Animal poop is great for the garden! Why? Think about it- they eat up all the organic matter and then spit it back out into a compact form of nutrients that are already broken down! If you have a friend with a horse, cow, goats, etc. see if they will give you their manure. Most people with large animals have more than they know what to do with, and will give it to you free if you offer to get it yourself. Just remember to compost new manure for around six months before using it in the garden. This natural fertilizer is so hot it will burn your plants!
I try to avoid this at all costs! As long as you know and understand the deposit/withdrawal cycle and make good use of what's around you, you may avoid this altogether. If the soil is so depleted that you must bring in fertilizers to give it a jump start on the road to recovery while your compost matures, look into organic fertilizers. I like my dirt as natural as possible.
Now that you know which things are withdrawals and deposits, let's look at creating a cycle that can repurpose as many nutrients as possible to get the most out of them and wasting as little as possible. There are ways to introduce other components into your yard that will create systems of nutrient self-sufficiency!
Withdrawals- eating grass, eating bugs, laying eggs for you to eat, becoming meat for you to eat
Deposits- feed that you buy for them, poop in the yard, hay bought to put in the coop
Rabbits are amazing little composting machines! And an added bonus is that rabbits are one of the few animals whose manure you can put into the garden immediately- no composting or waiting necessary. While you can put your green plants in the compost to break down, a much faster way is to feed it to a rabbit. When I pull up old plants in the garden (broccoli, tomatoes, beans, you name it!) I feed it to my rabbits. Then I scoop out that manure from under the cage the next day and till it back into the garden where I pulled up the plants. That's a one day turnaround of green plant to nutrients in the soil for the next season of planting! On top of that you will buy rabbit feed as another deposit into the system. We grow our rabbits for meat (an added level of productivity), but if you don't want to go that far rabbits make great pets and will do the same job.
Withdrawals- Meat that you eat, eating garden greens
Deposits- Best poop for gardens, rabbit feed
I won't go into all the details of aquaponics here, but aquaponics is a system of using container raised fish (more specifically their poop) to fertilize plants growing in water rather than dirt. The plants clean the water which cycles back to the fish in a completely self-sustaining system that grows fish and vegetables with the only input of fish food! If you have never heard of it, do a little research- it's awesome!
Withdrawal- Fish to eat, vegetables
Deposits- fish food
Bees are sneaky little nutrient ninjas! They fly around and take all of your neighbor's pollen (I don't think they will miss it- besides, they do them a favor by pollinating everything) and then bring all of the bounty back to your house where they turn it into honey and beeswax. This system creates a lot of output for a little input while increasing the productivity of all of your plants by pollinating them.
Withdrawal- honey, beeswax
Deposit- your neighbor's pollen
Backyard dairy goats can also play a role in nutrient making. They will be a fats composter for leaves and tree branches in the same way that rabbits are for all things green. The food you buy is a deposit for the manure they create as well as the milk and/or meat that you will get out of the system.
Withdrawals- Making milk, meat, eating leaves
Deposits- Feed, poop