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"Variable","Function","Allocation","Growth rate" | ||
"**(a) Assumed**",,, | ||
"Height","$H = \alpha_{{\rm l1}} \, \left(A_{\rm l} \, {\rm m^{-2}} \right)^{\alpha_{{\rm l2}}}$","$\frac{{\rm d}H}{{\rm d}A_{\rm l}} = \alpha_{{\rm l2}} \alpha_{{\rm l1}} \left(A_{\rm l} \, {\rm m^{-2}} \right)^{\alpha_{{\rm l2}}-1}$","$\frac{{\rm d}H}{{\rm d}t} = \frac{{\rm d}H}{{\rm d}A_{\rm l}} \, \frac{{\rm d}A_{\rm l}}{{\rm d}t}$" | ||
"Sapwoood area","$A_{\rm s} = \theta \, A_{\rm l}$","$\frac{{\rm d}A_{\rm s}}{{\rm d} A_{\rm l}} = \theta$","$\frac{{\rm d}A_{\rm s}}{{\rm d}t} = \frac{{\rm d}A_{\rm s}}{{\rm d} A_{\rm l}} \, \frac{{\rm d}A_{\rm l}}{{\rm d}t}$" | ||
"Bark area","$A_{\rm b} = \alpha_{{\rm b1}} \, \theta \, A_{\rm l}$","$\frac{{\rm d}A_{\rm b}}{{\rm d} A_{\rm l}} = \alpha_{{\rm b1}} \, \theta$","$\frac{{\rm d}A_{\rm b}}{{\rm d}t} = \frac{{\rm d}A_{\rm b}}{{\rm d} A_{\rm l}} \, \frac{{\rm d}A_{\rm l}}{{\rm d}t}$" | ||
"**(b) Derived**",,, | ||
"Leaf mass","$M_{\rm l} = \phi \, A_{\rm l}$","$\frac{{\rm d}M_{\rm l}}{{\rm d}A_{\rm l}} = \phi$","$\frac{{\rm d}M_{\rm l}}{{\rm d}t} = \frac{{\rm d}M_{\rm l}}{{\rm d}A_{\rm l}} \, \frac{{\rm d}A_{\rm l}}{{\rm d}t}$" | ||
"Sapwood mass","$M_{\rm s} = \rho \, \theta \, \eta_{\rm c} \, A_{\rm l} \, H$","$\frac{{\rm d}M_{\rm s}}{{\rm d}A_{\rm l}} = \rho \, \theta \, \eta_{\rm c} \, \big(H + A_{\rm l} \, \frac{{\rm d}H}{{\rm d}A_{\rm l}} \big)$","$\frac{{\rm d}M_{\rm s}}{{\rm d}t} = \frac{{\rm d}M_{\rm s}}{{\rm d}A_{\rm l}} \, \frac{{\rm d}A_{\rm l}}{{\rm d}t}$" | ||
"Bark mass","$M_{\rm b} = \alpha_{{\rm b1}} \, \rho \, \theta \, \eta_{\rm c} \, A_{\rm l} \, H$","$\frac{{\rm d}M_{\rm b}}{{\rm d}A_{\rm l}} = \alpha_{{\rm b1}} \, \rho \, \theta \, \eta_{\rm c}\big(H + A_{\rm l} \, \frac{{\rm d}H}{{\rm d}A_{\rm l}} \big)$","$\frac{{\rm d}M_{\rm b}}{{\rm d}t} = \frac{{\rm d}M_{\rm b}}{{\rm d}A_{\rm l}} \, \frac{{\rm d}A_{\rm l}}{{\rm d}t}$" | ||
"Root mass","$M_{\rm r} = \alpha_{{\rm r1}} \, A_{\rm l}$","$\frac{{\rm d}M_{\rm r}}{{\rm d}A_{\rm l}} = \alpha_{{\rm r1}}$","$\frac{{\rm d}M_{\rm r}}{{\rm d}t} = \frac{{\rm d}M_{\rm r}}{{\rm d}A_{\rm l}} \, \frac{{\rm d}A_{\rm l}}{{\rm d}t}$" | ||
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Description,Symbol,Unit,Code | ||
**Plant construction**,,, | ||
Crown-shape parameter,$\eta$,,eta | ||
Leaf mass per area,$\phi$,kg m$^{-2}$,lma | ||
Wood density,$\rho$,kg m$^{-3}$,rho | ||
Sapwood area per unit leaf area,$\theta$,,theta | ||
Height of plant with leaf area of 1m$^2$,$\alpha_{\rm l1}$,m,a_l1 | ||
Exponent of relationship between height and leaf area,$\alpha_{\rm l2}$,,a_l2 | ||
Root mass per unit leaf area,$\alpha_{\rm r1}$,kg m$^{-2}$,a_r1 | ||
Ratio of bark area to sapwood area,$\alpha_{\rm b1}$,,a_b1 | ||
**Production**,,, | ||
Leaf photosynthesis per area,$\alpha_{\rm p1}$,mol yr$^{-1}$ m$^{-2}$,a_p1 | ||
Saturation of leaf photosynthesis per area,$\alpha_{\rm p2}$,,a_p2 | ||
Yield = fraction of carbon fixed converted into mass,$\alpha_{\rm y}$,,a_y | ||
Biomass per mol carbon,$\alpha_{\rm bio}$,kg mol$^{-1}$,a_bio | ||
Leaf respiration per mass,$r_{\rm l}$,mol yr$^{-1}$ kg$^{-1}$,r_l | ||
Fine-root respiration per mass,$r_{\rm r}$,mol yr$^{-1}$ kg$^{-1}$,r_r | ||
Sapwood respiration per mass,$r_{\rm s}$,mol yr$^{-1}$ kg$^{-1}$,r_s | ||
Bark respiration per mass,$r_{\rm b}$,mol yr$^{-1}$ kg$^{-1}$,r_b | ||
Turnover rate for leaves,$k_{\rm l}$,yr$^{-1}$,k_l | ||
Turnover rate for sapwood,$k_{\rm s}$,yr$^{-1}$,k_s | ||
Turnover rate for bark,$k_{\rm b}$,yr$^{-1}$,k_b | ||
Turnover rate for fine roots,$k_{\rm r}$,yr$^{-1}$,k_r | ||
**Fecundity**,,, | ||
Seed mass,$\omega$,kg,omega | ||
Height at maturation,$H_{{\rm mat}}$,m,hmat | ||
Maximum allocation to reproduction,$\alpha_{\rm f1}$,,a_f1 | ||
"Parameter determining rate of change in$r(x, m_\textrm{l})$ around$H_{\rm mat}$",$\alpha_{\rm f2}$,,a_f2 | ||
Accessory cost per seed,$\alpha_{\rm f3}$,kg,a_f3 | ||
**Mortality**,,, | ||
Survival probability during dispersal,$S_{\rm D}$,,S_D | ||
Parameter influencing survival through germination,$\alpha_{\rm d0}$,kg yr$^{-1}$ m$^{-2}$,a_d0 | ||
Intrinsic or growth-independent mortality,$d_{\rm I}$,yr$^{-1}$,d_I | ||
Baseline rate for growth-dependent mortality,$\alpha_{\rm dG1}$,yr$^{-1}$,a_dG1 | ||
Risk coefficient for dry-mass production per unit leaf area in growth-dependent mortality,$\alpha_{\rm dG2}$,yr m^${2}$ kg$^{-1}$,a_dG2 |
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Description,Symbol,Unit,Code | ||
**Leaf turnover**,,, | ||
Global average leaf mass per area,$\phi_0$,kg m$^{-2}$,lma_0 | ||
"Rate of leaf turnover at average leaf mass per unit leaf area, $\phi_0$",$\beta_{\rm kl1}$,yr$^{-1}$,B_kl1 | ||
Scaling exponent for $\phi$ in leaf turnover,$\beta_{\rm kl2}$,,B_kl2 | ||
**Sapwood turnover**,,, | ||
Global average wood density,$\rho_0$,kg m$^{-3}$,rho_0 | ||
"Rate of sapwood turnover at average wood density, $\rho_0$",$\beta_{\rm ks1}$,yr$^{-1}$,B_ks1 | ||
Scaling exponent for $\rho$ in sapwood turnover,$\beta_{\rm ks2}$,,B_ks2 | ||
**Growth-independent mortality**,,, | ||
"Rate of instantaneous mortality at average wood density, $\rho_0$",$\beta_{\rm dI1}$,yr$^{-1}$,B_dI1 | ||
Scaling exponent for wood density in intrinsic mortality,$\beta_{\rm dI2}$,,B_dI2 | ||
**Photosynthesis**,,, | ||
Leaf nitrogen per unit leaf area,$\nu$,kg m$^{-2}$,narea | ||
Global average nitrogen per unit leaf area,$\nu_0$,kg m$^{-2}$,narea_0 | ||
"Potential CO$_2$ photosynthesis at average leaf nitrogen, $\nu_0$",$\beta_{\rm lf1}$,mol d$^{-1}$ m$^{-2}$,B_lf1 | ||
Curvature of light response curve,$\beta_{\rm lf2}$,,B_lf2 | ||
Quantum yield of leaf photosynthesis (CO$_2$ per unit photosynthetically active radiation),$\beta_{\rm lf3}$,,B_lf3 | ||
Scaling exponent for leaf nitrogen in maximum leaf photosynthesis,$\beta_{\rm lf5}$,,B_lf5 | ||
**Respiration**,,, | ||
CO$_2$ respiration per unit leaf nitrogen,$\beta_{\rm lf4}$,mol yr$^{-1}$ kg$^{-1}$,B_lf4 | ||
CO$_2$ respiration per unit sapwood volume,$\beta_{\rm rs1}$,mol yr$^{-1}$ m$^{-3}$,B_rs1 | ||
CO$_2$respiration per unit bark volume,$\beta_{\rm rb1}$,mol yr$^{-1}$ m$^{-3}$,B_rb1 | ||
**Reproduction**,,, | ||
Cost of seed accessories per unit seed mass,$\beta_{\rm f1}$,,B_f1 |
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Symbol,Unit,Description | ||
**Plant construction**,, | ||
$x$,,Vector of traits for a species | ||
$H_0$,m,Height of a seedling after germination | ||
$H$,m,Height of a plant | ||
$B$,kg,Biomass originating from parent plant | ||
$M_i$,kg,Mass of tissue type $i$ retained on plant | ||
$A_i$,m$^2$,Surface area or area of cross-section of tissue type $i$ | ||
"$q(z, H)$",m$^{-1}$,Vertical distribution of leaf area across heights $z$ for a plant with height $H$ | ||
"$Q(z, H)$",,Fraction of leaf area above height $z$ for a plant with height $H$Mass production, | ||
**Mass production**,, | ||
"$p,\bar{p}$",mol yr$^{-1}$ m$^{-2}$,Photosynthetic rate per unit area | ||
$r_i$,mol yr$^{-1}$ kg$^{-1}$ ,Respiration rate per unit mass of tissue type $i$ | ||
$k_i$,yr$^{-1}$,Turnover rate for tissue type $i$ | ||
**Environment**,, | ||
$a$,yr,Patch age | ||
$E_{a}$,,Profile of canopy openness within a patch of age $a$ | ||
$E_{a}(z)$,,Canopy openness at height $z$ within a patch of age $a$ | ||
**Demographic outcomes**,, | ||
"$g(x, H, E_{a})$",m yr$^{-1}$,Height growth rate of a plant with traits $x$ and height $H$ in the light environment $E_a$ in a patch of age $a$ | ||
"$f(x, H, E_{a})$",yr$^{-1}$,Seed production rate of a plant with traits $x$ and height $H$ in the light environment $E_a$ in a patch of age $a$ | ||
"$d(x, H, E_{a})$",yr$^{-1}$,Instantaneous mortality rate of a plant with traits $x$ and height $H$ in the light environment $E_a$ in a patch of age $a$ | ||
"$S_{\rm G} (x, H_0, E_{{\rm a}0})$",,Probability that a seed germinates successfully |
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Symbol,Unit,Description | ||
**Patch state variables**,, | ||
$K$,,Number of species in the metacommunity | ||
"$a, a^{\prime}$",yr,Patch age (time since disturbance) | ||
$a_0$,yr,Patch age when plant germinates | ||
$E_a$,,Profile of canopy openness within a patch of age $a$ | ||
$E_a(z)$,,Canopy openness at height $z$ within a patch of age $a$ | ||
**Plant state variables**,, | ||
$x$,,Vector of traits for a species | ||
$H$,m,Height of a plant | ||
$H_0(x)$,m,Height of a seedling with traits $x$ after germination | ||
$z$,m,Height in canopy | ||
$A_{\rm l}(H)$,m$^2$,Leaf area of a plant with height $H$ | ||
"$Q(z, H)$",,Fraction of leaf area above height $z$ for a plant with height $H$ | ||
**Abundance measures**,, | ||
$P(a)$,yr$^{-1}$,Frequency-density of patches of age $a$ | ||
$Y_{x}$,m$^{-2}$ yr$^{-1}$,Global birth rate for a species with traits $x$ | ||
"$N(H, x, a)$",m$^{-1}$ m$^{-2}$,Density of plants at height $H$ per unit ground area for given traits $x$ and patch age $a$ | ||
**Demographic rates**,, | ||
"$g(x, H, E_a)$",m yr$^{-1}$,Height growth rate of a plant with traits $x$ and height $H$ in the light environment $E_a$ in a patch of age $a$ | ||
"$f(x, H, E_a)$",yr$^{-1}$,Seed production rate of a plant with traits $x$ and height $H$ in the light environment $E_a$ in a patch of age $a$ | ||
"$d(x, H, E_a)$",yr$^{-1}$,Instantaneous mortality rate of a plant with traits $x$ and height $H$ in the light environment $E_a$ in a patch of age $a$ | ||
$d_{\rm P}(a)$,yr$^{-1}$,Instantaneous disturbance rate of a patch of age $a$ | ||
**Demographic outcomes**,, | ||
"$H(x, a_0, a)$",m,Height of a plant with traits $x$ in a patch of age $a$ having germinated at patch age $a_0$ | ||
$S_{\rm D}$,,Probability a seed survives dispersal | ||
"$S_{\rm G} (x, H_0, E_{{\rm a}0})$",,Probability the seed of a plant with traits $x$ germinates successfully at height $H_0$ in the light environment $E_{{\rm a}0}$ in a patch of age $a_0$ | ||
"$S_{\rm I} (x, a_0, a)$",,Probability a plant survives from patch age $a_0$ to patch age $a$ | ||
"$S_{\rm P} ( a_0, a)$",,Probability a patch remains undisturbed from patch age $a_0$ to patch age $a$ | ||
"$\tilde{R}(x, a_0, a)$",,Cumulative seed output for plants with traits $x$ from patch age $a_0$ to patch age $a$ | ||
"$R\left(x^\prime, x\right)$",,Basic reproduction ratio for a mutant plant with traits $x^\prime$ growing in a metapopulation of resident plants with traits $x$ | ||
**Miscellaneous constants**,, | ||
$k_{\rm I}$,,Light extinction coefficient | ||
$\bar{a}$,yr,Mean interval between patch disturbances |