Duty cycling is often used to reduce the energy consumption caused by idle listening in Wireless Sensor Networks (WSNs). Most studies on WSN protocols define a common duty cycle value throughout the network to achieve synchronization among the nodes. On the other hand, a few studies propose adaptation of the duty cycle according to uniform traffic conditions, which is beneficial assuming one-to-one traffic patterns that result in evenly distributed packet traffic. In this work, we consider the convergecast communication pattern commonly observed in WSNs. In convergecast communication, the packet traffic observed around the sink node is much higher than the traffic observed far from the sink, i.e., nodes with different distances to the sink node receive and must relay different amounts of traffic. Additionally, we utilize receiver-based protocols, which enable nodes to communicate with no synchronization or neighbor information, and hence do not require all nodes in the network to have the same duty cycle. In this paper, we model the expected energy consumption of nodes utilizing receiver-based protocols as a function of their duty cycle and their distance to the sink node. Using this analysis, we derive a closed-form formula for the duty cycle that minimizes the expected energy consumption at a given distance. Moreover, we propose an adaptation method for the derived distance-based duty cycle, based on local observed traffic. Performance evaluations of the two proposed duty cycle assignment methods show that they greatly improve the energy efficiency without sacrificing packet delivery ratio or delay significantly.