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Unformatted text preview: le -As time goes on, the exponent r becomes larger and larger!
-This is in contrast to fishery/bird population island models. Those models are
density dependent. High D = Slow Growth Exponential growth cannot continue unchecked, so
more complex models are needed
• Simplest model of
regulation is the
dt K N
K • Allee, Emerson, Park,
Park & Schmidt (1949),
“The Great APPES” Sigmoid growth, asymptotic
approach to carrying capacity (K) 20th In mid
logistic model was
viewed almost as an
ecological law… rN Historical perspective from first really
successful ecology textbook: N
Time -This logistic curve is representative of what happens in natural
p opulations when they are growing in DENSITY DEPENDENT fashions
-Similar to bird populations etc. 1 20/03/2013 Human projection from Allee et al. in 1940’s So, how did this prediction do?
2011: 7 billion and climbing! Best fit of logistic
equation to data
off at 2.6 billion -Assuming that the population was growing LOGISTICALLY, the upper estimate was: 2.6 BILLION
Extrapolating from logistic gave a very
poor prediction…why? * So far, human population growth
looks much more like exponential
growth than logistic. * -Our growth illustrates density INDEPENDENT growth! Are we experiencing an overshoot due to
delayed response? Or is K changing? • Statistical
– Extrapolating beyond the range of data is always
– Logistic is not a law, just a very simple possible
hypothesis for density dependence • Biological
– Logistic allows no overshoots
– Logistic assumes r and K to be constants -r and K will not always be constant: technology incre...
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This document was uploaded on 01/27/2014.
- Winter '14
- Annotated Lecture S