Question

Using the logistic equation (S-shaped curve), calculate population growth in one year when K = 1,000, N=100, r=0. Please show me how to calculate it!

0	100	35	1.00	0	0
1	65	?	0.65	0	0
2	45	15	?	3	1.35
3	30	20	0.30	1	?
4	10	10	0.10	1	0.10
5	0	0	0.00	1	0

Answer 1

For logistic growth model, the change in population size is represented by the following formula :

dN/dt = rN(K - N)/K

where dN/dt = Change in population size

r = rate of population growth

N = Population size

K = carrying capacity.

We must note that positive values for dN/dt indicate population growth and negative value for dN/dt indicated population decay or decrease. When dN/dt = 0 , then the population is said to be stable or no change in population size occurs.

Given in the above question, K = 1000, N = 100 and r = 0.

Substituting the values in the above equation we get :

dN/dt = 0 x 1000 (1000 - 100) / 1000 = 0

Thus there is 0 population growth since dN/dt = 0. The population is thus stable.

The missing values in the table are boldened and are as follows :

0	100	35	1.00	0	0
1	65	20	0.65	0	0
2	45	15	0.45	3	1.35
3	30	20	0.30	1	0.30
4	10	10	0.10	1	0.10
5	0	0	0.00	1	0