**Physical meaning of the equations**The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

*1. The prey population finds ample food at all times.*

*2. The food supply of the predator population depends entirely on the size of the prey population.*

*3. The rate of change of population is proportional to its size.*

*4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.*

*5. Predators have limitless appetite.*

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

**Prey**

When multiplied out, the prey equation becomes

*dx*/*dt* = *αx* - *βxy*

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this

exponential growth is represented in the equation above by the term

*αx*. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by

*βxy*. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = * - *

In this equation, *{\displaystyle \displaystyle \delta xy}* represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). *{\displaystyle \displaystyle \gamma y}* represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.