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Growth (成長)

Mount Usu / Sarobetsu post-mined peatland
From left: Crater basin in 1986 and 2006. Cottongrass / Daylily

[ photosynthesis | productivity | allometry | related to chemistry ]


Growth curve (成長曲線)

Growth analysis

Polynomial regression (Orloci & Kenkel 1987)
fw(T) = lnW = a + b1T + b2T2 ··· (1)
where W = the leaf area (LA) or sededling weight for a seed size class

T = the time at which the measurement is taken
a (constant) = the natural lograrithm of the initial leaf area or seedling weight
b1 and b2 (parameters) = related to the relative growth rate

Relative growth rate (RGR, f'w) of the leaf area and seedling weight ←
f'w(T) = dW/dt = b1 + b2T × 2 ··· (2)
here, b1: intercept of relative growth rate

b2: slope of the relative growth rate
b2 > 0: increase of RGR, b2 < 0: decrease of RGR

Tmax: relative growth rate = 0 (hypothesis)
Tmax = -b1/(2b2)
growth analysis

Productive ecology (生産生態学)

Productivity (生産力)

Gross primary productivity, GPP

= energy (or carbon) fixed via photosynthesis per unit time

Net primary productivity, NPP

= GPP - energy (or carbon) lost via respiration per unit time
= ΔB + L + G

ΔB = biomass change in the community between time 1 (t1) and time 2 (t2) = B2 - B1
L = biomass losses by death of plants or plant parts
G = biomass losses to consumer organisms

Net ecosystem productivity, NEP = NPP - heterotrophic respiration
Net biome productivity, NBP = NEP - loss due to disturbances

Allometry (相対成長, アロメトリー)

allometry = allo (different) + metric (measure)
isometry = iso (same) + metric (measure)
relationships between two growth parameters ← study to define the relationship between size and shape
y = αxβ ← logy = logα + βlogx

β: coefficient of relative growth (相対成長係数)
If this equation is found between the two parameters, we call that allometric relationship.

t = 0 ← α = y0/x0β
Differentiated by t
1/y·(dy/dt) = β·1/x·(dx/dt) (Huxley 1932)

Ex. Relative daiameter growth rate, RDGR (Harper 1977)
RDGR = (lnD2 - lnD1)/(t2 - t1)

D1, D2: diameters at time 1 and 2, respectively

(Huxley 1932)

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.

Ex. the relationships between surface area, volume and length