Nearly 200 years of sustained selection have not overcome the leaf area–stem size relationship in the poinsettia

Abstract Organismal parts often covary in their proportions, a phenomenon known as allometry. One way of exploring the causes of widespread allometric patterns is with artificial selection, to test whether or not it is possible to move populations into “empty” allometric space not occupied by the wild type. Domesticated organisms have been subject to many generations of selection, making them ideal model systems. We used the domesticated Christmas poinsettia Euphorbia pulcherrima in combination with wild populations to examine the origin of the proportionality between leaf area and stem size, which scales predictably across nearly all plants. In accordance with the stated aims of breeders to produce more compact plants, we predicted that domesticated poinsettias would have greater leaf area for a given stem volume than the tall, lanky wild ancestors. Our data rejected this prediction, showing instead that domesticates have leaf area–stem volume relationships identical to the wild ancestors. Presumably the metabolic dependence between stems and leaves makes the leaf area–stem volume relationship difficult to overcome. The relative fixity of this relationship leads to predictable covariation in other traits: The fuller outlines of domestic poinsettias involve significantly shorter internodes, and given a constant leaf area–stem volume relationship, smaller individual leaf areas. At the same time, domestic poinsettias are subject to selection favoring breakage resistance, which is achieved via thicker stems for a given length rather than stiffer stem tissue resistance to bending. Our results show that domesticated poinsettias differ from wild plants in a suite of traits including leaf size, internode distances, and stem length–diameter relations, but despite over 200 years of selection favoring rounded outlines, there has been no change in the total leaf area–stem volume relationship, helping to predict which changes are likely achievable and which will not be under continued artificial selection and in the wild.

subject to many generations of selection, making them ideal model systems. We used the domesticated Christmas poinsettia Euphorbia pulcherrima in combination with wild populations to examine the origin of the proportionality between leaf area and stem size, which scales predictably across nearly all plants. In accordance with the stated aims of breeders to produce more compact plants, we predicted that domesticated poinsettias would have greater leaf area for a given stem volume than the tall, lanky wild ancestors. Our data rejected this prediction, showing instead that domesticates have leaf area-stem volume relationships identical to the wild ancestors.
Presumably the metabolic dependence between stems and leaves makes the leaf area-stem volume relationship difficult to overcome. The relative fixity of this relationship leads to predictable covariation in other traits: The fuller outlines of domestic poinsettias involve significantly shorter internodes, and given a constant leaf area-stem volume relationship, smaller individual leaf areas. At the same time, domestic poinsettias are subject to selection favoring breakage resistance, which is achieved via thicker stems for a given length rather than stiffer stem tissue resistance to bending. Our results show that domesticated poinsettias differ from wild plants in a suite of traits including leaf size, internode distances, and stem length-diameter relations, but despite over 200 years of selection favoring rounded outlines, there has been no change in the total leaf area-stem volume relationship, helping to predict which changes are likely achievable and which will not be under continued artificial selection and in the wild.

K E Y W O R D S
adaptation, allometry, artificial selection, Constraint, corner's rules, domestication, Euphorbia pulcherrima, selection

| INTRODUC TI ON
The evolution of morphological diversity is bounded by biophysical and adaptive limits, including biases imposed by resource allocation tradeoffs, adaptive covariation, or the dynamics of development (Fusco, 2001;West-Eberhard, 2003;Arthur, 2004;Losos, 2011).
Whether selection is artificial or natural, understanding the breadth of developmental possibility is essential to understand why some morphologies are observed and others are not (Drake & Klingenberg, 2010;Olson, 2012). Situations in which the commonly observed morphologies represent only a tiny subset of the developmentally possible are consistent with the action of selection. Alternatively, the common morphologies could be the only ones, or among the few ones, that are developmentally possible. This second scenario could represent a situation in which selection has extinguished most variation, or one in which variation is or even was never possible, a phenomenon often discussed under the umbrella term "constraint" (Pigliucci, 2007;Pigliucci & Kaplan, 2006;Richardson & Chipman, 2003;Sansom, 2009;Schlichting & Pigliucci, 1998). Such mapping of developmental potential (understood as which variants can be produced and which cannot or are not) is also important for domestication efforts because they can inform regarding morphologies that are likely to be achievable and which are likely difficult or impossible.
Whatever the case, to identify the causes underlying developmental limits or biases must begin with a mapping of developmental potential (Olson, 2012).
For several reasons, domesticated organisms offer particularly attractive systems for exploring developmental limits and biases and their interaction with selection. One reason is that unlike in wild organisms, the features under selection are often well known and explicitly specified (Drake & Klingenberg, 2010). This means that it is possible to know what features breeders have attempted to accentuate or reduce, or which trait combinations are favored. In contrast, in wild populations it is often difficult to determine which attribute is actually under selection (MacColl, 2011). In addition, the wild ancestors of domesticated organisms are often living and can be compared directly to their descendants. The domesticates have often been under selection for hundreds if not thousands of years, and the possibility of comparing the products of such long periods of selection with their starting point is, in macroscopic organisms, found only in situations of domestication (Drake & Klingenberg, 2010; see also Frankino, Emlen, & Shingleton, 2010).
We use a well-known domesticated plant, the Christmas poinsettia (Euphorbia pulcherrima Willd. ex Klotzsch), to investigate the causes of one of the most pervasive trait relationships across the woody plants, the leaf size-stem size relationship. This relationship includes the observation that worldwide, the total leaf area supported by a twig is predicted by the diameter of the twig supporting them (Westoby & Wright, 2003). This pattern, known as Corner's rules, is pervasive, having been documented across virtually all flowering plant lineages, on multiple continents, in vastly differing vegetation types and climates (Ackerly, 1996;Ackerly & Donoghue, 1998;White, 1983a). Corner's rules state that plants with large leaves have thick twigs and branch sparingly; plants with small leaves have thin twigs that branch intricately (Leslie, Beaulieu, Crane, & Donoghue, 2014;Sun, Jin, & Shi, 2006;Westoby, Falster, Moles, Vesk, & Wright, 2002;White, 1983b;Wright, Falster, Pickup, & Westoby, 2006).
What causes Corner's rules is actively being elucidated (Smith, Sperry, & Adler, 2017), and documenting how plants fill leaf areastem size space is essential in this effort.
One essential assumption regarding the cause of the leaf sizestem size spectrum has to do with the mutual metabolic dependence between leaves and stems. Leaves meet the metabolic needs of stems and roots, whereas stems mechanically support leaves and supply them with water. Presumably this metabolic proportionality drives the generally strong leaf area-stem size relationship (Olson, Aguirre-Hernández, & Rosell, 2009). Stated in terms of developmental potential, the space that the leaf area-stem size relationship describes can be thought of as having three areas (see Olson, 2012;Olson & Arroyo-Santos, 2015 (Eggli, 2002). In other words, the largely empty space beneath the leaf area-stem size scaling line is accessible developmentally but apparently favored by selection only in extreme situations. What is not so clear is whether the area above the line is accessible. This area corresponds to plants with more leaf area for a given stem size than typical plants have. Unlike the reduced leaf area below the scaling line, few or no examples have been offered of plants with relatively high leaf area. If plants can be found that fall above the scaling line, then they would suggest that plants with "too much" leaf area are developmentally accessible, that is, that these variants can be produced. If they can be produced, then it makes it likely that their rarity in the wild is due to selection acting against them in most situations. Finding, on the other hand, that they apparently cannot be produced would open the door to study of the cause of this inaccessibility and would potentially modify the adaptive interpretation of the leaf size-stem size spectrum.
Because these alternative scenarios are very different, it is therefore very important to explore the accessibility of the area above the leaf area-stem diameter scaling line.
The poinsettia is ideal for examining whether leaf area can be increased for a given stem size because, in the stated goals of breeders, it has apparently been under selection in exactly this direction for nearly two centuries (Ecke, Matkin, & Hartley, 1990;Kobayashi, 2012;Lee et al., 1997;Taylor, López, Currey, & Janick, 2011). Wild poinsettias are lanky shrubs or small trees in mid-elevation tropical subdeciduous forests of the Mexican tropical Pacific slope with cane-like stems to over 6 meters long, mostly unbranched and clothed with distantly spaced leaves (Trejo et al., 2012; Figure 1). A rich historical record documents with illustrations the transformation from the lanky wild ancestor to the dense, rounded profile of the domesticates, as well as recording the aims of the breeders. The earliest efforts selected for, among other characteristics, homeotic replacement of the flower heads for colorful bracts, and shortened inflorescence internodes (e.g., Graham, 1836;Navarro, 1992).
Starting with the still tall and lanky early cultivars (Ecke et al., 1990;Taylor et al., 2011), poinsettia breeding has been directed at creating smaller, compact plants with more rounded outlines with a bushy habit (Kobayashi, 2012;also Taylor et al., 2011;Lee et al., 1997). As part of this program of shortening and creating a rounded profile, any heritable variant with short internodes and relatively high leaf area for a given stem size would be seized upon and accentuated.
This well-documented vector of domestication makes the poinsettia a particularly fertile system in which to look for deviation from the common global leaf size-stem size relationship. Changes in biological shape or size, such as the leaf area-stem size allometric relationship, also inevitably involve changes in the mechanical behavior of a structure (Rosell et al. 2012). Therefore, it is essential to understand how any differences in scaling between wild and domestic poinsettias could be associated with differences in the mechanical properties of their stems. We examine here the Young's modulus of the stem E stem, which is an index of how well the material that makes up a given structure resists deformation (Niklas, 1992;Vincent, 1992). Examining stem mechanical properties in poinsettia is likely to be informative because one of the well-documented vectors of selection of poinsettia breeders is to increase resistance to stem breakage during shipping (Ecke, 2011;Taylor et al., 2011). As a result, it seems possible that selection has altered stem mechanical properties in domesticates with respect to the wild ancestor in ways that might be linked to leaf area-stem diameter scaling.
We collected material from wild populations of poinsettia and compared the leaf size-stem size scaling patterns with morphologically divergent cultivars. Given this range, we fully expected to find marked deviation in leaf size-stem size scaling consistent with movement into the "too much leaf" zone. We found instead that while domestic poinsettias have smaller leaves, shorter internodes, and thicker stems than wild poinsettias, the leaf area-stem relationship remains identical between the two. We discuss reasons for why the leaf-stem relationship should be so difficult to move into the "too much leaf" area and how this fundamental relationship results in predictable patterns of covariation in other traits.

| Leaf area-stem volume scaling
Previous phylogeographic work (Trejo, Olson, & Bye, 2015;Trejo et al., 2012) mapped the relationships between wild and domesticated poinsettias. We used these data to select wild populations closely as well as distantly related to the modern cultivars. We sampled from the two largest wild poinsettia populations that we have been able to locate. One was from La Calera canyon in the semideciduous tropical forest. To maximize chances of finding departures from wild-type leaf-stem proportionality, we selected three of the main current and morphologically divergent cultivars, which in their commercial descriptions are described as spanning a range of leaf densities (Ecke, 2011). The cultivar Orange Spice is described as having a relatively sparse complement of narrow leaves.
Red Glitter is described as having a rounded, compact outline, and a high density of wide leaves. Finally, Polar Bear is noted as being similar to Red Glitter but more highly branched ( Figure 1). In all, we sampled one branch of each of 16-34 individuals per wild population or variety for a total of 118 individuals.
We sampled a range of stem diameters across populations and varieties to provide the necessary variation for fitting allometric models. We collected one branch per individual, measured its basal diameter fresh using digital calipers, labeled each leaf and bract, and pressed and dried the leaves and bracts in a herbarium press. In the laboratory, we measured leaf area, including bracts and petioles, using the program WinFolia Basic V2011a (Regent Instruments Inc 2011, Quebec, Canada). Noting the number of leaves per stem, we then summed the leaf area per branch. We represented stem volume using the basal diameter, stem length, and the formula for the volume of a cylinder. These data are available in Table S1.
We then fit multiple mixed-effects linear models predicting perbranch total leaf area (Bolker et al., 2009). We started with a model with the fixed effects log 10 stem volume, a binary cultivated/wild categorical variable, and a log 10 stem volume wild/cultivated interaction term. The random effect included the categorical variable population/variety to which the branch (and individual) belonged and had five levels (Concordia, La Calera, Orange Spice, Polar Bear, and Red Glitter). This random effect took into account that branches (and individuals) were nested within populations/varieties. This first model allowed the populations/varieties to have a random intercept.
We then fit another model allowing population/varieties to have a random slope in addition to a random intercept. We compared these two models (random intercept vs. random slope and intercept) using likelihood ratio tests and the Akaike Information Criterion (Zuur, Ieno, Walker, Saveliev, & Smith, 2009

| Mean individual leaf area-stem volume scaling
To ask whether selection for shorter, more rounded poinsettias has affected the mean size of individual leaves (as opposed to the total leaf area supported by stems), we followed a similar procedure as for total leaf area per branch. Using the data in Table S1, we calculated the mean area of leaves per branch and fit a model predicting log 10 mean individual leaf area based on log 10 stem volume, a binary cultivated/wild categorical variable, and a log 10 stem volume wild/ cultivated interaction term. As for the previous model, the random component included the categorical variable population/variety to which the branch belonged (the same levels as for models predicting total leaf area). We again compared random intercept versus random slope and intercept models. Once the best random component was identified, we tested the significance of the interaction term.

| Stem biomechanics
To test the notion that the domestication of poinsettia might involve differences in stem mechanical properties, we gathered samples from the large wild population at La Calera, and from Red Glitter and  (Vincent, 1992).
We tested the segments in three-point bending with an Instron 3345 mechanical test machine equipped with a 5-kN load cell. Stem Young's moduli (E stem ) were calculated using Instron System IX/s software (Instron Corporation, Canton, MA), using the basal diameter of the tested segment in the calculation of the second moment of area I (Niklas, 1992). Poinsettia stems have hollow piths, but we calculated I as though the stems were solid; this procedure underestimates the absolute E stem but the results are entirely comparable between individuals and segments. The mechanical demands made on a given stem segment are largely described by how far the segment is from the stem tip, because this distance is directly related to the bending moment that the segment is subjected to. Therefore, we measured the distance to the stem tip from the midpoint of our test segments and used this distance as the metric of comparison between wild and domesticated poinsettia mechanical properties.
These data are given in Table S2.
To examine the scaling of stem stiffness with distance from the tip, we used mixed-effects linear models following a similar procedure as previously explained. We predicted log 10 E struct based on log 10 distance from the tip, a binary cultivated/wild categorical variable, and a log 10 distance from the tip wild/cultivated interaction term. The random component of this model included the individual to which the segment belonged nested within the population/ variety (with five levels, Guerrero, La Calera, Polar Bear, Red Glitter, and Subjibi) to which the individual belonged. We followed the same procedure to select the best final model.

| Internode length-stem volume scaling
Plants with denser outlines could be achieved by selection favoring shorter internodes. If stem dimensions and mean individual leaf area remain unchanged, shorter internodes imply greater total leaf area.
When preliminary data suggested that domesticates bear slightly less rather than more total leaf area than similar-sized stems of wild  Table S3.
To examine whether for a given stem volume domestic and wild poinsettias differ in their internode distances, we calculated a mean internode distance per branch (and per individual) and fit mixed-effects linear models. In this case, we predicted log 10 internode distance based on log 10 stem volume, a binary cultivated/wild categorical variable, and a log 10 stem volume wild/cultivated interaction term. As for the leaf area models, the random component of this model included the population/variety to which the branch (individual) belonged (with eight levels La Calera, Casallas, La Anda, Amatlán, Texcal, Orange Spice, Red Glitter, and Lemon Snow). As for previous models, we identified the best random component and tested the significance of the interaction term.

| Stem length-stem diameter scaling
To examine whether domestic poinsettias have thicker stems for a given stem length, we predicted log 10 stem length based on log 10 stem diameter, a binary cultivated/wild categorical variable, and a log 10 stem diameter wild/cultivated interaction term. The random component included the population/variety to which the branch (individual) belonged (same levels as models predicting leaf areas). We followed the same procedure as for previous models.

| Total and individual leaf area-stem volume scaling
The 118  Our first model tested for differences in log 10 total leaf area for a given log 10 stem volume between cultivated and wild plants, nesting individuals within populations/cultivars, the variable that was included as a random effect. In our initial model, the log 10 stem volume cultivated/wild interaction term was nonsignificant (p = .126), indicating similar total leaf area-stem volume scaling between cultivated and wild plants (Table 1). We refit the model without the interaction term and examined whether cultivated and wild plants differed in intercept, which they did not (p = .570). With an R 2 of .83, the final model with just log 10 stem volume and the cultivated/ wild variable as fixed effects fit the data very well. The random component of this model indicated that populations/varieties had differences in intercepts but not in slopes (Table S4). Counter to our expectations, cultivated plants did not have a higher leaf area-stem volume intercept than the wild plants ( Figure 2a). Instead, despite their markedly different overall appearances, and the much fuller outlines of cultivated as compared to wild plants (Figure 1), domesticated poinsettias have the same leaf area for a given stem volume as do the wild ancestors.
Our subsequent model tested for differences in log 10 mean individual leaf area controlling for log 10 stem volume among cultivated and wild individuals. This model also fit the data very well with an R 2 of .76. The model suggested differences in slopes across populations (p = .004; Table 1). Although this slope difference precludes a direct comparison of intercepts to test our hypothesis, Figure 2b shows that fitted lines do not intersect and that the wild individuals tend to have larger leaves than cultivated ones along the sampled range, which includes most of the size range for these plants.

| Stem length-stem diameter scaling
Wild poinsettias have more closely spaced leaves than wild plants, contributing to their fuller outline, but they also have smaller leaves. Presumably there is a metabolic dependence between leaf area and the volume of metabolically active tissue within the stem.  (Table S4). The TA B L E 1 Mixed-effects models fit to test for differences in the allometry of wild and domestic poinsettias. Coefficients for fixed effects are shown with 95% confidence intervals in parentheses. All continuous variables were log 10 -transformed. In all cases, the model with a random intercept had a better fit than the model with a random slope and a random intercept, except for the model predicting stem length (see Table S4)  (Niklas, 1995).

| Stem biomechanics
Differences in the proportions of any biological structure will result in differences in mechanical behavior, so given the differences between domestic and wild poinsettias, we tested for differences in stem resistance to bending. Across the 85 segments tested, segments ranged in diameter from 5. The model examining E stem between domestic and wild plants had a nonsignificant interaction term (p = .126), indicating similar log 10 E stem -log 10 distance from the stem tip scaling slopes between cultivated and wild plants. We refit the model without the interaction term, finding that the domestic/wild binary variable was also not significant (p = .796), indicating no differences mean E stem for a given distance from the tip between wild and domesticated poinsettias (Figure 2e). These results show that domestic and wild poinsettias do not differ in their tissue level mechanical properties, that is, are made of "material" of the same resistance to bending.
Given that domestic poinsettias have a lower stem length-diameter intercept than wild plants, a segment of a given length of stem will be more resistant to bending in the domestic as compared to the wild plants by virtue of stem dimensions and not because they have stiffer tissues.

| D ISCUSS I ON
Our data clearly rejected our expectation that domesticated poinsettia plants should have greater leaf area controlling for stem volume than wild plants. Despite the sustained and explicit efforts of F I G U R E 2 The constant total leaf area-stem volume relationship and its influence on trait relationships between domestic poinsettias and their wild ancestors. (a). Despite nearly 200 years of breeding small poinsettias with full outlines, the relationship between total leaf area and stem volume has not been altered with respect to the wild ancestor. (b) Although their total leaf areas are the same for a given stem volume, domesticated plants have smaller individual leaf areas. (c) Smaller individual leaf area with similar total leaf area requires more numerous leaves in the domesticate, an expectation borne out by our data, which show that for a given stem volume, domesticates have not only smaller leaves but more of them per unit of stem length, as indicated by their significantly shorter internodes. (d). Likely reflecting selection favoring breakage resistance, domesticates also have thicker branches for a given stem length, the only way that domesticates could resist breakage better than wild plants, given that their stem tissue mechanical properties do not differ (e) breeders for 200 years along vectors of selection that would eagerly identify, preserve, and enhance variants with more leaf area per unit stem volume than the wild plants, in the cultivars we examined, no such tendency was detectable. Instead, the denser outline of cultivated plants is achieved in part via shorter internode length, together with smaller individual leaf area and thicker stems. We discuss how artificial selection on domestic poinsettias has led to manifold changes in proportionalities between parts, all in the context of a constant leaf area-stem volume relationship, and comment on why this relationship is unlikely to be overcome even under artificial selection.
The leaf area-stem size relation is nearly pervasive, being found across virtually all species that have been studied (Ackerly, 1996;Ackerly & Donoghue, 1998;Leslie et al., 2014;Sun et al., 2006;Westoby et al., 2002;White, 1983a,b;Wright et al., 2006). The only exceptions seem to be certain plants in warm drylands, which have greatly reduced leaf area for a given stem size (Eggli, 2002).
For example, species such as Adenium socotranum have crowns of very small leaf areas but very large stem diameters. Species such as Alluaudia procera or Fouquieria purpusii, which have thick, spiny stems clothed with small leaves, would also seem to be candidates that depart from the common leaf area-stem volume relationship. These examples also suggest that these highly water-storing plants likely have stem tissues of relatively low metabolic rate, a prediction consistent with the few data available, which show that woods with greater storage capacity are less metabolically active (e.g., Lambers, Scheurwater, Mata, & Nagel, 1998). These departures all are in the direction of less rather than more leaf area for a given stem size.
That domestic poinsettias also do not move into leaf area-stem volume scaling space that corresponds to "too much" leaf area suggests that while stem tissue can be largely devoted to storage and has low metabolic demands, leaves are a different matter. It suggests that as the sites of photosynthesis, which require water and mechanical support, leaf metabolic demands are necessarily relatively high and cannot in general, as in the case of storage stems, be significantly reduced. Storage stems provide examples of reduced metabolic demands permitting reduced leaf areas; a given amount of standard nonsucculent leaf, however, seems to require a given amount of stem volume to meet its metabolic needs. The mutual metabolic balance between stems and leaves, with stems having a much wider envelope of possible metabolic rates than leaves do with regard to their lower limits, would thus explain why the "too little" leaf area space is occupiable, albeit sparsely, whereas the "too much" leaf area is apparently not accessible, even, as in the case of the domestic poinsettia, under conditions of selection that would reasonably be expected to favor greater leaf area. The readily testable prediction that emerges from our results is therefore that metabolic rate should vary markedly in stems across species (being especially low in water-storing pachycauls with reduced leaf area; see, e.g., Poorter, Remkes, & Lambers, 1990;Lambers et al., 1998) but much less in leaves across plant functional types, from conventional plants to xerophytes with reduced leaf area and stems given over to storage (cf. Jin, Dai, Sun, & Sun, 2008).
That selection strongly maintains the leaf area-stem volume relationship means that selection on any aspect of vegetative allometry necessarily results in predictable changes in subsequent generations ( Figure 2). In the case of the poinsettia, selection favoring fuller outlines has resulted in shorter internodes. Shorter internodes clearly achieve the goal of fuller outlines, as compared to the wild plants.
Internodes in the wild plants we measured could reach nearly 10 cm, which would lead to a sparse appearance in a small potted plant.
Artificial selection has greatly reduced internode differences, with Also potentially accounting for the greater thickness of domestic poinsettia stems is that another stated goal of poinsettia breeders is to increase breakage resistance (Taylor et al., 2011).
Shipping poinsettias to market involves mechanical loads that can deform or break branches, leading to loss of revenue. When cultivars are presented to growers, among variables such as bract color, plant size, and flowering time, the resistance to stem mechanical deformation is also routinely reported (Ecke, 2011). Our results show that domestic poinsettia stems are indeed more resistant to bending but suggest that breeding efforts have not achieved these more resistant stems via greater materials stiffness, as reflected by E stem , but through thicker stems. The stiffness of a stem depends on two variables, the capacity of the material it is made up of to resist bending (as reflected by E stem ), and how well the material in a given stems is deployed in space to resist bending (as reflected by I, the second moment of area, Niklas, 1992). That E stem does not vary between domestic and wild poinsettias (Figure 2e), but that domestic plants have thicker stems (Figure 2d), allowed us to identify I, which scales with stem radius to the fourth power, as the crucial variable contributing to differences in resistance to bending between wild and domestic poinsettias. Selection favoring resistance to bending could thus plausibly have led to the thicker stems of domestic poinsettias. As mentioned above, thicker stems for a given length mean greater opportunities for deployment of leaf area, and therefore fuller outlines. As a result, selection favoring increase in leaf area could also increase stem volume for a given stem length. Whatever the exact cause, it illustrates how the constant leaf area-stem volume relationship produces a ripple effect, with any one change in the value of one of the variables making up part of the allometric network leading to predicable changes elsewhere ( Figure 2).
Such phenomena are often discussed under the rubric of "constraint," but we suggest that there is little to be gained by use of the term. The leaf area-stem volume relationship being "fixed" does indeed mean that changes in other traits such as leaf area, stem length-diameter proportions, or internode distances, lead to changes in the other traits that are predictable precisely because of the "fixed" leaf area-stem volume relationship. This predictability diagnoses limited or biased outcomes, exactly the notion that many definitions of constraint aim to capture (Olson, 2012). However, it seems likely that the leaf area-stem volume relationship is not "fixed" in any way beyond simply being one strongly favored by selection from among a range of developmentally possible contenders.
That the "too little" leaf area condition is possible to observe in nature shows vividly that such variants can be produced. Although the poinsettia does not provide an example of an occupant of the "too much" leaf area zone, there are other ways other than artificial selection of testing whether this area is accessible or not and the causes of this (in)accessibility. A comparative approach is the prediction that leaf metabolic rate should vary less across species than in the stem.
An experimental approach could examine our prediction that the leaf area-stem volume relationship is maintained because of the strong metabolic interdependence between stem and leaf, implying that leaves require a certain amount of stem volume (Donovan, Maherali, Caruso, Huber, & de Kroon, 2011;Olson, 2012). Experimental removal of stem tissue would help quantify the functional and fitness impacts of having "too much" leaf for a given stem volume. From this point of view, the leaf area-stem volume relationship is subject to stronger selection than others, including the total leaf area-leaf size relationship and stem length-diameter allometry. Although such situations are often described as representing "allometric," "selective," or "adaptive" constraint, use of these terms does not in fact add any mechanistic or detail or predictive power and we would advocate avoiding the vague term "constraint" in favor of describing the mechanism leading to any restriction or biasing of outcomes in as much detail as possible (Olson, 2012).
The apparently very strong selection favoring a constant leaf area-stem volume relationship implies that many trait combinations are unlikely to be achieved, both in nature and in the domestic poinsettia. That the combination of high leaf area and thin stems is not readily available seems underscored by horticultural practice in the poinsettia industry. In the apparent absence of breakage-resistant variants with greater leaf area per unit stem diameter, full and rounded outlines in domesticated poinsettias are achieved by pinching, which involves manual removal of apical meristems, thereby encouraging branching (Kobayashi, 2012;Lee et al., 1997), and even infection with phytoplasma, which also has the effect of encouraging branching (Lee et al., 1997). That poinsettia horticulturalists employ these labor-intensive and expensive techniques to produce plants of the requisite proportionalities strongly suggests that the desired increase in leaf area is not feasible and needs to be achieved through branching, illustrating how the mapping of patterns of covariation can guide applied breeding efforts in addition to shedding light on adaptive processes in nature.

| CON CLUS ION
Our data show that two centuries of selection on the Christmas poinsettia have altered neither the slope nor the intercept of the leaf area-stem volume relationship. The apparent fixity of this relationship means that selection favoring fuller outlines during the domestication of the poinsettia has favored shorter internodes, leading to branches more densely clothed with leaves. Shorter internodes require more leaves per unit stem length, and given a constant leaf area-stem volume relationship, more leaves necessarily require smaller leaves. At the same time, stem length-diameter relations have been altered, with domestic poinsettias having thicker stems, leading both to more breakage-resistant stems as well as shorter internodes. With elaborate pinching and phytoplasma infection practices, the poinsettia provides a vivid example of the expense and effort required to produce desired morphologies when the path to their breeding is blocked by powerful selection favoring the leaf area-stem volume relationship above all others.

ACK N OWLED G EM ENTS
This study was funded by National Geographic Committee for Research and Exploration Project 870-09 and Conacyt Project 132404. We thank Rocío Moreno for help with leaf area, Roberto Gómez Bermejo for help in the field, Ing. Luis Zapata for help in obtaining cultivars, and two anonymous reviewers for their helpful comments and suggestions.

CO N FLI C T O F I NTE R E S T
None declared.

DATA A RCH I V I N G
Data are available in Tables S1-S3.