Recent genetic profiling of 30,000 Icelandic cod have produced data which suggests that a Lambda coalescent rather than Kingman’s coalescent is a suitable model for their ancestral lineages. We will discuss a class of population models analysed in Schweinsberg, 2003, along with its applicability as a population model. We have also looked into issues which arise in using coalescent models for the large sample sizes modern sequencing technology has enabled. Work by Wakeley and Takahashi, 2003, showed a breakdown in the coalescent approximation when the sample size is on the same order as effective population size. We will show heuristic arguments that show why the breakdown appears so late in the Kingman regime and extend the arguments to the Lambda regime. Joint work with Bjarki Eldon and Alison Etheridge.