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We consider the problem of gathering correlated sensor data by a single sink node in a wireless sensor network. We assume that the sensor nodes are energy constrained and design efficient distributed protocols to maximize the network lifetime. Many existing approaches focus on optimizing the routing layer only, but in fact the routing strategy is often coupled with power control in the physical layer and link access in the MAC layer. This paper represents a first effort on network lifetime maximization that jointly considers the three layers. We first assume that link access probabilities are known and consider the joint optimal design of power control and routing. We show that the formulated optimization problem is convex and propose a distributed algorithm, JRPA, for the solution. We also discuss the convergence of JRPA. When the optimal link access probabilities are unknown, as in many practical networks, we generalize the problem formulation to encompass all the three layers of routing, power control, and link-layer random access. In this case, the problem cannot be converted into a convex optimization problem, but there exists a duality gap when the Lagrangian dual method is employed. We propose an efficient heuristic algorithm, JRPRA, to solve the general problem, and show through numerical experiments that it can significantly narrow the gap between the computed and optimal solutions. Moreover, even without a priori knowledge of the best link access probabilities predetermined for JRPA, JRPRA achieves extremely competitive performance with JRPA. Beyond the metric of network lifetime, we also discuss how to solve the problem of correlated data gathering under general utility functions. Numerical results are provided to show the convergence of the algorithms and their advantages over existing solutions.