ments are very similar. Phenotypes that maximize the potential for long-distance spore dispersal tend to minimize the bending moment on their vertical axes. Theoretically, therefore, walks that optimize R/M are comparatively direct and simple. From the formula for total phenotypic fitness F, the topology of the fitness-landscape resulting when all three tasks are considered simultaneously is more complex than those resulting when only one or two tasks are considered. Specifically, phenotypes that maximize long-distance spore dispersal (high fitness) also minimize their bending moments (high fitness) but minimize their ability to intercept sunlight (low fitness) because most of their branches are vertically oriented and therefore bunched together.
Once the topology of the fitness-landscape has been quantified, walks must be "seeded"—that is, they must be assigned a nonarbitrary point of origin. Once again, the fossil record for early tracheophytes is invaluable in this regard. The simplest and most ancient phenotype known for vascular land plants is epitomized by the Silurian fossil remains of Cooksonia. The sporophyte of this genus consisted of one, or more than one, short-branched cylindrical axes that terminated in sporangia and lacked leaves or roots (Banks, 1975; Edwards et al., 1992). This morphology can be taken as the point of origin for each walk, regardless how fitness is mathematically defined. Each walk proceeds as a sequence of N number of steps, each representing a morphological transformation to a more fit phenotype from the preceding phenotype. The sequence of steps in a walk, therefore, serves to identify more fit phenotypes. The magnitude of each phenotypic transformation can be depicted as the volume of the morphospace that must be searched by a computer-driven algorithm until the next more fit phenotype is reached. The volume searched by each step in a walk can be quantified by its diameter D. Each walk is permitted to branch when two or more phenotypes with equivalent fitness are identified by the algorithm. Each walk is brought to closure when it obtains all the phenotypic maxima within a single-function landscape or all the phenotypic optima within multi-function landscape. The mean diameter ¯D and the SE of D for all the steps in a walk quantify the mean variation in the phenotypic transformations required to achieve all maxima or optima within a particular fitness-landscape. The volume fraction VF of the entire morphospace occupied by a walk can be computed from the formula VF = [(ΣDi)V-1/T] × 100%, where VT is the total volume of the morphospace. Because the sample statistics obtained from single-and multiple-function fitness-landscapes (i.e., N, n, ¯D, VF) have unequal variances, the approximate t test, ¦t's¦, can be used to test for equality of sample means (Snedecor and Cochran, 1980; Sokal and Rohlf, 1981).