This is normal behavior at this time of the year which is nesting and mating season for swans. Usually, the male swan builds the nest. However, regardless of the presence or absence of a mate, swans will still nest. This behavior lasts until the sex hormones settle. So, the swan sitting on a nest that has no viable eggs will not last long. Is there any chance that there might be another swan you do not see, and the two are actually nesting? The Regal Swan