Figure 4

Comparison of the Poisson process and Markov approximation in terms of tree height. Histograms of the densities for tree height are shown for trees built from a simulated Poisson process (solid yellow) and Galton-Watson trees from the Markov approximation (blue striped) for the case of fixed fragment lengths. Each tree corresponds to one lattice path excursion away from 0 (also referred to as sequence islands or contigs). The simulations include average height θ = 6 with 14,466 trees simulated for each type (A), θ = 9 with 3,551 trees simulated for each type (B), θ = 12 with 1,429 trees simulated for each type (C), and θ = 15 with 217 trees simulated for each type (D).