1 Abstract Coalescent simulations are widely used to examine the effects of evolution and demographic history on the genetic makeup of populations. Thanks to recent progress in algorithms and data structures, simulators such as the widely-used msprime  now provide genome-wide simulations for millions of individuals. However, this software relies on classic coalescent theory and the corresponding assumptions that sample sizes are small relative to effective population size and that the region being simulated is short. Here we show that coalescent simulations of long regions of the genome exhibit large biases in identity-by-descent (IBD), long-range linkage disequilibrium (LD), and ancestry patterns, particularly when sample size is large. We present a Wright-Fisher extension to msprime , and show that it produces more realistic distributions of IBD, LD, and ancestry proportions, while also addressing more subtle biases of the coalescent. Further, these extensions are more computationally efficient than state-of-the-art coalescent simulations when simulating long regions, including whole-genome data. For shorter regions, efficiency and accuracy can be maintained via a flexible hybrid model which simulates the recent past under the Wright-Fisher model and uses coalescent simulations in the distant past.