1 / 23

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

base
Download Presentation

S-shaped growth

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related