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Mount Usu / Sarobetsu post-mined peatland
From left: Crater basin in 1986 and 2006. Cottongrass / Daylily
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Plant growthsize increase by cell division and enlargement, including synthesis of new cellular material and organization of subcellular organellesMeasuring growthfresh weightdry weight volume length height surface area |
[ photosynthesis | productivity | allometry | related to chemistry ] Absolute growth rate, AGR (絶対成長速度)AGR = dY/dt ≈ (Y_{2} - Y_{1})/(t_{2} - t_{1})
dY: size |
Growth analysisPolynomial regression (Orloci & Kenkel 1987)f_{w}(T) = lnW = a + b_{1}T + b_{2}T^{2} … (1) where W = the leaf area (LA) or sededling weight for a seed size class
T = the time at which the measurement is taken f'_{w}(T) = dW/dt = b_{1} + b_{2}T × 2 … (2) here, b_{1}: intercept of relative growth rate
b_{2}: slope of the relative growth rate ∴ T_{max} = -b_{1}/(2b_{2}) Relative growth rate (相対成長率, RGR)1958 Iwaki (岩城): dW = F(a - r_{f}) - C·r_{c}
dW: increase in dry weight (per day) ☛ compare with relative growth rate (RGR) |
1960 Hogetsu et al.
RGR ≈ ΔW/W = (F·a - F·r_{f} - C·r_{c} - D)/(F + C) ∵ W = F + C RGR can be estimated by productivity analysis 1) Logistic growth= geometric growth or logarithmic growth(Mitscherlich 1909) a) Mitscherlich equation (ミチェーリッヒ式)dY/dt = k(M - x) ⇒ Y = M - (M - x_{0})e^{-kt}
k: proportionality constant (considered as efficiency coefficient) b) simple logistic equationIssues on allometrySum is not the sumEx. considering two parts of biomass, e.g., stem (w_{1}) and leaf (w_{2})
If w_{1} = aD^{b} and w_{2} = cD^{d}, then w_{1+2} = w_{1} + w_{2} = aD^{b} + cD^{d} |
Shape: an object encompasses all of its geometric properties except its size, position and orientation
Morphological integration: The covariation of morphological structures in an organism or of parts in a structure, which may reflect developmental or functional interactions among traits allometry = allo (different) + metric (measure)isometry = iso (same) + metric (measure) relationships between two (growth) parameters → study to define the relationship between size and shape (s.s.) The dependence of shape on size, often characterized by a regression of shape on size y = αx^{β} ⇒ logy = logα + βlogx → Y = βX + a (linear equation)
β: coefficient of relative growth (相対成長係数) = dY/dX = dlogy/dlogx = (dy/y)/(dx/x) = (x/y)·(dy/dx) t = 0 → α = y_{0}/x_{0}β |
Differentiated by t 1/y·(dy/dt) = β·1/x·(dx/dt) (Huxley 1932)
Ex. Relative daiameter growth rate, RDGR (Harper 1977) D_{1}, D_{2}: diameters at time 1 and 2, respectively Isometry (等成長, アイソメトリー)Geometrically similar objects exhibit what is called isometric scaling; the relationships between surface area, volume, and length≡ β = 1 or integer Ex. the relationships between surface area, volume and length t-test, t = (b – β)/sb, sb = s^{2}·y·x·Σ(X – m)^{2} (Rensch 1950) Rensch's rule (レンシュの法則)Rule in the relationship between the extent of sexual size dimorphism and which sex is largerAcross species within a lineage, size dimorphism increases with increasing body size when the male is the larger sex, and decreases with increasing average body size when the female is the larger sex |
Boysen-Jensen, Peter 1932 proposed the three concepts for modeling plant production - to explain the determinantgs on plant growth
gross production (Bruttoproduktion, 総生産), P_{g} Four factors influencing production
Atmosphere: light, temperature and atmospheric CO_{2} P_{g} - R_{l} - D_{l} = D_{n} + R_{n}
R_{l}: leaf respiration 1953 stratified-clipping (層別刈取) → biomass profile (生産構造図)
profile of light penetration into the ecosystem K: determined by three parameters, horizontal leaf distribution, light penetration rate on leaf (m) and slope angle of leaf (α) 1960 considering productivity in a dayq = (bI)/(1 + aI)
q: photosynthesis in leaves (/area/day) |
Productivity (生産力)Gross primary productivity, GPP (総一次生産力)= energy (E) or carbon (C) fixed via photosynthesis per unit time Net primary productivity, NPP (純一次生産力)
= GPP - E or C lost via respiration (by plants) per unit time
ΔB = biomass change in the community between time 1 (t_{1}) and time 2 (t_{2}) = B_{2} - B_{1} = NPP - heterotrophic respiration Net biome productivity, NBP (純バイオーム生産力)
= NEP - loss due to disturbances |