Q1 What method should I use to estimate RGR? Q2 What statistical test should I use to test for differences in RGR? Q3 What is a simple parameter to express how variation in RGR at a growth-analytical level is brought about? Q4 What are reference values for growth parameters? Q5 How can I estimate RGR of Arabidopsis in a high-throughput manner? Q6 Do you have some exercises for RGR calculations?

Question 1: What method should I use to estimate RGR?

Question 2: What statistical test should I use to test for differences in RGR?

 A problem in the evaluation of RGR and NAR derived from a destructive growth analysis is that the plants measured at harvest 1 cannot be measured again at harvest 2. However, apart from an average RGR also some kind of variability around the mean has to be calculated before any test can be carried out. A simple solution is to pair plants of harvest 1 randomly with plants of harvest 2 and calculate a RGR and NAR for each pair. However, there is no justification for this approach. You may have paired the smallest plant of harvest 1 with the largest of harvest 2, thus overestimating variability. A statistically sound method for the classical approach has been described by Causton & Venus (1981), but this works for two harvests and two treatments only. In the functional approach, a 95% confidence interval is constructed around the computed curves for RGR, ULR and LAR. Rod Hunt from Sheffield has written a commercially available program for this analysis. If there is no overlap in the confidence intervals for two treatments, it is safe to conclude that they are significantly different. However, as a consequence of the method used, the 95% confidence intervals are small in the middle part of the curves and wide towards the outer sides. Most likely, you will find a significant difference in the middle part of the experiment, but non-significant differences at the beginning and the end. Clearly, such an approach is statistically sound, but does not bear any biological relevance. Moreover, one can only make pairwise contrasts, a statistically dangerous exercise. An alternative is to test differences in RGR with an Analysis of Variance, with ln-transformed dry weight as dependent variable, and Time (of harvest) and Treatment (or Species or Both) as independent variables. A difference in RGR will show up as a significant Time x Treatment interaction. Two remarks have to be made. First, an important requirement is that the design of your experiment is completely orthogonal. That is, you have to harvest the same number of plants for all treatments/species combinations throughout the experiment, preferably equally spaced in time. This is not easy, but remember that an orthogonal design is so powerful that it will be worth the effort anyway. Second, in the case of a large number of harvests, the interaction term may turn out to be non-significant, due to the large number of degrees of freedom. That is, the Sum of Squares of the interaction is rather large, but the Mean Square turns out to be small. This is a complication. Another complication is when harvests are not equally spaced in time. Both problems can be solved using orthogonal polynomials. Thus, the interaction SS can be factorized in a linear, a quadratic. etc., orthogonal polynomial, up to as high as the degrees of freedom for the interaction. Now, mostly, the polynomials with an order higher than 2 or 3 are not interesting and can be discarded as irrelevant fluctuations. Quite often it turns out that the linear and/or quadratic one, when considered separately from the rest, is highly significant, whereas the total interaction was not significant. Lies, damned lies and statistics! For more info see Poorter & Lewis (1986). An SPSS programme to break down the Treatment X Harvest interaction with orthogonal polynomials is:

Question 3: What is a simple parameter to express how variation in RGR at a growth-analytical level is brought about?

 A simple way to break down the RGR of a plant is by the technique of growth analysis. RGR can then be factorized into a ‘physiological’ (ULR) and a ‘morphological’ (LAR) component. LAR by itself is the product of the leaf area:leaf mass ratio (SLA) and the fraction of biomass allocated to leaves (LMF). It would be useful to have a simple parameter that tells us to what extent the variation in RGR between species (or treatments) is due to variation in any of these underlying parameters. One way would be to compute correlation coefficients between RGR on the one hand, and parameters like ULR and LAR on the other hand. A high correlation coefficient would imply that variation in RGR (in terms of deviation from the overall mean) scales well with variation in, say, deviations from the mean in ULR. The use of correlation coefficients has two drawbacks. First, in the case where only 2 species are analysed, the correlation coefficient will always be 1. Second, the correlation coefficient considers relative variation around the mean, but does not take into account the absolute size of the variation. That is, if RGR varies between 100 and 400 mg g-1 day-1 and ULR varies between 10 and 13 g m-2 day-1, correlation between RGR and ULR can be as high as when ULR varied between 10 and 40 g m-2 day-1. However, in the first case NAR would only marginally contribute to variation in RGR, whereas ULR would be the sole component responsible in the second case. To allow for this Poorter & Van der Werf (1998) introduce the ‘Growth Response Coefficient’ (GRC). They define GRCX as the proportional difference in a particular growth parameter X (ULR, LAR, SLA or LMF), scaled to the proportional difference in RGR. In formula: GRC will have a value of 1 if the increase in RGR is fully proportional to the change in X. A value of 0 indicates that the ‘change’ in RGR is not accompanied by any ‘change’ in X. Values below 0 and above 1 may occur also, for example if a higher RGR for a given species is accompanied by both a lower NAR and a more than proportionally higher LAR. How are GRCs calculated? In the case of two species A and B, each with a given RGR, ULR and LAR, calculation is as follows: If the growth analysis has been carried out well, and RGR really is close to the product of ULR and LAR, then the sum of GRCULR and GRCLAR is 1.0. In the case of a comparison with more than two species, GRCs are calculated as the slope of the regression line fitted through the the ln-transformed ULR or LAR values (dependent variable) and ln-transformed RGR values (indepedent variable). This slope is dimensionless. For more information see Poorter & Van der Werf (1998).

Question 4: What are reference values for growth parameters?

These values include observations for both tree seedlings and herbaceous species.

 RGR 20 - 350 mg g-1 day-1 ULR 2 - 25 g m-2 day-1 LAR 2 - 65 m2 kg-1 SLA 10 - 130 m2 kg-1 LMF 0.25 - 0.80 g g-1

Question 5: How can I estimate RGR of Arabidopsis in a high-throughput manner?

 A simple way to grow plants is to grow them in pots. However, for RGR measurements, and especially to break down RGR in components, it is imperative to know the biomass of the whole plant. For most plant species grown in pots this is already quite tedious, because you have to retrieve the roots from the soil, and for Arabidopsis, it is virtually ipossible as the roots are so thin. So life is much easier if plants are grown in hydroponics, because you can quickly remove the whole plant. Growth in hydroponics has many advantages, but it also this is not necessarily easy for Arabidopsis... So the alternative is to measure leaf area rather than total plant weight. Total area is easily estimated by a digital camera, and a program like ImageJ. When you do the leaf area measurements on different days, you can calculate RGR on a leaf area rather than a total plant weight basis. How different are these two variables? This simply depends on the change in LAR over time: when LAR remains constant than the leaf area:total plant weight ratio remains constant as well, and then RGR on a weight and leaf area basis are exactly the same. However, generally the LAR does not remain the same, but decreases with ontogeny. Fortunately, the change in LAR over time is in most cases not too large, so that the mistake you make is small. The advantage of this approach is that you assess growth non-destructively, so that you can follow growth of an individual over time, which makes the RGR measurement much more precise. The disadvantage is that you do not know anything anymore about the underlying parameters. Be aware that you cannot work with too large plants, as the total area of overlapping leaves will be underestimated in pictures taken from above. Moreover, make sure that you measure the plants each day at the same time, as leaf angle will change diurnally, and a higher leaf angle will result in a stronger underestimation of leaf area.

Question 6: Do you have some exercises for RGR calculations?

 You can download an Excel file with some exercises related to RGR by clicking HERE.