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Abstract：
Relative growth rate (RGR) has a long history of use in biology. In its logged form, RGR = ln[(M + ΔM)/M], where M is size of the organism at the commencement of the study, and ΔM is new growth over time interval Δt. It illustrates the general problem of comparing non-independent (confounded) variables, e.g. (X + Y) vs. X. Thus, RGR depends on what starting M(X) is used even within the same growth phase. Equally, RGR lacks independence from its derived components, net assimilation rate (NAR) and leaf mass ratio (LMR), as RGR = NAR × LMR, so that they cannot legitimately be compared by standard regression or correlation analysis.
The mathematical properties of RGR exemplify the general problem of \'spurious\' correlations that compare expressions derived from various combinations of the same component terms X and Y. This is particularly acute when X >> Y, the variance of X or Y is large, or there is little range overlap of X and Y values among datasets being compared. Relationships (direction, curvilinearity) between such confounded variables are essentially predetermined and so should not be reported as if they are a finding of the study. Standardizing by M rather than time does not solve the problem. We propose the inherent growth rate (IGR), lnΔM/lnM, as a simple, robust alternative to RGR that is independent of M within the same growth phase.
Although the preferred alternative is to avoid the practice altogether, we discuss cases where comparing expressions with components in common may still have utility. These may provide insights if (1) the regression slope between pairs yields a new variable of biological interest, (2) the statistical significance of the relationship remains supported using suitable methods, such as our specially devised randomization test, or (3) multiple datasets are compared and found to be statistically different. Distinguishing true biological relationships from spurious ones, which arise from comparing non-independent expressions, is essential when dealing with derived variables associated with plant growth analyses.
The mathematical properties of RGR exemplify the general problem of \'spurious\' correlations that compare expressions derived from various combinations of the same component terms X and Y. This is particularly acute when X >> Y, the variance of X or Y is large, or there is little range overlap of X and Y values among datasets being compared. Relationships (direction, curvilinearity) between such confounded variables are essentially predetermined and so should not be reported as if they are a finding of the study. Standardizing by M rather than time does not solve the problem. We propose the inherent growth rate (IGR), lnΔM/lnM, as a simple, robust alternative to RGR that is independent of M within the same growth phase.
Although the preferred alternative is to avoid the practice altogether, we discuss cases where comparing expressions with components in common may still have utility. These may provide insights if (1) the regression slope between pairs yields a new variable of biological interest, (2) the statistical significance of the relationship remains supported using suitable methods, such as our specially devised randomization test, or (3) multiple datasets are compared and found to be statistically different. Distinguishing true biological relationships from spurious ones, which arise from comparing non-independent expressions, is essential when dealing with derived variables associated with plant growth analyses.
摘要：
背景：相对生长速率（RGR）在生物学中的使用历史悠久。在其记录的形式中，RGR=ln[(M+ΔM)/M]，其中M是研究开始时生物体的大小，ΔM是时间间隔Δt上的新增长。它说明了比较非独立(混淆)变量的一般问题，例如(X+Y)与X.因此，RGR取决于甚至在相同生长阶段内使用的起始M(X)。同样,RGR缺乏与其派生组件的独立性，净同化率(NAR)和叶片质量比(LMR)，作为RGR=NAR×LMR，因此，它们不能通过标准回归或相关分析进行合法比较。
结果：X或Y的方差很大，或者正在比较的数据集之间的X和Y值几乎没有范围重叠。关系(方向，此类混淆变量之间的曲线性）基本上是预先确定的，因此不应将其报告为研究发现。用M而不是时间来标准化并不能解决问题。我们提出了固有增长率(IGR)，lnΔM/lnM,作为一个简单的，在同一生长阶段独立于M的RGR的稳健替代方案。
结论：尽管首选的选择是完全避免这种做法，我们讨论了将表达式与通用组件进行比较可能仍然有用的情况。如果（1）配对之间的回归斜率产生新的生物学兴趣变量，这些可以提供见解，(2)使用合适的方法支持该关系的统计显著性，比如我们专门设计的随机化测试，或（3）多个数据集进行比较，发现有统计学差异。区分真实的生物关系和虚假的关系，它们来自比较非独立表达式，在处理与植物生长分析相关的派生变量时是必不可少的。
结果：X或Y的方差很大，或者正在比较的数据集之间的X和Y值几乎没有范围重叠。关系(方向，此类混淆变量之间的曲线性）基本上是预先确定的，因此不应将其报告为研究发现。用M而不是时间来标准化并不能解决问题。我们提出了固有增长率(IGR)，lnΔM/lnM,作为一个简单的，在同一生长阶段独立于M的RGR的稳健替代方案。
结论：尽管首选的选择是完全避免这种做法，我们讨论了将表达式与通用组件进行比较可能仍然有用的情况。如果（1）配对之间的回归斜率产生新的生物学兴趣变量，这些可以提供见解，(2)使用合适的方法支持该关系的统计显著性，比如我们专门设计的随机化测试，或（3）多个数据集进行比较，发现有统计学差异。区分真实的生物关系和虚假的关系，它们来自比较非独立表达式，在处理与植物生长分析相关的派生变量时是必不可少的。
