  Spatial models where growth is limited to the edge of the expansions have
been instrumental to understand the population dynamics and the clone size
distribution in growing cellular populations, such as microbial colonies and
avascular tumours. A complete characterization of the coalescence process
generated by spatial growth is still lacking, limiting our ability to apply
classic population genetics inference to spatially growing populations. Here,
we start filling this gap by investigating the statistical properties of the
cell lineages generated by the two dimensional Eden model, leveraging their
physical analogy with directed polymers. Our analysis provides quantitative
estimates for population measurements that can easily be assessed via
sequencing, such as the average number of segregating sites and the clone size
distribution of a subsample of the population. Our results not only reveal
remarkable features of the genealogies generated during growth, but also
highlight new properties that can be misinterpreted as signs of selection if
non-spatial models are inappropriately applied.
