landscape topology and the dynamics of walks, particularly in terms of computer simulations. The first step is to simulate a multidimensional domain of all conceivable phenotypes—a "morphospace" (sensu Thomas and Reif, 1993). The next step is to determine the ability of every hypothetical phenotype to perform each of a few biologically realistic tasks, in addition to its ability to simultaneously perform various combinations of these tasks—that is, the fitness of phenotypes must be mapped to establish and quantify the topology of the fitness-landscape. Then, beginning with the same ancestral phenotype, a computer algorithm can be used to search the morphospace for successively more fit phenotypes. Simulations of this sort are brought to closure when each phenotypic maximum or optimum within the morphospace is reached by a walk, after which the number and magnitude of the phenotypic transformations in a walk, as well as the number of phenotypic maxima or optima within different fitness-landscapes, are computed and compared. Clearly, to be useful, this heuristic protocol requires nonarbitrary definitions for "morphology," "function," and "ancestor.'' It also must be cast in terms of a real evolutionary episode against which simulated walks and predicted phenotypic maxima or optima can be compared and contrasted with the actual morphological trends established by the fossil record.
The early evolution of vascular land plants is a case in point. The most ancient tracheophytes had cylindrical, bifurcating axes that lacked leaves and roots (Banks, 1975; Edwards et al., 1992; Stewart and Rothwell, 1993; Taylor and Taylor, 1993). These morphologies are easily simulated by means of a computer with only six variables (Niklas and Kerchner, 1984; Niklas, 1988). Referring to Figure 2, in which each axis of a bifurcate pair is distinguished by the subscript 1 or 2, the six variables are the probabilities of branching P1 and P2, the rotation angles subtended between each axis and the horizontal plane γ1 and γ2, and the bifurcation angles subtended between the longitudinal axis of each axial member and the longitudinal axis of the subtending member ø1 and ø2. Indeed, a morphospace containing 200,000 phenotypes, encompassing virtually the entire spectrum of early vascular land-plant morphology, can be simulated by establishing the limiting conditions (and increments) for these six variables: 0 ≤ P ≤ 1 (in increments of 0.01), and 0° ≤ g ≤ 180° and 0° ≤ ø ≤ 180° (both in increments of 1°). Within this morphospace, the simplest phenotype (i.e., a Y-shaped plant) results when P1 = P2 = 0 and ø1 = ø2. Higher values of P produce more complex, highly branched morphologies. Morphologies with equal (isometric) branching are simulated when P1 = P2. Plants with anisometric (unequal) branching, very much like those that appear in the Devonian Period, are obtained when P1P2 . And phenotypes with