Assuming you are in an environment where precipitation exceeds evaporation and an open pond is a reasonable thing to do, then you get into things like what are your temperature ranges, how many ducks/fish are you wanting to raise, what thoughts have you given to plants, etc.
Lawton, discussing fish ponds, says 1.5 to 2 meters deep is sufficient. He is talking about ponds intended for producing substantial quantities of fish and recommends not building wider than can be readily netted - I think he said 24 meters across, but don't hold me to it
I don't know what sort of inputs he is considering with these designs.
The kinds of fish you choose will impact your pond design - trout need loads of oxygen, but catfish not so much. Temperatures impact your fish choices, and if you're going for a natural pond, you will want to stick with
native species since you are not controlling them and anything in your natural pond can escape into your
local waterways.
The larger the load you put on the pond, the bigger the pond needs to be. While you want to minimize your inputs, the pond requires inputs, so what are the parameters of the naturally available inputs on your site? What kind of sun exposure, precipitation? What potential does your site have for natural oxygenating waterflows, such as from a higher pond running down through flowforms to pick up oxygen and carry it into the lower pond, or from swales where the overflow spillways are set to feed the pond, again, running through flowforms to maximize oxygenation on the way into the pond.
Do you have
trees overhanging the pond dropping fruit into the water to feed life in the pond? Insect populations, again, natural inputs of food for the fish and the ducks? Is your area warm enough for you to grow water chestnuts? They're a yield for you and for pond life, as well as habitat.
Oxygen levels are affected by turbulence, is your pond site in a windy location, or a still one? More wind means more turbulence and more oxygen. There are even some wind driven machines that could serve to agitate and oxygenate, if your pond has reliable wind. For example, a vertical wind turbine driving an archimedes screw could lift water and drop it back into the pond, thereby adding oxygen.
Are we speaking of a self-sustaining system? One where the fish population maintains itself through natural breeding cycles? How much do you want to be able to take out of the pond? Same questions for the ducks, looking for a self-sustaining population? How much do you want to be able to harvest?
Scaling the system is built on lots of parameters and a fair bit of guesswork
My gut instinct agrees with Tyler about building the largest I could manage, but I would still make every effort to analyze my site and design to take advantage of nature's inputs into the system One time
energy inputs that yield on going returns over the long term rather than on going inputs, sounds like
permaculture.