Modelling Variations in Individual Plant Productivity Within a Stand: Comparison of Top-Down and Bottom-Up Approaches in an Alfalfa Crop Louarn Gaëtan*, Frak Ela, Combes Didier, Escobar-Gutiérrez Abraham INRA UR4 P3F, BP6, F-86600 Lusignan, France *
[email protected]
Abstract — Modelling individual variations in plant productivity and resource-dependent mortality is a key issue in population dynamic models. The present study examined two classical approaches to account for plant productivity in functional-structural plant models (i.e. the up-scaling of a leaf photosynthesis model, and the down-scaling of a canopy production model) and compares them in their ability to account for the size-structure of a population of alfalfa plants competing for light. The two models differed mainly in their formulation of the plant carbon balance. Only the leaf approach included a respiration sub-model and was able to predict self-thinning and changes in radiation use efficiency among plants. Variations in plant mass were however mainly explained by differences in light interception. The two models behaved quite well to simulate the mass distribution of surviving plants, the leaf model being clearly more difficult to calibrate. Keywords— Gas exchange; Farqhar model; RUE; alfalfa
I. INTRODUCTION The development of a community of plants results from the growth of individuals, as altered by interactions among these individuals. Within a population, plants vary in size and mass. In even-aged populations (i.e. case of most cultivated plant populations), it has been shown that the distribution of masses results from a hierarchy of resource exploitation [1, 2]. Individuals can differ in their rates of resources capture as well as in their efficiency for resources use [3]. Furthermore, an increased resource-dependent mortality can occur for subordinate plants and contributes to the regulation of population size by self-thinning [1]. Modelling the interactions among individual plants is a topic of considerable interest in ecology, forestry and agronomy to explain the dynamics of natural or cultivated plant communities [4, 5]. Our ability to predict changes in productivity and species composition as a result of interand intra- specific competition is still limited, even in simple cultivated communities [6]. Functional-structural plant models could play a prominent role in the development of this modelling approach. They indeed naturally encompass the description and fate of elementary units controlling population dynamics: individual plants interacting with their biotic and abiotic environment [7, 8].
Few attempts have been made so far to extend functional-structural plant models at the community level [8, 9]. Furthermore, a profusion of models have been proposed, and we lack the benchmark to know which formalisms will be the most appropriate and robust to pass the up scaling change of focus on the plant to the community dynamics. For instance, simply considering the conversion process of captured resource (e.g. light interception) into new biomass, three contrasting views are generally encountered: the first relies on the up-scaling of models developed to describe organ functioning (e.g. leaf photosynthesis [10]), the second – and opposite – strategy consist in down-scaling relationships initially established at the canopy level [11, 12], and the third defines directly empirical relationships between resource capture and growth rate at the plant level [13]. To date, no critical appraisal of these strategies has been undertaken in the perspective of population integration. Studying a population of plants competing for light only, the objectives of the present paper were i) to assess to which extend light interception and radiation use efficiency respectively explain inter-plant variation in biomass accumulation and ii) to compare two contrasting modeling strategies in their ability to convert light interception into biomass and predict self-thinning. Alfalfa was taken as a model species because this herbaceous perennial is frequently cultivated in mixtures, the dynamic of which remains difficult to predict from current crop models and could benefit from individual-based plant models. II. MATERIALS AND METHODS A. Plant material studied The experiment was carried out outdoors between April and September 2009 at the INRA Lusignan station, France. Alfalfa (Medicago sativa L. cv Orca) was sown at 460 plants.m-2. Each plant was grown in an individual pot to facilitate excavation of individual plant roots. Three rows of border plants at the same density surrounded the sampled plants. Pots were ferti-irrigated three times a day with a complete nutrient solution. The nitrogen concentration of the solution (8 mM) prevented nodulation of alfalfa roots, so that plants were not able to fix atmospheric N.
B. Dry matter measurements The studied area consisted in two sub-plots, one dedicated to the study of plant dry matter production (Z1, 100 pots) and the other (Z2, 40 pots) used for the establishment of allometric relationships between shoot mass, shoot leaf area and shoot morphological traits (stem length and diameter, number of primary and secondary leaves, maximal leaf size, maximal shoot height). All plants were cut to 5 cm above soil level every 4-5 weeks during the growing season, at the early bloom stage of alfalfa. In addition, from the second regrowth on, 10 shoots of contrasting hierarchical position within the canopy were harvested weekly in Z2 to measure their leaf area and dry weight. At the same dates, the whole set of shoot morphological traits was measured for every shoots of the Z1 area. This made it possible to estimate above-ground plant mass in Z1 from non destructive measurements between two alfalfa cuts. Data are presented for the second re-growth (401 shoots followed on 100 plants). C. Light interception by canopy components 1) Envelope-based reconstruction of plant 3D structures A statistical envelope-based reconstruction method was used to build-up simplified 3D plants from the shoot morphological traits measured in Z1 [14, 15]. Basically, each shoot of a plant was represented by a turbid-medium delimited by a vertical cylinder (Fig. 1a,b). Shoot leaf area was randomly distributed inside the cylinder according to two distribution functions: a Gaussian distribution to account for clumping of leaf area in the center of the cylinder (µ=0, σ=1/6 of diameter) and a triangular distribution to account for the relative vertical distribution of leaf area along the vertical axis (peak of leaf area at 0.9 relative height). Leaf angles were assumed to follow a plagiophile distribution [16]. Leaf area, shoot height and diameter of the boundary envelope were interpolated between measurements dates as a function of thermal time (base 5°C). This allowed daily plant reconstructions, each plant being the sum of its constitutive shoots. a)
c)
2) Computation of light interception Leaf area within shoot envelopes was represented by a turbid medium of discrete, small 3D leaf elements (i.e. triangles of 0.5 cm2). Light interception was computed on the surfaces of these plant structures using the radiative transfer model CANESTRA [17] available in the Openalea platform [18]. Radiative budgets of leaf elements and of the soil compartment were calculated hourly using incoming light data from INRA Lusignan meteorological station (Fig. 1c). It was then possible to precisely sum up the amount of photosynthetically active radiation (PAR) intercepted by leaf elements and the distributions of leaf irradiances for each plant. 3) Assessment of light partitioning Nine PAR sensors were regularly distributed at the ground level within the Z1 sub-plot to measure light transmission to the soil and canopy light interception efficiency over time. These measurements were compared to the simulated light partitioning between soil and vegetation. In addition, 15 plants in Z1 were digitized at the end of the second alfalfa re-growth cycle using an electromagnetic 3D digitizer (3Space Fastrak, Polhemus Inc., Colchester, VT, USA). Light interceptions by each of these 3D plants within the canopy were compared to those estimated with the simple envelope-based reconstructions. D. Modeling of net assimilation: down-scaling a canopy model Using the same plant structures and PAR interceptions, two contrasting approaches were compared to predict whole plant net assimilation and dry matter accumulation from resource capture. The first relied on the Monteith equation frequently used in crop models [19] and sometimes introduced in plant population models [11, 12]. The second consisted of a more detailed leaf gas exchange model [20] up-scaled at the whole plant level [10, 21]. 1) Model description. The first approach was based on the linear relationship between dry weight accumulation (DW) and intercepted PAR radiation cumulated over time (PARc), which is consistently observed for crop canopies in conditions where neither water nor mineral nutrients are limiting: t =n
DW(t) =
∑ PAR (t ).ε (t ).RUE i
i
(1)
t =1 b)
Figure 1. Shoot envelopes at 30 (a) and 360 °C.d (b) in the second alfalfa re-growth and example of leaf irradiance distribution (c).
DW(t) =
PARc .RUE
(2)
Where PARi and εi stand for incoming PAR and canopy light interception efficiency at time t and RUE is the canopy radiation-use efficiency (g DW.PAR MJ-1). We assumed that the same linear conversion principle applies at the plant scale, so that Eq. 2 was valid for individual plants within a canopy.
2) Model parameterization. The values of RUE were assumed equal at plant and canopy levels. As alfalfa did not fix atmospheric N in our experiment, we chose a RUE of 2 g.MJ-1. This value is indeed generally observed for above-ground dry weight accumulation of non-fixing C3 plants [22]. E. Modeling of net assimilation: up-scaling a leaf gas exchange model 1) Leaf gas exchange model description The proposed model combines the biochemical photosynthetic model of Farquhar et al. [20] with a semiempirical stomatal conductance model (gs) proposed by Ball et al. [23] and later modified by Leuning [24]. Farquhar model assumes that leaf gross photosynthesis rate (A) depends on the carboxylation rate of the Rubisco (Vc) and of substomatal CO2 partial pressure (Ci): A=
Γ* Vc .1 − Ci
(3)
Vc is limited by one of three factors: (i) activation state, quantity and kinetic properties of Rubisco (Ac), (ii) ribulose-1,5 biphosphate (RuBP) regeneration in the Calvin cycle (Aj), or, (iii) the utilization of triose phosphate (Ap) [25].
Na I = N 0 I 0
s.N a + b
(5)
Where P25 stand for the parameter value (i.e. Vcmax, Jmax, TPU, respectively) at 25°C, Na is the leaf nitrogen content of the leaf (g.m-2) and s and b are slope and intercept of the relationship. The Leuning stomatal model defines gs as:
a1 . A (1 + VPD D0 ). C s − Γ *
(
)
(6)
Where g0 is the residual stomatal conductance in absence of assimilation, a1 and D0 are two empirical parameters, VPD the vapor pressure deficit and Cs the CO2 partial pressure at
0.223
(7)
Where N0 and I0 represent the nitrogen content and the daily average irradiance of sunlit leaves at the top of the canopy. Then, Na was used to calculate the photosynthetic parameters (Vcmax, Jmax, TPU) for each leaf irradiance class (Eq. 5). Gross assimilation rate was estimated hourly for each irradiance class and summed up for each plant according to their leaf area distribution in each class. 3) Respiration model description Plant respiration (r) was calculated based on the twocomponent respiration model which distinguishes specific growth (rg) and maintenance (rm) respirations [29]: r = rg + rm =
Parameters that determine leaf photosynthetic capacity are thus Vcmax (Rubisco maximal carboxilation rate), Jmax (maximum electron transport rate) and TPU (triose phosphate utilization rate), each characterizing one of the tree limiting states. The temperature dependence of the photosynthetic parameters was set as an Arrhenius function [26]. The nitrogen dependency of the photosynthetic parameters was introduced through a linear function [21].
gs = g0 +
2) Whole plant integration of gross assimilation Scaling-up gross assimilation from the leaf to the plant level was performed calculating leaf nitrogen content (Na) for each class of leaf irradiance (I) by using the empirical relationship established by Lemaire et al. [28]:
(4)
Vc = Min{Ac, Aj, Ap}
P25 =
leaf surface. Photosynthesis and stomatal conductance submodels were coupled through an iterative calculation of Ci involving a relationship between Cs, Ci and atmospheric CO2 partial pressure [27].
r1 . An + r2 .DW
(8)
where r1 and r2 are respiration rates parameters characterising the two components at 25°C and An represents plant net assimilation rate. The temperature dependence of dark respiration was set as an Arrhenius function [26]. Maintenance respiration was split between leaves, stem and roots and we used organ specific parameters. Leaf dark respiration rate was set dependent upon leaf nitrogen content (Eq. 5). For each plant, An was finally calculated as the difference between A integrated at the plant level and r. 4) Model parameterization. The parameterization of the leaf gas exchange model and of leaf dark respiration was performed on two independent experiments performed during the springs of 2010 and 2011. Plants were grown outdoors in the same conditions except that alfalfa pots were mixed with tall fescue pots (50/50). Photosynthetic parameters were determined performing response curves of An to substomatal CO2 concentration (A-Ci curves) on leaves of contrasting age and positions within the canopy at 25°C. Dark respiration was subsequently measured on the same leaves after dark acclimation. Parameters are summarized in
TABLE I. PHOTOSYNTHESIS AND RESPIRATION PARAMETER DEPENDENCES TO LEAF NITROGEN CONTENT
Parameter Vcmax Jmax TPU r2_leaf
s b 70.7 -35.1 123.4 -47.7 9.0 -3.2 0.22 0.19
n 30 30 30 10
2
r 0.94 0.85 0.87 0.95
n : number of samples
The stomatal conductance model was calibrated using a dataset of continuous leaf gas exchange measurements during contrasting meteorological sequences in spring 2011. Parameters are summarized in Tab. 2. TABLE II. LEUNING STOMATAL CONDUCTANCE MODEL PARAMETERS FOR ALFALFA
Self-thinning occurred within the canopy: mortality during the second re-growth represented 10% of the plants at emergence, all coming from the first quartile of the previous cut. Dynamics of individual plant growth (Fig. 3) clearly show how this final size structure of the population was shaped. The first quartile was composed by plants which stopped growing quickly after canopy closure, and even tended to decrease in biomass afterwards. On the contrary, in the fourth quartile plants grew continuously and tended to have a growth rate that increased with time. In between, a gradient of situations was observed, ranging from plants stopping their growth lately to plants with a more or less steady state growth rate. 0,30 1st quartile
0,25
Above ground plant mass (g)
Tab. 1. Temperature dependence parameters were taken from the literature [30]. Alfalfa growth respiration rate and dark respiration rates for other organs were taken from Lötsher et al. [31]. Roots were assumed to have the same respiration rate than fully developed shoots. The fraction fr of An partitioned to roots was assumed constant and was evaluated as the ratio between root mass and total plant mass cumulated over the first three re-growth cycles (fr=0.19).
0,20 0,4
0,15 0,10
0,2
0,05 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0
Value 0.02 12.5 2.86
units -2 -1 mmol.m .s -
III. RESULTS A. Dry mass distribution of individuals Figure 2 shows the dry mass distribution of individuals at the end of the second alfalfa re-growth cycle. The distribution was highly skewed, with plants in the first quartile of dry weights representing 2.5% of total yield whereas plants in the fourth quartile accounted for 75.5%.
Proportion of plants (%)
40
30
20
10
0 dead
0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
Above ground plant mass (g) Figure 2. Dry mass distribution of individuals at the third alfalfa cut
4
3rd quartile
4th quartile
3 2 1 0 0
Parameter g0 a1 D0
2nd quartile 0,6
100
200
300
400
0
100
200
300
400
Time after cut (°Cd)
Figure 3. Dynamics of plant growth as a function of thermal time during the second re-growth
B. Assessment of light partitioning To explain these differences of fate, we examined how the capture of resources (i.e. light was the only limiting resource in the experiment) and their conversion in biomass respectively contributed to the success (i.e. high ranking) of individuals. Light partitioning was estimated from the coupling of a simple envelope-based 3D model with a light transfer model. Figure 4a presents a comparison of observed and simulated partitioning of light between soil and vegetation during the second re-growth. The model simulated quite accurately the dynamic of canopy closure and the canopy light interception efficiency. Light partitioning between individual plants was also assessed just before harvest through a comparison with 3D digitized plants (Fig. 4b). Simplified shoot 3D structures proved to be accurate enough to estimate light interception at plant scale.
0,10 -1
PARc (MJ.plant- .day )
0,8
a) 0,08
1
Canopy light interception efficiency
a)
1,0
0,6 0,4 measured simulated
0,2 0,0 0
100
200
300
400
0,06 0,04 0,02 0,00
Plant RUE (g.MJ )
4
b)
-1
b)
0,4
TT = 360 °Cd 0,3
0,2
0,1
y = 1.04x+0.01 1:1 line
2
0
-2 3,5
0,0 0,0
0,1
0,2
0,3
0,4
Intercepted PAR with digitisations (MJ.plant-1.day-1) Figure 4. Comparison of measured and simulated light interception by the canopy during the second re-growth (a) and of light partitioning among individual plants at 360°Cd (b)
c)
3,0
Plant respiration -1 (g C. g C fixed)
Intercepted PAR with -1 -1 simulations (MJ.plant .day )
Time after cut (°Cd)
50-150°Cd 150-250°Cd 250-360°Cd
2,5 2,0 1,5 1,0 0,5
C. Light interception, RUE and respiration rate of plants according to their hierarchical position within the canopy Relationships between plant growth rate, resource capture and resource use efficiency are presented in Figure 5 for three periods in the course of the second re-growth. A strong positive relationship was found between plant growth rate and light interception (Fig. 5a). The relationship tended to be slightly curvilinear, plants with a large growth rate getting a more than proportional share of incoming light per unit new mass. Resource use efficiency was clearly not similar for all individuals (Fig. 5b). The most subordinate plants had RUE that quickly decreased, reaching negative values for plants with decreasing dry weights. A large variation in RUE was observed for plants with intermediate growth rate. Their RUE was in average higher than for subordinate and dominant plants. The plants with the highest growth rates presented RUE values close to 1.8 g.MJ-1.
0,0 -0,05
0,00
0,05
0,10
0,15
0,20
Plant growth rate (g DM.day-1) Figure 5. PARc (a), RUE (b) and respiration rates (c) of plants as a function of their growth rate over three periods during the second regrowth
Plant respiration rates, as calculated with the respiration model over the same periods, are plotted against measured plant growth rates in Fig 5c. A dramatic increase of respiration rate affected the most subordinate plants. This was clearly related to the decrease of RUE observed for these plants. On the other hand, no increase in respiration rate was shown for the dominant plants in parallel of their slight RUE decrease. Interestingly, the PARc, RUE and respiration relationships remained the same over the three periods studied and did not seem to vary with time in spite of the very different patterns of plant growth sampled by these periods.
-2
Simulated above ground DM (g.m )
dominant plants (DM>1.5g). By comparison (Fig. 6c), the leaf model did not improve the prediction of individual plant productivity (84% of inter plant variance explained). A slightly larger error was detected (RMSE=0.26g instead of 0.24g). Model errors were also dependent of the hierarchical positions of plants within the canopy. The productivity of dominant plants was correctly predicted whereas, contrary to the canopy model, the productivity of the subordinate plants was underestimated. The proportion of dead plants (i.e. reaching a negative mass) was also higher than observed (21% in the course of the second regrowth instead of 10%).
600 a) 500 400 300 200
canopy model y = 0.99x - 3 leaf model y = 1.01x +6 1:1 line
100 0 0
100 200 300 400 500 600 -2
Measured above ground DM (g.m ) 5 b)
y = 1,07x
-1
Simulated above ground DM (g.plant )
4 3 2
1 0,1
1
0,01 0,001 0,001 0,01
0,1
1
0,1
1
0 c)
y=1.04x - 0.1
4 3 2
1 0,1
1
0,01 0,001 0,001 0,01
0 0
1
2
3
4
5
Measured above ground DM (g.plant-1) Figure 6. Comparison of measured and simulated dry matter production at canopy (a) and individual plant (b, c) scales. Dots and squares are for the canopy and leaf models, respectively. Inserts present the same results with log scales.
D. Comparison of top-down and bottom-up approaches to predict plant productivity Figure 6 presents a comparison of measured and simulated above ground dry matters for the two models studied to account for net assimilation. At canopy scale (Fig. 6a), the prediction of the canopy model were remarkably accurate. The same trend was observed for the up-scaled leaf model. Variations in individual plant masses were also quite accurately predicted by the two models(Fig. 6b). Over 91% of interplant variance was explained by the canopy model which only considers differences in resource capture. The canopy model however clearly overestimated the dry matter production of the most subordinate plants, and presented a trend for the overestimation of the most
IV. DISCUSSION The experimental alfalfa plant population studied presented a skewed distribution of plant masses which was typical of grassland plant populations and of many dense natural plant populations structured by competition for light [32]. The size structure of the population emerged from the differential growth rates of individuals, and in particular from the selection of a minority of individuals able to sustain continuous growth whereas a large majority quickly stopped to accumulate biomass. We used a combination of field measurements and simple envelope-based 3D reconstructions to estimate light partitioning among individual plants over time and quantify the role of resource capture by individuals in the selection process observed at the population level. As recently demonstrated on a large range of canopy structures [15], simplified 3D representation proved faithful to infer light partitioning among individuals. They were good surrogates to the reference method of 3D plant digitization and allowed the dynamic follow-up of up to 100 neighbor plants. Although simple, the down-scaled canopy net assimilation model performed reasonably well to predict variations in individual plant productions. As plant RUE was the only parameter considered in this model, and because RUE was assumed constant for all plants, this result suggests that differences in resource capture (i.e. light interception) were the main cause of variation of individual plant mass during the re-growth. However, the constant RUE paradigm made the model suffer from several drawbacks. Contrary to the predictions at canopy scale, deviations were observed at plant scale for individuals at both ends of the distribution. As shown in Fig. 5b and in previous studies on crowded canopies [33], it is indeed unlikely that plant RUE remain the same for all plants irrespective of their hierarchical position within the canopy, or for one plant throughout its growing cycle. More importantly, the model was unable to predict self-thinning. In absence of respiration, any resource capture was transformed into DM increase. Such a zero-mortality rate represents a strong limitation to properly simulate population dynamics over longer periods. Up to 75% of
plants usually die in the first two years of an alfalfa crop [32]. The up-scaled leaf model presented a complete plant C balance. It was recently assessed at leaf scale both in grapevine [21] and in alfalfa (not shown). The up-scaling method was also validated for aboveground parts in grapevine against measurement of whole plant gas exchange [10, 21]. In spite of its detailed parameterization, the model did not perform better than the canopy model to predict individual variations in DM. The underestimation of subordinate plant growth and of plant mortality could be related to a problem in the respiration sub-model. Root respiration in particular was roughly considered in our approach (dark respiration rate assumed similar to shoots; partitioning of new assimilates between shoots and roots assumed constant over time and identical for all plants irrespective of their hierarchical position). This could be improved in future work. Nonetheless, the model also showed some very interesting properties. It did predict the self-thinning of observed dead plants. The change of RUE (as assessed by the An:PARc ratio) with plant hierarchical position also appeared as an emerging property of the model (not shown). To conclude, the positive points of the two models could probably be combined. The trade-off represented by a simple “gross RUE” conversation of light interception [22], latter reduced by a respiration sub-model, appears as a promising track to follow [11, 12]. Moreover, resource capture explained the larger part of inter-plant variability in our data, but the processes controlling it were not simulated (shoot heights and leaf area were taken as inputs). The asymmetric size structure of the population was shaped by plants that regularly stopped growing as a consequence of an entrance of their shoot apex in quiescence. This highlights the importance of further considering the morphogenetic control of plant growth in accounting for inter-plant competition for light.
ACKNOWLEDGMENTS This study was supported by the Conseil Régional Poitou-Charentes (http://www.poitou-charentes.fr), by Agropolis Foundation (ALEA Project) and by the AIP INRA-INRIA (Alinea Project). We would like to thank S. Carre, A. Eprinchard, A. Philiponneau V. Dunoyer and S. Denis for their help with the experiments and J. Prieto for fruitful discussions. REFERENCES [1] J.L. Harper, 1977. “Population Biology of Plants”. Academic Press, New York.
[2] G.B. Bonan, 1988. “The size structure of theoretical plant populations: spatial patterns and neighbourhood effects”. Ecology 69: 1721– 1730. [3] K. Hikosaka, S. Sudoh & T. Hirose, 1999. “Light acquisition and use by individuals competing in a dense stand of an annual herb, Xanthium canadense”. Oecologia 118(3): 388-396. [4] A. Lomnicki, 1988. “Population ecology of individuals”. Princeton University Press, Princeton, New Jersey, USA. [5] U. Berger, C. Piou, K. Schiffers & V. Grimm, 2008. ”Competition among plants: Concepts, individual-based modelling approaches, and a proposal for a future research strategy”. Perspectives in Plant Ecology, Evolution and Systematics 9 (3-4): 121-135. [6] E. Malézieux, Y. Crozat, C. Dupraz, M. Laurans, D. Makowski, H.Ozier-Lafontaine, B. Rapidel, de Tourdonnet S. & M. ValantinMorison, 2009. “Mixing plant species in cropping systems: concepts, tools and models. A review”. Agronomy and Sustainable Development 29(1): 43-62. [7] J. Perttunen, E. Nikinmaa, M.J. Lechowicz, R. Sievänen, C. Messier, 2001. “Application of the functional-structural tree model LIGNUM to Sugar Maple Sapling (Acer saccharum Marsh) growing in forest gaps”. Annals of Botany 88, 471-481. [8] P.-H. Cournède, A. Mathieu, et al. 2008. “Computing Competition for Light in the GREENLAB Model of Plant Growth: A Contribution to the Study of the Effects of Density on Resource Acquisition and Architectural Development”. Annals of Botany 101(8): 1207-1219. [9] S. Bornhofen, & C. Lattaud, 2009. “Competition and evolution in virtual plant communities: a new modeling approach”. Natural Computing 8(2): 349-385. [10] J.A. Prieto, 2011. “Simulation of photosynthesis and transpiration within grapevine (Vitis vinifera L.) canopies based on a 3D architectural model. Application to training system evaluation”. PhD Thesis, Montpellier SupAgro, France. [11] N. Colbach, A. Gardarin and N. M. Munier-Jolain, 2010. “FLORSYS: a mechanistic model of cropping system effects on weed flora based on functional relationships with species traits”. In: Proceedings of 15th International EWRS Symposium. Kaposvár, Hungary, 12-15 July 2010, 157-158 [12] N. M. Munier-Jolain, S. Guyot and N.Colbach, 2012. “A 3D model for crop-weed light competition in heterogeneous canopies. Model structure and evaluation”. Ecological Modelling [13] H.P. Yan, M.Z. Kang, P. de Reffye and M. Dingkuhn, 2004. “A dynamic, architectural plant model simulating resource-dependent growth”. Annals of Botany 93: 1–12. [14] G. Louarn, D. Combes, D. Da Silva and C. Godin, 2010. “Reconstruction methods to estimate light partitioning among individual plants in crowded canopies”, In: Proceedings of 6th international workshop on Plant Structural-Functional Models, Davies, CA, pp 74-76. [15] G. Louarn, D. Da Silva, C. Godin and D. Combes, 2012. “Simple envelope-based reconstruction methods can infer light partitioning among individual plants in sparse and dense herbaceous canopies”, Agricultural and Forest Meterology, In Press, doi 10.1016/j.agrformet.2012.06.014 [16] H. Sinoquet and B. Andrieu, 1993. “The geometrical structure of plant canopies: Characterization and direct measurements methods”. In: Varlet-Grancher, C., Bonhomme, R. and Sinoquet, H Editors, 1993. Crop structure and light microclimate: characterization and applications INRA, Paris, pp. 131–158. [17] M. Chelle and B. Andrieu, 1998. “The nested radiosity model for the distribution of light within plant canopies”. Ecological Modelling 111(1): 75-91. [18] C. Pradal, S. Dufour-Kowalski, F. Boudon, C. Fournier and C. Godin, 2008. “OpenAlea: a visual programming and componentbased software platform for plant modelling”. Functional Plant Biology 35(10): 751-760.
[19] J. Monteith, 1977. “Climate and the efficiency of crop production in Britain”. Philosophical Transactions of the Royal Society of London 281: 277–294. [20] G.D. Farquhar, S. von Caemmerer and J.A. Berry, 1980. “A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species”. Planta 149, 78-90. [21] J.A. Prieto, , G. Louarn, et al. 2012. "A leaf gas exchange model that accounts for intra-canopy variability by considering leaf nitrogen content and local acclimation to radiation in grapevine (Vitis vinifera L.)." Plant, Cell & Environment: 35(7) : 1313-1328. [22] G. Bélanger, F. Gastal, and F.R. Warembourg, 1994. "Carbon Balance of Tall Fescue (Festuca arundinacea Schreb.): Effects of Nitrogen Fertilization and the Growing Season." Annals of Botany 74(6): 653-659. [23] M.C. Ball, I.E. Woodrow and J.A. Berry, 1987. “A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions”. In Progress in Photosynthesis Research (ed J. Biggins), pp. 221-224. [24] R. Leuning, 1995. “A critical appraisal of a combined stomatalphotosynthesis model for C3 plants”. Plant, Cell & Environment 18, 339-355. [25] T.D. Sharkey, 1985. “Photosynthesis in intact leaves of C3 plants: Physics, physiology and rate limitations”. The Botanical Review 51, 53-105. [26] C.J. Bernacchi, E.L. Singsaas, C. Pimentel, A.R. Portis and S.P. Long, 2001. “Improved temperature response functions for models of Rubisco-limited photosynthesis”. Plant, Cell & Environment 24, 253-259.
[27] S.H. Kim and J.H. Lieth, 2003. “A coupled model of photosynthesis, stomatal conductance and transpiration for a Rose leaf (Rosa hybrida L.)”. Annals of Botany 91, 771-781. [28] G. Lemaire, B. Onillon et al. (1991). "Nitrogen Distribution Within a Lucerne Canopy During Regrowth: Relation With Light Distribution." Ann Bot 68(6): 483-488. [29] K.J. McCree, 1970. “An equation for the rate of respiration of white clover plants grown under controlled conditions”, In: Proceedings of the technical meeting IBP, Trebon (CSK), 1969, Centre for Agricultural Publishing and Documentation, Wageningen, (NDL), pp. 221–229. [30] S. Al-Hamdani and G.W. Todd, 1990. "Effect of Temperature Regimes on Photosynthesis, Respiration, and Growth in Alfalfa." Proc. Oklahoma Acad. Sci. 70, 1–4. [31] M. Lötscher, K. Klumpp, et al. 2004. "Growth and maintenance respiration for individual plants in hierarchically structured canopies of Medicago sativa and Helianthus annuus: the contribution of current and old assimilates." New Phytologist 164(2): 305-316. [32] G. Gosse, G. Lemaire, M. Chartier and F. Balfourier, 1988. “Structure of a lucerne population (Medicago sativa L.) and dynamics of stem competition for light during regrowth”. Journal of Applied Ecology 25, 609-617. [33] K. Hikosaka, S. Sudoh and T. Hirose, 1999. “Light acquisition and use by individuals competing in a dense stand of an annual herb, Xanthium canadense”. Oecologia 118(3): 388-396.
