Hi Zhen,
I focus on questions of leadership and group dynamics. This consists of very basic questions such as what is leadership and why/how did it evolve. Consequently, an evolutionary perspective has helped to refine the definition of leadership. This leads to increasingly complex questions such as did different leadership prototypes emerge for distinct "fitness relevant" coordination problems. For instance, conflict and cooperation are evolutionarily consistent (and important) group problems to manage, and the traits/skills necessary to successfully overcome conflict may not be the best traits/skills for brokering peace. In fact, we find certain gender-based differences which correspond to hormonal differences and facial perceptions of masculinity/femininity. This has contributed to contingency and implicit leadership theories. I would encourage you to look at some of my publications for a more detailed discussion as the above is simplified:
http://www.researchgate.net/profile/Brian_Spisak/
This, in turn, raises questions, for example, about voting bias, distributed leadership in organizations (to include issues of gender and age), and why formal leadership structures are the way they are.
Finally, instead of me being the sole respondent. Perhaps this would be a good starting point for discussion. I ask my colleagues in the group conducting OB and/or PS research form an evolutionary perspective to offer some other research questions and findings.
Brian