“One of the first conditions of happiness,” Leo Tolstoy once observed, “is that the link between Man and Nature shall not be broken.” Had Tolstoy lived in the digital age, he might have added the link between man and fellow man — or people, in today’s preferred parlance.

Both bonds, and their fragility, are thrown into stark relief in Abe Koogler’s “Deep Blue Sound,” a gently probing, bittersweet new play that had its premiere two years ago as part of Summerworks, a festival presented by the acclaimed theater company Clubbed Thumb. Director Arin Arbus has now brought her production, featuring a superb cast of rising and longstanding theater favorites — several new to this second staging — to the Public Theater for a more extended run.