Growth Analysis Calculators

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Growth analysis is the quantitative study of how plants accumulate biomass over time relative to their leaf area and resource use. Classic growth analysis uses destructive harvests at successive time points to calculate: relative growth rate (RGR = fractional biomass increase per day), net assimilation rate (NAR = biomass gain per unit leaf area per day), and leaf area ratio (LAR = leaf area per unit plant mass). The fundamental relationship: RGR = NAR × LAR. These indices reveal whether differences in growth between species or treatments come from photosynthetic efficiency (NAR) or leaf deployment (LAR).

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Key Growth Analysis Formulas

RGR = (ln W₂ − ln W₁) / (t₂ − t₁) (g g⁻¹ day⁻¹)

NAR = [(W₂−W₁)/(t₂−t₁)] × [ln(A₂/A₁)/(A₂−A₁)] (g m⁻² day⁻¹)

LAR = leaf area / total plant dry mass (m² g⁻¹)

RGR = NAR × LAR

Typical RGR Values

Fast-growing weeds: 0.20–0.40 g g⁻¹ d⁻¹. Crop plants: 0.10–0.25. Slow-growing stress-tolerators: < 0.05.

Crop Physiology Application

Crop growth rate (CGR) = RGR × biomass per area = NAR × LAI. Harvest index (HI) = economic yield / total biomass. Green Revolution increased HI (0.35→0.55 for wheat) by reducing stem allocation. Current research targets increasing total biomass (RGR) rather than HI (near biological ceiling).

Glossary

Relative Growth Rate (RGR)
(ln W₂ − ln W₁)/(t₂ − t₁) in g g⁻¹ day⁻¹; fractional biomass increase rate; RGR = NAR × LAR; fast-growing weeds 0.20–0.40; slow stress-tolerators < 0.05.
Net Assimilation Rate (NAR)
Dry mass gain per unit leaf area per day (g m⁻² day⁻¹); measures photosynthetic efficiency integrated over time; sun plants 5–15 g m⁻² day⁻¹; NAR × LAR = RGR.
Harvest Index (HI)
Economic yield / total above-ground biomass; modern wheat ≈ 0.50–0.55 (up from 0.35 before Green Revolution); near its biological ceiling; future yield gains depend on increasing total biomass.

Frequently Asked Questions

RGR = (ln W₂ − ln W₁) / (t₂ − t₁). Units: g g⁻¹ day⁻¹. It measures the fractional increase in plant dry mass per unit time — how fast the plant doubles its biomass. Example: dry mass increases from 0.5 g to 2.0 g in 7 days: RGR = (ln 2.0 − ln 0.5)/7 = (0.693 − (−0.693))/7 = 1.386/7 = 0.198 g g⁻¹ day⁻¹. Analogous to specific growth rate (μ) in microbiology and intrinsic rate of increase (r) in ecology.

RGR = NAR × LAR. NAR (net assimilation rate) = dry mass gain per unit leaf area per day — the photosynthetic efficiency. High NAR = leaves are efficient at converting light to biomass. LAR (leaf area ratio) = total leaf area per unit total plant mass — how much leaf is deployed per unit invested biomass. High LAR = plant has many thin light leaves. Ecological insight: fast-growing ruderal species achieve high RGR mainly through high LAR (many thin leaves per gram of biomass) rather than high NAR. Slow-growing stress-tolerators have low LAR but may have respectable NAR per unit leaf area.

NAR = [(W₂ − W₁)/(t₂ − t₁)] × [(ln A₂ − ln A₁)/(A₂ − A₁)]. The second factor corrects for changing leaf area during the interval. Units: g m⁻² day⁻¹. Typical values: sun plants in optimal conditions: 5–15 g m⁻² day⁻¹; shade plants: 1–5 g m⁻² day⁻¹. Requires measuring both dry mass (W) and leaf area (A) at each harvest. Can be combined with LAR: if W and A are both measured, calculate LAR = A/W, then NAR = RGR/LAR as a check.

In crop physiology: Crop growth rate (CGR) = NAR × LAI (leaf area index, the crop-level LAR). Rapid canopy closure → high LAI early in the season → high CGR → maximum yield potential. Harvest index (HI) = grain yield / total above-ground biomass. The Green Revolution (1960s–70s) increased wheat and rice yields primarily by increasing HI from ~0.35 to 0.50–0.55 through semi-dwarf varieties that invest less in straw and more in grain. Current research focuses on increasing total biomass accumulation (higher RGR through more radiation use efficiency) since HI is approaching its biological ceiling.