Unless your tank is evaporating so quickly that the filter is running dry, it's probably not going to be a significant amount.
The amount of ammonia that would bring 20 gallons of water to 4 ppm, put into 16 gallons of water, would be 5 ppm.
So if you loose about ~1/4 of your tank volume, you'd get about a 1ppm increase.
Were you able to seed the tank with anything from an established tan? (hardscape, substrate, plants, filter media, etc.)
And do you have anything in the tank that may be leaching ammonia (substrate? ferts?)