What purpose does the crab serve for the anemone?

Answer 1

If one can presume the concept of purpose is subsumed by salient factors that dictate the observable effects of purpose (the outward expressions of purpose, such as behaviors), it would be safe to posit that the crabs purpose is dictated by genetic programming, learned behaviors, and other factors. Examining causality tends to yield conclusions that the shared purpose of organisms is to survive, which reasoning descends into diverse postulates including the purpose of life itself. Regardless of the true source of the concept of purpose in the general sense, one is compelled to conclude that life itself is a reversal of entropy (all organisms, by definition, express a degree of organization or an apparent local reversal of entropy, whereas the second law of thermodynamics dictates that the entropy of a closed system will increase with time) and that a core principle of life is self-maintenance (for example, through reproduction). Advanced considerations in purpose of life tend to depart Biology into the fields of ontology and metaphysics, better answered in depth within the realm of philosophy.

To truly examine the purpose of a crab one might need to consider it from various disciplines. Based on the biological context, one could argue the purpose of a crab is to fill the niche that the crab is best suited to, a reasoning which naively appears circular. Some scientists have described the niche as an abstract "n-dimensional hypervolume" determined by environmental factors; which is to say that a crab would be bound by an upper and lower limit for each factor in terms of tolerance: temperature, salinity, oxygen partial pressure, etc. At the extremes of any of these, the crab, as with any organism, would begin to experience physiological stress and its survival would be challenging. There does exist overlap in these hypervolumes (notional niches) such that other organisms are in a position to compete with crabs for resources. Should the crab be arbitrarily removed and become extinct, other organisms would tend to find more success within the niche usually occupied by the crab since they would experience less competition from crabs.

Answer 2

There are many different species of crabs and many diffrent species of anenome. Without knowing the exact species I could not say but some species E.g. Carcinus maenas (The green shore crab) eat Actinia equina (The beadlet anenome).
While other crabs such as Hermit crabs can form a symbitoic relationship with the anenome in which both partys prosper (the crab feeds the anenome while the anenome protects the crab from predators)

Answer 3

Don't question it; just believe it.