  In populations competing for resources, it is natural to ask whether
consuming fewer resources provides any selective advantage. To answer this
question, we propose a Wright- Fisher model with two types of individuals: the
inefficient individuals, those who need more resources to reproduce and can
have a higher growth rate, and the efficient individuals. In this model, the
total amount of resource N, is fixed, and the population size varies randomly
depending on the number of efficient individuals. We show that, as N increases,
the frequency process of efficient individuals converges to a diffusion which
is a generalisation of the Wright- Fisher diffusion with selection. The
genealogy of this model is given by a branching-coalescing process that we call
the Ancestral Selection/Efficiency Graph, and that is an extension of the
Ancestral Selection Graph (Krone and Neuhauser (1997a), Krone and Neuhauser
(1997b)). The main contribution of this paper is that, in evolving populations,
inefficiency can arise as a promoter of selective advantage and not necessarily
as a trade-off.
