According to Tchaikovsky 's nephew Yuri Lvovich Davydov and his niece Anna Meck-Davydov , he had already written a little ballet called The Lake of the Swans at their home in 1871 . According to two of Tchaikovsky 's relativesâ '' his nephew Yuri Lvovich Davydov and his niece Anna Meck-Davydov â '' the composer had earlier created a little ballet called The Lake of the Swans at their home in 1871 .