached the conclusion that the carrying capacity would be 2.6 billion
Best fit of logistic equation to data suggests levelling at 2.6 billion
Slide 8
So far, human population growth looks more like exponential growth than logistic
The population didn’t fit the logistic model predicted by Allee in the 1940s
About 1000 years ago, there is a breaking point where things seem to grow
About 500 years ago, there was a dip in the European population due to the
bubonic plague
Our population rising so much is a very recent effect
Slide 9
Logistic is just an idea of how density-dependence might work but it’s just way
too simple for reality
Logistic model doesn’t allow overshoot, rather it always has a population
levelling off at K
It assumes that birth and death rates (which is equal to r) and the carrying
capacity (K) to be constant; this is oversimplified
Slide 10
These are 3 different versions of the logistic equation modified to reflect time
delays for when the resource limitation kicks in
Green: normal logistic; Blue: time delay; Red: stronger time delay
Time delays cause populations to overshoot the carrying capacity (K)
Blue and Red graphs both overshoot K
Blue smooths out eventually
Red graph reached carrying capacity so far over that it’s on the brink of
massive collapse
Slide 11
We can’t even model ourselves with the logistic model because reality is far
more complicated
Both r and K have been bumped up by technology and it’s an ongoing process
We can’t use r and K to describe the future because these numbers are both
Slide 12
2% per year growth was the fastest growth rate in history
The time scale on the graph ends at 2100 (end of the century)
Green peaking at 7.5 billion an dropping
Blue levelling at 9 billion
Red 14 billion by 2100 and growing
These projections by the UN are fairly optimistic because they don’t include big
population crashes; they basically include that birth rates will drop more or less
voluntarily as humans change their relationship with the world
Slide 13
Growth rates and their response to changing birth and death schedules depend
on population age structures
Population Momentum even if you get to the point where birth and death
rates are equal, the probability that a person produces offspring is exactly offset
by the probability of a person dying
oA population with a lot of pre-reproductive children in it is still going to
have population growth because those children are still going to reach
reproductive age and have babies
High Momentum this pyramid is typical of any rapidly growing population
oThis is the structure that most of the undeveloped countries are growing
oMany populations in the world fit this structure
oIf you reduce growth rate to zero, this population still grows for a
generation or two
Low Momentum might stop growing immediately if you make growth rate
oThis is what European countries are growing like