Figure 2 Variables used to simulate branched morphology of early vascular land plants: P, probability of branching; ø, bifurcation angle; γ, rotation angle (subscripts 1 and 2 distinguish parameters for each axis in a branch-pair). (A) Three-dimensional bifurcate pattern of branching for which the orientation of each axis is prescribed by ø and γ. (B) Transverse view of terminal branch-pair in A showing the geometric affect of γ.

horizontally flattened (planated) branching systems are simulated when γ1 = γ2 = 0°.

Because six variables are required to simulate ancient tracheophytes, hypothetical phenotypes occupy a multidimensional space. Although this makes the graphic display of simulated walks somewhat difficult, the situation is greatly simplified by initiating simulations of walks in the isometric domain of the morphospace (i.e., P1 = P2) and permitting optima within this domain to enter the anisometric domain of the morphospace (i.e., P1P2). Conceptually, this simulation is illustrated in Figure 3A.



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