Adaptive Walks Through Fitness Landscapes for Early Vascular Land Plants Karl J. Niklas American Journal of Botany, Vol. 84

Adaptive Walks Through Fitness Landscapes for Early Vascular Land Plants

Karl J. Niklas

American Journal of Botany, Vol. 84, No. 1. (Jan., 1997), pp. 16-25.

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http://www.jstor.org Tue Mar 25 09:35:07 2008 American Journal of Botany 84(1): 16-25. 1997.

ADAPTIVEWALKS THROUGH FITNESS LANDSCAPES FOR EARLY VASCULAR LAND PLANTS'

Section of Plant Biology, Cornell University, Ithaca. New York 14853

Hypothetical adaptive walks (i. e., morphological transformation series gaining increasing relative fitness) were simulated through a computer-generated domain for early vascular land plant morphologies to examine the relationship between the dynamics of adaptive walks and the topologies of fitness landscapes. A total of 15 hypothetical adaptive walks were simulated, assuming that relative fitness was based on performing one or more of four biological tasks: maximizing light interception, mechanical stability, and reproductive success, and minimizing total surface area. Morphologies occupying fitness peaks typically were similar to some early vascular land plant remains. The most stringent task (the minimization of total surface area) resulted in a few, comparatively small Y-shaped morphologies. Based on the 15 walks, the number of fitness peaks increased and their heights decreased as the number of tasks simultaneously performed increased. These results (which are consistent with prior computer-simulated walks treating light interception, mechanical stability, and reproductive success) suggest that the biological requirement to conserve water reduced the number of phenotypic options available to the earliest land plants, and that, once this adaptive hurtle was overcome, the simultaneous performance of two or more tasks, increased the number of phenotypic options with equivalent relative fitnesses that could be rapidly reached due to the comparatively small fitness differential between derived and ancestral morphologies.

Key words: computer simulations; land plants; relative fitness.

The central dogma of Darwinian evolution rests on Wright's metaphor in useful terms, however. Among the three premises: individuals within a population exhibit more obvious-of these are the requirement to quantify hereditary variation, some individuals are better equipped fitness in a biologically meaningful way, the naive ex- to survive or reproduce than others, and more progeny pectation that all "conceivable" variants have been iden- are produced per generation than the environment can tified, and that the components of fitness are nonepistatic sustain (Dobzhansky, 1937; Mays, 1942; Wallace, 1981). (Lewontin, 1974, 1977; Levin, 1978; Ewens, 1979; The logical consequences of these premises are threefold: Gould, 1980; Scharloo, 1991; Kauffman, 1993). In a few individuals are eliminated, the elimination is nonrandom cases, these obstacles have been overcome by treating with respect to hereditary variation, and individuals with evolving chemical systems as comparatively simple an- features that favor survival or reproductive success within alogs to more complex (organismic) systems (e.g., Eigen, the context of the their environment increase in number 1987; Gillespie, 1983, 1984; Kauffman and Levin, 1987). due to the elimination of less fit individuals. This dogma Chemical systems afford an opportunity to define fitness and its consequences were redacted into a powerful met- (e.g., catalytic rates) and to stipulate the topology of the aphor for adaptive evolution by Sewall Wright (1931, fitness landscape for all conceivable variants (e.g., per- 1932) who conceived of evolution as a "local search" missible protein configurations). Local searches in such by variants within a population for "fitness peaks" on a a chemical system, as for example those protein trans- landscape containing all conceivable variants within the formation series obtaining faster rates, may thus be used population. This metaphor draws attention to three criti- to explore the dynamics of chemical adaptive changes. cal requirements for understanding adaptive evolution: Prior research has shown that other heuristically useful the quantification of fitness in terms of the environment, systems are equally, if not more amenable to this kind of the resulting topology of the fitness landscape, and the approach. One such system employs computer-generated dynamics of local searches obtaining increased popula- branching morphologies fabricated to mimic early De- tion fitness. vonian vascular land plants for which the relative fitness Numerous obstacles confront attempts to cast Sewall of phenotypic variants can be uniformly quantified (Nik- las and Kerchner, 1984; Niklas, 1995). Branching pat- Manuscript received 26 March 1996; revision accepted 14 August terns are often correlated with major phyletic groups 1996. . (Rothwell, 1995), and, in comparison to more recently The author thanks William E. Stein, Jr. (The State University of New plants, those of early land plants are cornpara- York, Binghamton) who acted as Editor-in-Chief and supervised the review of this paper; and Nick Rowe (Laboratoire de PalCobotanique, tivel~ (Banks, 1975; Gensel and 1984; Institute des Sciences de l'Evolution, Montpellier) and one anonymous Stewart and Rothwell, 1993; Taylor and Taylor, 1993). reviewer for making many useful suggestions to improve an early draft Consequently, the construction of a morphological do- of this paper. The author dedicates this paper to Harlan I? Banks (Cor- main for early land plants is practical, while phenotypic nell University), a friend and colleague whose tripartite taxonomic treat- among these morphologies may shed ment of early vascular land plants continues to stand the test of time, and to David M. Raup (University of Chicago), who paved the way for light on phyletic relationships. ~ikewise,the various bi- the use of computer-generated morphological domains in understanding ological tasks that these plants must have had to perform evolution. to grow, survive, and reproduce (i.e., fitness components) January 19971 NIKLAS-FITNESSLANDSCAPES are comparatively well known (e.g., light interception, water conservation, and mechanical support of vegetative and reproductive structures) and are quantitatively trac- table in terms of biophysical laws and processes (Niklas, 1988, 1992). An advantage of this phenotypic rather than chemical system is that morphological components are arguably the principal foci of selection pressures. Another is that the evolutionary history of the early vascular land plants is comparatively well known and thus presents an opportunity to compare the reasonableness of hypothetical adaptive walks through the fitness domains of fabricated phenotypes. TWO conclusions have been drawn from previous ex- plorations of hypothetical adaptive walks through the early land plant domain (Niklas, 1995). First, the number of phenotypes occupying "adaptive peaks" increases in proportion to the number of biological tasks that must be simultaneously performed, and, second, the difference between the most and least fit variants in the domain declines as the number of tasks performed increases. Al- though intriguing, these conclusions are tentative because they were based on the differences among only seven adaptive walks predicated on performing one or more of three biological tasks (i.e., maximizing light interception, mechanical stability, and reproductive success, here de- Fig. 1. Physical description of the mathematical parameters used to construct hypothetical early land plant morphologies with equal and fined in terms of spore number and potential for long- unequal branching (left and right, respectively). Three variables were distance dispersal) whose properties were occasionally used: the bifurcation angle, 4, the rotation angle, y, and the frequency statistically insignificant. of branching, p. Unequally branching morphologies required separate This paper reports on the properties of an additional numerical values for each of these three variables, one set for each eight adaptive walks through the same computer-gener- member resulting from an apical bifurcation. ated domain for early land plant morphologies. Here, fitness was defined on the basis of performing one or more of four rather than three biological tasks, i.e., maximizing directly proportional to the frequency of branching (see Appendix). Ax- light interception, mechanical stability, and reproductive ial length and the frequency of branching thus automatically defined the total biomass of a morphology (i.e., biomass was the product of the success, and minimizing total plant surface area to con- number of axes per phenotype and the weights of axes that have uni- serve water by reducing evapotranspiration. By increas- form girth and density but different lengths), while the overall height, ing the number of biological tasks to four, a larger num- H, of each morphology was stipulated by three variables (y, 4, and p) ber of hypothetical adaptive walks could be statistically because each variable influenced the elevation or number of axial ele- compared to determine whether the number and access- ments per morphology. ability of fitness peaks increase in proportion to the com- The entire morphological domain for early vascular land plants was plexity of fitness landscapes (i.e., the number of tasks constructed by independently varying each of the three variables within simultaneously performed). each of the two subdomains. The spatial ordering of morphologies within the entire domain was predetermined by assigning ascending numer- MATERIALS AND METHODS ical values to each variable. Specifically, each variable was assigned numerical values increasing in uniform increments (e.g., the bifurcation The morphological domain-The procedures used to construct the angle varied from loto 180" in loincrements; the frequency of branch- domain for all conceivable early vascular land plant morphologies (= ing varied from 0.0 to 1.0 in 0.01 increments). The three variables were a "morphospace" sensu Thomas and Reif, 1993) have been described orthogonally plotted such that the location of each morphology was elsewhere (Niklas and Kerchner, 1984). Briefly, each morphology was specified by a Cartesian coordinate system (see Fig. 2). This protocol mathematically assembled from cylindrical axes stipulated to have uni- resulted in a total of =1.6 X lo9 morphologies whose spatial ordering form girth and density. Two broad categories of morphologies were thus within the domain permitted very small incremental transformations fabricated, those with equal branching (isodichotomous) and those with from one morphology to its neighboring morphologies (i.e., "saltation- unequal branching (Fig. 1). In the isodichotomous category, the position al" morphological transformations among neighboring morphologies and number of axes were determined by three variables: the rotation were not required). angle, y, which defined the orientation of each axis with respect to the . Because of the massive size of the entire domain and the desirability horizontal plane; the bifurcation angle, 4, which defined the angle of reducing computer computation time, all local searches began in the spanned between two adjoining axes resulting from the bifurcation of isodichotomous subdomain because this subdomain contained the Y- an apex; and the frequency of apical branching, p, which defined the shaped plant morphologies most reminiscent of the earliest currently number of times a branching system bifurcated. In the case of aniso- known vascular plants (Steganotheca and Cooksonia; see Edwards and dichotomously branching morphologies, the position and number of Fanning, 1985; Edwards, Davies, and Axe, 1992), which provided the branches required the same three variables, but the values of these vari- "ancestral" morphological condition. Local searches exhausting the ables were independently assigned to each of the two axial elements morphological possibilities within the isodichotomous subdomain pro- comprising each bifurcation (e.g., 4, and 4,; see Fig. 1). For both mor- ceeded into the anisodichotomous subdomain. The points of entry into phological categories, internodal (axial) length, I, was stipulated to be this subdomain were confined to the phenotype(s) with the closest mor- AMERICANJOURNAL OF BOTANY [Vol. 84 m combination of two or more tasks Methods for evaluating the performance of three of these tasks (maxlmlzlng light interception, L; maxi- ////// ///// mizing mechanical stablllty, M; and maxlmlzing reproductive success,

/ / ,/ ,/ ,/ ,/ A R) have been described elsewhere (see Appendix). Briefly, the abillty of each morphology to intercept light was computed on the basis of the integrated area under the curve plotting the quotient of the projected and total surface area against the elevation angle of the sun (from 0" to 180" in lo increments). The ability of each morphology to maximize the area under this curve was evaluated based on the diurnal pathway of the sun at equatorial latitude. Mechanical stability was gauged on the basis of the bending moment acting on the single vertical support axis subtending each morphology. The bending moment was calculated on the basis of the weight distribution resulting from the three-dimen- sional display of all axes whose weights were stipulated by assuming tissue density equals the density of water. Mechanical stability was taken as the inverse function of the bending moment. Reproductive success was gauged on the basis of the number of sporangia and their elevation on each morphology. A simple ballistic model for long-distance spore dispersal (taken from Okubo and Levin, 1989) was used to estimate the distance spores could be transported from each morphology Frequency of Branching, p based on the height of the sporangium from which they were released. Each terminal axis was assumed to bear a single sporangium at its tip; each sporangium was assumed to produce the same number of spores, each of which had the same terminal settling velocity. Thus, reproductive success was taken as a function of both the number and height of sporangia (see Appendix). The fourth biological task, which was added to the three previously considered tasks, was the minimization of total surface area, S. The rationale was that the conservation of water played an important role in the colonization of land by plants and that total surface area serves as a crude surrogate for this task in the absence of precise knowledge of cuticle thickness, chemistry, stomata1 number, location, and conduc- tance, the extent of vascular tissue development, and the availability of water. Noting that all axes have uniform girth, the numerical value of local S was solely stipulated by the frequency of branching because this vari- fitness able mathematically predetermined the number of axes per morphology maximum as well as their lengths, I. The relative fitness of each morphology performing a single task was calculated as a function of the ability to maximize light interception, mechanical stability, and reproductive success, and to minimize total surface area. It was further assumed that each of these four tasks contributed equally and independently to relative fitness and that relative fitness could be calculated as the geometric mean of the performance Arbitrary Units levels of two or more tasks. Thus, when fitness was defined on the basis Fig. 2. Cartesian coordinate system based on the three variables of simultaneously maximizing light interception and mechanical stabil- used to construct hypothetical morphologies. The spatial orderings of ity, relative fitness was computed as (Lm)'IZ,where L is the magnitude all morphologies within the domain described by this coordinate system of the integrated area under the light interception curve and m is the were defined by treating each variable as a continuous variable ranging reciprocal of the bending moment M. Likewise, when fitness was de- from minimum to maximum numerical value. Morphological transfor- fined on the basis of simultaneously maximizing light interception and mations among neighboring morphologies, here shown simply by the mechanical stability, and minimizing total surface area, relative fitness products of the numerical values of the three variables, thus did not was computed as (L~S)"~,where s is the reciprocal of total surface area require abrupt changes in the values of variables (lower diagram). S. Finally, the relative fitness of each morphology was computed as (LRms)Il4 when all four tasks simultaneously contributed to fitness. Al- phological correspondence to those occupying the terminal step of the though relative fitness is expressed as a percentage of maximum fitness search through the isodichotomous subdomain. Because the location of for each landscape, the units used to measure absolute fitness differed each morphology within both subdomains was invariable (i.e., regard- among the various landscapes (e.g., light interception was measured in less of the task used to quantify relative fitness, the spatial relationships. units of watt-hours, mechanical stability was measured in units of force- among morphological variants did not change), local searches were de- length; reproductive success was measured in units of transport distance terminate. That is, every computer-simulated "adaptive walk" through and spore number). a particular landscape obtained precisely the same series of morphological transformations. Nevertheless, because the topologies of the fitness Local searches ("adaptive walks")-As noted, each search for mor- landscapes (i.e., the numerical values of relative fitness) depend on how phologies with progressively higher relative fitness was initiated at the fitness was defined, searches through different landscapes identified dif- point within the isodichotomous subdomain corresponding to the Y-like ferent transformation series. morphology of Cooksonia. Each "step" in a search was restricted to Relative~5tness-The relative fitness of each morphology in the do- the space immediately surrounding the morphology identified in the main was evaluated for each of the four biological tasks and for each prevous iteration to have higher relative fitness. This was accomplished January 19971 NIKLAS-FITNESS LANDSCAPES

Fig. 3. Morphologies occupying adaptive peaks (with highest equivalent relative fitness) in fitness landscapes defined by maximizing the performance of one of four biological tasks. (A) Maximizing reproductive success. (B) Maximizing light interception. (C) Minimizing total surface area. (D) Maximizing mechanical stability. by a computer algorithm that calculated the relative fitnesses of all maximized the performance of one task, 3.3 phenotypes morphologies immediately neighboring the morphology in the step. If that optimized the performance of two tasks, and 6.5 phe- two or more morphologies had equivalent higher fitness, the search notypes that optimized the performance of three tasks. A branched and took separate trajectories. This process was reiterated until total of 20 phenotypes were identified by the local search local searches reached all attainable morphologies that were surrounded for morphologies that had near equivalent abilities to per- by others having lower relative fitnesses (i.e., morphologies occupying form all four tasks (Table 1). Statistical comparisons, "adaptive peaks"). However, because saltational morphological trans- based on the Tukey-Kramer test for the significance of formations were not permitted (i.e., searches could not "jump" over differences among means with different variances, indi- fitness "valleys"), it is possible that alternative fitness peaks went un- cated that the number of adaptive peaks significantly dif- detected in each fitness landscape. fered at the 0.5% level among the two, three, and four task-defined fitness landscapes. Likewise, one-way ANO- RESULTS VA indicated that the differences in the means of the The general appearance of morphologies identified as number of adaptive peaks for these three different cate- either maximizing or optimizing the performance of one gories of fitness landscape were statistically significant. or more tasks differed in size and shape among the 15 However, the mean numbers of adaptive peaks for the fitness landscapes (Figs. 3-6). The morphologies occu- one and two task-defined landscapes did not significantly pying adaptive peaks (those that maximized the perfor- differ (see Table I), although regression analysis showed mance of one task or that optimized the simultaneous that the number of adaptive peaks, n, exponentially in- performance of two or more tasks) in all fitness land- creased as the number of tasks, N,defining fitness in- scapes either solely or partially defined on the basis of creased and that these two parameters were overall sig- minimizing total surface area were fewer in number and nificantly correlated: n = 1.02 (109, r2 = 0.92. generally shorter and more sparsely branched than those The relative heights of adaptive peaks decreased as the found in landscapes for which this task played no role in number of tasks defining relative fitness increased (Table defining relative fitness. Morphologies occupying adap- 2). Noting that the "currency" in which fitness was mea- tive peaks in landscapes either solely or partially defined sured differed among the 15 fitness landscape (e.g., by light interception had, on average, much branched and amount of light intercepted, spore number and dispersal near horizontally oriented lateral systems. A characteris- distance, bending moment), it was not possible to draw tic feature of morphologies occupying adaptive peaks in direct comparisons among the relative heights of adaptive fitness landscapes either solely or partially defined by peaks in different fitness landscapes. However, it was maximizing mechanical stability was the near vertical ori~ possible to compare the heights of adaptive peaks on a entation of lateral branching systems. This feature also particular fitness landscape to the relative fitness of the characterized the most fit morphologies in landscapes de- ancestral Cooksonia-like morphology by taking the quo- fined on the basis of reproductive success. tient, h (i.e., relative peak height), of the peak fitness to The number of adaptive peaks located by searches in ancestral fitness. Comparisons among landscapes showed the 15 fitness landscapes surveyed increased as the num- that the relative peak heights of two and three task-de- ber of biological tasks upon which relative fitness was fined landscapes and the relative peak heights of three predicated increased. Local searches within the morpho- and four task-defined landscapes did not significantly dif- logical domain, on average, identified 2.5 phenotypes that fer. However, overall, h was inversely related to the num- Fig. 4. Morphologies occupying adaptive peaks (with highest equivalent relative fitness) in fitness landscapes defined by optimizing the performance of two of four biological tasks. (A) Mechanical stability and reproductive success. (B) Mechanical stability and total surface area. (C) Light interception and mechanical stability. (D) Light interception and total surface area. (E) Reproductive success and light interception. (F) Reproductive success and total surface area.

Fig. 5. Morphologies occupying adaptive peaks (with highest equivalent relative fitness) in fitness landscapes defined by optimizing the performance of three of four biological tasks. (A) Mechanical stability, light interception, and reproductive success. (B) Mechanical stability, light interception, and total surface area. (C) Mechanical stability, reproductive success, and total surface area. (D) Light interception, reproductive success, and total surface area. January 19971

Fig. 6. Morphologies occupying adaptive peaks (with highest equivalent relative fitness) in fitness landscapes defined by optimizing the performance of four biological tasks: maximizing light interception, mechanical stability, and reproductive success, and minimizing total surface area.

ber, N, of simultaneously performed tasks: h = 38.6 phological transformations, (4) local searches are unfet- N-1.78,r2 = 0.94. tered, such that all transformations among neighboring phenotypic variants are equiprobable, (5) fitness land- DISCUSSION scapes do not change during the course of local searches due to changes in environmental conditions that would The results reported here resonate with the prior hy- alter the currency by which relative fitness is measured pothesis that the number of phenotypes occupying fitness (Levins, 1968; Levin, 1978), and (6) density and fre- peaks increases while the heights of peaks decrease in quency-dependent effects on fitness are minimal or ab- proportion to the number of biological tasks contributing sent. Each of these stipulations is open to severe criti- to relative fitness. That these relationships generally hold cism; e.g., (1) the developmental repertoire of early vas- true for all morphological domains for all manner of or- cular land plants was diverse and, with the closure of the ganism is highly problematic because they are predicated Devonian, encompassed secondary growth and other in- on a highly simplified model for early land plants. novations, such as leaves (Stewart and Rothwell, 1993; Among the weaknesses of this model are the stipulations Taylor and Taylor, 1993; Rothwell, 1995), (2) the obvious that (1) all early land plant morphologies share the same epistatic relationships among photosynthesis, water con- developmental pattern and reproductive potential (apical servation, and reproductive potential flout the naive ex- dichotomization, terminal sporangia, and so forth), (2) the pectation that these and other biological obligations in- performance of each task contributed equally and inde- fluencing growth, survival, and reproductive success con- pendently to relative fitness, (3) local searches through tribute equally and independently to relative fitness (Le- the morphological domain involve nonsaltational mor- wontin, 1974, 1977), and, finally (3) genetic and

TABLE1. Summary statistics for the relationship between the number TABLE2. Summary statistics for the relationship between the relative of adaptive peaks, n, and the number of tasks, N, used to define heights of adaptive peaks, h, and the number of tasks, N, used to the relative fitness of hypothetical early vascular land plant mor- define the relative fitness of hypothetical early vascular land plant phologies. a = positive values denote pairs of means significantly morphologies. a = positive values denote pairs of means signifi- differ at the 5% level. cantly differ at the 5% level.

A) Number of morpholog~es Relative height Number of tasks occupying adaptive peaks Number of tasks of adaptive peaks defining fitness (Mean i SD) defining fitness (Mean 2 SD)

~ - - ~ - - 1 2.5 ? 0.63 1 35.3 ? 1.8 2 3.3 i 0.51 2 11.6 i 0.68 3 6.5 -C 0.63 3 7.7 t 0.14 4 20 4 2.4 B) Comparisons of means for all pairs (based on Tukey-Kramer test) B) Comparisons of means for all pairs (based on Tukey-Kramer test) N N 22 AMERICANJOURNALOF BOTANY [Vol. 84 developmental limitations on the acquisition of some of adaptive walks. Each morphological transformation morphologies undoubtedly exist such that, in theory, within an adaptive walk is computed in real time, but "saltational" morphological transformations would be re- there is no correspondence a priori between computation quired for a population to move across a fitness valley time and evolutionary time. Unfortunately, the relative toward an adaptive peak. heights of adaptive peaks (i.e., the topological relief of a Because the hypothesis entertained here is engendered fitness landscape) also do not afford a realistic basis for by a potentially idiosyncratic computer-generated (ab- estimating the speeds of different adaptive walks because stract) flora, the important issue is whether adaptive two alternative interpretations are equally plausible. On walks for this abstract flora have any bearing on the in- the one hand, fitness landscapes with high topological terpretation of early vascular land plant evolution. Mod- relief (those that are defined by one or a few tasks) afford els such as the one presented here are extremely difficult steep fitness differentials among neighboring variants to reify even when designed to parody natural systems upon which natural selection may quickly act. Mathe- amenable to direct experimental manipulation. Because matical models based on population genetics indicate that the biomimetic model for early vascular land plant evo- rapid passage, even across fitness valleys, reduces the ef- lution is not subject to direct experimental challange, the fectiveness of natural selection (Lande, 1985) and can properties of hypothetical adaptive walks for the abstract lead to rapid speciation via a founder effect (see Temple- flora cannot be experimentally validated, even though ton, 1980, 1982). If so, then adaptive walks may be faster many of the hypothetical phenotypes identified to occupy on single task-defined landscapes compared to walks on adaptive peaks bear a morphological correspondence with landscapes defined by the performance of manifold tasks. the fossil remains of some well-known early vascular On the other hand, "smooth" landscapes with little to- plants. pological relief resulting from simultaneously performing Some of these correspondences are intriguing in light many tasks may permit comparatively rapid morpholog- of the functional tasks believed to influence relative fit- ical innovation because natural selection is similarly "re- ness at certain points in early land plant evolution. For laxed," due, in this case, to little differences among the example, all fitness landscapes predicted solely or in part relative fitnesses of neighboring phenotypes. on the biological obligation to conserve water by mini- Although no definitive resolution between these alter- mizing total surface area identify the occupants of fitness natives exists, the tempo of early land plant morpholog- peaks as small, sparsely branched morphologies. Most of ical and anatomical innovation appears to favor the latter these hypothetical morphologies bear a reasonable cor- of these two plausibilities. If the first land plants evolved respondence to some of the earliest known rhyniophytes in the early Silurian (or possibly earlier in the Ordovi- and zosterophyllophytes (e.g., Cooksonia and Renalia, cian) as some believe (see Gray and Boucot, 1977; Gray, see Figs. 3-4). It is not unreasonable to believe that the 1985), then the comparatively low morphological diver- colonization of the terrestrial landscape imposed restric- sity by late Silurian times argues in favor of slow phe- tions on the transpiring surface areas of sporophytes and notypic innovation presumably when water conservation thus restricted plant size (i.e., defined in terms of either took precedence over other biological tasks. The appear- height or number and size of axes) until such time that ance of bona fide vascular plants by the end of the Si- cuticles and stomata evolved and restricted and regulated lurian and certainly by early Devonian times was fol- water loss from aerial axes (see Gates, 1965; Nobel, lowed by a morphological diversification virtually unpar- 1983; Raven, 1984, 1985). Once these early land plant alleled by any subsequent period of land plant evolution, features were evolutionarily acquired, it is not difficult to with the possible exception of the early radiation of the envision selection pressures favoring larger morphologies flowering plants (Knoll et al., 1984). Thus, taken at face capable of optimizing the requirements for water conser- value, the fitness landscapes defined for the earliest land vation, mechanical stability, and the simultaneous eleva- plants by performing one or a few tasks appear to have tion of photosynthetic and reproductive axes. If so, then reduced the tempo of adaptive walks compared to evo- the results reported here predict that the fitness landscape lutionary times when numerous tasks contributed equally for the earliest land plant contained comparatively few to the relative fitness of subsequently evolving vascular but relatively high fitness peaks dominated by the per- land plants. Bereft of a internal chronometer, the simu- formance of a single task (water conservation) only to be lations reported here indicate that single-task landscapes subsequently transformed into fitness landscapes contain- favor anagenesis and convergence on one or a few opti- ing comparatively many but relatively low fitness peaks mal phenotypes. Conversely, manifold-task landscapes molded by the simultaneous performance of manifold favor cladogenesis and phenotypic divergence. rather than one or a few biological obligations. As noted, The hypothetical adaptive walks are consistent with some of the morphologies occupying fitness peaks, es- engineering theory treating systems analysis. This theory pecially those in landscapes defined by the performance as well as the results of engineering practice predicts that of two or more tasks, resemble vascular plants appearing few design options exist for artifacts that must perform in the middle and late Devonian (e.g., lepidodendrids, a single task in comparison to the number of design op- sphenopsids, ferns, and progymnosperms; see Fig. 6). tions for artifacts that must perform manifold tasks This similarity is at least consistent with the notion that (Brent, 1973; Meredith et al., 1973; Gill, Murray, and the fitness landscape of Devonian plants changed from Wright, 1981; Niklas, 1994). The reason for this high- one defined by a single (or few) tasks to one in which lights the sharp logical distinction between "maximiza- all tasks contributed in some measure to relative fitness. tion" and "optimization" (Horn, 1979). The design re- The simulations used in this study have no internal quirements that permit an artifact to maximize the per- chronometer with which to measure the absolute speed formance of a single task tend to be highly specific and January 19971 NIKLAS-FITNESs LANDSCAPES 23

thus give little latitude in the appearance of the artifact. HORN,H. S. 1979. Adaptation from the perspective of optimality. In In contrast, the performance of manifold tasks often en- 0.T Solbrig, S. Jain, G. B. Johnson, and l? H. Raven [eds.], Topics tails antagonistic design specifications that can be rec- in plant population biology, 48-61. Columbia University Press, New York, NY. onciled in various ways to optimize the global perfor- KAUFFMAN,S. A. 1993. The origins of order. Oxford University Press, mance of an artifact. Thus, single-task-defined artifacts Oxford. have fewer alternative designs compared to manifold- , AND S. A. LEVIN.1987. Towards a general theory of adaptive task-defined artifacts. Herein lies a potential explanation walks on rugged landscapes. Journal of Theoretical Biology 128: for the proportional relationship between the number of 11-45. adaptive peaks on a landscape and the number of biolog- KNOLL,A. H., K. J. NIKLAS,P. G. GENSEL,AND B. H. TIFFNEY.1984. ical tasks that must be simultaneously performed. Also, Character diversification and patterns of evolution in early vascular plants. Paleobiology 10: 34-47. herein lies a potential explanation for the inverse rela- LANDE,R. 1985. Expected time for random genetic drift of a population tionship between the complexity of the fitness landscape between stable phenotypic states. Proceedings of the National and its topological relief. Single-task-defined artifacts are Academy of Sciences, USA 82: 7641-7645. especially efficient at what they do; manifold task-defined LEVIN,S. A. 1978. On the evolution of ecological parameters. In P. E artifacts are globally efficient yet comparatively poor at Brussard [ed.], Ecological genetics: the interface, 3-26. Springer- doing any one task due to their design reconciliations. Verlag, New York, NY. The supposition that early land plant biology sub- LEVINS,R. 1968. Evolution in changing environments. Monographs in Population Biology, Number 2. scribed to the logic underlying engineering systems anal- LEWONTIN,R. C. 1974. The genetic basis of evolutionary change. Co- ysis is undoubtedly naive at many levels, but it does pro- lumbia University Press, New York, NY. vide a potentially useful heuristic tool with which to ex- . 1977. Adaptation. Scientijic American 239: 159-169. plore the otherwise intractably complex relationship be- MAYR,E. 1942. Systematics and the origin of species. Columbia Uni- tween organic form and function and the environmental versity Press, New York, NY. conditions attending their evolution. Early land plants af- MEREDITH,D. D., K. W. WONG,R. W. WOODHEAD,AND R. H. WORTMAN. ford an outstanding venue for this exploration owing to 1973. Design and planning of engineering systems. In N. M. New- mark and W. J. Hall [eds.], Civil engineering and engineering me- their comparatively simple morphologies, our ability to chanical series. Prentice-Hall, Englewood Cliffs, NJ. redact their biological functions in terms of mathematical NIKLAS,K. J. 1988. Biophysical limitations on plant form and evolu- descriptions based on physical laws and processes known tion. In L. D. Gottlieb and S. K. Jain [eds.], Plant evolutionary to influence living plants, the breadth and depth of our biology, 185-220. Chapman and Hall, London. understanding of the their fossil record, and the seminal . 1992. Plant biomechanics: an engineering approach to plant role they played in shaping and populating the terrestrial form and function. University of Chicago Press, Chicago IL. landscape. . 1994. Plant allometry: the scaling of form and process. Uni- versity of Chicago Press, Chicago IL. . 1995. Morphological evolution through complex domains of LITERATURE CITED fitness,. In W. M. Fitch and E J. Ayala [eds.], Tempo and mode in evolution: genetics and paleontology 50 years after Simpson, 145- BANKS,H. l? 1975. Reclassification of Psilophyta. Taxon 24: 401-413. 165. National Academy Press, Washington, DC. BRENT.R. P. 1973. Algorithms for maximization without derivatives. , AND V. KERCHNER.1984. Mechanical and photosynthetic con- Prentice-Hall, ~n&wod Cliffs, NJ. straints on the evolution of plant shape. Paleobiology 10: 79-101. DOBSHANSKY,TH. 1937. Genetics and the origin of species, 1st ed. NOBEL,P. S. 1983. Biophysical plant physiology and ecology. W. H. Columbia University Press, New York, NY. Freeman, New York, NY. EDWARDS,D., AND U. FANNING.1985. Evolution and environment in OKUBO,A,, AND S. A. LEVIN.1989. A theoretical framework for data the late Silurian-early Devonian: the rise of the pteridophytes. analysis of wind dispersal of seeds and pollen. Ecology 70: 329- Philosophical Transactions of the Royal Society of London 309B: 338. 147-165. RAVEN,J. A. 1984. Physiological conelates of the morphology of early EDWARDS,D., K. L. DAVIES,AND L. AXE. 1992. A vascular conducting vascular plants. Botanical Journal of Linnean Society 88: 105-126. strand in the early land plant Cooksonia. Nature 357: 683-685. 1985. Comparative physiology of plant and arthropod land EIGEN,M. 1987. New concepts for dealing with the evolution of nu- . cleic acids. In l? Barker and D. Brown [eds.], Cold Spring Harbor adaptation. Philosophical Transactions of the Royal Society of Lon- Symposia on Quantitative Biology 52: 307-320. don B 309: 273-388. EWENS,W. 1979. Mathematical population genetics. Springer-Verlag, ROTHWELL,G. W. 1995. The fossil history of branching: implications New York, NY. for the phylogeny of land plants. In l? C. Hoch and A. G. Ste- GATES,D. M. 1965. Energy, plants, and ecology. Ecology 46: 1-16. phenson [eds.], Experimental and molecular approaches to plant GENSEL,P. G., AND H. N. ANDREWS.Plant life in the Devonian. Praeger biosystematics, 71-86. Missouri Botanical Garden, St. Louis, MO. Press, New York, NY. SCHARLOO,W. 199 1. Canalization, genetic and developmental aspects. GILL,l? E., MURRAY,W., AND N. H. WRIGHT.1981. Practical optimi- Annual Review of Ecology and Systematics 22: 265-294. zation. Academic Press, London. STEWART,W. N., AND G. W. ROTHWELL.1993. Paleobotany and the GILLESPIE,J. H. 1983. A simple stochastic gene substitution model. evolution of plants, 2d. ed. Cambridge University Press, Cam- Theoretical Population Biology 23: 202-215. bridge, England. . 1984. Molecular evolution over the mutational landscape. TAYLOR,T. N., AND E. L. TAYLOR.1993. The biology and evolution of Evolution 38: 11161129. fossil plants. Prentice-Hall, Englewood Cliffs, NJ. GOULD,S. J. 1980. The evolutionary biology of constraint. Daedalus TEMPLETON,A. R, 1980. The theory of speciation via the founder ef- 109: 39-52. fect. Genetics 94: 101 1-1038. GRAY,J. 1985. The microfossil record of early land plants: advances . 1982. Adaptation and the integration of evolutionary forces. in understanding of early tenestrialization, 1970-1984. In W. G. In R. Milkman [ed.], Perspectives on evolution, 15-3 1. Sinauer, Chaloner and J. D. Lawson [eds.], Evolution and environment in Sunderland, MA. the Late Silurian and Early Devonian. Philosophical Transactions THOMAS,R. D. K. AND W.-E. REIF. 1993. The skeleton space: a finite of the. Royal Society of London B 309: 167-195. set of organic designs. Evolution 47: 341-360. , AND A. J. BOUCOT.1977. Early va,scular land plants: proof and WALLACE.B. 198 1. Basic population genetics. Columbia University conjecture. Lethaia 10: 145-174. Press, New York, NY. [Vol. 84

WRIGHT,S. 193 1. Evolution in Mendelian population. Genetics 16: 97- 159. . 1932. The role of mutation, inbreeding, crossbreeding, and selection in evolution. Proceedings of the Sixth International Con- gress on Genetics 1: 356-66.

APPENDIX Light interception and total surface area-Each plant morphology was mathematically considered to be a collection of Y-shaped telomes. The orientation of each axis within each telome with respect to the solar angle, 8, is defined by two variables, the bifurcation angle, 4, swept between the two axes subtended by another, and the rotation angle, y, of the axis with respect to the horizontal plane (see Fig. 1). The ability of each axis to intercept sunlight was determined on the basis of the area under the curve resulting from plotting the quotient of the projected surface area Sp to the total surface area S against 0 (for 1" 5 0 5 180"). For each telome this quotient can be mathematically expressed as 4J 9 = @(cos 8 - sin 0 sin-cos y +cos 8 cos-+ S 4 2 2 4J + sin 8 sin-cos y + cos 8 cos-+ 2 2 4J + sin 8 sin-cos y + cos 0 Fig. A.1. Physical description of moment arms (X) on the axes of 2 an equally branching morphology with uniform bifurcation angle, 4, and a rotation angle, y,resulting in a planated geometry. Subscripts for moment arms denote ascending orders of branching.

function of the incident direction of radiation, S. Denoting 8, the rotation 4J + 2sin 0 cos 0 sin-cos-cos+ y - cos28 angle of the sun about the overall morphology, 2 2

4J - 2sin 8 cos 8 sin-cos-cos+ y - cos28 cos2- 2 2 where

where d and 1 are the diameter and the length of each axis (internode), The (x, y, z) coordinates of an axis were transformed into the (a, 0) respectively. coordinate system such that For purposes of computing Sp/S, the projected outlines of axes were specified by a series of (a, b) coordinates computed such that v = o(x, y, z). (A.8) The interception of light was calculated over a surface grid (with coordinates [i, j]), oriented normal to 9, upon which the outlines of axes where 1 is axial length and fi is the vector representing the direction of were projected. The grid system was "moved" as the ambient incident the axis: angle of the "sun" shifted during its diurnal path. The total power or flux F intercepted by the total surface area of all axes was calculated p, = (sin +)(cos d) as

p, = (sin +)(sin d)

pi = cos +, (-4.3) where d now denotes a complex function of and y. The transformed + where Ai and Aj are changes in the dimensions of the grid system as (a, b) coordinates become the "sun" shifts position, W is the solar inadiance (in watt-hours) measured on surfaces perpendicular to the solar angle 8, t is the transmit- tance of axial-tissues, and n is the number of axes through which light passes. The value of n was calculated as the number of axes whose where outlines blocked a point (i, j) on the grid system. When cast in terms of Sp/S and 8 and taking t = 0, Eq. A.9 becomes c, = sin d c,. = -cos d (A.10) c, = 0 d=cxp. (-4.5) The total surface area of each simulated morphology was calculated on the basis of a uniform axial girth and the lengths and numbers of The vectors ii and V were used to represent the coordinate system'em- axial elements resulting from stipulated values for the frequency of ployed to calculate the amount of light intercepted by an axis as a branching (see Eq. A.15). January 19971 NIKLAS-FITNESSLANDSCAPES

Bending moments-The bending moment, M, for any (but a per- fectly vertical) axis is the product of a bending force and the magnitude of the moment arm, X, at right angles to the direction of the bending force. Referring to the notation provided for the simple, two-dimen- sional branching system shown in Fig. A.l, the individual moment arms are

Thus, assuming 4 = 30°, the numerical value for the bracketed term in Eq. A.13 equals 0.26, 1.80, 6.85, 19.22, and 44.56 when N = 1, 2, 3, and 4, respectively.

Reproductive success and the frequency of branching-The ele- mentary ballistic model of Okubo and Levin (1989) was used to estimate the distance, x, spores elevated to a height, H, would be transported for a given horizontal wind speed, U: U x = H-, (A. 13) which are additive in terms of the moment arms on subtending axes, T e.g., where T is the terminal settling velocity of spores. The terminal settling velocity was held constant at 0.15 m/s (which is the average settling velocity of Lycopodium spores). Theory and measurements indicate that U typically varies as a logarithmic function of H according to the formula

(A.14a)

where u* is the velocity shear, k is Von Karman's constant, d is the zero plane displacement, and z, is the roughness parameter. Equation A.14a was simplified by assuming u* = 0.5H, k = 0.40, d = 0.63H, and z, = 0.13H, so that

(A.14b)

Thus, x Hz. The elevation of sporangia was not constant within or among plant morphology because each terminal axes was assumed to bear a sporangium and because the elevations of terminal sporangia were functions of the frequency of branching, p. For the purposes of this paper, higher order branching systems were simulated by the computer program TREE BAS (see Niklas and Kerchner, 1984). Each plant morphology Because the bending force is the mass acceleration force resulting from was restricted to ten bifurcation events; the resulting maximum number the weight of each axis, the bending moments accrued at the base of of axial elements could thus equal 2N = 1048576. The basal-most sup- branched morphology resulting from a single first-, second-, and third- porting axial element was designated as level 10; all terminal axes were ordered axis are level 1. Branching patterns with varying degrees of bifurcation were simulated by stipulating the frequency of bifurcation, p (at each suc- cessively lower nodal level) according to the linear formula

where p,_,,+,, is the probability of termination at the next generated (lower) nodal level and N + k designates the previously generated nodal level. The frequency of bifurcation was varied from 0.0 to 1.0 (respectively, the highest and lowest frequencies of bifurcation). Axial length was taken as a linear function of p such that the basal-most axial elements were always as long or longer than any more distal axial element. + cos 90" - - (A. 12a) No closed form solution could be found for the mathematical rela- i 3:j1 tionship between p and H, however, because the latter also depended where g is the gravity acceleration constant, p is tissue bulk density, on the rotation angle, y, which was not a correlated function of p. TREE and r is the radius of each axis. It follows that the general case for any BAS computed the H of each terminal axis by means of brute numerical order of branching, N, is given by calculation.