Alexander, known as Alasdair Beag, was born about 1854, the son of John MacLean and Christina MacLeod of 12 Ruisgarry (Quay). When Alasdair was aged ten, the family moved to 18 Ruisgarry (Brusda).

Alasdair became a fisherman and farmer, living on his father's croft. He married Margaret MacLeod in 1881, with whom he was to have ten children. He became a merchant in addition to his crofting activities. In 1900 he obtained 8 Borve.