(Upload on January 10 2019) [ 日本語 | English ]

## Growth (成長)

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

#### Plant growth

size increase by cell division and enlargement, including synthesis of new cellular material and organization of subcellular organelles
fresh weight
dry weight
volume
length
height
surface area

#### Absolute growth rate, AGR (絶対成長速度)

AGR = dY/dt ≈ (Y2 - Y1)/(t2 - t1)

dY: size
dt: time (e.g., year)
Y1 and Y2: size at t1 and t2, respectively
t1 and t2 time at 1 (beginning)and 2 (end), respectively

### 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)

##### 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 - x0)e-kt

k: proportionality constant (considered as efficiency coefficient)
t → ∞ → Y = M (M: maximum possible growth)

#### Issues on allometry

##### Sum is not the sum
Ex. considering two parts of biomass, e.g., stem (w1) and leaf (w2)

If w1 = aDb and w2 = cDd, then w1+2 = w1 + w2 = aDb + cDd
This equation is satisfied only when b = d [not realistic]

## Productive ecology (生産生態学)

#### 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 (純一時生産力)

= GPP - E or C lost via respiration (by plants) 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 (純生態系生産力)

= NPP - heterotrophic respiration

Net biome productivity, NBP (純バイオーム生産力)

= NEP - loss due to disturbances
☛ productivity of biome type

### Allometry (相対成長, アロメトリー)

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 = αxβ ⇒ logy = logα + βlogxY = βX + a (linear equation)

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

= dY/dX = dlogy/dlogx = (dy/y)/(dx/x) = (x/y)·(dy/dx)

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

##### 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 = (bβ)/sb, sb = s2·y·x·Σ(Xm)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 larger
Across 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