In mobile ad hoc networks (MANET), nodes move freely and the distribution of access requests changes dynamically. Replica allocation in such a dynamic environment is a significant challenge. The communication cost has become a prominent factor influencing the performance of replica allocation in the MANET environment. In this paper, a dynamic adaptive replica allocation algorithm that can adapt to the nodes motion is proposed to minimize the communication cost of the object access. When changes occur in the access requests of the object or the network topology, each replica node collects access requests from its neighbors and makes decisions locally to expand the replica to neighbors or to relinquish the replica. This algorithm dynamically adjusts the replica allocation scheme towards a local optimal one. To reduce the oscillation of replica allocation, a statistical method based on history information is utilized to choose stable neighbors and to expand the replica to relatively stable nodes. Simulation results show that our algorithms efficiently reduce the communication cost of object access in MANET environment.