Sustainability means meeting today's needs without compromising the ability of future generations to meet theirs. For renewable resources, use must stay within the rate of replenishment over time.
Renewable resources include sunlight, wind, forests and fish. Forests and fish can replenish on a human timescale if harvest does not exceed regrowth over time. Coal, oil, natural gas and metal ores are non-renewable on that timescale, though metals can often be recycled.
An ecological footprint estimates the productive land and water needed to support a person or country. One ecological footprint estimate puts humanity's annual demand at about 1.7 Earths' worth of biocapacity. This estimate depends on accounting methods and includes the area needed to absorb CO2 emissions.
For waste, the order matters. Reduce first, then reuse, then recycle. Recycling aluminum saves about 95% of the energy needed to make new aluminum from ore, but never making the can saves all of it.
Worked example. A fish population grows logistically, dtdN=rN(1−KN), with r=0.4 per year and K=10,000. At N=9,000, growth is 0.4×9,000×0.1=360 fish per year. At N=2,000, it is 0.4×2,000×0.8=640. At N=5,000, it is 0.4×5,000×0.5=1,000. In this model, growth peaks at K/2, so the maximum sustainable yield is 1,000 fish per year if the population is held at 5,000. Real populations vary, and their growth and carrying capacity are uncertain. Atlantic cod off Newfoundland declined after heavy fishing, and a fishing moratorium began in 1992.