8
Morphological Evolution Through Complex Domains of Fitness
Karl J. Niklas
… the central problem of evolution … is that of a mechanism by which the species may continually find its way from lower to higher peaks.
Sewall Wright
The history of life is to be studied by a great variety of means, among which special importance attaches to the actual historical record in rocks and the fossils contained in them.
George Gaylord Simpson
A powerful metaphor, proposed by Sewall Wright (Wright, 1931, 1932; Provine, 1986), conceives of evolution as a ''local search" for "adaptive peaks" by progressively fitter mutants. This image of a walk over a fitnesslandscape forcefully draws attention to the relation between the number and location of fitness peaks, on the one hand, and the number and magnitude of phenotypic transformations among neighboring variants required to increase fitness, on the other (Kauffman, 1993; Maynard Smith, 1970). However, comparatively few attempts have been made to quantify the relation between the topology of landscapes and the dynamics of walks (Eigen, 1987; Gillespie, 1983; Kauffman and Levin, 1987). Among the numerous obstacles to quantitative analyses of Wright's metaphor are (i) the de minimus requirement for mapping all possible genotypes onto their corresponding pheno
Karl J. Niklas is professor of botany at Cornell University, Ithaca, New York.
types for a complete analysis of phenotypic variation (Scharloo, 1991), (ii) the possibility that the fitness contributed by performing one task depends upon the ability to perform other tasks simultaneously (i.e., epistatic fitnesscontributions; Ewens, 1979; Franklin and Lewontin, 1970; Lewontin, 1974), (iii) the likelihood that the dynamics of a walk depend upon the walk's point of origin on the landscape in addition to intrinsic genetic or developmental barriers to phenotypic transformations, and (iv) the requirement to treat biological realistic temporal and spatial variations in the topology of fitnesslandscapes, as well as (v) the complex interactions among a panoply of physical and biological variables that collectively define fitness (Kauffman, 1993; Gould, 1980; Levin, 1978).
Nonetheless, the image of the fitnesslandscape continues to inspire questions about the tempo and mode of evolution—for example, what is the relation between the number of fitness peaks and the number of functional tasks that an organism must simultaneously perform to grow, survive, and reproduce? Although there is no a priori reason to assume that the number and location of phenotypic optima depend upon the number of tasks an organism must perform, there are good reasons to believe that manifold functional obligations author "coursegrained" landscapes with many phenotypic optima. For example, engineering theory shows that the number of equally efficient designs for an artifact generally is proportional to both the number and the complexity of the tasks than an artifact must perform (Meredith et al., 1973) because the efficiency with which each of many tasks is performed must be relaxed due to unavoidable conflicting design specifications for individual tasks (Gill et al., 1981), and, as the number of tasks increases, the number of configurations that achieve equivalent or nearly equivalent performance levels increases (Brent, 1973). If such relationships hold true for organisms, these relations may account for the morphological and anatomical diversity seen among even closely related species. Indeed, the sharp logical distinction between "optima" and "maxima," on the one hand, and the observation that a multitask artifact may assume diverse appearances, on the other, suggest the hypothesis that the imposition of manifold obligations increases the number of equally fit phenotypes.
Although the problematic analogy between engineered and biological systems speaks to the topology of fitnesslandscapes, it sheds no light on questions related to the dynamics of walks—for example, what is the relation between the number of tasks that an organism must perform and the magnitude of the morphological transformations between neighboring variants required to reach fitness optima? Are walks confined to nearestneighbor variants or are they free to reach compara
tively distant morphologies? At some level, the number and magnitude of phenotypic transformations comprising a walk must depend upon both the location of fitness peaks and the extent to which the fitness of neighboring variants are correlated. However, it is evident also that the extent to which a walk proceeds depends upon the ability of an organism to alter its phenotype. Although the developmental repertoire of most organisms permits some latitude in external shape and internal structure, walks undoubtedly are governed by genetic or developmental mechanisms that establish barriers to transformations among neighboring variants on the landscape (Alberch, 1980, 1981, 1989; Odell et al., 1981; Oster et al., 1980). Thus, morphological transformations among phenotypes are not equiprobable, and walks cannot be governed exclusively by the topology of the fitnesslandscape.
Plants as a Venue for Simulated Walks
The extent to which walks are genetically or developmentally unfettered is a matter of relative rather than absolute degree because it undoubtedly varies among organisms and changes over evolutionary time. For example, the developmental "plasticity" of plants appears extremely high in comparison with most animals (Schmid, 1993; Sultan, 1987; Van Tienderen, 1990). By the same token, certain periods of evolutionary time are characterized by exceptionally high rates of phenotypic innovation as, for example, the colonization of the terrestrial landscape by the first vascular plants (Figure 1). Indeed, one is left with the impression that the walks of plants, in general, and those of early tracheophytes, in particular, feature phenotypic transformations sufficient to achieve many, perhaps most, of the morphological optima widely scattered over their fitnesslandscapes.
An added advantage to dealing with plants is that their fitness calibrates closely with the operation of physical laws and processes governing the exchange of mass and energy between the plant body and the external environment, which have remained constant over evolutionary time (Gates, 1965; Brent, 1973; Alberch, 1980, 1981, 1989; Oster et al. , 1980; Gill et al., 1981; Odell et al., 1981; Nobel, 1983; Sultan, 1987; Van Tienderen, 1990; Niklas, 1992; Schmid, 1993). Thus, the broad outlines of the fitnesslandscape for plants likely have remained comparatively constant. If so, then plants may be the ideal venue for examining the relation between the topology of fitnesslandscapes and the dynamics of more or less unrestricted walks.
The assumption that walks are unimpeded over stable fitnesslandscapes greatly simplifies attempts to explore the relation between
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 fitnesslandscape. 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 fitnesslandscapes, 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 P_{1} and P_{2}, the rotation angles subtended between each axis and the horizontal plane γ_{1} and γ_{2}, and the bifurcation angles subtended between the longitudinal axis of each axial member and the longitudinal axis of the subtending member ø_{1} and ø_{2}. Indeed, a morphospace containing 200,000 phenotypes, encompassing virtually the entire spectrum of early vascular landplant 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 Yshaped plant) results when P_{1} = P_{2} = 0 and ø_{1} = ø_{2}. Higher values of P produce more complex, highly branched morphologies. Morphologies with equal (isometric) branching are simulated when P_{1} = P_{2}. Plants with anisometric (unequal) branching, very much like those that appear in the Devonian Period, are obtained when P_{1}P_{2} . And phenotypes with
horizontally flattened (planated) branching systems are simulated when γ_{1} = γ_{2} = 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., P_{1} = P_{2}) and permitting optima within this domain to enter the anisometric domain of the morphospace (i.e., P_{1}P_{2}). Conceptually, this simulation is illustrated in Figure 3A.
Turning attention to the topology of the fitnesslandscape, the functional obligations assuring growth, survival, and reproduction must be known and quantified. For early vascular land plants, these obligations can be inferred from living tracheophytes and undoubtedly include the requirement to intercept sunlight, to mechanically sustain the weight of aerial organs, and to be able to produce and disperse diaspores some distance from parental plants. Fortunately, each of these tasks can be quantified by means of closedform equations derived from biophysics or biomechanics. For example, the efficiency E of a computersimulated phenotype to intercept solar irradiance (of intensity I measured perpendicular to its surfaces) is given by the formula
where S_{p} is the total unshaded surface area of the phenotype projected toward incident light, S is the total surface area of the phenotype, and Θ is the incident solar angle, which varies between 0° and 180° in each diurnal cycle (Niklas and Kerchner, 1984). Because the magnitude of I is independent of Θ (assuming atmospheric conditions are clear), Eq. 1a reduces to
Although the total projected area S_{p} of each morphology varies as a function of Θ, it also depends upon the orientation of axes in addition to the extent to which neighboring axes shade one another. All of these variables can be dealt with by even the most simple computer.
In terms of mechanical stability, the maximum bending stresses σ_{max} that develop in a cylindrical plant axis may be computed from the formula
where M is the bending moment, which has units of force times length, and + and  denote tensile and compressive stresses, respectively (Niklas, 1992). For any value of d, the bending stresses are directly proportional to the bending moment that, when expressed in terms of Φ and γ, is given by the formula
where ρ is the bulk density of tissues used to fabricate a plant and g is gravitational acceleration. Assuming that the bulk density varies little from one plant to another, M α γ^{1} sin Φ. Thus, the bending moment and therefore the maximum bending stresses are minimized when Φ = 90° (i.e., a vertically oriented axis).
In terms of spore dispersal, an elementary ballistic model suffices:
where x is the lateral distance of transport, H is the height at which spores are released from the parent plant, U_{T} is the average settling velocity of spores, and U_{h} is the horizontal wind speed averaged between H and ground level, which is assumed to parabolically diminish from the top to the base of the plant (Okubo and Levin, 1989). Assuming that U_{T} is independent of H and that U_{h} is proportional to H, the maximum lateral transport distance for spores is proportional to the square of plant height, x α H^{2}, indicating that even a small increase in plant height confers a selective advantage to spore dispersal. However, the number of spores a plant produces is as important to its reproductive success as the distance spores are transported (Niklas, 1986). Thus, the fitness contribution of the number of spores produced per plant must be considered in addition to the fitness contributed by elevating spores above ground level. Assuming that spores are produced at the tips of branches and that the number of spores per sporangium varies little among hypothetical phenotypes, reproductive fitness R is maximized by maximizing both the number n and height of branch tips: R = f(n, H).
The foregoing implicitly assumes that fitness is proportional to E and R and inversely proportional to M. Assuming that each of these three functional obligations contributes equally and independently to fitness, the most parsimonious mathematical expression for the total fitness F of a phenotype is the geometric mean of E and R divided by M—i.e., F = [(E)(R)]^{1/2}M^{1}. Importantly, the topology of the fitnesslandscape for each of the three functional tasks differs because different functional obligations can have different phenotypic requirements. For example, phenotypes that maximize light interception also maximize their bending moments. However, a phenotype with a high fitness in terms of its ability to garner irradiate energy for photosynthesis will have a low fitness in terms of its high probability for mechanical failure. Consequently, when both of these functions are considered simultaneously, the objective of a walk is to optimize E/M. Although E cannot be maximized without maximizing M, some functional obligations reinforce the same morphological solution because their phenotypic require
ments are very similar. Phenotypes that maximize the potential for longdistance 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 fitnesslandscape 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 longdistance 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 fitnesslandscape 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, shortbranched 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 computerdriven 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 singlefunction landscape or all the phenotypic optima within multifunction 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 fitnesslandscape. The volume fraction VF of the entire morphospace occupied by a walk can be computed from the formula VF = [(ΣD_{i})V1/T] × 100%, where VT is the total volume of the morphospace. Because the sample statistics obtained from singleand multiplefunction fitnesslandscapes (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).
Single Versus Multitask Walks
Unfettered walks over stable fitnesslandscapes are illustrated in Figs. 3 and 4 for a morphospace containing 200,000 phenotypes mimicking early vascular land plants. As noted, the morphospace is multidimensional, consisting of a domain occupied by "ancient" isometrically branched phenotypes and another occupied by more "derived" anisometrically branched morphologies (Figure 3A). Consequently, the plots
TABLE 1 Sample statistics for simulated walks in Figs. 3 and 4

Sample statistics^{*} 


N 
n 
D(± SE) 
VF 
Singletask walks 




Light interception, E 
116 
3 
5.81 ± 0.152 
0.568 
Mechanical stability, M 
81 
3 
5.49 ± 0.186 
0.335 
Reproductive success, R 
56 
1 
4.37 ± 0.130 
0.117 
± SE 
84.3 ± 17.4 
2.33 ± 1.15 
5.22 ± 0.44 
0.34 ± 0.13 
Multitask walks 

EMR 
49 
7 
14.4 ± 0.58 
3.65 
ER 
41 
5 
15.1 ± 1.02 
3.53 
EM 
40 
5 
21.6 ± 1.26 
10.1 
MR 
13 
1 
13.7 ± 1.63 
0.84 
± SE 
35.8 ± 7.85 
4.50 ± 1.26 
16.2 ± 1.82 
4.52 ± 2.26 
^{*}N, number of steps in walk; n, number of phenotypic maxima or optima in landscape; D, mean diameter of steps in walk; VF, volume fraction of morphospace occupied by walk. 
of walks are graphic reactions of mathematically more complex features. Every walk proceeds through the same morphospace; walks differ solely as a consequence of differences in fitness topologies. Specifically, walks are shown for three singletask and four multitaskdefined fitnesslandscapes. The three individual tasks are light interception E, mechanical stability M, and reproduction R (Figure 3). In turn, these tasks have four combinatorial permutations (Figure 4), three of which give twotask landscape (i.e., EM, ER, MR) and one of which is a threetask landscape (i.e., EMR).
The most apparent differences between simulated single and multitask walks are the number and magnitude of their phenotypic transformations, on the one hand, and the number of phenotypic maxima and optima they reach within landscapes, on the other (Table 1). Singletask walks have many small phenotypic transformations within landscapes that contain what appear to be comparatively few phenotypic maxima. By contrast, multitask walks have few, but large, transformations within landscapes that, at first glance, appear to contain comparatively many phenotypic optima. Also, the mean morphospace volume occupied by multitask walks is greater than that occupied by singletask walks (Table 1). Statistical comparisons indicate that the hypothesis that multitask walks require significantly larger phenotypic transformations than those of singletask walks can be accepted (Table 2). However, statistical comparisons show that the mean number of phenotypic maxima in singletask landscapes does not significantly differ from that of optima in multitask landscapes. In part, this is due to the small sample sizes for each of these two categories of fitnesslandscape and to
TABLE 2. Summary of tests for the equality of values (see Table 1)

Parameter^{*} 


N 
n 
D 
VF 
1.55 
2.17 
5.87 
9.46 

3.66 
3.69 
3.25 
3.19 

^{*}, Absolute value of the t test for sample mean; , approximate critical value of t distribution; > indicates that mean values significantly differ at the 5% level. 
the fact that the topology of fitness resulting from performing two tasks, mechanical stability and reproduction, contains a single phenotypic optimum (Figure 4A) that dramatically depresses the mean and inflates the SE for the mean number of optima. Nonetheless, the largest number of optima observed among all simulated landscapes is attained when fitness is quantified in terms of all three tasks, suggesting that the hypothesis would have been accepted had walks been simulated in landscapes for which fitness was defined in terms of other biological tasks in addition to light interception, mechanical stability, and reproduction.
It is instructive to compare the fitness of phenotypic maxima with the fitness of phenotypic optima. Although every simulated walk is permitted to reach all the maxima or optima in a particular landscape, the elevation of peaks (maxima or optima) differs from one landscape to another because fitness is defined in different terms in each landscape. Because phenotypic maxima and optima occupy fitness peaks, their absolute fitnesses define a landscape's elevation and, therefore, the gradient of the phenotypic transformations attending a walk. In theory, the magnitudes of the fitness of phenotypic maxima are greater than the magnitudes of the fitness of phenotypic optima. Therefore, the observation that the fitness of phenotypic maxima is greater than that of phenotypic optima is somewhat trivial. What is not unimportant, however, is that the "currency" in which fitness is measured differs among landscapes—that is, fitness was measured in different units (e.g., quanta of light absorbed, probability of mechanical failure, distance of spore dispersal). Therefore, comparisons among the elevations of different landscapes can be made only in relative, rather than absolute, terms. The ratio of the fitness of a phenotypic maximum (or optimum) and the fitness of the ancestral phenotype is useful because it normalizes the elevation of peaks and can be used to crudely compare the topologies of very different landscapes.
Noting that the normalized fitness values are ratios, a comparison for the fitnesslandscapes shown in Figure 3 with those shown in Figure 4 indicates that the topologic relief of singletask landscapes is, on the average, 10 times greater than that of multitask landscapes—that is, the fitnesses of phenotypic maxima with respect to the fitnesses of their ancestral condition are 10 times greater than the fitnesses of phenotypic optima with respect to their ancestral condition. Thus, the fitness of phenotypic optima apparently falls closer to the mean fitness of all the phenotypes within a landscape as the functional complexity of the phenotypes under selection increases. As noted, this result is consistent with engineering theory that indicates that the performance levels of artifacts designed to perform individual functional tasks are higher than those of artifacts designed to simultaneously perform two or more of the same tasks. Additionally, within both categories of fitnesslandscapes, the relative fitness values of phenotypes occupying fitness peaks decreases as the number of peaks increases (r = 0.82; N = 25 maxima and optima)—that is, the number of phenotypic maxima (or optima) increases as the elevation of a landscape declines.
These observations are crudely summarized in Figure 5; they suggest that both the number and the accessibility of phenotypic optima increase as the number of functional obligations contributing to total fitness increases. Put differently, as the complexity of optimal phenotypes increases, the fitness of these optima falls closer to the mean fitness of all the phenotypes under selection. One implication of this conclusion is that the majority of walks over complex fitnesslandscapes occurs over fitness plateaus and, therefore, is largely undirected by gradients of fitness until walks approach the foothills of fitness peaks.
Weaknesses and Strengths of Simulated Walks
However entertaining they may be, computersimulated walks have four obvious weaknesses. First, "fitness" was measured in terms of comparatively few biological tasks that were further assumed to contribute to fitness in an independent and equal manner. The obvious epistatic relation between photosynthesis and reproduction (Gates, 1965; Nobel, 1983), therefore, was entirely neglected, as was the possibility that some tasks are more important to fitness than others (Franklin and Lewontin, 1970; Lewontin, 1974; Ewens, 1979). Second, walks were simulated as continuous processions among more fit phenotypes. Alternatively, plausible types of walks were not considered (Gillespie, 1983, 1984; Kauffman, 1993). Third, fitnesslandscapes were assumed to be spatially stable in pointed neglect of evident changes in the environment that are predicted to shift the location of fitness optima
and accelerate evolution, particularly in very large panmictic populations (Wright, 1932). And fourth, all walks were assumed to be unfettered by genetic or development constraints. Even for plants, which arguably may be more phenotypically ''plastic" than animals, this is a naive expectation (Maynard Smith et al., 1985).
On the other hand, the approach taken here has some obvious strengths. First, walks were simulated over a dimensionally complex morphospace containing phenotypes representative of the entire spectrum of vascular landplant morphology. Second, although only three were considered, the functional obligations elected to define and quantify fitness are biologically realistic for the majority of past and present terrestrial plant species. Third, although the environment, living and nonliving, is in constant flux, the particular episode of plant evolution focused upon here most likely was dominated by the operation of physical laws and processes. Metaphorically, the fitnesslandscape of the first occupants of the terrestrial landscape was painted in the primary colors of biophysics rather than the subtle hues of complex
biotic interactions characterizing subsequent plant history. And fourth, the morphological trends predicted by the phenotypic transformations attending simulated walks are, in very broad terms, compatible with those actually seen in the fossil record of early tracheophytes. This correspondence is important on two accounts. First, it suggests that the developmental repertoire of early vascular plants was capable of phenotypic transformations sufficiently dramatic to warrant the assumption that the walks entertained by these organisms were largely developmentally unfettered. Second, if the hypothetical relations between fitness topologies and the dynamics of walks forecast by computer simulations have any relevancy, then they must, at the very least, mimic trends evinced in the fossil record of plants.
There can be little doubt that the phenotypic optima reached by simulated walks, particularly those over the tripartite fitnesslandscape, are morphologically complex (Figure 4D) nor that all phenotypic maxima or optima are attainable by walks proceeding essentially from the archetypal vascular land plant (i.e., Cooksonia). Fossil remains from the Late Silurian Period indicate that the first tracheophytes were comparatively short, consisting of equally branched, naked axes that simultaneously functioned as photosynthetic and reproductive organs. During much of the Devonian Period, the maximum stature of sequentially younger plant taxa steadily increased. This intertaxonomic trend in plant size was attended by significant evolutionary changes in branching morphology, among which unequal branching and horizontally planated lateral branching systems are notable. Importantly, unequal branching is a requisite for and, therefore, prefigures the elaboration of a main vertical axis for mechanical support. By the same token, the planation of lateral branches, which facilitates light interception, has been traditionally interpreted as a precursor to the evolution of megaphylls (Stewart and Rothwell, 1993). Therefore, it is not unreasonable to suppose that the transition from equal to unequal branching, which was evolutionarily rapid and invariably adopted by simulated walks, was a requisite for subsequent morphological trends and likely positioned derived phenotypes at the foothills near (rather than within the valleys between) fitness peaks (Figure 6).
By the latest Devonian Period arborescent species bearing planated lateral branching systems and true leaves were not uncommon (Stewart and Rothwell, 1993; Taylor and Taylor, 1993). This fact is consistent with the observation that the majority of the phenotypic maxima in multitask landscapes have horizontally planated lateral branching systems, as do the phenotypic maximum in the fitnesslandscape defined by light interception. Virtually every major vascular landplant lineage evolved arborescent, leafbearing species, although these species obviously
differed in morphological, as well as anatomical, details. In very broad terms, the appearance of ancient tracheophyte lineages evincing parallel or convergent phenotypic evolution is a feature mimicked by simulated walks. In all but two fitnesslandscapes, walks repeatedly branched to obtain many phenotypic maxima or optima, most of which have a treelike appearance (i.e., unequally branched with a main vertical "stem") with many lateral, planated "branches" or "leaflike appendages." Some walks even converge on and cross through the same
regions in the hypothetical morphospace of early vascular land plants (see Figure 4B).
Another, although highly problematic, parallel that can be drawn between simulated walks and the early evolution of tracheophytes relates to the "dilated" terminal steps of each branch in the walks through multitask landscapes. These terminal steps indicate that the last phenotypic transformations required to reach optima within a landscape are more sensational compared with prior phenotypic transformations. This hypothesis is consistent with the fact that the highestpertaxon origination rates as well as the highest rates of appearance of morphological (as well as anatomical) characters occur toward the end of the Devonian Period, which marks the closure of early landplant evolution (Niklas et al., 1980; Knoll et al., 1984). Interestingly, a significant temporal lag between the first appearance and rapid taxonomic diversification of animal, as well as plant, lineages is not atypical (Sepkoski, 1979; Tiffney, 1981). It should be noted, however, that simulated walks have no temporal component—steps in walks are vectors whose magnitudes are measured in space, not time. Although the volume of the morphospace occupied by a step denotes the phenotypic variance required to reach the next more fit phenotype, the "time" required to achieve this variance cannot be specified.
However tantalizing the similarities between simulated walks and the broad morphological trends seen in early landplant evolution, they cannot be taken as prima facie evidence that the mathematical and statistical properties of simulated walks reflect reality, nor can they be taken as evidence that the early evolution of vascular plant shape was governed by the biological obligations to intercept sunlight, remain mechanically stable, or to disperse large numbers of spores over great distances. However important these biological tasks may be to plant growth, survival, and reproductive success, the correspondence between simulated and empirically determined morphological trends for early tracheophytes may be simply fortuitous. And, under any circumstances, correlation can never be taken as evidence for a causeeffect relationship.
With these caveats clearly in mind, the following hypotheses are tentatively proposed for future study: (1) The fitnesslandscapes defined by a single biological task require comparatively small, but numerous, morphological transformations to reach phenotypic maxima (i.e., singletask landscapes are "finegrained," yet steep), whereas manifold functional obligations obtain "coursegrained," but less steep, fitnesslandscapes; (2) coursegrained landscapes contain a greater number of phenotypic optima than the number of phenotypic maxima in finegrained landscapes; (3) multitaskdriven walks occupy a greater volume
of the morphospace than do singletaskdriven walks; (4) multitask optima have a lower overall fitness than singletask phenotypic maxima; (5) organisms evincing developmental plasticity (and therefore the potential for significant phenotypic variation) (i) evolutionarily benefit by their ability to walk "rapidly" through and occupy a greater volume of the theoretically available morphospace, (ii) will be at increasing advantage as the number of manifold functional obligations increases, but (iii) are at a disadvantage whenever circumstances abruptly change to favor a single functional obligation rather than the full complement of functions.
Wright's metaphor suggests a "trial and error mechanism on a grand scale by which the species may explore the region surrounding the small portion of the fitness field which it occupies" (Wright, 1932). Attempts to cast this and other evolutionary mechanisms in terms of biologically realistic models by means of computer simulations are still very much in their infancy. As heuristic tools, however, simulations designed to forecast opportunistic phenotypic transformations over the topologies of fitnesslandscapes illustrate some of the initial steps required to adapt Wright's metaphor to understanding the evolution of plant morphology.
Summary
Computer simulated phenotypic walks through multidimensional fitnesslandscapes indicate that (1) the number of phenotypes capable of reconciling conflicting morphological requirements increases in proportion to the number of manifold functional obligations an organism must perform to grow, survive, and reproduce, and (2) walks over multitask fitnesslandscapes require fewer but larger phenotypic transformations than those through singletask landscapes. These results were determined by (1) simulating a "morphospace" containing 200,000 phenotypes reminiscent of early Paleozoic vascular sporophytes, (2) evaluating the capacity of each morphology to perform each of three tasks (light interception, mechanical support, and reproduction) as well as the ability to reconcile the conflicting morphological requirements for the four combinatorial permutations of these tasks, (3) simulating the walks obtaining all phenotypic maxima or optima within the seven "fitnesslandscapes," and (4) computing the mean morphological variation attending these walks. The results of these simulations, whose credibility is discussed in the context of early vascular landplant evolution, suggest that both the number and the accessibility of phenotypic optima increase as the number of functional obligations contributing to total fitness increases (i.e., as the complexity of optimal phenotypes in
creases, the fitnesses of optima fall closer to the mean fitness of all the phenotypes under selection).
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