what is or how can we find out what the minimal space requirements of a species to give them an natural live in a captive setting?
Active animals would need more space, I guess. Large, open ocean species like whale sharks often need a lot of space to get by in captivity. Some of the larger animals like rhinos and elephants need a good amount of space to move or they risk developing foot problems. Looking at the ranges of the animals in the wild is a start, but take it with a grain of salt, since many animals only move so much to get to resources. A highly intelligent animal might need more space. At the very least, they need more enrichment, which often necessitates more space.
By zoo practice. It is when animals are healthy, don't develop behavior stereotypies, and breed well and groups are cohesive (there is enough space for subordinate animals to avoid dominant ones). More space is needed for animals which move a lot, which live in large groups, and which chase each other during their pairing. Zoos usually want to give animals more space than minimum. There is also a certain level of giving more space to 'favorite' animals. For example, gorillas as more 'valuable' get larger exhibits than chimps which may be more active. More important than space is however, how this space is developed - giving animals simulation and chance for all the natural behaviors. Range of animal in the wild is very poor prediction of its needs in a zoo. Not least because single species can have territories differing dramatically in size depending from locality, and larger home ranges are usually in marginal habitats. For example, elephants in semi-desert have very large territories, but in rich forests have much smaller ones. If home range in the wild was an indication, then domestic geese and ducks would be impossible to keep in captivity, for they migrate for winter over hundreds of kilometers.