  Collecting genomics data across multiple heterogeneous populations (e.g.,
across different cancer types) has the potential to improve our understanding
of disease. Despite sequencing advances, though, resources often remain a
constraint when gathering data. So it would be useful for experimental design
if experimenters with access to a pilot study could predict the number of new
variants they might expect to find in a follow-up study: both the number of new
variants shared between the populations and the total across the populations.
While many authors have developed prediction methods for the single-population
case, we show that these predictions can fare poorly across multiple
populations that are heterogeneous. We prove that, surprisingly, a natural
extension of a state-of-the-art single-population predictor to multiple
populations fails for fundamental reasons. We provide the first predictor for
the number of new shared variants and new total variants that can handle
heterogeneity in multiple populations. We show that our proposed method works
well empirically using real cancer and population genetics data.
