The area of the brain stem that is important in controlling breathing is the:

Medulla.

Explanation:

The primary role of the medulla is regulating our involuntary functions that keeps us alive such as breathing, swallowing and heart rate. As part of the brain stem, it also helps transfer neural messages to and from the brain and spinal cord. It is located at the junction of the spinal cord and brain.

Hope this helps :))

searching efficiency (a)

Explanation:

The other word for Lotka-Volterra is predator-prey in which they have a combination of the differential equation which consists of nonlinear and should be the first ordered sequence.

It is used to tell the biological system changes where the two species interacted with each other. The one is the predator and the other one is prey.

Now according to the question the rate at which the  predator-prey change is searching efficiency (a) as it shows the changes of predator species with the respect that how quick they determine, attack it and consumed it