Activity 52. 2 What Models Can You Use to Calculate How Quickly a Population Can Grow?



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  Activity 52.2 What Models Can You Use to Calculate How Quickly a Population Can Grow?

1. In the simplest population growth model (dN/dtrN).

a. What do each of the terms stand for?
Term Stands for:

dN Change in the number of individuals

dt Time interval during which the change occurred

r Per capita population growth rate  b – d

N Initial population size

b. What type of population growth does this equation describe?

Exponential growth of a population (J-shaped curve)

c. What assumptions are made to develop this equation?

Unlimited space (habitat) and resources

2. Population growth may also be represented by the model, dN/dtrN[(KN)/K].

a. What is K?

Carrying capacity, or the number of individuals that can be sustained over time. K is a function of the environment.

b. If NK, then what is dN/dt?

dN/dt  0; that is, there is no change in the population size over time.

c. Describe in words how dN/dt changes from when N is very small to when N is large relative to K.

When N is very small, the population is growing exponentially. The actual number of new individuals added is relatively small, however, because N is so small. As N nears the value of K/2, dN/dt approaches its maximum. As N approaches K, dN/dt decreases.
d. What assumptions are made to develop this equation?

The logistic model assumes that resources and space limit the growth of a population and that these factors determine the maximum number of individuals that can be sustained over time.

POPULATION GROWTH PROBLEMS

Answers:

1) r is increasing. r=0.045

2) 172 frogs

3). dN/dt= (b-d)N

(1134-1492)/1 = (b- 0.395) 1492

so b= 0.155.

Not suitable, because birth rate is much lower than death rate.

4a) 8.5 turkeys/acre

4b) 110 turkeys/ year

4c) 890 turkeys

5) One dandelion plant can produce many seeds, leading to a high growth rate for dandelion populations. If a population of dandelions is currently 40 individuals, and rmax= 80 dandelions/month, predict dN/dt if these dandelions would grow exponentially.

Equation to use, exponential growth: dN/dt= rmax N

dN/dt= 80 x 40= 3200

3200 dandelions

6) Imagine the dandelions mentioned in #5 cannot grow exponentially, due to lack of space. The carrying capacity for their patch of lawn is 70 dandelions. What is their dN/dt in this logistic growth situation?

Equation to use, logistic growth: dN/dt= r max N (K-N/K)

dN/dt= 80 x 40 (70-40/70)

dN/dt= 3200 (30/70)

dN/dt= 1371



1371 dandelions


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