In biology nature determines the system:

‘A group of related natural objects or forces within a defined zone, a regularly interacting or interdependent group of items forming a unified whole.’

 www.biologyonline.org

Wolves in Yellowstone Park – Ecologists recognize that wolves are an apex predator and act as integral part of the food web in Yellowstone Park. From a biological perspective, removing wolves from the system would imply physically removing the wolves from the park so that they no longer influence the system.

In physics the scientist chooses the system:

‘We will often consider a particular system, by which we mean a particular object or set of objects;  everything else in the universe is called the “environment.”’

  Giancoli, Physics for Scientists   and Engineers, 3rd Edition, pg 445.

Atwood’s Machine – Physicists recognize that when applying the principle of energy conservation it can be very important to make a strategic system choice.  When analyzing the energy story of a pushing a box up a ramp a physicists might choose to put the person outside of the system.  This does not imply that the person is not influencing the motion of the box.  By putting the person in the environment the physicist chooses to only consider the energy that the person transfers to the box and not other energy changes of the person.