The Biosphere 2 project attempted to make a materially isolated system in which the animals, including people, produce carbon dioxide and consume oxygen; the plants produce oxygen and consume carbon dioxide; and the entire set of interactions between animals, plants, and microbes recycles the materials necessary to life. It enclosed more than 3 acres. The originally planned recycling failed and many species of animals became extinct in the enclosure while other animals and plants wildly increased in number.
There were a number of planning failures. The concrete had not fully cured, which reduced the oxygen content of the air. Air conditioning was inadequate for a huge greenhouse in the desert which caused over heating.
It seems that the main original difficulty was underestimating the problem of establishing a stable recycling system of plants and animals in imitation of the wild recycling system on Earth. More regular study of the various animals and plants to be put into such a system is required to learn all of their specific needs and products. Proper research should be done in smaller scale enclosures with regular records being kept. Just how difficult it is to produce a closed recycling life support system as originally planned for Biosphere 2 will be learned when the goal is accomplished.
It might not be an efficient way to proceed to try to learn everything about every plant and animal necessary for a recycling life support system. Some experiments with incompletely known combinations of plants animals and microbes can expand knowledge in this area. Already commercial organizations offer sorts of self-contained sealed aquariums. These may be more entertainment than science but they suggest possibilities. Small scale experiments with some containment of some of the living species might yield results. Food, gasses, water, and nutrients could be transferred by experimenters with remotely controlled mechanisms. The amounts of substances needed to be added to make up for imperfect recycling and the amounts of waste products could be recorded. Whatever progress has been made in this area so far, there is a possibility of practical recycling to meet all of settlers needs on Mars. The requirement on Mars is not that of complete material closure, but getting by with only the materials that can be generated by industry from the atmosphere dirt and rocks of Mars. Success in producing such a system would be bigger news than the troubles that occurred in Biosphere 2.
There have been several simulated long duration space missions, most of which ran into problems with interpersonal relationships. In 2021 NASA is planning the CHAPEA missions to study this problem. 
Various Problems Encountered
Biosphere suffered from a number of problems. In no particular order:
--- Oxygen levels dropped quickly from curing concrete and from oxygen breathing bacteria. This made physical labour challenging.
--- There were insect species which grew out of control. These included ants and cockroaches.
--- Air conditioning was inadequate. It got very hot inside.
--- The team split into two factions, those who wished to continue as planned, and those who wanted to bring in materials from outside to make things better. This division grew more acrimonious as time went on and eventually ended the mission early.