Relative growth rate (RGR) and other confounded variables: mathematical problems and biological solutions

Area of Science:

• Biology
• Ecology
• Plant Science

Background:

• Relative growth rate (RGR) is a widely used metric in biological studies.
• The calculation of RGR, especially in its logged form, involves non-independent variables, leading to potential 'spurious' correlations.
• RGR is mathematically linked to other growth components like net assimilation rate (NAR) and leaf mass ratio (LMR), precluding their independent analysis via standard regression.

Purpose of the Study:

• To address the mathematical limitations of Relative Growth Rate (RGR) in biological studies.
• To propose a new, robust metric for growth rate analysis that overcomes the issue of non-independent variables.
• To differentiate between true biological relationships and artifactual correlations in growth data.

Main Methods:

• Analysis of the mathematical properties of Relative Growth Rate (RGR).
• Introduction and definition of Inherent Growth Rate (IGR) as an alternative metric: IGR = lnΔM/lnM.
• Development of a randomization test for assessing statistical significance.

Main Results:

• Relative Growth Rate (RGR) is inherently dependent on starting organism size (M) and its components, leading to predetermined relationships.
• The proposed Inherent Growth Rate (IGR) is independent of initial size (M) within the same growth phase, offering a more reliable measure.
• Standardizing RGR by size (M) does not resolve the issue of non-independence.

Conclusions:

• The mathematical structure of RGR can create spurious correlations, masking true biological insights.
• Inherent Growth Rate (IGR) provides a statistically sound alternative for analyzing growth dynamics.
• While direct comparison of confounded variables is discouraged, specific statistical methods can reveal utility in certain comparative analyses.