Introduction

The study of tree architecture has a long history. Whole crown size and shape and how it changes with tree size, age, and crowding have long been studied in forestry to evaluate competition and wood yield (e.g., Raulier et al. 1996; Rouvinen and Kuuluvainen 1997) as well as wind-throw risk (King 1986; Stathers et al. 1994; Ancelin et al. 2004). It has been found that crown shape changes with tree age and size (Smith et al. 2014) and is altered by crowding (e.g., Rouvinen and Kuuluvainen 1997). Horn (1971) argued that crown structure should differ between shade-tolerant and -intolerant species as an adaptation to light capture.

At the other extreme, the study of fine-scale branching patterns has revealed regularities. For example, Leonardo da Vinci noted that the sum of the cross sections of daughter branches is the same as that of the parent branches (Richter 1970 cited in Eloy 2011), a relation now known as the pipe-model theory (Shinozaki et al. 1964a, b; Chiba 1998). The pure geometric perspective was given impetus by Mandelbrot (1978, 1983) who showed that iterative branching systems could be described using fractal geometry. This inspired many studies of branching patterns (Borchert and Slade 1981; Zeide 1998) and computer programs that can create visually realistic-looking simulated trees (Fisher 1992; Perttunen and Sievänen 2005) with an emphasis on light capture and space-filling patterns.

The other main line of enquiry has explored and classified branching as a biological process (Fisher and Honda 1979a, b; Fisher and Hibbs 1982; Borchert and Tomlinson 1984; Tomlinson 1987). It has been found that flowering at terminals of branches, for example, forces branching, and that branching patterns during development can be predicted for some species and differ between species. These branching patterns have been related to light capture as well (e.g., Fisher and Honda 1979a, b).

In contrast to the vast literature on branching patterns (either idealized or observed), there are only a handful of studies on the mechanical properties of wood and implications for branching architecture and ecology (e.g., McMahon and Kronauer 1976; Fisher and Stevenson 1981; Niklas 1998; Dean et al. 2002; Alméras et al. 2005; Read and Stokes 2006; Alméras and Fourier 2009; Eloy 2011). It is here shown that further exploration of biomechanics yields multiple insights into the architecture of trees based on costs and constraints on growth. A linkage can also be made with life history theory of trees which provides further insights into how damage risk is weighted in the overall biomass allocation process. It is also shown that many branching patterns respond to competition and biomechanical stresses. However, it is argued that there are certain limits on such responses because of the mechanical properties of wood.

Mechanical constraints

It has long been known (e.g., Greenhill 1881) that vertical structures, such as a tree, are subject to buckling. In the absence of wind loading (e.g., in a dense stand of trees), the main trunk dimensions tend to be close to the allometric coefficients for elastic similarity (McMahon and Kronauer 1976; Eloy 2011), though larger and open-grown trees can show deviations from this relation in the direction of greater taper, which produces a greater margin of safety, likely related to wind stress effects.

Recent work on mechanical properties of wood and growth responses to stress shows that branch growth and, therefore, crown geometry cannot be understood as either a simple iterative branching process (Borchert and Slade 1981) or a simple cantilever beam system such as modeled by Eloy (2011). Mechanical stresses on branches differ from those on the main trunk and change with branch size and wood maturity (Alméras et al. 2005; Alméras and Fourier 2009).

While Eloy (2011) did not consider mechanical stress responses in trees in his models, because he did not see a mechanism for such a response, there is actually strong evidence for such mechanisms at all levels of organization. At the tissue level, Coutand et al. (2014), Hamant (2013), and Hamant and Traas (2010) have shown that there are receptors for tension and pressure in and near cell walls (as well as otherwise) and that these sensory modes are essential to generating the coordinated responses that produce plant tissues and growth. Experiments show that the direct sensing of gravity is also utilized by trees and leads to growth responses (see Groover 2016). Detailed studies of the mechanisms of tree responses to bending and the several wood properties involved have recently been published (e.g., Alméras et al. 2004, 2005, 2009; Alméras and Fourier 2009; Coutand et al. 2014; Pot et al. 2014).

At the macro scale, there are also clear dynamic responses of woody tissues. For a cantilever beam (branch), as in Fig. 1, at any point along the branch, there are tensive and compressive forces. These forces can be aggravated by wind. To remain upright, the branch must resist these forces. To some degree, these forces can be resisted by the default branch wood properties, but as branch size increases the forces become greater than the elastic similarity of the wood (Alméras and Fourier 2009). At this point, growth responses take place. In angiosperms, the dominant response is the growth of reaction wood on the top of the branch which pulls back toward the base of the branch, acting like a support cable. Reaction wood in young elm branches can convert a nearly horizontal branch into a vertical one. In contrast, in gymnosperms, compression wood is formed underneath the branch or at the bottom of the branch-trunk juncture. Compression wood can resist but not reverse drooping of a branch and is less efficient than reaction wood (Alméras et al. 2005; Alméras and Fourier 2009). Growth responses also involve eccentric wood growth around the branch or trunk, stiffening as wood matures, and change in the modulus of elasticity of new wood (Alméras et al. 2005; Coutand et al. 2014; Pot et al. 2014). The dynamic response to wind is more easily demonstrated in trunks, where wind-exposed trees have greater safety margins than protected trees (King 1986).

Fig. 1
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For any branch at any point, there is tension (pull) on the top of the branch and compression on the bottom. n neutral plane

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Reaction wood formation within gymnosperms is not uniform. Cycadales and Gnetales do not produce it (Groover 2016). In Araucariaceae and Pinaceae, compression wood is formed by shortening of tracheids and reduction in lumen diameter, which reduces hydraulic conductance (Pittermann et al. 2006). This tradeoff means that reaction wood formation has both an energetic cost and a hydraulic efficiency cost. In contrast, it was found that in Cupressaceae and Podocarpaceae, the wood is hydraulically over-engineered, being much denser than necessary, such that this tradeoff does not exist (Pittermann et al. 2006).

Other changes also take place. Young branches are highly flexible. It is not possible to “break” a young branch of many angiosperms. Instead, it crushes but with intact fibers which must be torn lengthwise to break the branch. Older branches become progressively stiffer, but are still hard to “break” until they are quite large. Thus, mild storm damage to angiosperms consists mainly of dead branches and smaller branches that separate at a juncture point with a larger branch. These juncture points are weaker than the branch because rather than long fibers, the wood fibers exhibit a change in direction. It is also a point where a flexible branch can no longer flex and thus where forces are concentrated rather than dissipated by waving.

In contrast, the use of compression wood by conifers means that most twigs (e.g., in Pinus) are stouter and more rigid. This leads to small branches that are more easily broken in two by hand, and which are more likely to snap at their midpoint due to wind or ice loading.

As wood matures further, it becomes stiffer (Bao et al. 2001; Alméras and Fourier 2009). This varies by species and can clearly be adaptive (see Loehle 2000). Some species, such as pines, can reinforce their heartwood with resin over time, making the main trunk and branch junctures much more rigid than would be the case for their wood per se, as well as much more decay resistant (Loehle 2000). Bao et al. (2001), for example, documented greater changes between young vs. mature wood for conifers than for broadleaf trees.

The geometry of branching has a strong effect on the forces the branch must resist. For a branch of length L viewed as a cylinder, where all the smaller branches are folded up into the cylinder (or conversely have been partitioned out of the cylinder), the center of mass is at approximately ½L. For branches with leaves or fruit, the center of mass will be farther out. Just considering the mass of the wood, for an angle of 15° (Fig. 2a), the moment arm for torque is only 0.13L, with mostly compressive forces at the base of the branch. For a 45° angle (Fig. 2b), the moment arm is 0.354L (2.72 times as long) and the tension and compression forces are equal. For a horizontal branch, the moment arm is 0.5L which is 3.86 times as long as for the 15° angle, with almost all tension force. Thus, branch angle and length strongly affect the forces the branch must resist.

Fig. 2
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With greater angle from the vertical, the moment arm is larger; L is length of branch viewed as a beam; force for torque based on center of mass

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As Alméras and Fourier (2009) noted, for smaller branches, the increased forces on the lower part (closer to trunk) are partially met by the increasing stiffness of maturing wood. As the branch gets larger, however, additional wood as tension or compression tissue must be added. These tissues must be added not just at the trunk juncture but along the branch, which further increases the weight of the branch. This may put a limit on branch length, explored below. Because compression wood is less efficient than tension wood at resisting tension forces, conifer branch geometry may be even more constrained by these forces, as will be shown.

Implications of energetics for architecture

Based on the preceding analysis of wood properties and energetic costs in terms of growth and branching, some implications can be drawn. A detailed explanation for conifer crown shape can be derived from wood properties. The idealized crowns for light capture derived from branching ratios can be shown to be constrained by wood properties, especially for larger trees. Optimal crown width can be shown to be affected by the nonlinear nature of the increasing moment arm and increasing support tissue with branch length that cause diminishing returns to investments in wider crowns. While optimal and maximal tree heights have been analyzed in terms of energetics, effects of wind in particular on support costs and risk of damage also affect tree height and crown structure.

Conifer crowns

The gymnosperms commonly exhibit a central trunk with radiating branches. In spruces and firs, the crown is strictly conical. One can ask (sensu Farnsworth and Niklas 1995) if there is some evolutionary reason for this branching habit. Since conifers span hot to cold, wet to dry, and shade to sun environments, it is difficult to see how optimal design could be involved. Instead, it is here argued that conifer crowns are constrained by their wood properties. The use of compression wood rather than reaction wood for resisting bending forces means that very large and very long side branches cannot be supported, as they can be in angiosperms. In older angiosperms, for example, it is not unusual to find side branches or forks greater than 1 m in diameter and extending more than 10 m (vertical projection) horizontally. This is almost never seen in large conifers. The stress due to torque on the relatively weaker wood of a conifer will simply snap in such a configuration. With large branches and forks precluded, an excurrent growth form (spire, cone, sphere, and half-sphere) is the only form available. Long, graceful, and flexible branches, such as seen in elm (Ulmus spp.), are likewise precluded in conifers. Thus, the primitive (since universal across the taxon) trait of compression wood forms a strong constraint on conifer growth form. The success of this group is thus due to high ability to tolerate extremes of temperature and moisture rather than due to crown geometry or its flexibility.

The unique dense wood of Cupressaceae and Podocarpaceae compared to other gymnosperms means that these taxa are much less constrained by branch geometry and mechanics. While many species in these taxa do exhibit the default excurrent form proposed here, exceptions can be found. For example, large individuals of Podocarpus totara can look like a typical spreading angiosperm tree.

Smith and Brewer (1994) argued that a conical crown is an optimal design for light interception, especially in high latitudes with low sun angles. Since conifers are constrained to a more or less conical crown by mechanical limitations, it is difficult to argue that this is an adaptation per se. Instead, the low sun angles may give the already conical crowns of spruces and firs an advantage. This will also be true in slightly lower latitudes (e.g., Oregon, Washington USA), where conifers are photosynthetically active during the cooler months (since summers are dry), when sun angles are also low, that is, the wood structure limitation on conifer crown shape coincidentally confers an advantage in certain settings.

Conical crowns might also provide an advantage with respect to wind loading. Hydrodynamic drag is not simply a function of surface area but is also influenced by shape. A narrow spire, such as the top of a spruce crown, produces less drag (and thus force) than other shapes of the same plan area. Niklas (1998) showed that for the same volume and height, a cone produces 16 % less drag than a cylinder and has a lower center of the moment arm due to the wind, which means less torque. This could provide a significantly lower risk of wind damage in places, such as mountains, where conifers are often found growing in exposed locations.

Wood properties also explain a secondary feature of conifer crowns: drooping lower branches. To prevent lower branches from exceeding the safety margin for breakage, a conifer must limit its growth as it gets taller. Since a branch system must still grow at the tips each year and add wood along the branch, such a limitation on growth (probably hormonal, see Groover 2016) will necessarily either lead to lower branches becoming shaded out and dying or lead to the branches being progressively unable to support their weight and drooping over time (Fig. 3). Thus, it is argued here that this drooping is not adaptive per se but rather results from wood strength constraints in conifers.

Fig. 3
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Spruce crown showing drooping lower branches

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Sillett et al. (2015) provide data suitable for testing this theory. They mapped crown structure in a set of very large conifers. In the set of 55 Sequoia sempervirons trees ranging from 110 to 1830 years old and up to 110 m tall, older branches tended to droop and only a few forks were mapped, with these growing close to and parallel to the main trunk, probably due to historical damage. No massive horizontal branches were evident. For Sequoiadendron giganteum, trees up to 1000 years old followed this same pattern. However, the extremely stout older trees (up to 9 m basal diameter and 3240 years old) did show huge side branches. It appears that given massive size, large branches can be produced in conifers, but not in typical scenarios. It is also possible that this species differs in wood properties compared to typical conifers.

Given the costly nature of branch support in taxa, such as Pinaceae and Araucariaceae, some other morphological traits can also be more clearly understood. In certain habitats, tree establishment may be difficult due to rocks, bogs, snow, or other features. Individual trees will thus not be crowded. Whereas angiosperms will tend to expand their crowns under such conditions, many conifers can be seen to develop a bottle-brush shape, with a high crown ratio but a very narrow crown. Figure 3 illustrates this shape, with many conifers being even more elongated than this. For example, very tall conifers, as the redwood examples show, have a very long, narrow crown when large. The path fraction, a measure of average distance of branch tips from the trunk, is minimized by such shapes (Smith et al. 2014). This shape can, therefore, be seen to minimize the cost of constructing side branches and, therefore, to be a different strategy than a space-filling growth form. A related argument can be made that pendant secondary branches (Fig. 4) likewise reduce the construction costs for branch support.

Fig. 4
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Pendant secondary branches on a spruce tree

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Wind, tree height, and crown form

Except in protected locations, wind poses a constant risk of damage or mortality for trees. Wind loading exerts both tension (for steady wind) and torsional (twisting) loading (for asymmetric crowns) (Skatter and Kucera 2000). Wind effects can be exacerbated by snow loading (Nishimura 2005) and vibrational amplification (swaying) (Ancelin et al. 2004). In dense stands, trees protect each other but any tree emerging above the average canopy height or exposed by death or removal of neighbors will be exposed to the wind, which, furthermore, increases with height above ground. Increases in height also increase the moment arm which interacts multiplicatively with the wind force to create torque. Scott and Mitchell (2005), for example, showed that after partial harvesting of conifer stands in British Columbia, Canada, risk of windthrow went up with tree height, and down with stem diameter and height to live crown (since deeper crowns catch more wind). This means that more support tissue (thicker trunk) will progressively be needed as the tree grows taller. This will lead to the violation of geometric similarity as the tree grows (see Niklas 1995). Another way to put this is that larger trees develop a progressively larger margin of safety (trunk taper) compared to simple elastic similarity (see King 1990, Fig. 5). This trend will be even greater for exposed or emergent trees. This requirement for extra support can take photosynthate away from height and crown growth. Since greater height is both a competitive advantage and aids seed dispersal (King 1990; Loehle 2000), this cost is a disadvantage. It is noteworthy that very tall angiosperms also maintain a single trunk growth form when young (Loehle 1986, 2000) via a combination of apical dominance and crowding effects.

Wind damage is a significant source of mortality for trees. Peterson (2000) in a study of the effects of two tornadoes in Pennsylvania found that of trees destroyed by wind, 65.6 vs. 34.4 % were via uprooting vs. breakage in one and 62.7 vs. 37.3 % in the other event. The only conifer, Tsuga canadensis, was reduced by about 90 % in the more severe storm, much more than the other species. In the less severe storm, the dominant species composition was unchanged after the storm. He also found that the smaller and larger diameter trees were more likely to be killed. This is probably because the smaller trees would have had less taper, being in the understory, and the largest trees were more exposed to the wind. In a related study, Peterson (2007) found that species consistently differed in wind-throw risk. There was a weak tendency for conifers and early successional species to be at greater risk.

In a survey following hurricane-related downbursts in the mountains of North Carolina, Greenberg and McNab (1998) found that uprooting was much more common than breakage among mostly angiosperm species. Very little major limb damage was seen. Almost all stem breakages were above 1.8 m in height.

Nishimura (2005) conducted a survey of wind damage in two conifers in the mountains of northern Japan, where heavy snow and strong winter storms cause wind mortality predominantly in winter. All mortalities he documented were due to wind. He found that most mortality was due to breakage, perhaps due to frozen soil which increased root stability. Harcombe and Marks (1983) studied normal (not extreme storm) mortality in a beech-magnolia forest in southeast Texas. They found that only 11 % of mortality was due to wind, with a further 10 % of small tree mortality due to crushing by falling trees or limbs. Franklin and DeBell (1988) evaluated 36 years of mortality in an old-growth conifer forest in southern Washington, USA. They found 23.3 % of mortality due to windthrow, 21.5 % due to stem breakage, and 10 % due to excessive snow loading, for a total of 62 % of the mortality due to mechanical failure.

Franklin et al. (1987) found wind-related mortality to be much higher in moist sites (83, 33, 41, and 46 % of totals) in Oregon and Washington compared to the drier ponderosa pine sites in Oregon (10, 18 %). This may be because trees on the drier site are always exposed to the wind as they grow due to low stand density. In addition, wetter soils are more likely to cause tipping.

From these studies, it is clear that wind-caused mortality outside of tornadic events ranged from 10 to 100 % of total mortality in different forests due to wind exposure and other factors. Species differ in their susceptibility due to root, wood, and crown factors. There is evidence for a weak trend for conifers and early successional species to be less wind firm. I suggest that crown allometry and optimal light capture models need to factor in the effects of wind on tree and crown development.

It is proposed here that mechanisms may exist by which trees reduce the impact of wind. The first mechanism is to simply not invest in full safety factors. For fast-growing species, the advantage of fast growth may outweigh the risk of mortality. This is particularly true if the species is short-lived. Thus, for example, King (1986) showed that the early successional trembling aspen (Populus tremuloides) has much lower stability safety factors than sugar maple (Acer saccharum) and greater risk of breakage. At the crown level, I predict that fast-growing species, such as aspen, should treat small to mid-size branches as expendable and allow them to break off in high winds as a tradeoff with rapid growth. This is supported by the casual observation of frequent small branch damage or loss in the fastest growing species, such as aspen, compared, for example, to oaks and maples. This concept is further supported by the known relationship between lower investment in wood defenses in fast-growing species, including wood strength and density (Loehle 1996, 2000).

A second mechanism for coping with wind is hypothesized to be the shift to an open crown form for taller and more exposed trees that allows the wind to pass through. The more energetically and hydraulically efficient compact crown shape suggested by theoretical models (e.g., Horn 1971; Fisher 1992; Pearcy et al. 2005) as ideal for light capture will catch the wind as a big sail and the whole tree can sway in the wind (Ancelin et al. 2004). This concentrates stress on the whole trunk. In contrast, an open architecture with separated clusters of leaves will break up the wind, allow much of the wind to pass through, and break up the timing of the forces propagating down the trunk (i.e., branches will sway out of sync), lessening the risk of whole tree breakage. For example, Stathers et al. (1994) suggested that thinning a crown by 20–30 % can greatly reduce wind-throw risk. Yang et al. (2015) showed that larger early successional trees in a Chinese forest showed foliage clustering, as hypothesized here, though they did not quantify the scale of clustering or the effect on drag.

A population of open-grown cottonwood (Populus deltoides) growing near a river in downtown Naperville, IL, USA, was examined. These trees were all about 90–100 years old, based on a cut stump of one tree, and ranged from 1.2 to 2 m in diameter breast height and about 30 m tall. Those that could be photographed successfully (not blocked by other trees) all showed large separations of foliage clusters (see Fig. 5 as an example). Dead and broken branches had been trimmed out of these trees by the parks department, leaving live branch spacing clearly evident. Foliage clusters were often separated by up to 5–10 m, and the crown clearly was open to the wind.

Fig. 5
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Open-grown large eastern cottonwood (Populus deltoides) showing open crown configuration

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When a case of open crown development is observed, it is necessary to ask if it is an adaptation or a coincidence, because an open crown is both energetically and hydraulically inefficient. It is possible that the action of the wind, by causing branch breakage, leads to an open crown configuration. However, this seems unlikely to be more than a partial explanation. It is also possible that continued growth in a large tree simply leads to divergence of growing sections and an open configuration, especially in a shade-intolerant tree, such as cottonwood. However, such an open crown is both energetically and hydraulically inefficient. Since some species maintain a more or less compact crown when large (Fig. 6), it seems that crown openness is not an inevitable consequence of size, though the downward arching branches of cottonwood (Fig. 5) could result from unrestrained foraging for light. This can be considered an open question at this time. If three-dimensional data on crown structure could be obtained for larger trees, methods, such as developed by Zeide (1998) or Godin et al. (1999), could be used to characterize the spatial pattern of foliage and how it changes with tree size.

Fig. 6
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Large elm (Ulmus sp.) showing compact crown

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Kane et al. (2014) in a study of mechanical deflection of large Acer saccharum trees found that branching characteristics of individual trees significantly influenced damping and other swaying responses. These results are not directly related to the open crown question but do show that it cannot be assumed that tree response to wind is a simple crown surface area phenomenon. If branching pattern affects sway responses, it could affect mortality risk from wind. In this case, branching architecture might be an evolved response to wind damage as well as light capture.

In addition to crown shape effects, leaf architecture can damp wind damage risk. It has been found that for many species, the response of leaves in wind is to fold up into a conical shape, reducing drag, with clusters of leaves in Populus forming stable cones (Vogel 1989, 2007). The twisted petiole of poplars allows the leaves to tremble in the wind and to be highly resistant to tearing at wind speeds that damage leaves of other species (Vogel 1989). This unique feature of poplar leaves reduces drag more than other species at the leaf level (Niklas 1991; Vogel 1989). This feature of leaves may reduce wind resistance (drag) of such crowns as poplar significantly and reduce wind damage even in fast-growing species with weak wood. The fluttering of leaves, such as poplar, has been claimed to increase carbon gain (Roden 2003) and to displace herbivores (Yamazaki 2011). This trait might, therefore, provide a triple benefit, at least, which may help account for the widespread distribution and success of Populus, especially in open, windy habitats.

There may also exist limits on tree adaptations to wind. If the highest wind-induced mortality is in winter (e.g., Nishimura 2005), there may be selective pressures on tree architecture but no possibility for dynamic (stress-induced) growth responses, since the trees are dormant. If extreme wind damage is rare, such as due to tornadoes, there may not be a response for three reasons: (1) normal wind stresses will not give an indication of tornadic wind strength, so appropriate growth responses will not be invoked; (2) the wood cost of preventing death compared to the risk of such an extreme event may mean that selection is not advantageous; and (3) if the dominant failure mode is uprooting due to lack of soil strength, there may be no growth response that can prevent this source of mortality.

Crown width

From a purely light-capturing perspective (Honda and Fisher 1978), there is no obvious limitation to an advantageous crown width. For young trees, it might be expected that proportional growth of the species’ preferred crown shape would exhibit geometric similarity (see Smith et al. 2014). For larger trees, the progressively larger investments needed to support branches should put constraints on branch length such that crown width is limited. Simple proportionate scaling up of a young tree crown would yield an impossibly wide crown. This is particularly true for emergent trees. For conifers, maximum crown width is further constrained by wood properties, as mentioned previously. Even for saplings, however, optimal leaf display for carbon assimilation can be constrained by the energetic costs of support tissue (e.g., Pearcy et al. 2005). Gehring et al. (2015) showed that the distal leaf mass per branch mass ratio decreases with branch diameter in Castanea sativa Mill, an expected result if mechanical support costs increase faster than linearly. They also found that this ratio went down with branch height in the tree, which would support a hydraulic constraint argument. There is thus some evidence for limitations on crown width and branches, as suggested here, but studies done on young trees will not reveal these limitations.

Architectural models and optimal design

In the introduction, the large literature on branching geometry was mentioned. Fisher (1992) showed that some young trees follow simple branching rules that can be simulated. As well, statistical and geometric regularities have been observed in branch size distributions which can be characterized (e.g., Fisher and Honda 1979a, b; Fisher and Hibbs 1982) and simulated in some cases (Takenaka 1994). Fisher (1992) noted, however, that successful prediction or description of form for larger trees has been elusive, an issue he attributes to damage and plastic response to the environment. Several recent studies have documented variability in crown shape and allometric scaling with species, size, age, environment, and other factors, compared to predictions of self-similarity or optimal space-filling designs for light capture (e.g., Anderson-Teixeira et al. 2015; Bentley et al. 2013; Smith et al. 2014). I believe many of the differences noted could be the result of biomechanical cost constraints and tradeoffs. I would suggest that many of the studies showing constant allometry, branching patterns, optimal branching, or crown scaling were based on young trees, often growing in plantations, where they are protected from the wind. I argue that as trees get larger or with increased exposure to wind, these observed scaling relations will be violated as additional support tissue is added.

Some authors attribute tree branching patterns to optimal hydraulic adaptations (e.g., Enquist 2002). While hydraulic considerations are not irrelevant, Sperry et al. (2008) argued that real tree crowns do not exhibit the most efficient hydraulic architecture due to the limitations of mechanical safety. They suggest that even minimal mechanical support (e.g., a tree trunk just at elastic similarity) provides adequate hydraulic support and that larger trees are less hydraulically efficient due to greater structural support tissue. I concur with their assessment and would extend this argument to branches, as well.

Conclusions

Mechanical support is a key constraint on tree growth. As a tree gets larger or is exposed to wind, increasing amounts of assimilate must go to support tissue. This greater investment in support limits crown width and tree height. Crown width is especially limited in conifers due to their wood structural limitations. The effect of wind on tree crowns leads to the proposal that large trees, especially of fast-growing species, should exhibit an open crown structure to dissipate wind. Some evidence exists to support this conjecture.

The arguments made here about mechanical constraints lead to several proposals to modify current allometric and scaling theory for trees. In the application of the pipe-model theory, Ogawa (2015) noted that taper in the lower stem, while traditionally attributed to “unused pipes” due to shed branches, has not been fully explained. I would suggest that taper in the trunk is not just a passive consequence of unused xylem elements but rather reflects the need for mechanical support. This can be shown by the fact that trees of the same size show greater taper when growing exposed to the wind. This argument extends to branches, as well. This means that tree allometry (at the whole tree scale) or branching pattern at finer scales will be size, environment, and wind dependent, as documented by Antin et al. (2013), Niklas (1995), and others discussed above. Crown size, shape, and scaling should also depend on mechanical limitations, competition, successional status (see Yang et al. 2015), wind exposure, and other factors. The need for mechanical support leads to specific guidance for how scaling should change with conditions and tree size (contra Enquist 2002) and how the pipe model (Chiba 1998; Ogawa 2015) or other models (Sievänen et al. 2000; Perttunen and Sievänen 2005) need to be modified to be more realistic for larger trees. It explains why bifurcation ratios and path fraction differ as the tree grows (Borchert and Slade 1981). It explains why conifers, with their more rigid wood-induced growth constraints, are more easily simulated. It suggests that light capture, while a primary goal of tree architecture, is constrained by both wood properties and hydraulic considerations. These costs and tradeoffs can produce multiple solutions to the problem of optimal growth form, such as conical vs. spherical crowns.

Author contribution statement

Craig Loehle performed all the work and writing on the manuscript.