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Lecture 7. Population dynamics Part 2. posted

# Lecture 7. Population dynamics Part 2. posted - Population...

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Population dynamics Part 2.

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Intuitively, a population increases in size when its birth rate exceeds its death rate: b >  d   or when r is positive; r = 0 when b = d r > 0 when b > d r < 0 when b < d Population size -200 0 200 400 600 800 1000 1200 0 1 2 3 4 5 6 7 8 9 10 11 time r = 0 r = -0.3 r = 0.3 r = 0.2 r = 0.1 Small changes in r make a big difference -100 0 100 200 300 400 500 600 700 800 Population Size 0 1 2 3 4 5 6 7 8 9 10 11 time N 0 = 5 r = 0.5 N 0 =50, r = 0.1 N 0 vs r : effects on pop’n growth __dN/dt = rN
Changing differential equation into a form we can use more easily Integrate from 0 to time t to predict population size at tim N t = N 0 e rt N t = # at some time in the future N 0 = # at time = 0 e = 2.717 (base of natural log, or ln) r = intrinsic rate of increase t = time

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1. Elephants live about 90 years 2. Elephants become sexually mature and can reproduce at about age 30 3. Thus, an elephant has a reproductive lifetime of about 60 years 4. A pair of elephants produce about 6 offspring in their lifetimes. 5. An elephant has a volume of about 5 cubic meters After 2500 yrs, there would be 73 x 10 18 elephants Which would occupy 1/3 of the volume of the Earth (actual population size currently around 500,000) Darwin: After 500 yrs there would be 15 million elephants (more like 16,000)… not such a great mathematician, but: an populations increase forever without limit?

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Density dependent regulation : per individual birth and death rates dependent on density As density increases: Limits to population size Per individual birth rate _decreases__ Per individual death rate __increases_
What causes birth and death rates to change with increasing density? Waste product accumulation _Space limitation__ Predators _ intraspecific (cannibalism) interspecific (predation or disease) ___Dispersal or emigration_ Resource depletion (energy limitation): decreases per individual birth rate(fecundity)_ __Decrease individual growth_ (fewer offspring) Increased death rate due to starvation

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Lecture 7. Population dynamics Part 2. posted - Population...

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