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Copyright © 2011 Pearson Education, Inc. Slide 8-1 Unit 8C Real Population Growth.
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Transcript of Copyright © 2011 Pearson Education, Inc. Slide 8-1 Unit 8C Real Population Growth.
Copyright © 2011 Pearson Education, Inc.
Slide 8-1
Unit 8C
Real Population Growth
8-C
Copyright © 2011 Pearson Education, Inc.
Slide 8-2
Definitions
Overall Growth RateThe world population growth rate is the difference between the birth rate and the death rate:
growth rate = birth rate – death rate
For any particular species in a given environment, the carrying capacity is the maximum sustainable population—that is, the largest population the environment can support for extended periods of time.
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Slide 8-3
Logistic Growth RateA logistic growth model assumes that population growth gradually slows as the population approaches the carrying capacity.
When the population is small relative to the carrying capacity, logistic growth is exponential with a fractional growth rate close to the base growth rate, r.
populationLogistic growth rate 1
carrying capacityr
Logistic Growth Rate
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Slide 8-4
In the exponential case, the growth rate stays equal at all times. In the logistic case, the growth rate starts out equal and as time progress the growth rate becomes smaller, until it finally reaches zero as the population levels out at the carrying capacity.
Exponential versus Logistic Growth
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Slide 8-5
The phenomenon where a real population increases beyond the carrying capacity in a relatively short period of time is overshoot. If the overshoot is substantial, a rapid and severe decrease in the population can occur—a phenomenon known as collapse.
Overshoot and Collapse
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Slide 8-6
SOURCE: T.H. Hollingsworth, Historical Demography (Ithaca, NY: Cornell University Press, 1969).
The historical population of Egypt
Difficulties of Population Prediction
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Slide 8-7
What is the Carrying Capacity?
The carrying capacity depends on consumption of resources such as energy. However, different countries consume at different rates.
The carrying capacity depends on assumptions about the environmental impact of the average person. A larger average impact on the environment means a lower carrying capacity.
The carrying capacity can change with both human technology and the environment.
The earth is such a complex system that precisely predicting the carrying capacity may be impossible.
Any estimate of carrying capacity is subject to greatuncertainty, for at least four important reasons:
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Copyright © 2011 Pearson Education, Inc.
Slide 8-8
Example
Suppose a country’s birth rate (per 1000) is 9.2 and its death rate (per 1000) is 11.8. Determine the population growth rate.
9.2 11.8 2.60.0026
1000 1000 1000
Since the country’s death rate exceeds its birth rate, the population growth rate is negative. Thus, the population is decreasing.
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Slide 8-9
Example
Consider a population that begins growing exponentially at a base rate of 4.0% per year and then follows a logistic growth pattern. If the carrying capacity is 50 million, find the actual growth rate when the population is 5 million.
growth rate
population1
carrying capacity
r
0.040.056
51
50
r
Solve the Logistic growth rate formula for r.
Use a growth rate of 4.0% = 0.04.
