1. AGU meeting 2014
LM3-PPA: scaling from individuals to ecosystems with height-structured competition for light
Ensheng Weng1, Sergey Malyshev1, Jeremy Lichstein2, Caroline Farrior1, Ray Dybzinski1, Tao Zhang2, Elena Shevliakova1, Stephen W. Pacala 1
1Princeton University, Princeton, NJ 08544, USA
2University of Florida, Gainesville, FL 32611, USA
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2. Modeling terrestrial ecosystems in ESMs
Grid-cell BGC
Biomass
Litter
Soil Carbon U
CO2
PFTs, Allocation, Turnover (Mortality)
Leaf photosynthesis
Scale to Canopy ?
Grid-cell BGC
Leaf
Tree
Population
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3. Perfect Plasticity Approximation model (PPA)
Crown area = land area
Height-structured competition for light:
Crown is “perfect plastic”;
Each layer is filled by crowns according to the order of tree height;
Trees in the canopy layer have full sunshine; the trees in understory are shaded.
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Strigul et al. 2008; Purves et al. 2008

4. Evolutionarily Stable Strategy of Allocation
Dybzinski et al. 2011
Farrior et al. 2014
An evolutionarily stable strategy (ESS) is the strategy that can competitively exclude all others.
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5. A coupled model: LM3-PPA
LM3, Land component of GFDL ESMs
PPA
Photosynthesis
Respiration
Energy balance
Water cycle
etc.
Canopy layering
Competition
Optimal strategy
NPP
Vegetation states
Reproduction
Growth
Mortality
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6. From photosynthesis to the 3-D sizes of a tree:
Canopy photosynthesis
Whole tree respiration
Allometry & Allocation:
Crown area
Tree height
Trunk diameter
Tree biomass
NPP
Crown area, LAI, fine roots, sapwood
Allometry:
Biomass partitioning:
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7. Growth of diameter, height, and crown area
NSC
Fine Roots
Fast Soil C
Slow Soil C
Leaves
(Photosynthesis)
Sapwood
Heartwood
Seeds
Height:
Crown area:
When θC=1.5 and θZ=0.5, trunk diameter growth rate (dD/dt) is independent of D.
The height and crown area growth rates are functions of D.
The diameter growth equation bridges the C dynamics and tree allometry by translating NPP into growth rates.
Carbon pools
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8. Arrangement of trees in a limited space and population dynamics
Land Tile
Cohort
Solar radiation
Layer
New born cohort:
Growth:
Mortality:
Individuals to cohorts;
Flat-topped canopy: zero crown join height ;
Sort by height and fill the space with crown area;
Different light intensity for varied canopy layers.
LM3-PPA
Weng et al. submitted to Biogeosciences
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9. Simulation tests at a deciduous temperate forest site (Willow creek, WI, USA): I. Individual growth, population dynamics, and succession II. Evolutionarily stable strategies of allocation at two atmospheric [CO2] levels
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10. Test I: Individual growth, population dynamics, and succession
Three species:
Trembling aspen (pioneer)
Red maple (intermediate)
Sugar maple (late)
Parameter
Trembling aspen
Red maple
Sugar maple
Vcmax
30.0E-6
25.0E-6
22.0E-6 ρW
230
265 µC
0.065
0.02
0.012 µU
0.162
0.081
0.049
φRL
0.8
SRA 80
LMA
0.045
0.038
0.035
LAImax
3.0
3.5
3.8
Differences:
Vcmax
LAImax
µC and µU
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11. Simulated diameter growth rates
θC=1.5; θZ=0.5
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12. Tree size distribution
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13. Succession with three species
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14. Test II: Evolutionarily stable strategy at different [CO2]
Red maple variants: varied only in target fine roots (different φRL);
Polyculture runs: initiated with five variants (φRL = 0.5, 0.6, 0.7, 0.8 and 0.9) all having the same initial population density (250 seedlings ha-1);
Monoculture runs: performed for each of the five above variants (φRL = 0.5, 0.6, 0.7, 0.8 and 0.9) to identify the most productive strategy in monoculture;
Invasion runs: performed at two [CO2] levels (280 and 560 ppm) to confirm the identity of the most competitive strategy. Each invasion run included two different variants: a “resident” variant and an “invader” variant.
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15. Polyculture runs
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16. Growth rates and woody NPP
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17. DBH growth rates in invasion tests
ESS of allocation φRL shifts from 0.7 to 0.9 when CO2 concentration is doubled;
The optimal φRL has a higher growth rate when invading the non-optimal than when it is resident;
Even the ESS’s have lower growth rates, the non-optimal strategies can’t successively invade them.
ESS φRL = 0.7
ESS φRL = 0.9
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18. Reason: soil water conditions
Two opposing forces on ESS root allocation: (1) increased period of wet season favors decrease in root allocation, vs. (2) increased leaf productivity during the water-limited period makes increased root allocation more profitable.
The latter effect dominates, and the most competitive strategy shifts to the one with greater allocation to fine roots
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19. Summary
LM3-PPA simulates vegetation dynamics and biogeochemical processes by explicitly scaling from individuals to ecosystems with a mathematically tractable model of height-structured competition for light.
The partitioning of space by plant crowns simplifies the simulation of light competition among trees, allowing the model to include biodiversity and therefore to predict the competitive strategies.
The carbon sinks caused by CO2 fertilization in forests can be down-regulated if allocation tracks changes in the competitive optimum.
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20. Thank you for your attention!
Acknowledgments
Development of the theories: Caroline Farrior, Ray Dybzinski, Stephen Pacala
Development of LM3: Sergey Malyshev, Elena Shevliakova
Work together to make it possible: Jeremy Lichstein and Stephen Pacala
Help in FIA data analysis: Tao Zhang, Jeremy Lichstein
Financial support: Forest Service Northern Research Station, and Princeton Environment Institute
Thank you for your attention!
11/24/2018

21. Growth rates at different allometry of crown area
Crown area ∝ D1.5
Crown area ceases to expand when D>0.8 m
θC=1.5; θZ=0.5
Farrior et al. 2013
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