# Corner's rules as a framework for plant morphology, architecture and functioning - issues and steps forward

Pierre-Éric Lauri

► To cite this version:

Pierre-Éric Lauri. Corner's rules as a framework for plant morphology, architecture and functioning - issues and steps forward. New Phytologist, 2019, 221 (4), pp.1679-1684. 10.1111/nph.15503. hal-02618964v2

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Letters

Corner's rules as a framework for
plant morphology, architecture
and functioning – issues and steps
forward

The Durian theory and Corner's rules governing plant
architecture

In the middle of the twentieth century E. J. H. Corner developed 'The Durian theory' (Corner, 1949) and 'The Durian theory extended' (Corner, 1953, 1954a,b) named after the large spiny fruit of *Durio zibethinus* (Bombacaceae) containing light-brown seeds covered by a fleshy and edible white or yellow aril. Following a first intuition that 'such fruits must have been borne on massive twigs' Corner (1949) established two 'complementary principles', later referred to as Corner's rules, that were 'susceptible to mathematical treatments'. The 'axial conformity' rule states that 'the stouter, or more massive, the axis in a given species, the larger and more complicated are its appendages'. The 'diminution on ramification' rule states that 'the greater the ramification the smaller become the branches and their appendages'. These two rules delineated the poorly branched pachycaul trees with 'thick' stems and 'big' leaves and axillary organs (inflorescence, fruit) (Fig. 1a), and the highly branched leptocaul trees with 'slender primary axis and branches' and 'small' leaves and axillary organs) (Fig. 1b,c).

The Durian theory was merely based on a general view on trees and encompassed an evolutionary aspect theorizing about the primitive character of pachycaul forms. Corner's hypothesis that leptocaul trees constitute an evolutionary outcome of pachycaul trees has been criticized considering that pachycaul forms may also derive from selective pressures in extreme environments (Mabberley, 1974) or questioning the plesiomorphic characteristic of the large fruits (Nyffeler & Baum, 2000).

Here, it is outlined that although this evolutionary view is discussed, Corner's rules inspired interspecific and ontogenetic studies from a morphological (organ size and shape), architectural (relations with branching) and functioning (relations with hydraulics and biomechanics) perspectives.

Corner's rules canonical relationships

Corner's rules provided a structural vision of woody plants building upon previous works on relationships among morphological traits such as the positive relationships between the diameter of the apical meristem and leaf size (Sinnott, 1921). Noticeably, Corner's rules

were at the origin of the conceptual modeling of whole-plant architecture developed by Hallé and colleagues on existing species (Hallé & Oldeman, 1970; Hallé et al., 1978), recently extended by Chomicki et al. (2017) on Paleozoic taxa. These rules are still providing a heuristic framework for the quantification of plant form and function at various plant scales (e.g. in relation to plant hydraulics; Lehnebach et al., 2018).

Most research works referring to Corner's rules are focused on two canonical relationships (Table 1). The first ones are between stem traits (namely diameter used in a majority of studies or directly derived from it, such as cross-sectional area and radius, mass, length, shape) and the number and/or size of appendages (leaf, inflorescence). The second ones are between leaf area and the number and/or size of appendages whether vegetative (branch) or reproductive (inflorescence, seed, fruit, cone). A few studies document across-scales relationships such as stem diameter or leaf area vs tree height (Table 1). Although most works are developed on woody plants a few aim at assessing these relationships on herbaceous plants (Barcellos de Souza et al., 1986). Studies are developed at two main scales. The first one considers the whole-plant including the branch or the leafy shoot at the end of primary growth and is used for phylogenetic studies based on interspecific comparisons (e.g. across *Acer* accessions; Ackerly & Donoghue, 1998). The second one considers the metamer, that is, the complex formed by the internode, the attached leaf or leaves and the axillary production(s), and is used to study ontogenetic changes during the development of an individual, whether a tree (Brouat et al., 1998; Brouat & McKey, 2001) or a herbaceous plant (Barcellos de Souza et al., 1986).

The link with hydraulics

For a great majority of authors, the quantitative relationships between stem diameter, loosely termed stem 'size' in several articles (Brouat et al., 1998; Westoby et al., 2002; Westoby & Wright, 2003), and the appendages the stem supports are primarily interpreted in terms of the vascular supply joining the roots to the appendages through the stem. These relationships have been extensively discussed in past decades using the conceptual framework of the pipe model theory (Shinozaki et al., 1964), including very recently by Lehnebach et al. (2018). This theory predicts that 'the amount of leaves existing above a certain horizontal level in a plant community (is) always proportional to the sum of the cross-sectional area of the stems and branches found at that level' (Shinozaki et al., 1964). The pipe model theory does not strictly consider the process of heartwood (non-conducting wood) formation, which is independent of pipe production and deactivation, and more studies are needed to differentiate between conducting and storage sapwood (Lehnebach et al., 2018). However, as a whole, this theory showed its high heuristic value in stimulating research on relations between structure and functions among plant
<figure><img src="image_3.png" /><figcaption>**Fig. 1** Corner's rules at various scales. At the whole plant scale, (a) large and thick internodes with low slenderness are related to large leaves and no or poor branching (e.g. monocaulous pachycaul tree fern, *Cyathea* sp.), whereas (b) small and slender internodes are associated with small leaves and high branching (e.g. (b, c) leptocaul beech tree, *Fagus sylvatica*); and (d) relationships that determine the correlation space between stem and appendages are initiated in the shoot apical meristem (SAM) where cell number positively affects meristem size which, in turn, positively affects stem diameter and leaf area (blue arrows; Schnablová *et al.*, 2017). The axillary meristem, which is initiated in the boundary regions between the adaxial base of the leaf primordium and the SAM, is closely associated with leaf polarity and also results from signals from the SAM (yellow arrows; Yang & Jiao, 2016; Chomicki *et al.*, 2017). To what extent leaf and stem size and shape, and axillary production size and fate, are pre-determined in the SAM or result from later interactions among growing organs needs to be further investigated. Photograph credits: Pierre-Éric Lauri.</figcaption></figure>

compartments. For example, the statement of isometry between leaf area and stem cross-sectional area is well supported by findings of Brouat *et al.* (1998) over the ontogenetic gradient on two caesalpinioid legume trees, and by Petit *et al.* (2018) on shoots of two deciduous angiosperms and of two evergreen conifers at different distances from the apex.

## Further insights from Corner's rules

Based on a literature review that quantified Corner's rules among stem, leaf and appendages, it is proposed that three further insights might benefit from Corner's rules-based studies.

### Insight 1. Questions raised by biomechanics: the need to consider stem shape and not only stem diameter or cross-sectional area

Beside hydraulics, the relationships between stem diameter and appendage size or number are also interpreted in terms of biomechanics. Biomechanical properties of a stem are related to

two main factors. One factor is wood density 'with denser woods being stiffer and stronger than stems with equivalent cross-section composed of less-denser wood' (Niklas & Spatz, 2012). Another factor is shape which determines that for a stem with a same weight of appendages and same construction material properties, the higher the slenderness, that is, ratio between length and diameter, the lower the mechanical stability. This limitation on length by cross-sectional area is well known by foresters in studies at the whole-tree scale to evaluate the critical buckling height (Niklas, 2013). Therefore, from the morphological point of view, considering only stem diameter (Brouat *et al.*, 1998; Fan *et al.*, 2017) as a proxy for stem biomechanical strength is misleading. In his initial articles, Corner (1949, 1953, 1954a,b, 1975) most often used the words 'massive' or 'stout' as opposed to 'slender' to qualify stems of pachycaul and leptocaul trees, respectively. These words, although imprecise, strongly suggested that to maintain same biomechanical characteristics of the stem with regards to appendages a difference in size must be accompanied by a difference in shape. Therefore, not only stem diameter, or even volume or mass, but also shape should be considered in relation to the size of appendages. Working
<table><caption>**Table 1** Canonical relationships among morphological and architectural traits illustrating Corner's rules at various scales.</caption><thead><tr><th rowspan="2">Organ</th><th rowspan="2"></th><th rowspan="2">Relationships among<br/>morphological and architectural traits</th><th colspan="2">Scale</th></tr><tr><th>Tree, branch or leafy shoot (also called twig)</th><th>Individual<br/>metamer</th></tr></thead><tbody><tr><td rowspan="5">Stem</td><td rowspan="2">Diameter</td><td>vs inflorescence<br/>number or size</td><td>Bond &amp; Midgley (1988); Midgley &amp; Bond (1989);<br/>Normand et al. (2009)</td><td rowspan="5">White (1983a,b);<br/>Barcellos de Souza<br/>et al. (1986); Brouat<br/>et al. (1998); Brouat &amp;<br/>McKey (2001)</td></tr><tr><td>vs leaf area</td><td>Bond &amp; Midgley (1988); Westoby et al. (2002);<br/>Westoby &amp; Wright (2003); Olson et al.<br/>(2009); Fajardo (2016); Trueba et al. (2016); Fan et al. (2017);<br/>Messier et al. (2017); Osada &amp; Hiura (2017);<br/>Schnablová et al. (2017); Smith et al. (2017);<br/>Poorter et al. (2018)</td></tr><tr><td>Mass</td><td>vs tree height</td><td>Brouat et al. (1998); Brouat &amp; McKey (2001)</td></tr><tr><td>Length</td><td>vs leaf mass</td><td>Normand et al. (2008); Fan et al. (2017)</td></tr><tr><td>Shape</td><td>vs leaf area</td><td>Trueba et al. (2016)</td></tr><tr><td rowspan="4">Leaf</td><td rowspan="4">Area</td><td>vs reproductive organ<br/>(seed, fruit, cone,<br/>inflorescence) size</td><td>Bond &amp; Midgley (1988); Midgley &amp; Bond (1989); Ackerly &amp;<br/>Donoghue (1998); Cornelissen<br/>(1999); Westoby &amp; Wright (2003); Duivenvoorden &amp;<br/>Cuello (2012); Leslie et al. (2014)</td><td rowspan="4">Barcellos de Souza<br/>et al. (1986)</td></tr><tr><td>vs branching intensity</td><td>Ashton (1976a,b); Yagi (2006); Takahashi &amp; Mikami<br/>(2008); Messier et al. (2017);<br/>Osada &amp; Hiura (2017)</td></tr><tr><td>vs leaf number</td><td>Fajardo (2016)</td></tr><tr><td>vs stem mass</td><td>Yang et al. (2010)</td></tr><tr><td></td><td></td><td>vs tree height</td><td>Hodgson et al. (2017)</td><td></td></tr></tbody></table>

Only articles referring explicitly to 'Corner's rules' or 'The Durian theory' are selected.

In the case various expressions cover correlated traits or are imprecise, a single expression is retained after checking of the Materials and Methods in each article: 'stem diameter' also includes 'stem cross-sectional area' and 'radius'; 'leaf area' also includes 'leaf size'; 'branching intensity' also includes 'degree of branching'.

on a rosette-stoloniferous plant, *Callisia fragrans* (Commelinaeae), Barcellos de Souza *et al.* (1986) analyzed ontogenetic changes considering individual metamers. They showed that if, as hypothesized, leaf area was positively related to stem-cross sectional area supporting the hydraulic relations, it was negatively related to internode slenderness supporting the biomechanical relations. Variations of these three traits thus appeared as good markers of the successive stages this species goes through during its ontogeny, large leaves being associated to short internodes with a low slenderness ratio typical of the erect rosette phase, whereas small leaves were associated to long internodes with a high slenderness ratio typical of the stolon phase growing at the soil surface.

At the whole-plant and branch scales, if the relationships between stem diameter and size and number of appendages are well established (Table 1), the relations with stem shape needs to be more documented. For example, Niklas *et al.* (2006) hypothesized that the high slenderness ratio of some pachycaul species, comparable to some leptocaul species, were likely related to the absence or paucity of branching. However, this study did not detail relationships between stem traits and appendages.

## Insight 2. The definition of a realistic biological-based phenotypic correlation space to better design plant architectural ideotypes

The earlier mentioned literature confirms that some main relationships, such as stem diameter vs leaf area and the coordinated

changes of these two traits, are observed from both the phylogenetic or interspecific and the ontogenetic points of view. Combined with hydraulics and biomechanics, these results support the idea that Corner's rules likely cover a universal network of biological relationships shaping plant architecture and functioning.

The definition of ideotype, that is, the best-adapted biological model in a given agricultural and socio-economic environment (Donald, 1968), is crucial to optimize plant cultivation and yield. Among architectural traits that affect yield, canopy porosity to light is a main variable governing light interception by the plant and therefore partly affects yield (Sinoquet *et al.*, 2007). In the apple, canopy porosity depends on leaf-area distribution within the canopy that is directly related to branch orientation and branching density (Willaume *et al.*, 2004). These morphological and architectural traits can be phenotyped in progenies and can also be manipulated in the orchard through tailored precision management procedures (Lauri & Laurens, 2005). Recent attempts that aim at designing plant ideotypes to improve light interception using plant numerical models conclude on the interest of ideotypes with long internodes (e.g. tomato, Sarlikioti *et al.*, 2011; Chen *et al.*, 2014; apple, Picheny *et al.*, 2017) possibly combined with high leaf area (apple, Picheny *et al.*, 2017) and/or with narrow leaves, that is, high length to width ratio (e.g. tomato, Sarlikioti *et al.*, 2011). Such assertions confirm previous horticultural knowledge on positive relationships between light interception and stem slenderness (e.g. apple, Lespinasse, 1992; Lauri *et al.*, 1997). These works raise interest to explore further the correlation space among
morphological and architectural traits that are biologically mean-
ingful, especially here where the extent to which stem length can be
positively related to leaf number and area without endangering
biomechanical and hydraulic stability. For example, in the apple
case, increasing both stem length and leaf area as proposed by
Picheny et al. (2017) is biologically realistic and agronomically
relevant only up to a critical value of stem slenderness.

Beyond relationships among vegetative organs, Corner's rules also encompassed quantitative relationships between vegetative and reproductive organs (e.g. stem diameter positively correlated with the size of reproductive appendages; Midgley & Bond, 1989). It has been shown that flowering rate increases and then decreases when the bearing stem diameter (Normand et al., 2009) or length (Lauri & Trottier, 2004) increases following a quadratic function. These results suggest that Corner's quantitative relationships established for mature and well differentiated vegetative and reproductive organs are likely to be prepared during floral induction and through more complex relationships.

Insight 3. The respective contributions of organogenesis and growth mechanisms in determining the phenotypic correlation space

Schnablová et al. (2017) working on the shoot apical meristem (SAM) conclude that stem diameter and leaf size, and in the case of a reproductive meristem seed mass, are ‘linked to each other by rules such as Corner’s rules’. These relationships are primarily related to cell number in the SAM from which organs are derived with a minor role of cell size (blue arrows in Fig. 1d; e.g. Gonzalez *et al.*, 2012; Schnablová *et al.*, 2017). However, we still have poor knowledge on the stage of organogenesis at which stem and leaf shape are determined, and to what extent they result from interactions at the metamer or at the whole-stem scale. Furthermore, axillary meristem initiation from which a branch or an inflorescence develops is tightly related to the boundary regions between the SAM and the leaf primordium (yellow arrows in Fig. 1d; Yang & Jiao, 2016) suggesting that the growth, and likely fate of the axillary production, is not passive but partly determined by interactions between the SAM and newly initiated organs at a very early stage. This is supported by findings on branch plagiotropy in *Araucaria* and *Coffea* likely resulting from an early SAM signal (see discussion in Chomicki *et al.*, 2017). However, results obtained on individual metamers of peach (*Kervella* *et al.*, 1995) and apple (Lauri & Térouanne, 1998) show that the growth dynamics of the leaf or of both the internode and the leaf, respectively, affect the axillary bud fate (namely, latent, vegetative, floral; Lauri & Normand, 2017). The challenge is now to better investigate when and how the phenotypic correlation space is built during plant development and growth and in particular to analyze whether organ size and shape, and axillary production size and fate, are fully pre-determined in the SAM or depend on interactions among growing or mature organs at later stages.

Future directions

It is argued that agricultural plants constitute a remarkable
biological material to develop Corner's rules based on

knowledge-oriented and applied research. A research agenda is
proposed with two main goals.

Goal 1. Domestication effects

Most agricultural plants result from long-term domestication by human societies, which includes both selection of wild plant material and intentional breeding (Zeder et al., 2006). In a majority of cases, domestication and especially breeding strategies have been oriented towards an increase of the weight of grain (e.g. wheat, Schoppach et al., 2017) or fruit (e.g. apple, Cornille et al., 2014) relative to the whole plant biomass. It is hypothesized that this increase in ‘yield efficiency’ is related to changes in size and shape of vegetative organs that support reproductive organs and likely also in branching. As a premise for such studies it is noteworthy that the decrease in trunk slenderness of domesticated *Carica papaya* is interpreted as a mechanical response to the domestication-related increase of large fruit clusters (Niklas & Marler, 2007). Such research can be extended to various agricultural plants benefiting from collaboration between geneticists, breeders and archeobotanists.

Goal 2. Environmental effects

Generally speaking, Corner’s rules-based research works (Table 1) consider the plant entity without explicitly integrating the effects of the environment. Changes in environmental conditions arise from climate change and the associated global warming (Intergovernmental Panel on Climate Change (IPCC), 2014) but also result from growing conditions. This is especially true in agriculture with the development of more sustainable and diversified agroecosystems that generally increase competitions among plants for above-ground and below-ground resources (Barot et al., 2017). The plasticity in responses to environmental constraints is well studied on annuals (e.g. contrasted patterns of plasticity in allocation, morphology, physiology and architecture in improving light capture or nitrogen acquisition, respectively; Freschet et al., 2018) but far less on woody plants on which the abiotic (e.g. temperature) and biotic (e.g. proximity of neighboring plants) environments have a cumulative effect on tree morphology and architecture over consecutive growing seasons. It has been shown that besides their effect on budburst phenology (Legave et al., 2015) mild winter temperatures compared to cold winter temperatures significantly decrease branching frequency on stems with similar size and shape (e.g. apple, Dutra Schmitz et al., 2014). Similarly, shading by neighboring trees in natural or agricultural systems increases stem slenderness and decreases branching (MacFarlane & Kane, 2017). Such studies document the variation spectra of morphological and architectural traits, here stem size or shape and branching frequency, and their relationships. However, how these changes in vegetative growth are related to reproductive growth over the tree lifespan is still little studied. Works on woody plants, typically forest and fruit trees in pure stands or in multispecies systems, typically agroforestry systems, would permit an evaluation of the level of plasticity of organs size and shape and of their relationships.
Domestication and adaptation to environmental changes both address morphological and architectural relationships at stem and whole plant scales (Insights 1 and 2) with applied issues. For example, based on research works on apple tree architecture showing a relation between low branching frequency and regular flowering over consecutive years, practical guidelines are proposed for system and plant management in the context of sustainable production (Lauri & Simon, 2018; Lauri et al., 2018). At a finer scale (Insight 3), it has been shown that meristem plasticity to environmental changes affects differently leaf growth and relative growth rate in *Festuca* depending on the fast- or slow-growing pattern of the species (Sugiyama & Gotoh, 2010). A further step could benefit from Corner's rules-based studies on the extent to which this environment- or domestication-related meristem plasticity also affects organ fate and growth distribution in time (ontogeny) and in space (plant architecture) with consequences for plant cultivation (e.g. onset of flowering during plant ontogeny).

## Acknowledgements

The author is deeply indebted to Prof. F. Hallé and to Prof. E. J. H. Corner who during the 1980s oriented him to the study of plant morphology and architecture, and functioning, and to the potential interest for agricultural plants. The author is grateful to three anonymous reviewers for their helpful criticisms and advice on a first version of this article.

## ORCID

Pierre-Éric Lauri ID http://orcid.org/0000-0002-7549-0484

Pierre-Éric Lauri ID

SYSTEM, Univ Montpellier, INRA, Cirad, Montpellier SupAgro, CIHEAM-IAMM, 2 Place Pierre Viala, Montpellier 34060, France
(tel +33 (0)4 99 61 30 54; email pierre-eric.lauri@inra.fr)

## References

Ackerly DD, Donoghue MJ. 1998. Leaf size, sapling allometry, and Corner's rules: phylogeny and correlated evolution in maples (Acer). *The American Naturalist* 152: 767-791.

Ashton PS. 1976a. Ecology and the Durian theory. *Gardens' Bulletin* 29: 19-23.

Ashton PS. 1976b. The crown characteristics of tropical trees. In: Tomlinson PB, Zimmermann MH, eds. *Tropical trees as living systems*. Cambridge, UK: Cambridge University Press, 591-615.

Barcellos de Souza I, Lauri PÉ, Blanc P. 1986. Évolution de paramètres morphologiques au cours du cycle de croissance de *Callisia fragrans* (Commelinaceae). *Canadian Journal of Botany* 64: 1664-1670.

Barot S, Allard V, Cantarel A, Enjalbert J, Gauffreteau A, Goldringer I, Lata JC, Le Roux X, Niboyet A, Porcher E. 2017. Designing mixtures of varieties for multifunctional agriculture with the help of ecology. A review. *Agronomy for Sustainable Development* 37: 13.

Bond W, Midgley J. 1988. Allometry and sexual differences in leaf size. *The American Naturalist* 131: 901-910.

Brouat C, Gibernau M, Amsellem L, McKey D. 1998. Corner's rules revisited: ontogenetic and interspecific patterns in leaf-stem allometry. *New Phytologist* 139: 459-470.

Brouat C, McKey D. 2001. Leaf-stem allometry, hollow stems, and the evolution of caulinary domatia in myrmecophytes. *New Phytologist* 151: 391-406.

Chen TW, Nguyen TMN, Kahlen K, Stützel H. 2014. Quantification of the effects of architectural traits on dry mass production and light interception of tomato canopy under different temperature regimes using a dynamic functional-structural plant model. *Journal of Experimental Botany* 65: 6399-6410.

Chomicki G, Coiro M, Renner SS. 2017. Evolution and ecology of plant architecture: integrating insights from the fossil record, extant morphology, developmental genetics and phylogenies. *Annals of Botany* 120: 855-891.

Cornelissen JHC. 1999. A triangular relationship between leaf size and seed size among wood species: allometry, ontogeny, ecology and taxonomy. *Oecologia* 118: 248-255.

Corner EJH. 1949. The Durian theory or the origin of the modern tree. *Annals of Botany* 13: 367-414.

Corner EJH. 1953. The Durian theory extended – I. *Phytomorphology* 3: 465-476.

Corner EJH. 1954a. The Durian theory extended – II. The arillate fruit and the compound leaf. *Phytomorphology* 4: 152-165.

Corner EJH. 1954b. The Durian theory extended – III. Pachycauly and megaspermy conclusion. *Phytomorphology* 4: 263-274.

Corner EJH. 1975. Prototypic organisms XIII – tropical trees – thick twig, big leaf. *Theoria to Theory* 9: 33-43.

Cornille A, Giraud T, Smulders JMJ, Roldàn-Ruiz I, Gladieux P. 2014. The domestication and evolutionary ecology of apples. *Trends in Genetics* 30: 57-65.

Donald CM. 1968. The breeding of crop ideotypes. *Euphytica* 17: 385-403.

Duivenvoorden JF, Cuello NL. 2012. Functional trait state diversity of Andean forests in Venezuela changes with altitude. *Journal of Vegetation Science* 23: 1105-1113.

Dutra Schmitz J, Guédon Y, Gilberto Herter F, Berenhauser Leite G, Lauri PÉ. 2014. Exploring bud dormancy completion with a combined architectural and phenological analysis – the case of apple trees in contrasted winter temperature conditions. *American Journal of Botany* 101: 398-407.

Fajardo A. 2016. Are trait-scaling relationships invariant across contrasting elevations in the widely distributed treeline species *Nothofagus pumilio*. *American Journal of Botany* 103: 821-829.

Fan ZX, Sterck F, Zhang SB, Fu PL, Hao GY. 2017. Tradeoff between stem hydraulic efficiency and mechanical strength affects leaf-stem allometry in 28 *Ficus* tree species. *Frontiers in Plant Science* 8: 1619.

Freschet GT, Violle C, Bourget MY, Scherer-Lorenzen M, Fort F. 2018. Allocation, morphology, physiology, architecture: the multiple facets of plant above- and below-ground responses to resource stress. *New Phytologist* 219: 1338-1352.

Gonzalez N, Vanhaeren H, Inzé D. 2012. Leaf size control: complex coordination of cell division and expansion. *Trends in Plant Science* 17: 332-340.

Hallé F, Oldeman RAA. 1970. *Essai sur l'architecture et la dynamique de croissance des arbres tropicaux*. Paris, France: Masson.

Hallé F, Oldeman RAA, Tomlinson PB. 1978. *Tropical trees and forests. An architectural analysis*. Berlin, Germany: Springer-Verlag.

Hodgson JG, Santini BA, Marti GM, Pla FR, Jones G, Bogaard A, Charles M, Font X, Ater M, Taleb A *et al*. 2017. Trade-offs between seed and leaf size (seed-phytomer-leaf theory): functional glue linking regenerative with life history strategies and taxonomy with ecology? *Annals of Botany* 120: 633-652.

Intergovernmental Panel on Climate Change (IPCC). 2014. Pachauri RK, Meyer LA, eds. *Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change*. Geneva, Switzerland: IPCC. [WWW document] URL http://www.ipcc.ch/pdf/assessment-report/ar5/syr/AR5_SYR_FINAL_All_Topics.pdf [accessed: 9 October 2018].

Kervella J, Pagès L, Génard M. 1995. Growth context and fate of axillary meristems of young peach trees. Influence of parent shoot growth characteristics and of emergence date. *Annals of Botany* 76: 559-567.

Lauri PÉ, Barkaoui K, Ater M, Rosati A. 2018. Agroforestry for fruit trees in the temperate Europe and dry Mediterranean. In: Mosquera-Losada M, Prabhu R, eds. *Agroforestry for sustainable agriculture*. Cambridge, UK: Burleigh Dodds Science Publishing (in press).
Lauri PÉ, Laurens F. 2005. Architectural types in apple (Malus × domestica Borkh.). In: Dris R, ed. *Crops: growth, quality and biotechnology*. Helsinki, Finland: World Food Limited, 1300–1314.

Lauri PÉ, Lespinasse JM, Laurens F. 1997. What kind of morphological traits should be sought in apple seedling progenies in order to select regular bearing cultivars? *Acta Horticulturae* 451: 725–729.

Lauri PÉ, Normand F. 2017. Are leaves only involved in flowering? Bridging the gap between structural botany and functional morphology. *Tree Physiology* 37: 1137–1139.

Lauri PÉ, Simon S. 2018. Advances and challenges in sustainable apple cultivation. In: Lang G, ed. *Achieving sustainable cultivation of temperate zone tree fruits and berries*. Cambridge, UK: Burleigh Dodds Science Publishing (in press).

Lauri PÉ, Térouanne É. 1998. The influence of shoot growth on the pattern of axillary development on the long shoots of young apple trees (Malus domestica Borkh.). *International Journal of Plant Sciences* 159: 283–296.

Lauri PÉ, Trottier C. 2004. Patterns of size and fate relationships of contiguous organs in the apple (Malus domestica Borkh.) crown. *New Phytologist* 163: 533–546.

Legave JM, Guédon Y, Malagi G, El Yaacoubi A, Bonhomme M. 2015. Differentiated responses of apple tree floral phenology to global warming in contrasting climatic regions. *Frontiers in Plant Science* 6: 1054

Lehnebach R, Beyer R, Letort V, Heuret P. 2018. The pipe model theory half a century on: a review. *Annals of Botany* 121: 773–795.

Leslie AB, Beaulieu JM, Crane PR, Donoghue MJ. 2014. Cone size is related to branching architecture in conifers. *New Phytologist* 203: 1119–1127.

Lespinasse Y. 1992. Breeding Apple tree: aims and methods. In: Rousselle-Bourgeois F, Rousselle P, eds. *Proceedings of the Joint conference of the EAPR breeding and varietal assessment section and the EUCARPIA potato section*. Landerneau, France: INRA, 103–110.

Mabberley DJ. 1974. Branching in pachycaul Senecios: the durian theory and the evolution of angiosperm trees and herbs. *New Phytologist* 73: 967–975.

MacFarlane DW, Kane B. 2017. Neighbour effects on tree architecture: functional trade-offs balancing crown competitiveness with wind resistance. *Functional Ecology* 31: 1624–1636.

Messier J, Lechowicz MJ, McGill BJ, Violle C, Enquist BJ. 2017. Interspecific integration of trait dimensions at local scales: the plant phenotype as an integrated network. *Journal of Ecology* 105: 1775–1790.

Midgley J, Bond W. 1989. Leaf size and inflorescence size may be allometrically related traits. *Oecologia* 78: 427–429.

Niklas KJ. 2013. Biophysical and size-dependent perspectives on plant evolution. *Journal of Experimental Botany* 64: 4817–4827.

Niklas KJ, Cobb ED, Marler TE. 2006. A comparison between the record height-to-stem diameter allometries of *Pachycaulis* and *Leptocaulis* species. *Annals of Botany* 97: 79–83.

Niklas KJ, Marler TE. 2007. *Carica papaya* (Caricaceae): a case study of the effects of domestication on plant vegetative growth and reproduction. *American Journal of Botany* 94: 999–1002.

Niklas KJ, Spatz HC. 2012. Mechanical properties of wood disproportionately increase with increasing density. *American Journal of Botany* 99: 169–170.

Normand F, Bissery C, Damour G, Lauri PÉ. 2008. Hydraulic and mechanical stem properties affect leaf-stem allometry in mango cultivars. *New Phytologist* 178: 590–602.

Normand F, Pambo Bello AK, Trottier C, Lauri PÉ. 2009. Is axis position within tree architecture a determinant of axis morphology, branching, flowering and fruiting? An essay in mango. *Annals of Botany* 103: 1325–1336.

Nyffeler R, Baum DA. 2000. Phylogenetic relationships of the durians (Bombacaceae-Durioneae or/Malvaceae/Helicteroideae/Durioneae) based on chloroplast and nuclear ribosomal DNA sequences. *Plant Systematics and Evolution* 224: 55–82.

Olson ME, Aguirre-Hernández R, Rosell JA. 2009. Universal foliage-stem scaling across environments and species in dicot trees: plasticity, biomechanics and Corner's Rules. *Ecology Letters* 12: 210–219.

Osada N, Hiura T. 2017. How is light interception efficiency related to shoot structure in tall canopy species? *Oecologia* 185: 29–41.

Petit G, von Arx G, Kiorapostolou N, Lechthaler S, Prendin AL, Anfodillo T, Caldeira MC, Cochard H, Copini P, Crivellaro A et al. 2018. Tree differences in

primary and secondary growth drive convergent scaling in leaf area to sapwood area across Europe. *New Phytologist* 218: 1383–1392.

Picheny V, Casadebaig P, Trépos R, Faivre R, Da Silva D, Vincourt P, Costes E. 2017. Using numerical plant models and phenotypic correlation space to design achievable ideotypes. *Plant, Cell & Environment* 40: 1926–1939.

Poorter L, Castilho CV, Schietti J, Oliveira RS, Costa FRC. 2018. Can traits predict individual growth performance? A test in a hyperdiverse tropical forest hyperdiverse tropical forest. *New Phytologist* 219: 109–121.

Sarlikioti V, de Visser PHB, Buck-Sorlin GH, Marcelis LFM. 2011. How plant architecture affects light absorption and photosynthesis in tomato: towards an ideotype for plant architecture using a functional-structural plant model. *Annals of Botany* 108: 1065–1073.

Schnablová R, Herben T, Klimešová J. 2017. Shoot apical meristem and plant body organization: a cross-species comparative study. *Annals of Botany* 120: 833–843.

Schoppach R, Fleury D, Sinclair TR, Sadok W. 2017. Transpiration sensitivity to evaporative demand across 120 years of breeding of Australian wheat cultivars. *Journal of Agronomy and Crop Science* 203: 219–226.

Shinozaki K, Yoda K, Hozumi K, Kira T. 1964. A quantitative analysis of plant form – the pipe model theory. I. Basic analyses. *Japanese Journal of Ecology* 14: 97–105.

Sinnott EW. 1921. The relation between body size and organ size in plants. *American Naturalist* 55: 385–403.

Sinoquet H, Stephan J, Sonohat G, Lauri PÉ, Monney P. 2007. Simple equations to estimate light interception by isolated trees from canopy structure features: assessment with 3D digitised apple trees. *New Phytologist* 175: 94–106.

Smith DD, Sperry JS, Adler FR. 2017. Convergence in leaf size versus twig leaf area scaling: do plants optimize leaf area partitioning? *Annals of Botany* 119: 447–456.

Sugiyama SI, Gotoh M. 2010. How meristem plasticity in response to soil nutrients and light affects plant growth in four *Festuca* grass species. *New Phytologist* 185: 747–758.

Takahashi K, Mikami Y. 2008. A weak relationship between crown architectural and leaf traits in saplings of eight tropical rain-forest species in Indonesia. *Journal of Tropical Ecology* 24: 425–432.

Trueba S, Isnard S, Barthélémy D, Olson ME. 2016. Trait coordination, mechanical behaviour and growth form plasticity of *Amborella trichopoda* under variation in canopy openness. *AoB PLANTS* 8: plw068.

Westoby M, Falster DS, Moles AT, Vesk PA, Wright IJ. 2002. Plant ecological strategies: some leading dimensions of variation between species. *Annual Review of Ecology and Systematics* 33: 125–159.

Westoby M, Wright IJ. 2003. The leaf size – twig size spectrum and its relationship to other important spectra of variation among species. *Oecologia* 135: 621–628.

White PS. 1983a. Corner's rules in eastern deciduous trees: allometry and its implications for the adaptive architecture of trees. *Bulletin of the Torrey Botanical Club* 110: 203–212.

White PS. 1983b. Evidence that temperate East North American evergreen woody plants follow Corner's rules. *New Phytologist* 95: 139–145.

Willaume M, Lauri PÉ, Sinoquet H. 2004. Light interception in apple trees influenced by canopy architecture manipulation. *Trees – Structure and Function* 18: 705–713.

Yagi T. 2006. Relationships between shoot size and branching patterns in 10 broad-leaved tall tree species in a Japanese cool-temperate forest. *Canadian Journal of Botany* 84: 1894–1907.

Yang D, Niklas KJ, Xiang S, Sun S. 2010. Size-dependent leaf area ratio in plant twigs: implication for leaf size optimization. *Annals of Botany* 105: 71–77.

Yang M, Jiao Y. 2016. Regulation of axillary meristem initiation by transcription factors and plant hormones. *Frontiers in Plant Science* 7: 183.

Zeder MA, Emshwiller E, Smith RD, Bradley DG. 2006. Documenting domestication: the intersection of genetics and archaeology. *Trends in Genetics* 22: 139–155.

**Key words:** agricultural plants, Corner's rules, domestication, environment, ideotype, phenotypic correlation space, plasticity, shoot apical meristem (SAM).

Received, 1 June 2018; accepted, 24 September 2018.