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S-shaped growth Flowers. dA / dt = r * A * (K-A) / K If A<<K then (K-A) / K ~1 And we have exponential growth Logistic Equation r net growth rate for.

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Presentation on theme: "S-shaped growth Flowers. dA / dt = r * A * (K-A) / K If A<<K then (K-A) / K ~1 And we have exponential growth Logistic Equation r net growth rate for."— Presentation transcript:

1 S-shaped growth Flowers

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

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

6

7 S-shaped growth FlowersVerifys

8 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.

9 Sales of Widgets Stella

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

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

12 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth

13 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth

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

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

16 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth

17 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth

18 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? A.Series 1 B.Series 2 C.Series 3 D.Series 4

19 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? A.Series 1 B.Series 2 C.Series 3 D.Series 4

20 A.Series 1 B.Series 2 C.Series 3 D.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 %?

21 A.Series 1 B.Series 2 C.Series 3 D.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 %?

22 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? A.Series 1 B.Series 2 C.Series 3 D.Series 4

23 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? A.Series 1 B.Series 2 C.Series 3 D.Series 4

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