Recessive hereditary deafness, assortative mating, and persistence of a sign language

We model the cultural transmission of sign language when there is one-locus genetic variation for deafness and hearing. Our premises are that the deaf are more motivated to learn sign language than the hearing, and that a vertically transmitted sign language, unlike recessive hereditary deafness, cannot "jump a generation." Conditions are obtained for persistence (i.e. protection from loss) of signers. These conditions are more easily satisfied the greater the fraction of the hearing who also learn sign language and as the frequency of the recessive gene for deafness increases. Persistence is also facilitated by assortative mating for deafness, but not by assortment for signing. With vertical transmission only, it is necessary that one signer parent be able to transmit sign language with greater than one-half the efficiency of two. Under the assumption that the hearing do not learn sign language, the following additional results are obtained. Persistence is more likely with dominant as opposed to recessive inheritance. When recessive hereditary and acquired deafness co-occur, increasing the frequency of the latter has opposite effects depending on the degree of assortment. Opportunities for the deaf to learn sign language outside the family seem not to affect the conditions for persistence.