I thank Pedro Aphalo for replying to my statements regarding the invalid use of the MRGR technique. The following is my reply. (1) Pedro states that the MRGR techniqe does not compensate for effects of of size on MRGR. He states that this invalidates the interpretations of the results obtained using this method (when the researcher) assumes that mean RGR is independent of seedling size. I FULLY AGREE. MOST INTERPRETATIONS MADE FROM USING THE MRGR ARE INVALID BECAUSE MOST RESEARCHERS ASSUME THAT THE MRGR VALUES ARE INDEPENDENT OF SIZE. (2) Pedro states that "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)." OF COURSE THE MRGR WILL BE INDEPENDENT OF SEEDLING SIZE IN THOSE CASES WHERE THE RESEARCHER FORCES THE SEEDLINGS TO GROW WITH A STEADY-STATE MRGR. HOWEVER, MOST RESEARCHERS WHO USE THE MRGR TECHNIQUE AS AN AID IN GROWTH ANALYSIS DO NOT USE EXPONENTIAL FERTILIZATION TO FORCE THEIR SEEDLINGS INTO A FIXED EXPONENTIAL GROWTH CURVE. IF FACT, I WOULD ARGUE THAT INGESTAD USES MRGR AS A INDEPENDENT VARIABLE (TREATMENT) AND DOES NOT ANALYZE THE MRGR VALUES AS DEPENDENT VARIABLES. (3) Pedro stated that MRGR technique is a valid method when the X-axis is some measure of size (instead of time). I AGREE THAT CHANGING THE BASIS OF COMPARISON (X-AXIS) FROM THAT OF TIME TO THAT OF SIZE IS A VALID TECHNIQUE. THIS WOULD DO MUCH TO HELP REDUCE INVALID INTREPTATION OF THE DATA. WE HAVE USED SUCH A METHOD IN THE PAST (FOREST SCIENCE 37(2):655-668.) HOWEVER, I ARGUE THAT WHEN THE X-AXIS IS WEIGHT (SIZE), THERE IS NO NEED TO PLOT MRGR ON THE Y-AXIS, YOU CAN JUST PLOT ABSOLUTE GROWTH ON THE Y-AXIS. WHY PLOT (AG/W) AGAINST (W) WHEN YOU CAN PLOT (AG) AGAINST (W)? WHY HAVE W REPRESETED ON BOTH THE X AND Y AXIS? (4) Perhaps another question for Pedro is to provide a citation with all of the following: (a) MRGR was analyzed as a independent variable (b) time was plotted on the x-axis (c) intrepretations from the results were valid THANKS AGAIN PEDRO FOR YOUR REPLY The following is the original text. DAVID SOUTH > >> 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." PEDRO >> >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). DAVID SOUTH > >> 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. PEDRO >> >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). DAVID SOUTH > >> 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. >> PEDRO >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. > DAVID SOUTH >> 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 PEDRO > >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
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