1. So if R o = 1.5 and N t = 500, then N t+1 = : 2. At the second generation, N

Question

1. So if Ro = 1.5 and Nt = 500, then Nt+1= :

2. At the second generation, Nt+2, the size of the population would be:

3. What would the population size be for Nt+3, and Nt+4?

4. So as you can see, much depends on Ro. Considering the equation above, what happens to the population if

a. Ro < 1 (4)

b. Ro > 1 (5)

c. Ro = 1 (6)

5. If Ro = 2, what does that mean for population growth? In other words how many generations would it take to double in size?

6. Solve this riddle. Suppose you had a pond that was being overgrown by an aggressive weed that doubled its numbers every day (Ro = 2). If the weed went unchecked, it would cover the pond in 30 days. The weed's growth is very slow--almost negligible--to begin with, so you decide not to remove the weed until the pond is half covered. When would that be?

7. All of the calculations on this worksheet were based on R0. What is the difference between r and Ro?

8.What is the formula for population size at Nt+1 if given r and Nt?

Explanation / Answer

Nt+1 = RoNt

Nt: Population size of individual at age time t.

Nt+1: Population size at the time t+1

Ro: Net reproductive rate is the number of offspring produced per generation

Nt+1 = R0 * Nt

1) Nt+1 = 1.5 * 500 = 750

2) Nt+2 = 750 * 1.5 = 1125,

3) Nt+3 = 1125 * 1.5 = 1687.5, Nt+4 = 1687.5 * 1.5 = 2531.25

4) If Ro = 1 then,  birth rate equals the death rate.

Ro > 1, population increases

Ro < 1, population declines.

5) If Ro = 2, population size is increasing. In each generation population size get doubled

6) Weeds get doubled on each day and if it takes 30 days to cover the pond then on 15 days pond would be half covered. Therefore, on 15th day you start to remove the weed.

7)  r is the intrinsic rate of population increase under prevailing conditions

Ro = population net reproductive rate

8) Nt+1 = RoNt

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