**Author details**

Kai-Lan Hsu1,2, Chih-Wei Chang1,2,3\*, Chyun-Yu Yang1,3 and Jou-Hua Wang1

\*Address all correspondence to<EMAIL_ADDRESS>
1 Department of Orthopaedic Surgery, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan

2 Department of Biomedical Engineering, College of Engineering, National Cheng Kung University, Tainan, Taiwan

3 Bone and Joint Center, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan


There is dispute whether height growth stimulation produced by decrease in R:FR has a cost in terms of reduced biomass growth in other parts of the plant. Maliakal et al. (1999) working with *I. capensis* and Ballaré et al. (1991) with *Amaranthus quitensis* both report that stimulation of height growth does not cause a reduction in root or leaf growth. On the other hand, Vermeulen et al. (2008a) found through experimental manipulation of R:FR, an increase in petiole length and petiole mass for *Potentilla reptans* but decrease in root, stolon, and total biomass. They also report that petiole length can be limited by the productive capacity of plants. Direct application of gibberellic acid to stems of *Phaseolus vulgaris* produced the expected increase in stem elongation but a concomitant reduction in total mass, pod number, and pod mass (Cipollini and Schultz, 1999).

Whether there is a carbon cost to R:FR-induced height growth could be important in considering its possible effect on competition. Dudley and Schmitt (1996) manipulated R:FR supplied to seedlings of *I. capensis* to produce stem-elongated and nonelongated plants. These seedlings were transplanted to within both high- (plants 3 cm apart) and low- (20 cm apart) density arrays. Lifetime fitness was calculated as number of reproductive structures produced over the lifetime of the plant. Elongated plants were more fit at high density and non-elongated plants at low density. Dudley and Schmitt (1996) suggested the advantage of elongated plants at high density was that greater height resulted in greater light capture, while their disadvantage at low density may be the result of the additional carbon cost of increased height. In a comparison of eight genotypes of *P. reptans* grown in a mixture to form single-species stands,Vermeulen et al. (2008b) found that genotypes with relatively more leaves in the top layer of the canopy were, on average, more efficient in light capture per unit leaf weight.

Photomorphogenetic-induced height increase can change plant population structures through increasing survival of smaller plants. However, the extent of this effect on the competition process, as a whole, is likely affected by the conditions of growth, particularly spacing, and the genetic structure of the population. We need to know the balance between change in R:FR in relation to PAR level for particular instances and to define how this relationship may change as the plant stand increases in height and

total foliage amount. Interestingly, Dudley and Schmitt (1995) showed that while populations of *I. capensis* from more open conditions, where there was likely considerable competition for light, showed photomorphogenetic-induced height growth, populations from more shaded conditions did not. Schmitt (1997) cites additional examples of similar ecotypic variation. Certainly, we can anticipate limitation to the effect that a decrease in R:FR may have in rescuing the growth of over-topped plants since we know that small plants do die due to the effects of competition.

### **ARCHITECTURAL VARIATION IN INTERCEPTION AND UTILIZATION OF LIGHT**

Much research has been conducted into variation in plant structure on light absorptance but primarily with a standpoint of examining the efficiency of whole canopies rather than possible effects on competition within a stand (Niinemets, 2010). However, there are reasonable grounds for considering that architectural variation found between competing plants may influence competition through their effects on interception and utilization of light, e.g., Bendix et al. (2010). Leaf angle and the spatial distribution of leaf biomass can be affected by plant density (Vandenbussche et al., 2005; van Zanten et al., 2010) as well as leaf orientation, e.g., in maize (Drouet and Moulia, 1997) and cucumber (Kahlen et al., 2008). Some rosette species show hyponastic leaf growth in response to crowding, i.e., where leaves bend upwards, which can reduce the impact of competition: Pierik et al. (2003) planted hyponasty loss-of-function transgenic plants along with wild-type *Nicotiana tabacum* at the rosette stage of development and demonstrated that the transgenic was outcompeted.

Anten and Hirose (1998) calculated light absorption by individual plants in natural monospecific stands of *X. canadense*, a fast-growing, shade-intolerant annual. Dominant plants absorbed more light both per unit leaf area (area) and per unit mass (mass) and that the greater area more than compensated for the lower leaf area ratio of dominant plants. They concluded that the greater mass of dominant plants is quantitative evidence that success in competing for light is disproportionally related to the size of shoots. The proportion of mass in leaf lamina, the leaf mass ratio (LMR), decreased with increasing height but solitary plants had higher LMR than competing plants of the same height. Anten and Hirose (1998) concluded that LMR is not determined by biomechanical constraints but results from a plastic shift in allocation in response to competition.

From the perspective of competition, the production of foliage has two functions: certainly one is production of photosynthate for growth but the other can be simply shading neighbors even if there is no net gain in photosynthesis to the producing plant. Trends in development of *Zea mays* hybrids provide an example where reduced competition may contribute to an increased in total crop yield. Commercial hybrids have been selected, and commercially planted, in the central corn belt of the United States (Duvick et al., 2004) at increasingly closer spacing from ∼30,000 plants ha−1 in the 1930s to ∼75,000 plants ha−1 or higher by the 1990s. Production has increased markedly over this period and while a number of phenotypic characters have changed (Duvick et al., 2004) whole canopy efficiency (yield per ground area) has increased. Ford et al. (2008) compared the major hybrid used in the 1960s with that in the 1990s and found the 1990 hybrid had smaller leaves. Maize leaves are curved and Ford et al. (2008) found less curvature and more uprightness for the 1990 hybrid compared with that for the 1960 hybrid and so, potentially a reduced competitive influence. Interestingly, experimental manipulation of foliage of the same 1960s hybrid, by tying leaves into a more upright position, produced an increase in yield (Pendleton et al., 1968). Curvature is a plastic character in response to plant density and while Ford et al. (2008) found both hybrids had less curvature at higher planting density the effect was greatest for the 1990 hybrid. Fellner et al. (2003, 2006) show that this plasticity is related to an interaction between light quality and auxin particularly in the development of the leaf auricle.

How can a decrease in leaf size and an increase in leaf inclination increase productivity of a whole stand and do these changes reduce competition between individuals? Generally, increased leaf inclination from the horizontal will reduce incident quantum flux density on the leaf surface although the exact effect depends upon sun angle, foliage inclination, and the azimuth between sun and plane of the laminar surface. The effect of more upright foliage may be more appropriately thought of as reducing the duration of high incident quantum flux density.

Lateral extension of uppermost leaves may reduce light received by neighbors, but that light may be intercepted by the larger plant at intensities in excess of the light saturation point of the photosynthesis curve. An increase in inclination of these leaves, and reduction in their size, may reduce total light intercepted but not necessarily the total amount of whole-plant photosynthesis since uppermost leaves may still receive light close to the light saturation point of photosynthesis for considerable periods and more light will reach lower, more shaded, foliage. Reduced exposure of foliage to high irradiance may reduce the possibility of photo-damage and/or high evaporative demand on the foliage, e.g., Falster and Westoby (2003) for sclerophyllous plants.

Conifers also have consistent modifications to foliage in response to differences in ambient light levels. In the *Pinacea* foliage, needles are clumped around the supporting shoot at higher light levels and more spread out at lower levels and this is measured by the silhouette to area ratio (STAR), e.g., Stenberg et al. (2001) for *P. sylvestris*. In the *Cupressaceae*, which has foliage in fronds, there are multiple variations in foliage and branch structure as light varies, e.g., Edelstein and Ford (2003) for *Thuja plicata*.

In summary, although investigations of plants as competitors have shown the importance of considering competition as a 3-D and not 2-D process we still lack investigations of canopy formation, particularly of the effects of differences in resource acquisition plasticity. The three features of plants as competitors (resource acquisition plasticity, morphogenetic plasticity, architectural variation in interception and utilization of light) should not be considered separately although the history of the subject shows that they have been—which is not surprising given the details of the research required.

### **DEVELOPMENT OF THEORY FOR THE EFFECTS OF PLANT ARCHITECTURE ON COMPETITION**

Competition theory based on studies of populations and stands has been challenged and found wanting. This is not surprising. Competition can affect the component parts of plants differently (sec Plants as Competitors) and the effect on the individual, as a whole, results from the integration of many such interactions. The size of an individual is only an approximate indication of competitive status and can neither be used to indicate the component interactions that will occur nor how their effects may be integrated.

Nevertheless, studies of stands undergoing competition provide essential descriptions of what needs to be explained. They show that the process has multiple effects on stand structure in the numbers of plants that survive or reproduce, the distribution of plant sizes, and the spatial distribution of individuals. These effects are interrelated but the relationships may vary between species and conditions of growth. Unfortunately, some research into the properties of plants as competitors has selected just one component of stand development as an indicator of competition. This can lead to a biased view of the process as a whole and inadequate understanding of the role of particular properties.

This section outlines a theory for analyzing the dynamics of architectural effects on competition. However, prior to that it is necessary to define what the theory should be able to explain both in general terms and in details of stand development.

### **WHAT SHOULD THE THEORY BE ABLE TO EXPLAIN?**

There are considerable challenges in establishing a relationship between plant architecture and competition. Plant morphology is diverse and this presents us with a conundrum. If competition for light is ubiquitous then why has there not been evolution for an obviously successful architecture? Niklas (1997) suggests the requirement to conserve water reduced phenotypic options available to the earliest land plants. However, once this adaptive hurdle was overcome the next requirement was to achieve effective performance of multiplefunctions simultaneously—such as maximizing both light interception and reproductive success and ensuring mechanical stability—which took place where plants were growing together in communities. This increased the number of phenotypic options that had equivalent relative fitness. A system with a single defined task has fewer alternative designs compared to that for systems with manifold tasks which may be globally efficient yet comparatively poor at doing any one task. This implies there are multiple answers to the apparently simple question of what makes an effective competitor and a theory for the effects of plant architecture on competition should be required to show how different combinations of features may have similar results.

Population- and stand-level studies illustrate that the intensity of competition and the results it produces change over time. For practical purposes, this requires that investigations and studies should be assessed on rates of change rather than outcomes at a single point in time. Consider a study that compares plants with different architectures, e.g., the pioneering study by Geber (1989) which compared effects of differences in morphology between two species of *Polygonum* on competition. We can ask:

In practice, competition has multiple effects and more than one metric should be used. Techniques for multi-criteria assessment are discussed by Reynolds and Ford (1999) specifically for competition; Ford and Kennedy (2011) for FSPMs; Kennedy and Ford (2012) as a general strategy of investigation.

### **STRUCTURE FOR A THEORY TO INVESTIGATE THE EFFECTS OF PLANT ARCHITECTURE ON COMPETITION**

Five groups of postulates are required to analyze the effects of differences in architecture on competition. These are given in general terms here and specific postulates would need to be developed for particular questions.

### *Group 1*

Competition for light takes place at the level of foliage and foliated axes rather than whole plants—save for small plants that have only a single foliated axis.

This is the foundation postulate for attempts to explain competition through architecture and provides a clear distinction from population or whole-plant-based theories. It ensures that explanations for differences that we may see in competition will be sought in differences in the processes of plant growth. A corollary is that the effects on the whole plant depend upon integration of affects across all foliage and foliated shoots (see Group 4). Section "Architectural Models and Competition Dynamics," on modeling illustrates the importance, and difficulty, of explaining how this integration in the growth of the whole plant takes place.

### *Group 2*

The outcome of competition is determined by interaction between two processes:

• *Exertion of dominance* through growth of foliage or a foliated axis that intercepts light that would otherwise could be utilized by neighboring foliage and;

• *Reaction to shading* through changing form and/or physiological characteristics.

This postulate is fundamental to determination of the dynamics of the competition process. Exertion of dominance can occur through resource acquisition plasticity and may be affected by efficiency of interception and utilization of received PAR. Reaction to shading can be through morphogenetic plasticity. Both process *Exertion of dominance* and *Reaction to shading* may occur on different parts of the same plant (see Group 4) and the resultsfor plant growth and/or survival depend upon the integration of effects. It is important that studies claiming to define competition as some result of a particular architecture should define both processes. We have many studies (see Plants as Competitors) demonstrating that one or the other of these processes occur but their effects on the competition process require analysis of both components in the dynamic system.

The implication of specifying competition in this way is that the primary process is the exertion of dominance and that morphogenetic plasticity is a *reaction* to that but does not halt it or stop its effects completely. So we can expect to see stand structural characteristics that indicate competition has occurred even in roseate plants such as *Arabidopsis* (e.g., Stoll and Bergius, 2005). The intensity of competition might be considered as the extent to which *Exertion of dominance* exceeds *Reaction to shading*. The rate at which these two processes proceed may change during stand development. This is the central group of postulates that defines the work to be done to develop understanding of architectural effects on competition because it indicates the dynamics of interaction.

### *Group 3*

Architectural properties of a species determine both *Exertion of dominance* and *Reaction to shading.*

Comparative analysis of species seems to be an important approach to analyze the effects of architecture on competition. Research has shown (see Plants as Competitors) that plant species exhibit different responses to being crowded but analysis of architectural effects on competition requires that exertion of dominance and responses to shade be quantified simultaneously.

### *Group 4*

For an individual plant, the outcome of competition depends upon integration of effects of *Exertion of dominance* and *Reaction to shading* across the component foliage and foliated shoots.

Individual plants may simultaneously exhibit, in different parts, both resource acquisition plasticity, differences in interception and utilization of PAR, and forms of morphogenetic plasticity depending on their size, modularity of construction and architecture. In Section "Architectural Models and Competition Dynamics," the importance of understanding the integration of plant growth is illustrated.

### *Group 5*

Mortality is a time-delayed response to suppression. It is an important result of competition, particularly in dense stands or those where competition persists for long periods as in stands of trees. However, it is not generally studied in relation to architectural effects.

### **ARCHITECTURAL MODELS AND COMPETITION DYNAMICS**

Simulating competition provides an excellent test for functional– structural plant models (FSPMs; Godin and Sinoquet, 2005) because it requires effective representation of plants as conditions change. Two types of problems have been encountered: how to represent the integration of plant function and how to define precise relationships for operation of morphogenetic plasticity.

### **INTEGRATION OF WHOLE-PLANT FUNCTION**

Trees are interesting subjects for the study of plant competition. Their size and longevity raise questions about how effects of different parts of trees and how the effect of such competition is integrated in the growth of the whole tree.

Sorrensen-Cothern et al. (1993) investigated the extent to which morphogenetic plasticity affected competition. They simulated competition for light in a young stand of dense, naturally regenerated *Abies amabilis.* The model simulated growth of each individual tree in annual height and branch, including foliage increments, and the 3-D spatial location of branch and foliage was calculated.

Light was considered in contiguous vertical columns and absorption depended upon the total leaf area density and its interception characteristics that had morphogenetic plasticity depending on whether the tree was classified as a "sun," "intermediate," or "shade" individual, according to its relative height in the stand. No direct calculation of photosynthesis was made but a conversion efficiency, which varied between the three trees classes, was applied to the light absorbed to give a surrogate variable for photosynthate. The accounting system for the penetration and absorption of light, represented in vertical columns, allowed for spatial variability of light to have an effect on growth.

Height and individual branch increments were estimated through parameters applied respectively to the sum of the surrogate variable for the whole tree and the branch being considered. Branches grew as expanding fans of foliage with foliage density depending on the light level at each point within the branch, i.e., for the relevant 10 cm × 10 cm × 10 cm section. Model parameters were calculated using an extended sensitivity analysis.

When no plasticity was incorporated into the model, suppressed trees lost the structure found in empirical investigations. It was essential to incorporate plasticity in the amount of light absorbed per unit foliage as well as foliage survival in relation to light level to simulate observed changes in crown apex angles of suppressed trees, and correct crown lengths and to simulate the frequency distribution of tree heights and mortality.

In a subsequent uncertainty assessment of the model, Reynolds and Ford (1999) found it important to assign the plastic characteristics of foliage based on the local light level rather than based on classification of complete trees as sun, intermediate, or shade. The effectiveness of this model depended upon the interaction between resource acquisition plasticity and morphogenetic plasticity. Resource acquisition plasticity occurred because of the modular construction so that branches extended and grew into areas of greater illumination. This occurred through the depth of the canopy.

To simulate tree mass, further architectural information is required, particularly details on the structure of the tree body, i.e., the development of branches by increasing order, and representation of how branches thicken. Sievänen et al. (2008) developed LIGNUM (Perttunen et al., 1996) parameterized for *P. sylvestris* based on growth of successive metamers (Room et al., 1994) each comprising a woody pipe in the modular segment (node plus internode) terminated with apical and axillary meristems and covered with needles. LIGNUM was designed and. Wood increment to the body of the tree was calculated using the pipemodel theory (Shinozaki et al., 1964) which specified that the amount of foliage carried on a shoot section was matched by the cross-sectional area of sapwood of the shoot and that this crosssectional area was propagated down through all more proximal shoots, branches, and the trunk. Based on empirical investigation, the sapwood area per unit foliage requirement declined with increasing branching order. The length, radius, and amount of foliage on new shoots were in proportions derived from empirical investigations. Segments became shorter as branching order increased. The length, and consequently other dimensions, was determined by the availability of photosynthate. After considering respiration losses, the photosynthate available for growth was considered in one pool and all of it distributed to growth.

The model simulated growth and development of trees over four decades giving effective 3-D images. However, Sievänen et al. (2008) noted a number of discrepancies from expected quantities. Generally, branch diameters and branch lengths were greater than expected, and the number of surviving branches was greater. Branch mortality in the model only occurred close to the base of the live crown, whereas field studies showed it to be distributed over more of the crown length. Increasing the density of trees in the plot decreased tree diameter as expected. An interesting result was that increase in foliage density along shoots caused lower photosynthesis per unit mass. Shoot extension was greater with lower foliage mass which increased both photosynthesis, by decreasing crowding, and production of woody material.

Sievänen et al. (2008) commented that considering the resources available for growth in one pool may not be appropriate. If resources are low then all growing segments grow less so that, for example, a branch producing less than it consumes in respiration decreases the growth of branches that produce a surplus. This does not agree with branch autonomy (Sprugel et al., 1991). Sievänen et al. (2008) noted that the larger dimensions of branches produced by the model than found in measurements may be due to inadequacy in the light model component or application of the pipe model.

Competition for a number of species (*Fagus sylvatica*, Letort et al., 2008; *Pinus tabulaeformis*, Guo et al., 2012) have been studied using the GREENLAB model (Yan et al., 2004) which comprises a formal grammar to describe plant structure. Mathieu et al. (2009) presented a version where increment to the plant body depends upon the ratio of biomass produced to demand from new meristems. The plant grew as a collection of sinks competing for allocation of photosynthate. Net photosynthate production was calculated from radiation interception which depended upon a calibrated radiation use efficiency and a coefficient related to the projected ground surface area of the plant. Biomass was stored in a common pool and distributed among new and existing organs according to calculated sink values. Distribution to the cambium was computed according to the pipe-model theory. A feedback between growth and development was included whereby the number of branches and the composition of growth units depended upon the ratio of the increment pool of biomass/plant demand which is the sum of all sinks in the current growth cycle.

Plants were simulated in a homogenous stand and competition was the result of shading which affects biomass increment and, as plant density increases, a greater priority in allocation was given to height growth. Mathieu et al. (2009) discussed four issues. First, organogenesis may not be strictly controlled by the ratio of available biomass to demand. Second, the inability of the model to reproduce the spatially heterogeneous expression of plasticity, which they comment cannot be neglected in large trees. Third, the hypothesis of a common pool of photosynthate may not be adequate. Fourth, in some instances the supply of photosynthate may be regulated by demand.

### **CANOPY DEVELOPMENT, LIGHT INTERCEPTION, AND COMPETITION**

Models that simulate penetration of light into canopies based on absorption, reflection, and transmission for individual structural elements of the canopy particularly that of Chelle and Andrieu (1998) have stimulated research into canopy development and competition. When combined with a model for detailed geometry of the foliage canopy estimates can be made of light conditions at the organs of individual plants and their light-dependent growth. In the two cases reviewed here, the investigators reported advances in understanding provided by modeling as well as improvements they consider should be made to models.

From empirical investigations with spring wheat Evers et al. (2006) reported that the probability of tiller appearance decreased earlier in crop development at higher population density. Their simulation study (Evers et al., 2007) was designed to investigate the form of the relationship between R:FR and the relative extension of a tiller bud. Evers et al. (2007) used an architectural model, ADEL-wheat (Fournier et al., 2003) calibrated for spring wheat (Evers et al., 2006, 2007) and the nested radiosity light interception model (NR) of Chelle and Andrieu (1998). ADEL-wheat simulates production and growth from a given initial planting of phytometer units comprising a leaf (blade and sheath) inserted on a node, an internode, and a tiller bud. ADEL-wheat calculates leaf size and shape, basal angle, and curvature, and blade and tiller azimuth angles. Each leaf is defined by a set of polygons with coordinates that establish their position in space. This geometry was interfaced to NR which calculates irradiance on, and energy absorbed by, each simulated plant organ.

Evers et al. (2007) hypothesized that the growth of tiller buds was arrested when R:FR received fell below a threshold value. Tiller bud extension was represented in ADEL-wheat by an exponential growth function

$$L = L\_0 e^{F.RFR\_{\mathbb{P}}.t},$$

where *L* is the bud length, *L*0 is the initial bud length, RERp is the potential relative extension rate (oCd)−1, *t* is the thermal time (oCd) since the initiation of the bud. *F* was a function of R:FR so that *F* decreased as R:FR decreased and threeforms were examined, a threshold value and curvilinear or linear decrease.

Simulations were conducted for a range of initial planting for which the time course of numbers of tillers.plant−1 had been measured in field experiments. Evers et al. (2007) noted that a threshold function with an R:FR value of 0.8–0.9 was required to simulated both a comparable tillering rate to field data and a final tiller number to that found experimentally. This was considerably higher than found in measurements and they suggest this may be due to use of a higher above canopy R:FR, 1.2, than is actually found under natural conditions.

Dauzat et al. (2008) combined the modeling strategy of using an architectural and a light penetration model with analysis of canopy structure using the 3-D Fastrack digitizer (Polhemus Inc., Sinoquet and Rivet, 1997). They studied growth of cotton at three densities, 1, 2, and 4 plants m−2. They anticipated that greater morphogenetic plasticity would occur at higher planting densities and investigated the effects of these changes on crop efficiency in intercepting light over a growing season. Measurements were made of crop cover, time courses of plant height growth, and leaf area.

They observed that morphogenetic plasticity varied with plant density and stage of development of the stand with a transition between increasing internode lengths in the lower part of the stem and decreasing internode lengths in the upper part. Dauzat et al. (2008) suggested that while the pattern of increasing internode lengths early in development was consistent with decreasing R:FR this was counteracted by plant carbon limitations during the latter phase. They noted that internode length and leaf area increment decreased simultaneously. The transition between the two phases occurred when average leaf irradiance decreased below 60% of incident PAR.

### **CONCLUSION**

Although it seems intuitively obvious that plant architecture should affect competition for light between plants we have little knowledge about the effects that different architectural features may have on the competition process. Not surprisingly, pioneering studies that demonstrated such effects (Ellison and Rabinowitz, 1989; Geber, 1989) used plants with large contrasts. Niklas (1997) description of how multiple plant forms may have arisen suggests that obtaining an understanding of competition effects may be a considerable challenge. Nevertheless, explaining competition effects is one of the important challenges faced by FSPMs because of the range of information that must be integrated into a model.

Much research into competition has been conducted with a standpoint of population biology and such work enables us to define some effects of competition on stands and individual plants. However, it has not provided an analytical framework for analysis of the effects of architecture on the process. Studies of plant functioning in stands undergoing competition have shown interesting responses to changes in the environment as a stand develops. However, the assessment of effects on competition in such work has typically been limited to measurements that only give a partial representation of the competition process and interactions between different aspects of physiology and morphology have largely been ignored.

Section "Development of Theory for the Effects of Plant Architecture on Competition," of this review outlines a basic structure of a theory for analyzing the influences that architecture may have on competition and how such a theory may be assessed. The research reviewed here was conducted on multiple species growing under different conditions. The proposed theory is a synthesis from this wide ranging work. Postulates for two groups of ideas are central. Group I—that competition for light takes place at the level of foliage and foliated axes—defines competition as a local event within the canopy. To a considerable extent, it tallies with theories of plant growth based on modular development of plants and branch and foliage reiteration. Use of this postulate in models for competition would reorient how such models are constructed.

Group II defines the outcome of competition as determined by the interaction between the exertion of dominance, particularly through resource acquisition plasticity, and reaction to shading through changing form and/or physiological characteristics. This suggests it is essential to study *interactions* between these processes rather than just one or another. The pioneering work of Casal et al. (1986) did this, at least to the extent of showing the importance of a certain level of PAR being necessary for a response to changes in R:FR. It was unfortunate that this duality in approach was not continued as it led to larger claims being made for the importance of morphogenetic plasticity than are warranted. The field study of Dauzat et al. (2008) showing a change over time in the control of internode length, from R:FR to carbohydrate limitation reinforces the need for this approach.

Work with tree species illustrates that considerable development of the Group 4 postulates on integration of plant growth is essential. Although it seems reasonable that competition for light should be accounted at the level of foliage and the foliage-bearing structure, understanding and representing how such units are sustained requires considerable work. The idea of a whole-plant carbon pool and the pipe-model theory for addition of wood need to be replaced and this suggests that further research is required into the interactions between carbohydrate metabolism and the structures produced for water conduction.

Section "Development of Theory for the Effects of Plant Architecture on Competition" illustrates the value of models, when combined with field investigations. Laboratory-based investigations present us with possibilities that certain processes may be important—but the experimental conditions under which they are established may not reflect those found in developing stands. Stand conditions do need to be documented carefully.

### **ACKNOWLEDGMENTS**

The author is grateful to Shawn Behling for the drawing in **Figure 1** and for her helpful discussions considering plants as distributed systems. The author is particularly grateful to two anonymous reviewers for their questions and encouragement and to Katrin Kahalen for their helpful comments.

### **REFERENCES**

**Conflict of Interest Statement:** The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 18 December 2013; accepted: 26 May 2014; published online: 17 June 2014. Citation: Ford ED (2014) The dynamic relationship between plant architecture and competition. Front. Plant Sci. 5:275. doi: 10.3389/fpls.2014.00275*

*This article was submitted to Plant Biophysics and Modeling, a section of the journal Frontiers in Plant Science.*

*Copyright © 2014 Ford. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

### Optimizing illumination in the greenhouse using a 3D model of tomato and a ray tracer

### *Pieter H. B. de Visser 1\*, Gerhard H. Buck-Sorlin2 and GerieW. A. M. van der Heijden3 †*

1 Department of Greenhouse Horticulture, Wageningen University and Research Centre, Wageningen, Netherlands

2 Institut de Recherche en Horticulture et Semences, AGROCAMPUS OUEST, Angers, France

3 Biometris, Wageningen University and Research Centre, Wageningen, Netherlands

### *Edited by:*

Katrin Kahlen, Hochschule Geisenheim University, Germany

*Reviewed by:*

Veerle De Schepper, Ghent University, Belgium Tsu-Wei Chen, Leibniz Universität Hannover, Germany

#### *\*Correspondence:*

Pieter H. B. de Visser, Department of Greenhouse Horticulture, Wageningen University and Research centre, Droevendaalsesteeg 1, 6700 AA Wageningen, Netherlands e-mail<EMAIL_ADDRESS>
### *†Present address:*

Gerie W. A. M. van der Heijden, UMR1345 Institut de Recherche en Horticulture et Semences (IRHS), AGROCAMPUS OUEST, Centre d'Angers, Angers, France

Reduction of energy use for assimilation lighting is one of the most urgent goals of current greenhouse horticulture in the Netherlands. In recent years numerous lighting systems have been tested in greenhouses, yet their efficiency has been very difficult to measure in practice. This simulation study evaluated a number of lighting strategies using a 3D light model for natural and artificial light in combination with a 3D model of tomato.The modeling platform GroIMP was used for the simulation study. The crop was represented by 3D virtual plants of tomato with fixed architecture. Detailed data on greenhouse architecture and lamp emission patterns of different light sources were incorporated in the model. A number of illumination strategies were modeled with the calibrated model. Results were compared to the standard configuration. Moreover, adaptation of leaf angles was incorporated for testing their effect on light use efficiency (LUE). A Farquhar photosynthesis model was used to translate the absorbed light for each leaf into a produced amount of carbohydrates. The carbohydrates produced by the crop per unit emitted light from sun or high pressure sodium lamps was the highest for horizontal leaf angles or slightly downward pointing leaves, and was less for more upward leaf orientations. The simulated leaf angles did not affect light absorption from inter-lighting LED modules, but the scenario with LEDs shining slightly upward (20◦) increased light absorption and LUE relative to default horizontal beaming LEDs. Furthermore, the model showed that leaf orientation more perpendicular to the string of LEDs increased LED light interception. The combination of a ray tracer and a 3D crop model could compute optimal lighting of leaves by quantification of light fluxes and illustration by rendered lighting patterns. Results indicate that illumination efficiency increases when the lamp light is directed at most to leaves that have a high photosynthetic potential.

**Keywords: photosynthesis, greenhouse crop, HPS, LED, light distribution, LUE**

### **INTRODUCTION**

The spatial distribution of assimilation lights in greenhouse horticulture, especially in countries with a deficiency in natural sunlight, is a controversially debated topic (Hovi-Pekkanen and Tahvonen, 2008; Trouwborst et al., 2010; de Visser and Buck-Sorlin, 2011). However, there is general agreement that lamp type, density, positioning and orientation with respect to plant orientation are important and that an optimization of these factors can help improve crop light interception and thus reduce energy costs. Finding the optimal solution experimentally is nearly impossible due to the large number of possible combinations and the high financial, and time investment per experiment. Computer-aided design coupled with 3D modeling of plants and light distribution could be a more rapid and cost-effective solution in order to test the effect of possible lamp configurations in the greenhouse on crop light interception. Software tools (e.g., computer aided design – CAD) that enable 3D visualization of objects in a 3D scene, including the simulation of the trajectories of light rays using ray tracing methods, are well established and tested. Commonly used methods to simulate light distribution in plant

canopies are Monte Carlo ray tracing (Veach, 1997) and nested radiosity (Chelle and Andrieu, 1998). The exponential increase in computing power also allowed the further development of simple crop models into more elaborate versions, so-called functionalstructural plant models (FSPM; Vos et al., 2010). FSPM refers to a paradigm for the description of a plant by creating a (usually object-oriented) computer model of its structure and selected physiological and physical processes, at different hierarchical levels: organ, plant individual, canopy (a stand of plants), and in which the processes are modulated by the local environment. With respect to greenhouse crops FSPMs for tomato (Sarlikioti et al., 2011a,b), cut rose (Buck-Sorlin et al., 2011) cucumber (Kahlen et al., 2008; Kahlen and Stützel, 2011; Wiechers et al., 2011) and *chrysanthemum* (de Visser et al., 2007) have been devised. Although in greenhouse practice a small number of 3D models of greenhouse structure including lamps are available, the model by de Visser et al. (2012) is to our knowledge the only one that considers the greenhouse interior (lamps, slabs) as well as the 3D structure and physiology of the plants. The reported model simulates the light distribution of natural (diffuse and direct)

daylight and artificial light within a realistic 3D representation of a crop.

deVisser et al. (2012)simulated some energy saving light strategies by optimization of position of local LED lights in the crop, but the options of lamps with specific angles to better illuminate the leaves at angles changing with age were not addressed. Moreover, answers are needed on effects of leaves oriented toward the path, as raised by Sarlikioti et al. (2011b) and whether leaf positions are equally important for High-pressure sodium (HPS) and LED lamps. With the upcoming technology of LEDs as a (partial) alternative for HPS lamps, growers have an instrument to adapt the angles of the LED modules to account for local leaf angles. The 3D modeling can be used to find promising set-ups of LED lighting in a tomato crop that may result in increased light absorption and crop growth, concomitantly supporting a more energy saving lighting strategy.

### **MATERIALS AND METHODS**

The GroIMP interactive modeling platform, initially developed and described by Kniemeyer (2008) and maintained by the University of Göttingen (Germany), was used for the simulations. A virtual greenhouse was constructed within GroIMP on basis of an existing greenhouse compartment at the Improvement Center, Bleiswijk, The Netherlands, by explicitly considering the positions, shapes and optical properties of all its constituting objects (see

below) in a 3D scene. The light distribution at a given time step was then computed by the GroIMP radiation model, which is based on an inversed Monte Carlo path tracer, similar to the one used by Cieslak et al. (2008). Sunlight was modeled as a direct and a diffuse component, depending on the 10-year average recorded outside light level. Diffuse light came from a sky object consisting of 72 directional lights arranged in a hemisphere around the greenhouse, whilst direct sun light was provided by a single directional light. The power of both light sources, as well as the position of the sun was a function of latitude, day of year, and time of day (Goudriaan and van Laar, 1994).

Optical properties of all greenhouse objects as well as leaves entailed reflection, transmission and absorption of the fraction of photosynthetic radiation (PAR) generated by a light source, and were measured on subsamples with a Lambda 1050 spectrophotometer (Perkin-Elmer Inc) coupled to a snap-in light integrating sphere.

Net photosynthesis was simulated for each leaflet on the basis of absorbed light, air temperature and CO2 according to Kim and Lieth (2003), with a leaf-age-depended value for Jmax, the potential rate of electron transport (in μmol electrons m−2 s −1). Measured light-response curves (3 heights in the crop, *n* = 3, 10 PAR levels from 0 to 2000 μmol m−2 s −1, measured with a Licor 6400 by gas exchange) at 700 ppm CO2 (annual average in greenhouse air) for winter and summer were used to calibrate

**FIGURE 1 |The modeled 3D scene of the tomato crop: (A)** A crop of 32 plants (wireframe with black leaves, green unripe trusses and red ripe trusses) on two double rows of slabs at 0.8 m above the floor, with LED (red squares) inside the double row at 2.4 m height and HPS lamps (brown squares) at 1.5 m above the crop, **(B)** cross-section

of four plants with leaf angles increasing with height (LED position at brown square), **(C)** rendered image of a single leaf with its rachis at a specific angle (red arrow) with the main stem, and consisting of leaflets that hang down by 30−50◦ (see blue arrow) relative to the horizontal.

parameters *f* (spectral correction factor, dimensionless) and Jmax in the photosynthesis model by reducing least square differences between modeled and observed photosynthesis.

The virtual greenhouse consisted of a glass roof, side walls, floor, energy-saving screen, gutters, assimilation lamps, and a crop consisting of static virtual plants (**Figure 1A**). The light pattern emitted by the HPS lamps of 1000 W concisely matched (per 10◦ interval) that of a SON-T in a wide angle reflector (data from Hortilux ©), see Buck-Sorlin et al. (2009) for details. The HPS lamps were placed in a grid of 6 m (in row direction) × 2.5 m (across rows) at 1.5 m above top of the crop. The emission pattern of LED light was simulated using simple, horizontally shining spotlights which had an opening angle similar to what has been measured on the 150 cm, commercially available, production module RB (data from Philips ©), and emitted PAR was calibrated to 60 μmol m−2 s −1 greenhouse. The strings with LEDs were at a height of 2.1 m above the ground, LEDs were 40 cm horizontally apart within each double plant row and placed in row direction. Ca. 3 leaves were situated below the LEDs which is regularly occurring in practice. The crop was represented as a static structure, corresponding to measurements on a tomato crop cv. Kommeet in our research facilities in Bleiswijk, The Netherlands: for the HPS and LED scenarios in winter, as measured on six plants on January 11th in 2011, for the sunlight scenarios in summer in another crop as measured on August 9th in 2011. The average value and its variation of leaf angles, length, width, internode length, and phyllotaxis were measured with ruler and protractor. The data were incorporated in GroIMP as average values per phytomer and the associated random variation, using a set of growth rules that created 32 (summer) or 36 (winter) phytomers per plant, of which eight were trusses and the rest consisted of leaves (**Figure 1B**). Each leaf was composed of 15 leaflets of a fixed geometry, yet their size increased in proportion to the length of the terminal leaflet of the composite leaf (**Figure 1C**). The modeled scene of 4 by 3.2 m ground area consisted of 32 plants with their lowest leaf oriented at a random azimuthal direction, an observed phyllotaxis of 130◦ between leaves, leaf angle of 90◦ (i.e., horizontal position) for lowest leaves and becoming slightly higher, maximizing at 130◦ for upper leaves (**Figures 1B,C**). Plants were placed on slabs at 0.8 m above the floor, and pairs of slabs, with internal distance 0.4 m, were divided by a path, giving 1.6 m distance from center to center between slab pairs (**Figure 1A**). On a slab, plants were 0.4 m apart, and had only one stem without a split. Crop density was 2.5 stems per m2 ground floor; the top of the canopy was situated at maximally 4.5 m above the floor. Plant rows were oriented east-west as observed. An infinite canopy was simulated by placing perfect mirrors around the scene.

### **SCENARIOS**

Based on the above described default setup, different scenarios were examined to gain insight in the influence of plant architecture and light source specifics on crop light absorption and photosynthesis:

(1) Leaves were tilted by angles of +30% of default (i.e., from default 90 to 117◦ (lowest leaves) and from 130 to 169◦ (upper leaves), 0 and -30% (runs a, b, and c) relative to default, combined with different light sources: (1.1) daily course on June 21st of 10 year averaged sun light (70% direct, 30% diffuse), (1.2) HPS top light (130 μmol m−2 s −1PAR), (1.3) LED inter-lighting (60 μmol m−2 s −1 PAR)

(2) Leaves were forced to orientate toward the path (2a) or parallel to the slab (2b), combined with LED inter-lighting. Each of the leaf directions is imposed with a uniform continuous random variation between −10◦ and +10◦ in the horizontal plane, i.e., left and right of the main leaf direction.

(3) Inter-lighting with LED modules illuminating the plants at different angles [LEDs heading from upward by 30◦ (scenario 3a) to downward −30◦ (3f) in steps of 10◦]

Each scenario was replicated five times, and at each run leaf angles were randomly varied in vertical direction between −10◦ and+10◦ of the measured angle, and each plant was turned around its axis randomly between −180 and +180◦. Each run took ca. 10 s on a standard PC. Apart from percentage of emitted light per light source absorbed by the crop, per scenario the average net photosynthesis per MJ absorbed or emitted PAR light, referred to as light use efficiency (LUE) in its most usual unit, is calculated. Analysis of variance and *t*-test for differences were carried out in GenStat, 16th Edition.

### **RESULTS**

The tomato leaves reflected and transmitted 8 and 3% of PAR light, respectively. The greenhouse floor reflected on average ca. 40% of PAR light and the white plastic 75%. For the relatively small area of stem surface we assumed similar optics as for leaves.

With the 3D structure of the measured crop, results of the scenarios on leaf angles showed an effect of maximally 3% relative to the control for most situations (**Table 1**). In the control situation, the rachis of mature leaves has an almost horizontal position (see indicated angle in **Figure 1C**), and the attached leaflets hung down by another 30–50◦. Modeling a larger angle of the rachis relative to the main stem (scenario 1.1a) made the leaves point a little upward, which was detrimental for light interception (**Table 1**; **Figure 2**). Leaves that pointed more downward (scenario 1.1.c) did not increase light absorption of sun light compared to default, horizontal leaves. Averaged over the day, this scenario, however, showed absorption to decrease 2% around noon and increase 2% in morning and afternoon relative to default. For sun light the leaf angle changes, similar to light absorption, only decreased LUE for steeper leaves (scenario 1.1.a). The day average of LUE for absorbed light was relatively low as compared to other scenarios, and despite 20% higher photosynthetic potential in summer, due to the higher light levels which at noon (at 1400 μmol PAR m−2 s −1) resulted in light saturation.

For winter the measured crop structure had similar leaf angles, yet smaller LAI (2.7 vs. 3.4), longer internodes (0.11 vs. 0.08 m on average) and a 20% lower maximum photosynthesis relative to summer, and was used for HPS and LED scenarios. For HPS lighting, raising the leaves from −30 to +30% from default, decreased light absorption but hardly affected LUE (**Table 1**). The latter means that between these leaf angle scenarios the light-absorbing leaves all have a similar leaf age and thus similar photosynthetic

**Table 1 | Light absorption (% of input) and light use efficiency (LUE) per unit absorbed or emitted light per mentioned light source of the tomato crop for the different scenarios.Within each group (1.1, 1.2, 1.3, 2, or 3) letters behind a mean indicate a significant difference between scenarios (***p <* **0.05). DM, dry matter.**

#For sunlight scenarios a measured summer crop structure was used instead of the default winter structure

potential. On the contrary, for the LED scenarios with horizontal and steeper leaves (scenarios 1.3.a,b) the increased absorption did not increase but lighting more upper leaves were illuminated as shown by increased LUE relative to down-hanging leaves (scenario 1.3.c).

Leaves oriented to the path (scenario 2.a) had only 2% more interception than leaves oriented toward the slab (**Table 1**), yet utilization per MJ emitted light was lower than leaves oriented parallel to the row and slab (scenario 2.b).

Directing LEDs more upward up to 20◦ (scenario 3.b) resulted in higher absorption of LED light by the crop and the highest LUE per MJ emitted light of all scenarios. In this scenario no increased loss of light to the sky was simulated since the LEDs were positioned rather low in the crop. Pointing the light more downward did dramatically decrease light interception (only 78% of input at scenario 3.g) and led to less photosynthesis due to the lower performance of the lower leaves (**Table 1**).

The light model computed considerable horizontal differences in light intensity within the crop. For HPS lamps without plants, the visual rendering seemed to indicate large intensity differences

in the area between lamps as shown by illumination of a horizontal plane (**Figure 3**), yet the sensed light level showed only modest differences (**Figure 4**). When plants are introduced in the model, the sensed light level between positions in and outside the plant row were large (**Figure 4**). Also for LEDs, after light penetration through the plant, hardly any light remained to illuminate the neighboring row (data not shown), suggesting each double plant row should contain a LED module for homogeneous illumination.

### **DISCUSSION**

A 3D model of light including leaf photosynthesis has seldom been used to predict effect of artificial light on LUE of the crop (Delepoulle et al., 2008; de Visser and Buck-Sorlin, 2011). The present, unique model indicates that HPS lamps result in a higher photosynthesis per unit absorbed light than LEDs. This is caused by the higher LUE of upper leaves, catching more light for HPS than for LEDs. Yet, per emitted MJ, LED lighting is more efficient than HPS lighting due to a higher fraction of absorbed light. Apart from HPS lamps illuminating the upper

leaves with high photosynthetic capacity, an additional advantage of HPS relative to LED is that they combine PAR and heat radiation, thus supporting both assimilate supply by photosynthesis and temperature driven organ development. Despite the efficiency of LED light interception, their PAR emission should be accompanied by a certain level of heating, reducing their energysaving advantages. Only a 3D model incorporating energy balance calculations can fully estimate the energy efficiency of a LED strategy.

Tilting the leaves upward decreased light interception of the downward light from sun and HPS lamps, but not for LEDs. Very probably leaves have less surface exposed to the sun, alike more erect leaves in arid, sunny climates that prevent excess light heating the leaves. The decreased light interception did not affect LUE because still the same leaves were illuminated, at similar photosynthetic potential. In contrast, light interception was not affected for LEDs when leaf angles were changed. Yet, when down by −30%, the lowest leaves were illuminated more which resulted in a lower computed LUE due to lower photosynthetic capacity of these leaves. The winter crop structure was different from summer structure in terms of internode length and leaf area, but not in terms of leaf angles. We expect that the longer internodes in winter do result in a wider spread of LED light.

The turning of leaves predominantly toward the path slightly increased LED light interception relative to default leaf positions, whereas leaves predominantly oriented parallel to the rows did not alter light interception relative to default. Leaves may orient toward LED light or turn away at too high light level (e.g., Trouwborst et al., 2011), thus impacting the interception of LED light.

For LEDs, the beaming angle had a strong effect on light absorption and LUE. The highest light interception was modeled at 20◦ up from horizontal position, and a significant decrease from 0◦ toward −30◦ angle due to loss to the ground. This effect may have been lower if the LEDs were positioned higher in the crop, showing the sensitivity of our results to the particular situation of LED placement and crop architecture. Placement of LEDs should be carefully planned, taking into consideration the given plant structure. A similar conclusion was drawn by Sarlikioti et al. (2011b) who observed strong effects of plant structure on light interception, in particular for internode lengths and leaf shape. The same authors found that leaves orientate themselves toward the path to intercept more light (Sarlikioti et al., 2011a), which agrees to our findings of a modest 2% light interception increase relative to orientation parallel to the plant row, as calculated for LED light.

Optimal lighting of leaves is driven by a combination of spatial emission pattern and crop characteristics such as structure and optical properties. We did not test the effect of the emitted light spectrum and its transformation (selective absorption, transmission, and reflection) as the light rays pass through the canopy. A recent extension of GroIMP, the GPUFlux light model (van Antwerpen et al., 2011), is a spectral Monte Carlo light tracer, which offers this possibility. The light tracer utilizes available computing resources through OpenCL. For each object, the model either computes a fully discretized absorption spectrum or several integrated weighted spectra, which are subsequently used in a photosynthesis model.

An important factor in optimization of light use is the positioning of light sources close to leaves with highest photosynthetic potential. It is standard practice that lamp power is accommodated such that the light level on nearby leaves is not at a saturating level but still in the linear trajectory of the light-response of photosynthesis. This is now also accommodated for LED modules when using interlighting, resulting in an average supplement of about 60 μmol PAR m−2 s −1 greenhouse. Whether this light amount will not lead to deleterious, high light levels on nearby leaves could be verified using the present model, ultimately leading to an advice to, e.g., use lower intensities and save energy. Yet, leaves can adapt their photosynthetic properties in response to their history of perceived local light, resulting, e.g., in sun-adapted leaves with high amounts of Rubisco and a high photosynthetic capacity. In a high-wired and dense crop, leaves normally decrease their photosynthetic capacity as well as their compensation point following adaptation to decreasing levels of perceived light lower in the canopy (Trouwborst et al., 2011). However, prolonged high light levels on aging cucumber leaves halted the decrease of photosynthetic capacity (Hovi-Pekkanen and Tahvonen, 2008). This is also aimed at with LED interlighting, yet this has to be confirmed experimentally. Maintenance of photosynthetic capacity would be another advantage of interlighting, adding to the lower light losses as shown in this study.

The computer graphical representation of tomato leaves that we used in our model was a combination of textured cylinders (petioles and rachies) and flat boxes (leaflets). This was clearly a simplification as tomato leaflets are in reality variously convexly or concavely curved surfaces: such curved surfaces will increase diffuse reflection and probably lead to better LUE in a dense canopy. Such an effect can at present not be considered by our model, but the representation of leaves as complexly curved surfaces is technically possible (Gerhard Buck-Sorlin and Michael Henke, unpublished work).

In conclusion, based on the present simulation study we would be able to give the following, tentative, recommendations to improve the efficacy of assimilation light in the greenhouse: LEDs should be preferred over HPS as the light interception efficiency is bigger; the crop's LUE for HPS is higher than for LED due to lighting a higher fraction of leaves with higher photosynthetic capacity; light interception of LED interlighting is increased if LEDs are sufficiently high above the greenhouse floor and pointing slightly upward, thereby avoiding loss of light to the ground.

### **ACKNOWLEDGMENTS**

This work was funded by the energy program of the Product Board for Horticulture (PT) and Ministry of Energy, Agriculture and Innovations of The Netherlands, the Biosolar Cells Program.

### **REFERENCES**

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 31 August 2013; accepted: 31 January 2014; published online: 18 February 2014.*

*Citation: de Visser PHB, Buck-Sorlin GH and van der Heijden GWAM (2014) Optimizing illumination in the greenhouse using a 3D model of tomato and a ray tracer. Front. Plant Sci. 5:48. doi: 10.3389/fpls.2014.00048*

*This article was submitted to Plant Biophysics and Modeling, a section of the journal Frontiers in Plant Science.*

*Copyright © 2014 de Visser, Buck-Sorlin and van der Heijden. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

### Meeting present and future challenges in sustainable horticulture using virtual plants

### *Gerhard Buck-Sorlin\* and Mickaël Delaire*

*Agro Campus OUEST Centre d'Angers, Institut de Recherche en Horticulture et Semences, Institut National d'Horticulture et de Paysage, UMR 1345, Angers, France*

*\*Correspondence<EMAIL_ADDRESS>
### *Edited by:*

*Katrin Kahlen, Research Center Geisenheim, Germany*

*Reviewed by:*

*Hartmut Stützel, Leibniz Universität Hannover, Germany*

**Keywords: apple, FSPM, typology, classification, horticulture, models, biological**

### **THE PURPOSE OF MODELS AND THE MODELING EXERCISE**

In order to better understand the significance of models in practical horticulture we have to put ourselves into the position of the horticulturist (orchard grower, consultant . . . ) and appreciate first of all some skepticism toward modeling. This does not necessarily mean a downright refusal to use models: on the contrary, it is often the result of an initial keen interest coupled with high expectations in modeling as such, frequently followed by disillusionment that the high hopes were not satisfied; that *the* model as a response to very specific problems and questions does not exist; that the models offered were remote from practice, unreliable, or too complicated to use. The special case of orchards as perennial production systems, poses a further challenge, for two reasons. Firstly, a rapidly increasing complexity: if considered it renders the model difficult to parameterize, intransparent and expensive; if, on the other hand, it is neglected it is fair to question the model's added value compared to the extensive experience of a grower. Secondly, a perennial production system represents the integral of a unique combination of location and history of production, and the interaction between the genotype with the local environment, making a generalization more difficult than for annual crops. So, what should be done about it? First of all, models are tools, equivalent to other experimental tools, not ultimate purposes: it is up to the researcher to get this message across to the user, to remove any misunderstandings regarding models as "perfect solutions" delivering "absolute answers," and to lower exaggerated hopes. Next, a common language between the researcher and the practitioner must be found, because in practice wires get crossed, not only with respect to the technicalities of the modeling approach but also with respect to the goals of the modeling exercise. Despite that, modelers and people from practice do actually pursue the same goal: trying to integrate the complex information (measured and observed) about a given system, in order to obtain a result (admittedly, opinions as to what is an acceptable result diverge, ranging from a decision-support tool to a publication...).

### **THE "TRUE" CHALLENGES OF MODELING**

In order to advance modeling as a scientific technique and to render its products more accessible to practice—in other words to come down the ivory tower of theoretical biology and applied mathematics in which many biological models and their authors reside—it is important to communicate the true challenges of modeling (which go beyond the predictions coming out of the black box of the model). The three principal challenges are:

• To design models as tools of information exchange between the different types of experts and practitioners of a horticultural sector (e.g., orcharding). Using the formalism developed to construct the model it must be possible to confront the different implicit representations of the stakeholders and to further let these representations evolve using a co-construction approach (similar to developing the Wikipedia), considering at the same time representations added from the "outside" (by scientists) and those belonging to the stakeholders working in practice. In this respect it is crucial that the modelers provide communication tools that permit to state explicitly and simply the conceptual bases of the formalism used to construct the model. This type of models is usually referred to as decision-support tools (DST), but actually DST is a too general and too advanced term for them as DST can also be derived from scientific and pedagogic models (**Figure 1**). We will instead call them prototype tools as they allow us to integrate and structure different knowledge types about a particular system into a simplified representation that serves as a first step toward developing either true DSTs or scientific tools. A prototype tool, like the prototype of a new car, can thus be conceived as an early version of the model, in which the boundaries, elements, behavior and levels of the system are already roughly specified.

and consequences of pruning and shoot bending). We will term this type educational tool.

All of the three types can be developed into DSTs (**Figure 1**), depending on the level of prior knowledge of the user, the design of the model and the modeling paradigm used (e.g., a decision tree, a conceptual model, or an object-oriented model), and the kind of decision-support envisaged (e.g., initial orchard design, prediction of fruit quality, scheduling of pest control measures as part of integrated biological production. . . ).

An additional challenge for biological modeling is the change of scale, i.e., the integration from a lower to a higher scale, and the differentiation from a higher to a lower scale. Integration of knowledge from the gene to the field, or even to the production region or the natural ecological zone is fanciful among plant scientists and this despite the lack of a clear methodology. From the shelter of their disciplines (genetics, physiology, ecophysiology, agronomy, ecology), scientists hypothesize that modeling might be the best choice to try to simplify the complexity encountered at each level and at the transgression from one level to the next. Accordingly, models have been developed to document the knowledge of a certain discipline and at a certain hierarchical scale. However, the concepts and tools to scale up and down, let alone to integrate "horizontally," i.e., to meaningfully link two or more disciplines (beyond the use of a common database. . . ), are still in their infancy.

### **WHAT TYPE OF MODELING?**

Different approaches to crop modeling have been developed in the past (Vos et al., 2010). The most recent approach among them, functional-structural plant modeling or "virtual plants" currently seems the most promising, especially in horticulture which distinguishes itself from agriculture by its enormous genetic and structural diversity (cultures and production methods) and a high technological investment (see greenhouse horticulture). FSPM refers to a paradigm for the description of a plant by creating a computer model of its structure and selected physiological and physical processes, at different hierarchical levels: organ, plant individual, canopy, and in which the processes are modulated by the local environment (Buck-Sorlin, 2013). Within the modeling paradigm of FSPM there exist types and gradations along the following opposite pairs: descriptive versus explanatory, stochastic versus deterministic, or dynamic versus static. From a programming paradigm point of view the most meaningful criterion is the one which distinguishes procedural, objectoriented, and rule-based approaches. Independent of the paradigm chosen in the end, all approaches have in common that they serve to represent a complex reality by decomposing, modularizing and simplifying it into (arguably) atomic units, in order to make it easier to handle, to understand, and to anticipate changes. The method of decomposition necessarily is often biased and depending on the eye and the intention of the observer, thence the importance of fixing the objectives of the model ahead of the actual modeling exercise. On the other hand, a deliberate effort can be made to approach the description of the system in an "objective" way, i.e., trying to be independent of any intention or subjective bias (knowing fully well, of course, that this is only possible as an approximation since all system descriptions are ultimately subjective). It is in this respect useful to make a distinction between procedural and object-oriented modeling: In procedural modeling (equivalent to classical crop modeling: applied in horticulture and agriculture since more than forty years) the available information is structured according to a chain of more or less concrete processes; ultimate aims of the model are fixed beforehand and the process of knowledge acquisition (and subsequent use in the model) is deductive and top-down. Contrary to this, in object-oriented modeling the available information is structured around objects (their traits and relations to each other) that have been identified a priori as relevant and/or characteristic, and in which knowledge acquisition is inductive and bottom-up.

### **THE NOTION OF STRUCTURE IN FSPM**

Though perfectly clear to everyone involved in research on FSPM, the idea of structure in Functional-Structural Plant Models regularly leads to misunderstandings outside the community. *Structure* in an FSPM, especially with respect to woody plants, corresponds to plant architecture, more precisely at the organ and plant individual level, not more and not less. This notion of architecture comprises the topology and the geometry of plant organs in relative and absolute coordinates and also helps to improve the definition of the interfaces with the microenvironment, which latter is both surrounding and being modified by the architecture of the plant (part) located inside it. The precise description of organ location and orientation by topology and geometry is the basis for quantitatively modeling the transport of carbon, water and minerals between sources and sinks. Many FSPM exist that have implemented the process chain from light interception to photosynthesis, assimilate distribution and growth in terms of organs extension or increase in biomass. On the other hand, FSPMs which also consider the feedback of a change in architecture (organogenesis by bud break) on, e.g., photosynthesis rate are rare.

### **A MULTI-SCALE OBJECT-ORIENTED FSPM OF THE APPLE PRODUCTION SYSTEM**

Heterogeneity, within the tree and in different years, in apple (*Malus* × *domestica*) fruit production poses a number of challenges: fruit quality and number (fruit load) can vary as a function of genotype, climate, or an interaction between these factors. Previous experimental work conducted by the ecophysiology team at Angers has shown that the carrying branch or limb is an apt experimental system for the investigation of these phenomena if certain key variables at the next lower (organ) and next higher (plant) scale are considered at the same time.

We have recently started to create a prototype model of the apple limb, in order to improve our knowledge about the role of plant architecture for the formation of fruit quality. This model is object-oriented and covers three hierarchical, consecutive scales: organ, branch, and plant; a number of physiological processes is defined for each organ (e.g., photosynthesis, growth, respiration. . . ); transport of sugar, water and minerals will be defined at the organ level using rules that apply rate equations to pairs of topologically joined organs (leaf–internode, internode–internode, internode–petiole, petiole–fruit), whilst the equations will be integrated in parallel with an embedded ODE solver (Hemmerling, 2012). At the level of the organ type "fruit" a modification of the "Virtual Fruit" model (Génard et al., 2007) will be employed. Since we are interested in the production (quantity and quality) of a given year, without having to reconstruct the history of the tree at each simulation run, we devised an initiation rule which at the start of each run puts in place the initial (measured) plant architecture as encountered in spring before bud break, of that year.

### **OUTLOOK**

The modeling exercise described here is exemplary for many modeling projects in horticulture, independently of whether these are departing from existing modules or from scratch. In the first place a conceptual model is elaborated and then qualitatively validated. Existing modules that have been parameterized for a certain fruit (e.g., peach) eventually need to be reparameterized, as in the Virtual Fruit model, where also a partial rewriting of the equations is necessary to make it applicable for apple. After proper calibration of modules (this can be done by doing sensitivity analyses under standard conditions), the latter can be tentatively combined, recalibrated and eventually validated using an external data set, with the ultimate aim to obtaining a model which can predict fruit quality as a function of the genotype and a specific production environment.

### **REFERENCES**

*Received: 08 July 2013; accepted: 16 October 2013; published online: November 2013. 05*

*Citation: Buck-Sorlin G and Delaire M (2013) Meeting present and future challenges in sustainable horticulture using virtual plants. Front. Plant Sci. 4:443. doi: 10.3389/fpls.2013.00443*

*This article was submitted to Plant Biophysics and Modeling, a section of the journal Frontiers in Plant Science.*

*Copyright © 2013 Buck-Sorlin and Delaire. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*


*2.3. Synthesis of [Cu2(ACR)(NO3)2]*

ACR dendrimer (0.219 g, 0.1 mmol) was dissolved in 20 mL of ethanol and Cu(NO3)2·3H2O (0.113 g, 0.6 mmol) was added to the solution. The mixture was stirred for 2 h, and the solid formed was filtered, washed with ethanol three times, and dried under vacuum. Yield: 0.225 g, 88.1%

FT-IR cm−1: 1638, 1691, 1531, 1466, 1367, 1298, 1173, 1037, 826, 754, 661.

Analysis: C144H152N26O12Cu2 (2564.8 g mol−1) Calculated (%): C 67.43, H 5.93, N 14.20; Found (%): C 67.54, H 5.88, N 14.28