In his message dsouth@Forestry.Auburn.EDU (David South) writes: > Many forest researchers use mean relative growth rates as a method of > growth analysis. I contend that this is not a valid technique since in most > cases, the MRGR is a function of tree size. Usually the MRGR declines as > seedling size increases. Therefore, using this technique does not "eliminate > differences in growth rates due to seedling size." > Well, it does only in the sense that it scales growth to seedling size, but it does not compensate for effects of size on RGR. This does NOT invalidate mean RGR as a method of growth analysis, it invalidates the interpretations of the results obtained using this method that assume that mean RGR is independent of seedling size. In the very special case of small seedlings growing at an exponential rate the assumption is valid (see Ingestad's et al. many papers on controlled nutrition experiments using steady-state RGR). > I solicit replies from anyone who still believes that comparing > mean relative growth rates is a valid technique for comparing growth of > seedlings that differ in initial size. > It all depends on how you present your data, and what you conclude from it: if you use functional growth analysis and get estimates of RGR at different seedling sizes, or calculate mean MRGR for intervals between succesive harvests, then you can plot RGR vs seedling dry weight (or other measure of size). > In particular, I am looking for anyone who can demonstrate that > > (1) MRGR is independent of seedling size. > see Ingestad's work on seedlings growing exponentially. > or > > (2) When MRGR is a function of seedling size, any valid explanation > for why this method of growth analysis should be used when comparing > growth response to various treatments. > Umm... If the initial average size of seedlings in different treatments is the same, then it doesn't matter much whether you use mean RGR or logs of the final size in your statistical analysis (with initial size as a covariate if available). If the initial average size of the seedlings was significantly different when the treatments were applied then the experiment was not properly randomized, and any results obtained from it are biased... You do have to use a log transform to make the error ditribution of growth data approximate a Normal distribution. It is not valid to use ANOVA or other tests that assume normality of error distribution on "raw" growth data. > I do not accept "tradition" as a valid scientific justification for using > this method of growth analysis. Neither do I, but a clear distinction should be made between: 1) design of experiments 2) method of calculation 3) interpretation of the result of these calculations So as long as one knows the limitations and assumptions involved one can get a sound interpretation of the results. If one uses growth analysis (or statistics) as a magic black box, then it is very easy to missuse them. Growth analysis is a valid method of calculation, what it can tell about an experiment depends on how the experiment was designed. I hope this has made things a little clearer, or at least stimulates further discussion. > David South FAX: 205-844-1084 > School of Forestry Telephone: 205-844-1022 > Auburn University, AL 36849-5418 Email: dsouth@forestry.auburn.edu > USA Pedro Aphalo Finnish Forest Research Institute Sunenjoki Research Station SF-77600 SUONENJOKI FINLAND Internet: Pedro.Aphalo@metla.fi
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