  Population genetics theory has laid the foundations for genomics analyses
including the recent burst in genome scans for selection and statistical
inference of past demographic events in many prokaryote, animal and plant
species. Identifying SNPs under natural selection and underpinning species
adaptation relies on disentangling the respective contribution of random
processes (mutation, drift, migration) from that of selection on nucleotide
variability. Most theory and statistical tests have been developed using the
Kingman coalescent theory based on the Wright-Fisher population model. However,
these theoretical models rely on biological and life-history assumptions which
may be violated in many prokaryote, fungal, animal or plant species. Recent
theoretical developments of the so called multiple merger coalescent models are
reviewed here ({\Lambda}-coalescent, beta-coalescent, Bolthausen-Snitzman,
{\Xi}-coalescent). We explicit how these new models take into account various
pervasive ecological and biological characteristics, life history traits or
life cycles which were not accounted in previous theories such as 1) the skew
in offspring production typical of marine species, 2) fast adapting
microparasites (virus, bacteria and fungi) exhibiting large variation in
population sizes during epidemics, 3) the peculiar life cycles of fungi and
bacteria alternating sexual and asexual cycles, and 4) the high rates of
extinction-recolonization in spatially structured populations. We finally
discuss the relevance of multiple merger models for the detection of SNPs under
selection in these species, for population genomics of very large sample size
and advocate to potentially examine the conclusion of previous population
genetics studies.
