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This paper describes a technique to save energy in the distributed Information_Driven maximum likelihood algorithm used for the localization of a diffusive source in Wireless Sensor Networks. First, the accurate Information_driven maximum likelihood distributed estimation based on the Gauss- Newton method is derived and called Modified Information-driven Collaborative Processing (MIDCP). In this method, a neighborhood region is defined and the information of all sensor nodes in this area is used to increase the algorithm accuracy. Then, a method for decreasing the energy consumption of this algorithm is proposed and called Energy Efficient MIDCP (EFMIDCP). In this algorithm, for estimation update, first, the neighboring radius is set to communication range of sensor nodes. After that, based on the covariance of estimation error in each iteration, this radius is decreased. Therefore, the amount of energy consumption is abated because of less transmission. Simulation results show the low energy consumption in the second proposed algorithm while its accuracy is rather well.