S-shaped growth
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Transcript of 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.
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