How to Calculate the Relative Growth Rate of Plants
Understanding plant growth kinetics is fundamental for botany, agronomy, and crop science. Unlike simple absolute growth rate (which measures total gain per day), the Relative Growth Rate (RGR) measures the efficiency of the plant's growth relative to its existing size. It is the most widely used index for comparing growth potential between different species or treatments.
What is Relative Growth Rate (RGR)?
Relative Growth Rate represents the increase in plant mass per unit of mass present per unit of time. It acts like "compound interest" for plant biology. A high RGR indicates that a plant is rapidly investing its biomass into creating more biomass.
RGR is typically expressed in units such as g·g⁻¹·day⁻¹ (grams of new growth per gram of existing plant per day) or simply day⁻¹.
The RGR Formula
The calculation relies on the natural logarithm (ln) to account for the exponential nature of biological growth. The standard formula is:
Where:
- ln = Natural logarithm
- W₁ = Initial size (biomass, height, leaf area) at the start
- W₂ = Final size at the end of the period
- t₁ = Start time
- t₂ = End time
Example Calculation
Let's say you are measuring the dry weight of a corn seedling.
- On Day 1 (t₁), the dry weight is 0.5 grams (W₁).
- On Day 8 (t₂), the dry weight is 2.8 grams (W₂).
- The time interval is 8 – 1 = 7 days.
Using the calculator above:
- ln(2.8) ≈ 1.0296
- ln(0.5) ≈ -0.6931
- Difference: 1.0296 – (-0.6931) = 1.7227
- Divide by 7 days: 1.7227 / 7 = 0.246 g·g⁻¹·day⁻¹
Why is RGR Important?
1. Removing Size Bias: Larger plants naturally gain more absolute weight per day than smaller plants simply because they are bigger. RGR levels the playing field, allowing you to compare the physiological efficiency of a small seedling versus a larger plant.
2. Physiological Analysis: RGR can be broken down into two components: Net Assimilation Rate (NAR) and Leaf Area Ratio (LAR). This helps researchers understand if growth is driven by better photosynthesis or by leafier structure.
3. Stress Detection: A decline in RGR is often one of the first indicators of environmental stress (drought, salinity, nutrient deficiency) before visible symptoms appear.
Tips for Accurate Measurement
- Use Dry Weight: While height or fresh weight can be used, dry biomass is the gold standard because it represents actual carbon accumulation, excluding water fluctuations.
- Consistent Conditions: Ensure measurements W₁ and W₂ are taken at the same time of day to avoid diurnal variations in water content.
- Sample Size: Because measurement often involves destructive harvesting (drying the plant), ensure your sample size is large enough to represent the population statistically.