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.