The region of the ancient Sahul continent (present day Australia and New Guinea, and surrounding islands) is home to extreme linguistic diversity. Even apart from the huge Austronesian language family, which spread into the area after the breakup of the Sahul continent in the Holocene, there are hundreds of languages from many apparently unrelated families. On each of the subcontinents, the generally accepted classification recognizes one large, widespread family and a number of unrelatable smaller families. If these language families are related to each other, it is at a depth which is inaccessible to standard linguistic methods. We have inferred the history of structural characteristics of these languages under an admixture model, using a...