An overlay network platform facilitates a multi-party videoconference. End users participate using client-based browser or mobile application rendering software, such as a web browser, and using a protocol such as WebRTC. Dynamic speaker selection among the participants is facilitated by continuously determining the “relevance” of a participant's stream with respect to other participants in the conference. Thus, for example, a particular participant stream might be deemed to have a higher relevance if it is the stream corresponding to a person that is currently speaking, that has spoken recently, or that is about to speak. Streams with higher relevance are then selectively delivered at higher quality relative to less relevant streams. Preferably, individual client machines determine which streams are requested and at which quality based in part on their local resource capabilities.