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Ecology

Ecology. Exponential and Logistic Growth Carrying Capacity Survivorship Curves Competition-Predator Prey. Exponential Growth. We have many birds in our population The amount of birds is N (population size) How many birds do we have? What will happen over time to the population of birds?

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Ecology

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  1. Ecology Exponential and Logistic Growth Carrying Capacity Survivorship Curves Competition-Predator Prey

  2. Exponential Growth • We have many birds in our population • The amount of birds is N (population size) • How many birds do we have? • What will happen over time to the population of birds? • Increase (Birth) • Decrease (Death) • Stay the same (environment is stable)

  3. Exponential Growth • r= birth-death/N • r = growth rate • Lets assume that we have 5 baby birds birthed • Lets assume that 2 birds got eaten by our owls • r = (5-2)/10  .3 • GROWTH RATE IS .3 • Factors where our growth rate is increasing

  4. Exponential Growth • 10 x .3 = 13 • We now cannot use 10 as our value for N, we have to use 13 • We will now represent this by: • dN/dt=rN

  5. Exponential Growth • dN/dt=rN • dN/dt=.3(13) • dN/dt=3.9 which rounds up to 4 (4 new birds) • Which brings our total population to 17

  6. Exponential Growth • dN/dt=rN • dN/dt=.3(17) • dN/dt=5.1 which rounds up to 5 (5 new birds) • Which brings our total population to 22

  7. Exponential Growth • dN/dt=rN • dN/dt=.3(22) • dN/dt=6.6 which rounds up to7 (7 new birds) • Which brings our total population to 29

  8. Exponential Growth • Now lets look at some questions: • What’s the population going to be at year 10? • AHHH HELP! • N(t) = N(1+r)t • 10(1+.3)10 • 10(13.78) • 137.8

  9. Logistic Growth • What happens after exponential growth? • The environment cannot handle continuous growth…reach a carrying capacity (K) and population starts to level off • Run into limiting factors • Abiotic • Biotic

  10. Logistic Growth • dN/dt = rN • HOWEVER • We need to take into account K or the carrying capacity

  11. Logistic Growth • dN/dt = rN (K-N/K) • Lets say our carrying capacity is 10 and r is 1

  12. When to use what… • So how do you know when to use exponential growth or logistic growth? • Look at r • If r is greater than 0 then it is exponential growth • If you ever see k then you know to use logistic • Also look at r and k selected species… • R- grows as quickly as it can • K- does not grow fast

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