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S-shaped growth

S-shaped growth. Flowers. Logistic Equation. dA / dt = r * A * (K-A) / K. r net growth rate for non-stressed growth K carrying capacity Ao initial population (or Area). If A<<K then (K-A) / K ~1 And we have exponential growth. dA / dt = r * A * (K-A) / K

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S-shaped growth

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  1. S-shaped growth Flowers

  2. Logistic Equation dA / dt = r * A * (K-A) / K r net growth rate for non-stressed growth K carrying capacity Ao initial population (or Area) If A<<K then (K-A) / K ~1 And we have exponential growth

  3. dA / dt = r * A * (K-A) / K = r*A - r*A*(A/K) If A<<K then (K-A) / K ~1 And we have exponential growth

  4. r net growth rate for non-stressed growth K carrying capacity Ao – initial population (or Area)

  5. S-shaped growth FlowersVerifys

  6. Problems with Logistic Equation • Simple One example of s-shaped growth • The linear decrease in growth rate is often not true in real life. • The logistic equation fails to highlight the mechanisms responsible for limited growth. i.e. is it a decrease in birth rate or an increase in death rate.

  7. Sales of Widgets Stella

  8. Exponential growth • Exponential decay (goal seeking) to zero • Exponential decay (goal seeking) to a non-zero level • S-shaped growth

  9. Exponential growth • Exponential decay (goal seeking) to zero • Exponential decay (goal seeking) to a non-zero level • S-shaped growth

  10. Exponential growth Exponential decay (goal seeking) to zero Exponential decay (goal seeking) to a non-zero level S-shaped growth

  11. Exponential growth Exponential decay (goal seeking) to zero Exponential decay (goal seeking) to a non-zero level S-shaped growth

  12. Growth rate=rate*(1-stock/100) Exponential growth Exponential decay (goal seeking) to zero Exponential decay (goal seeking) to a non-zero level S-shaped growth

  13. Growth rate=rate*(1-stock/100) Exponential growth Exponential decay (goal seeking) to zero Exponential decay (goal seeking) to a non-zero level S-shaped growth

  14. Exponential growth Exponential decay (goal seeking) to zero Exponential decay (goal seeking) to a non-zero level S-shaped growth

  15. Exponential growth Exponential decay (goal seeking) to zero Exponential decay (goal seeking) to a non-zero level S-shaped growth

  16. The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80? Series 1 Series 2 Series 3 Series 4

  17. The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80? Series 1 Series 2 Series 3 Series 4

  18. Series 1 • Series 2 • Series 3 • Series 4 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80 and an intrinsic growth rate of 5 %?

  19. Series 1 • Series 2 • Series 3 • Series 4 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80 and an intrinsic growth rate of 5 %?

  20. The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 100 and an initial value of 4? Series 1 Series 2 Series 3 Series 4

  21. The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 100 and an initial value of 4? Series 1 Series 2 Series 3 Series 4

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