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One of the major challenges in handling realistic forward simulations for plant and animal breeding is the sheer number of markers. Due to advancing technologies, the requirement has quickly grown from hundreds of markers to millions. Most simulators are lagging behind in handling these sizes, since they do not scale well. We present a scheme for representing and manipulating such realistic size genomes, without any loss of information. Usually, the simulation is forward and over tens to hundreds of generations with hundreds of thousands of individuals at each generation. We demonstrate through simulations that our representation can be two orders of magnitude faster and handle at least two orders of magnitude more markers than existing software on realistic breeding scenarios.