Calculating Logistic Growth

growth = G = rN[(K-N)/K]

population size = N = 10 individuals

carrying capacity =
              K = 1,000 individuals

rate of growth = r = 0.1 individuals/ individual/year

(K-N)/K = (1,000 – 10)/1,000 = 0.99

G = rN[0.99] = 0.1 x 10 x 0.99 = 0.99

New N = G + N = 0.99 + 10 = 10.99

Generation 2

(K-N)/K = (1,000 – 10.99)/1,000 = 0.989

G = 0.1 x 10.99 x 0.989 = 1.086

New N = 1.086 + 10.99 = 12.076

Generation 3

(K-N)/K = (1,000 – 12.076)/1,000 = 0.987

G = 0.1 x 12.076 x 0.987 = 1.19

Generation 30

(K-N)/K = 0.862;      G = 11.91;     New N = 150.21

Generation 50

(K-N)/K = 0.456;     G = 24.81;      New N = 568.53

Generation 70

(K-N)/K = 0.097;     G = 8.79;     New N = 919.50

When N = 1,000;     (K-N)/K = 0;

                   Therefore G = 0 and no individuals are added to the population.