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Edited by: José M. Grünzweig, The Hebrew University of Jerusalem, Israel

Reviewed by: Heather R. McCarthy, University of Oklahoma, USA; Cyrille B. Rathgeber, Institut National de la Recherche Agronomique, France

*Correspondence: Hendrik Poorter, Plant Sciences (IBG-2), Forschungszentrum Jülich, 52425 Jülich, Germany. e-mail:

This article was submitted to Frontiers in Functional Plant Ecology, a specialty of Frontiers in Plant Science.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and subject to any copyright notices concerning any third-party graphics etc.

Plants can differentially allocate biomass to leaves, stems, roots, and reproduction, and follow ontogenetic trajectories that interact with the prevailing climate. Various methodological tools exist to analyze the resulting allocation patterns, based either on the calculation of biomass ratios or fractions of different organs at a given point in time, or on a so-called allometric analysis of biomass data sampled across species or over an experimental growth period. We discuss the weak and strong points of each of these methods. Although both approaches have useful features, we suggest that often a plot of biomass fractions against total plant size, either across species or in the comparison of treatment effects, combines the best of both worlds.

How plants partition newly fixed carbohydrates among organs and biochemical fractions is likely to be as important to whole plant performance and ecology as photosynthesis itself. Carbohydrates may be employed to fuel leaf respiration, or can be stored as starch or fructans for later use. Alternatively, they can be transported elsewhere in the plant to be used to promote vegetative growth, maintenance processes, and/or reproduction. Integrated over time, the partitioning of carbohydrates to the various processes culminates in a plant with a given size and a so-called “biomass allocation” pattern. Detailed discussions on the terminology of allocation patterns and processes can be found in Litton et al. (

As plants can invest most of their C only once, there are likely to be benefits and penalties under given sets of conditions for any specific distribution pattern of photosynthates to the various organs. The most effective biomass partitioning therefore depends on above- and below-ground resource availability. The investment pattern is thought to be optimal for resource foraging if all organs limit growth to the same extent (Bloom et al.,

Two classes of methods are in common use for analyzing biomass allocation patterns. The first class of methods, which we will denote as the “allocation approach,” employs biomass ratios, with the shoot:root ratio (S:R; Brouwer,

The second class of methods is based on fitting so-called allometric equations. In its most typical form, the scaling among organs (i.e., relationship between the absolute size of one organ as a function of the size of another) is described by a power law with two parameters:

With these two contrasting approaches available, it is important to know their weak and strong points for presenting and interpreting biomass allocation patterns. There have been several explicit statements in the literature pointing to the weak aspects of ratios, thereby promoting the allometric approach as superior (e.g., Jasienski and Bazzaz,

Evaluation of allocation patterns is often done for a given species treated with different levels of an environmental factor (e.g., Müller et al.,

The second dataset consists of leaf, stem, and root dry mass data for a diverse array of plant species of very different sizes and ages. This dataset consists of average values of harvests from a wide range of experiments, and, in the case of large trees, for plants harvested from plantations or other forest plots, with ∼5230 data entries for ∼250 herbaceous and ∼330 woody species. This database was previously used by Poorter et al. (

Ratios are often used in the literature to standardize biological data. They are flexible in that they can be applied to two variables, even when the variables have disparate units (Liermann et al.,

Possible pitfalls, disadvantages, and/or points requiring attention in the application of ratios such as S:R fall into two categories. First, there are some statistical issues:

By nature, ratios are non-normally distributed (Sokal and Rohlf, _{2} transformation on the two plants’ S:R values results in values of 1 and −1, with 0 as an average, and a back-transformed S:R of 1, which is the appropriate estimate of the average in this case.

Ratios such as S:R with values less than 1 are less easy to visualize and work with, and thus, depending on species and conditions, some studies present R:S rather than S:R values. Although both are equally valid in representing data, alternative use of these inversely related expressions becomes confusing when one tries to make generalizations across a body of literature, as a seemingly large increase in S:R from 2 to 3 is exactly equivalent to a R:S decrease from 0.50 to 0.33.

Variability in both the numerator and the denominator contribute to the total variance of a ratio (Sokal and Rohlf,

LM | SM | RM | TM | |
---|---|---|---|---|

LM | – | |||

SM | – | |||

RM | – | |||

TM | – | |||

LM | – | 0.94 | ||

SM | – | 0.93 | ||

RM | – | |||

TM | – | |||

LM | – | 0.68 | 0.71 | 0.70 |

SM | – | 0.93 | ||

RM | – | |||

TM | – |

The second group of issues relate principally to the biological interpretation:

Ratios can encapsulate only the two quantities from which they are calculated. Most plants have distinct leaf, stem, and root organs contrasting in their functions. When relying on one ratio, two of the organs have to be combined (such as leaves and stems in the S:R ratio, or one organ has to be neglected (such as in the leaf:root ratio). In all cases, the use of one ratio entails a loss of information about the actual allocation pattern in the plant. For example, Poorter et al. (

Ratios can be affected in various ways, as a shift in the ratio can be due to a change in the numerator or the denominator, or both. In the case of the experiment with

Ratios can be potentially misleading when plants of different sizes are compared (Packard and Boardman,

Some of the problems mentioned above can be avoided by using fractions or percentages rather than unbounded ratios. Fractions and percentages are omnipresent in many facets of social, financial, and political life, for good reason as they provide a very easily interpretable variable. The reason for that is that the component values always add up to 1.0 or 100, thereby providing an easy-to-understand scaling. In any framework based on the C-economy of plants, fractions are easy to apply and come close to completely summarizing how plants partition available photosynthates over the various organs. The use of fractions avoids some of the complications related to ratios. Specifically, fractions are not confined to representing only two of many components (see point

Statistical pitfalls, disadvantages, and/or points requiring attention in the application of fractions include:

Fractions are not normally distributed, although the distribution is far less skewed than in the case of ratios (see point

Biomass fractions have also been criticized, as the mass of the organ of interest influences both the numerator and denominator. Hence, numerator and denominator are not fully independent (Müller et al.,

Pitfalls and shortcomings of fractions related to the biological interpretation are partly overlapping with those mentioned for ratios.

It is unclear whether changes in fractions are more strongly influenced by changes in the numerator, the denominator, or both (see point

Fractions can be misleading for considering changes in biomass allocation in growth treatments, as this approach cannot tease apart baseline developmental changes during ontogeny from active reprogramming of biomass allocation in given treatments (see point

The main alternative to ratios and fractions is the analysis of allocation within an allometric framework. Time

Statistical pitfalls, disadvantages and/or points requiring attention in the application of allometry include:

As mentioned above, the analysis is typically carried out by fitting a straight line through the log-transformed data for organ mass values. Although plots of mass values of plant components may often be linear on a log–log scale, or at least appears so, careful consideration may reveal this is not always true (Causton and Venus,

Beyond the choice of the structural model (i.e., linear versus quadratic fit to the log–log data), different statistical tests for fitting that model to data may give different estimates of parameters such as the slope of the line (Niklas, ^{2} of the relationship is very high, either line-fitting method will produce similar parameters (McArdle,

A related, but little-discussed problem with the SMA-derived parameters may show up when various fitted allometries are combined algebraically, e.g., if leaf area is estimated from stem diameter based on algebraically determining a leaf area-stem diameter relationship from fitted allometries for leaf area versus plant height, and for plant height versus stem diameter. This estimation can be poor if based on SMA-derived allometric parameters, especially at lower ^{2}. The algebraically derived allometric slope will then deviate from the data (see Table

Partial or complete extrapolation of fitted trends can result in misleading analyses of treatment effects. As an example, Müller et al. (

In many cases in the literature, the conclusion of comparison of allometries for plants of given species grown in different treatments is that the differences in biomass allocation which were observed as S:R or LMF at a common point in time disappeared after allometric correction (e.g., Gunn et al.,

Issues related to the biological interpretation are the following:

Generally, the growth of different organs is very well coordinated (Brouwer,

As discussed above, the allometric slope β for log

It is very important to understand that a fitted allometry represents a central trend, and for log–log allometries, a high ^{2} can simply be caused by a wide range of size values, For example, McCarthy et al. (^{2} of the allometric relation represents the variation in biomass ^{2} of 0.97 indicates that on this scale with an 8-fold order of variation in magnitude, one is very well able to predict the average shoot mass if one knows the average root or total plant mass. In other words: plants with large leaf mass are very likely to have large stem and root mass, and plants with small leaf mass will also have small stem and root mass. However, the ^{2} value does not necessarily indicate the precision of the actual biomass ^{2} of 0.99 in the allometric plot of leaf mass versus plant size (Figure ^{2} of 0.71. The risk of misinterpretation of high correlations over large ranges of values is not limited to plant or animal sizes only. In the analysis of genome-wide correlations of RNA expression among treatments or genotypes, any random comparison will show correlation coefficients of 0.80 or higher (Giorgi et al.,

Another point of concern is that most allometric analyses stop at the point of statistical analysis showing the

Low-N | High-N | ||
---|---|---|---|

LMF (plants in 10–30 mg range) | 0.444 | 0.504 | *** |

No. of plants in 10–30 mg range | 30 | 20 | |

LMF (plants in 30–100 mg range) | 0.369 | 0.491 | *** |

No. of plants in 30–100 mg range | 73 | 31 | |

LMF (plants in 100–300 mg range) | 0.333 | 0.472 | *** |

No. of plants in 100–300 mg range | 48 | 48 | |

Log(α) | 0.077 | 0.059 | ns |

β | 0.811 | 0.945 | * |

If one were interested only in a correction for plant size for biomass allocation, presentation of the results is straight forward. But what if one would like to correct a range of very different variables for ontogeny? Following the same allometric methodology, for the analysis of leaf N concentration, one would plot total leaf N versus total leaf mass, for root C it would be total root C against root mass, and for photosynthesis it would be total carbon fixation against total leaf area. For other variables, such as δ^{13}C values, there is no obvious counter variable of choice. Presenting this variety of plots, all with different

Having discussed the potential pitfalls of the two main types of analysis, we next focus on two additional approaches that incorporate aspects of both biomass allocation fractions and allometry. As mentioned above, the allometric analysis offers the unique advantage that the exact relationship between two compartments can be analyzed, without interference from changes in other compartments. Thus, the allometric relationships provide clarity on the developmental coordination of the growth of different organs, and how this coordination is affected by treatments, or how it varies across species. However, in most ecophysiological research, it is not only the coordination of growth processes that is important, but also the actual values of LMF, SMF, and RMF

Plotting LMF directly against log-transformed total plant mass, as shown in Figure

We recommend that for studies emphasizing biomass allocation (and not the coordination of the growth of organs,

A further approach to analyzing allocation over time is a graphical analysis of how the mass of a particular organ changes when plotted against total plant mass (Huxley,

We described several ways to analyze biomass allocation, and their strengths and weaknesses. However, it is not possible to conclude which of these methods is best, as each has strengths and pitfalls, and the pertinent analysis will also depend on the specific question asked. Even in the case of one-harvest experiments, it is relevant to determine the biomass fractions, as such information is essential to understand the C-budget of such plants, of which LMF is a component. If information is desired on the impacts of treatments or the differences among species, independent from variation in plant size, then an analysis that corrects for size is necessary. This requires multiple harvest data, where analyses of graphs of biomass fractions over time and against plant size, as well as allometric plots will provide important insights. Of these three, we suggest that the plots of biomass fractions against plant size often provide the most direct and instructive information. Allometric plots may provide additional information on the coordination of growth processes, with both fractions and allometry subject to the assumptions and pitfalls described above.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The Supplementary Material for this article can be found online at

We thank Jacek Oleksyn for providing part of the data of Figure

_{2}environments: no evidence for optimal partitioning

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_{2}-enrichment?

_{2}, nutrients and water: a quantitative review