The interaction of spices has been modeled by the equations

and .

(a)

For the stable population :

Stable population means there is no change in population.

Therefore and .

(b)

The caribou goes extinct refers to, the population of caribou is zero.

Therefore .

(c)

For stable population and .

Consider .

Substitute and in the above expression.

or

or .

Consider .

.

Substitute and in the above expression.

.

or .

or .

The two populations can live in balance if .

The pair of and .

It is possible for the two species live in balance. 

(a) For the stable population   and .

(b)

(c) and .

It is possible for the two species live in balance.