Data gathering is a basic task in Wireless Sensor Networks (WSNs). Data gathering trees capable of performing aggregation operations are also referred to as Data Aggregation Trees (DATs). Recent paper focus on constructing DATs according to different user requirements under the Deterministic Network Model (DNM). However, due to the existence of many probabilistic empty links in WSNs, it is more practical to obtain a DAT under the realistic Probabilistic Network Model (PNM). Moreover, the load-balance factor is neglected when constructing DATs in current literatures.