Question

A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 200 deer. Absent constraints, the population would grow by 70% per year.Estimate the population after one year

Answer 1

If a population is growing in a constrained environment with a carrying capacity K, and absent constraint would grow exponentially with growth rate r, then the population behavior can be described by the logistic growth model which is expressed as

Pn = Pn - 1 + r(1 - (Pn - 1)/K *P(n - 1)

n - 1 is a subscript

n is the number of years

Po represents initial population

K is the carrying capacity

r is the growth rate

From the information given,

Po = 50

K = 200r = 70% = 70/100 = 0.7

After 1 year, n = 1

Thus,

P1 = 50 + 0.7(1 - 50/200) * 50

P1 = 76.25

By approximating,

P1 = 76

The population after 1 year is 76