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We study the impact of physical layer (PHY) transmit rate control on energy efficient estimation in wireless sensor networks. A sensor network collects measurements about an unknown evolving process. Each sensor controls its sampling rate and its PHY transmit rate to the next hop or to the Fusion Center (FC). The FC performs estimation of the unknown process based on sensor measurements and needs to adhere to an estimation accuracy constraint. The objective is to maximize sensor network lifetime. The tradeoff is that, high PHY transmit rates consume more energy per transmitted bit, but they increase the amount of transmitted sensor measurement data per unit time, and thus they aid in improving estimation quality and in satisfying the estimation error constraint. First, we study a single-hop network where sensors transmit directly to the FC. In this case, sensor sampling rates are directly mapped onto PHY transmit rates. We identify fundamental structural properties of the optimal solution, and we propose a distributed, iterative sensor PHY rate adaptation algorithm for reaching a solution, based on light-weight feedback from the FC. Next, we consider the multi-hop version of the problem, where the sensor measurement (sampling) rates, PHY transmit rates and data flows to the FC are controlled. We extend the distributed optimization framework above to include all controllable parameters, and we devise an iterative algorithm for maximizing network lifetime.