Good photo. There are several possibilities of what is occurring. Your swans may be "migrating" to a nesting station. Your pond may not have a food source or suitable nesting site (too open from the photos of the island)for hiding a nest and cygnets. You can possibly keep them on your pond by doing the following:

Throw them plenty of lettuce, some bread and make sure they have accessibility to cracked corn and poultry layer pellets. In the spring, aquatic plant life flourishes. The swans may have found this aquatic vegetation in the other ponds. Lettuce will help supplement their vegetation needs. You might plant some grazing vegetation, i.e., petunias, rye grass, impatiens or choleaus (all insectide, fungicide and pesticide free) around your lake and on the island. As for nesting materials, you might plant a small tree or large bush and provide them with plenty of hay (do not use pine needles as the resin can harm feathers)or straw. Place the nesting material near the tree or bush. The male will begin to build the nest from the hay material. By providing an ample food source and shelter for the pen during the nesting season, you will enhance the probability that the swans will remain on your pond and on the island for nesting. The Regal Swan