  Evolutionary models for populations of constant size are frequently studied
using the Moran model, the Wright-Fisher model, or their diffusion limits. When
evolution is neutral, a random genealogy given through Kingman's coalescent is
used in order to understand basic properties of such models. Here, we address
the use of a genealogical perspective for models with weak frequency-dependent
selection, i.e. N s =: {\alpha} is small, and s is the fitness advantage of a
fit individual and N is the population size. When computing fixation
probabilities, this leads either to the approach proposed by Rousset (2003),
who argues how to use the Kingman's coalescent for weak selection, or to
extensions of the ancestral selection graph of Neuhauser and Krone (1997) and
Neuhauser (1999). As an application, we re-derive the one-third law of
evolutionary game theory (Nowak et al., 2004). In addition, we provide the
approximate distribution of the genealogical distance of two randomly sampled
individuals under linear frequency-dependence.
