  We model spatially expanding populations by means of a spatial
$\Lambda$-Fleming Viot process (SLFV) with selection : the k-parent SLFV. We
fill empty areas with type 0 "ghost" individuals, which have a strong selective
disadvantage against "real" type 1 individuals. This model is a special case of
the SLFV with selection introduced in [19, 22] : natural selection acts during
all reproduction events, and the fraction of individuals replaced during a
reproduction event is constant equal to 1. Letting the selective advantage k of
type 1 individuals over type 0 individuals grow to +$\infty$, and without
rescaling time nor space, we obtain a new model for expanding populations, the
$\infty$-parent SLFV. This model is reminiscent of the Eden growth model [13],
but with an associated dual process of potential ancestors, making it possible
to investigate the genetic diversity in a population sample. In order to obtain
the limit k $\rightarrow$ +$\infty$ of the k-parent SLFV, we introduce an
alternative construction of the k-parent SLFV adapted from [38], which allows
us to couple SLFVs with different selection strengths.
