s-shaped growth

S-shaped growth

Flowers

dA / dt = r * A * (K-A) / K

If A<<K then (K-A) / K ~1And we have exponential growth

Logistic Equation

r net growth rate for non-stressed growthK carrying capacityAo initial population (or Area)

dA / dt = r * A * (K-A) / K = r*A - r*A*(A/K)

If A<<K then (K-A) / K ~1And we have exponential growth

r net growth rate for non-stressed growthK carrying capacityAo – initial population (or Area)

S-shaped growth

FlowersVerifys

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.

Sales of Widgets

Stella

A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-

zero levelD. S-shaped growth

A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-

zero levelD. S-shaped growth

A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-

zero levelD. S-shaped growth

A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-

zero levelD. S-shaped growth

A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-

zero levelD. S-shaped growth

Growth rate=rate*(1-stock/100)

A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-

zero levelD. S-shaped growth

Growth rate=rate*(1-stock/100)

A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-

zero levelD. S-shaped growth

A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-

zero levelD. S-shaped growth

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 1B. Series 2C. Series 3D. 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?

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

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

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

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 1B. Series 2C. Series 3D. 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 100 and an initial value of 4?

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