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Title: Scaling the leaf length-times-width equation to predict total leaf area of shoots
Abstract Background and Aims

An individual plant consists of different-sized shoots, each of which consists of different-sized leaves. To predict plant-level physiological responses from the responses of individual leaves, modelling this within-shoot leaf size variation is necessary. Within-plant leaf trait variation has been well investigated in canopy photosynthesis models but less so in plant allometry. Therefore, integration of these two different approaches is needed.


We focused on an established leaf-level relationship that the area of an individual leaf lamina is proportional to the product of its length and width. The geometric interpretation of this equation is that different-sized leaf laminas from a single species share the same basic form. Based on this shared basic form, we synthesized a new length-times-width equation predicting total shoot leaf area from the collective dimensions of leaves that comprise a shoot. Furthermore, we showed that several previously established empirical relationships, including the allometric relationships between total shoot leaf area, maximum individual leaf length within the shoot and total leaf number of the shoot, can be unified under the same geometric argument. We tested the model predictions using five species, all of which have simple leaves, selected from diverse taxa (Magnoliids, monocots and eudicots) and from different growth forms (trees, erect herbs and rosette herbs).

Key Results

For all five species, the length-times-width equation explained within-species variation of total leaf area of a shoot with high accuracy (R2 > 0.994). These strong relationships existed despite leaf dimensions scaling very differently between species. We also found good support for all derived predictions from the model (R2 > 0.85).


Our model can be incorporated to improve previous models of allometry that do not consider within-shoot size variation of individual leaves, providing a cross-scale linkage between individual leaf-size variation and shoot-size variation.

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Author(s) / Creator(s):
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Annals of Botany
Medium: X Size: p. 215-230
["p. 215-230"]
Sponsoring Org:
National Science Foundation
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Spreadsheet: annual precip_drainage Description: Precipitation measured from nearby Kellogg Biological Station (KBS) Long Term Ecological Research (LTER) Weather station, over 2009-2016 study period. Data shown in Figure 1; original data source for precipitation ( Drainage estimated from SALUS crop model. Note that drainage is percolation out of the root zone (0-125 cm). Annual precipitation and drainage values shown here are calculated for growing and non-growing crop periods. Variate    Description year    year of the observation crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” precip_G    precipitation during growing period (milliMeter) precip_NG    precipitation during non-growing period (milliMeter) drainage_G    drainage during growing period (milliMeter) drainage_NG    drainage during non-growing period (milliMeter)      2. Spreadsheet: biomass_corn, perennial grasses Description: Maximum aboveground biomass measurements from corn, switchgrass, miscanthus, native grass and restored prairie plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2015. Data shown in Figure 2.   Variate    Description year    year of the observation date    day of the observation (mm/dd/yyyy) crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” replicate    each crop has four replicated plots, R1, R2, R3 and R4 station    stations (S1, S2 and S3) of samplings within the plot. For more details, refer to link ( species    plant species that are rooted within the quadrat during the time of maximum biomass harvest. See protocol for more information, refer to link ( For maize biomass, grain and whole biomass reported in the paper (weed biomass or surface litter are excluded). Surface litter biomass not included in any crops; weed biomass not included in switchgrass and miscanthus, but included in grass mixture and prairie. fraction    Fraction of biomass biomass_plot    biomass per plot on dry-weight basis (Grams_Per_SquareMeter) biomass_ha    biomass (megaGrams_Per_Hectare) by multiplying column biomass per plot with 0.01 3. Spreadsheet: biomass_poplar Description: Maximum aboveground biomass measurements from poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2015. Data shown in Figure 2. Note that poplar biomass was estimated from crop growth curves until the poplar was harvested in the winter of 2013-14. 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Data for nitrogen leached and volume-wtd mean N concentration shown in Figure 3a and Figure 3b, respectively. Note that ammonium (nh4) concentration were much lower and often undetectable (<0.07 milliGrams_N_Per_Liter). Also note that in 2009 and 2010 crop-years, data from some replicates are missing.    Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” crop-year    year of the observation replicate    each crop has four replicated plots, R1, R2, R3 and R4 no3 leached    annual leaching rates of nitrate (kiloGrams_N_Per_Hectare) don leached    annual leaching rates of don (kiloGrams_N_Per_Hectare) vol-wtd no3 conc.    Volume-weighted mean no3 concentration (milliGrams_N_Per_Liter) vol-wtd don conc.    Volume-weighted mean don concentration (milliGrams_N_Per_Liter) 5. 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Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” no3 leached    annual leaching rates of nitrate (kiloGrams_N_Per_Hectare) don leached    annual leaching rates of don (kiloGrams_N_Per_Hectare) N unleached    N unleached (kiloGrams_N_Per_Hectare) in other sources are not studied % of N applied N lost to leaching    % of N applied N lost to leaching 6. Spreadsheet: annual DOC leachin_vol-wtd conc Description: Annual leaching rate (kiloGrams_Per_Hectare) and volume-weighted mean N concentrations (milliGrams_Per_Liter) of dissolved organic carbon (DOC) in the leachate samples collected from corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2016. Data for DOC leached and volume-wtd mean DOC concentration shown in Figure 5a and Figure 5b, respectively. Note that in 2009 and 2010 crop-years, water samples were not available for DOC measurements.     Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” crop-year    year of the observation replicate    each crop has four replicated plots, R1, R2, R3 and R4 doc leached    annual leaching rates of nitrate (kiloGrams_Per_Hectare) vol-wtd doc conc.    volume-weighted mean doc concentration (milliGrams_Per_Liter) 7. Spreadsheet: growing season length Description: Growing season length (days) of corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in the Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2015. Date shown in Figure S2. Note that growing season is from the date of planting or emergence to the date of harvest (or leaf senescence in case of poplar).   Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” year    year of the observation growing season length    growing season length (days) 8. Spreadsheet: correlation_nh4 VS no3 Description: Correlation of ammonium (nh4+) and nitrate (no3-) concentrations (milliGrams_N_Per_Liter) in the leachate samples from corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2013-2015. Data shown in Figure S3. Note that nh4+ concentration in the leachates was very low compared to no3- and don concentration and often undetectable in three crop-years (2013-2015) when measurements are available. Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” date    date of the observation (mm/dd/yyyy) replicate    each crop has four replicated plots, R1, R2, R3 and R4 nh4 conc    nh4 concentration (milliGrams_N_Per_Liter) no3 conc    no3 concentration (milliGrams_N_Per_Liter)   9. Spreadsheet: correlations_don VS no3_doc VS don Description: Correlations of don and nitrate concentrations (milliGrams_N_Per_Liter); and doc (milliGrams_Per_Liter) and don concentrations (milliGrams_N_Per_Liter) in the leachate samples of corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2013-2015. Data of correlation of don and nitrate concentrations shown in Figure S4 a and doc and don concentrations shown in Figure S4 b. 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  4. Premise

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    Our results demonstrate that vein‐to‐blade ratio is a strong allometric indicator of leaf size and plasticity in grapevines measured across years. Grapevine leaf primordia are initiated in buds the year before they emerge, and we found that total precipitation and maximum air temperature of the previous growing season exerted the largest statistically significant effects on leaf morphology. Vein‐to‐blade ratio is a promising allometric indicator of relationships between leaf morphology and climate, the robustness of which should be explored further.

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  5. Abstract

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