Danny Tholen, Laurentius A.C.J. Voesenek, and Hendrik Poorter. 2004. “Ethylene Insensitivity Does Not Increase Leaf Area or Relative Growth Rate in Arabidopsis, Nicotiana tabacum , and Petunia x hybrida .” Plant Physiology (134), 1803-1812.
Hunt et al. 2002. A Modern Tool for Classical Plant Growth Analysis. Annals of Botany 90, 485-488.
“ In many phenomena of nature we find processes in which the rate of change of some quantity is proportional to the quantity itself.”
“ It is clear that in the case of an ordinary plant the leaf area will increase as growth proceeds, and with increasing leaf area the rate of production of material by assimilation will also increase; this again will lead to still more rapid growth, and thus to a greater leaf area and a greater production of assimilating material, and so on.”
Blackman’s Equation “ Apart from any question of autocatalysis it is obvious that the increase in size of the assimilating surface of the young plant must constantly accelerate the rate of growth, and that the consideration of this acceleration is essential for the proper comparison of the final weight of different plants and of the same plants grown for different periods.” “ The rate of interest (r of the equation) is clearly a very important physiological constant. It represents the efficiency of the plant as a producer of new material, and gives a measure of the plant’s economy in working.” Blackman 1919
“ The growth of an annual plant, at least in its early stages, follows approximately the ‘compound interest law’ … The plant is continually unfolding its leaves and increasing its assimilating power. Successive increases in the weight of the plant cannot therefore be treated as a discontinuous geometric series, as if the new material (interest) were added at the end of daily or weekly periods.”
“ A small difference in the “efficiency indices” of two plants (resulting, for example, from a slightly greater rate of assimilation or a more economical distribution of material between leaves and axis) may lead to a large difference in final weight.”
“ It would be of great interest to determine to what these differences in efficiency are due. They may be the result of differences in the rate of assimilation per unit area of leaf surface, or differences in the rate of respiration, of differences in the thickness of the leaves, or of differences in the distribution of material to leaves on the one hand and to the axis on the other.
The larger the proportion of new material that the plant can utilize in leaf production the greater, other things being equal, should be its efficiency.”
“ The fall in efficiency after the first few weeks of growth may perhaps be correlated with the mechanical relations connected with larger size. A doubling of the leaf area would require a stem of more than twice the weight to attain equal strength.”
“ Different growth analyses can be carried out, depending on what is considered a key factor for growth (Lambers et al. 1989). Leaf area and net assimilation rate are most commonly treated as the “driving variables” … however, we can also consider the plant’s nutrient concentration and nutrient productivity …”
“ We first concentrate on the plant’s leaf area as the driving variable for the relative growth rate (RGR, the rate of increase in plant mass per unit of plant mass already present) (Evans 1972). According to this approach, RGR is factored into two components: the leaf area ratio (LAR), which is the amount of leaf area per unit total plant mass, and the net assimilation rate (NAR), which is the rate of increase in plant mass per unit leaf area …”
“ The NAR, which is the rate of dry mass gain per unit leaf area, is largely the net result of the rate of carbon gain in photosynthesis per unit leaf area (A) and that of carbon use in respiration of leaves, stems, and roots (LR, SR, and RR) which, in this case, is also expressed per unit leaf area. If these physiological processes are expressed in moles of carbon, the net balance of photosynthesis and respiration has to be divided by the carbon concentration of the newly formed material, [C], to obtain the increase in dry mass.”
“ Although the net assimilation rate is relatively easy to estimate from harvest data, it is not really an appropriate parameter to gain insight into the relation between physiology & growth. Rather, we should concentration on the underlying processes: photosynthesis, respiration, and allocation.”
“ In a broad comparison of herbaceous species, there is no clear trend of NAR with RGR. Rate of photosynthesis per unit leaf area also shows no correlation with RGR…
Slow-growing species, however, use relatively more of their carbon for respiration, especially in their roots, whereas fast-growing species invest a relatively greater proportion of assimilated carbon in new growth, especially leaf growth.”
“ Fast-growing species allocate relatively less to their stems, both in terms of biomass and N, when compared with slower-growing ones. Similarly, high-yielding crop varieties generally have a low allocation to stems (Evans 1980). A high allocation to stem growth reflects a diversion of resources from growth to storage…”
NAR Variation Lambers 2008 Next to the variation in LAR (SLA and LMR), this difference in the amount of carbon required for respiration is the second-most important factor that is associated with inherent variation in RGR.”
“ On two time points, leaf number, leaf area, and the dry and fresh mass of roots, stem and leaves of each plant were measured. From these measurements, the following growth parameters can be calculated. The net dry biomass increase per unit dry mass per day is the RGR (mg g -1 d -1 ). RGR was calculated using the classical approach (Hunt, 1982):
where M 1 and M 2 is the plant dry mass at time t 1 and t 2 , respectively. RGR can be factorized into three components (Evans, 1972).”
“ The first component is the leaf area per leaf dry mass or SLA (m 2 kg -1 ). The second is the fraction of total biomass allocated to the leaves or LMF (g g -1 ). The third is the increase of biomass per unit leaf area per day or ULR (g m -2 d -1 ). The formula for RGR then becomes:”
“ The third factor is the increase in biomass per unit leaf area per day and is called the unit leaf rate (ULR). ULR is driven by the carbon fixation in the process of photosynthesis. A part of the carbon fixated is respired by shoots and roots, providing energy for biosynthesis and maintenance; the remaining carbon being incorporated into the biomass of the plant.
In contrast with SLA, variation in ULR appears to be of minor importance for explaining differences in RGR between species.
It has been shown previously that a decrease of the ULR due to environmental factors such as low light or CO 2 levels can be compensated by an increase in SLA.”
ULR can also be calculated from measurements of gas exchange and carbon concentration:
Tholen 2004 The ULR depends on (1) photosynthesis per unit leaf area (PS A ; mol C fixed m -2 leaf area d -1 ); (2) fraction of daily fixed carbon that is not respired but incorporated into the biomass of a plant (FCI; mol C incorporated mol -1 C fixed); and (3) the amount of biomass that can be formed with 1 mol carbon, referred to by the carbon concentration ([C]; mol C g -1 dry mass).
“ The SLA is calculated as the leaf area divided by the leaf mass. The SLA is also the reciprocal product of leaf thickness (m) and leaf density (kg m -3 ). Leaf density is dependent on the amount of air space inside the leaf tissue (leaf porosity) and the amount of water per dry mass (leaf water content).”
“ Leaves vary in SLA, which affects the amount of photosynthetically active radiation captured per unit of mass. For example, a leaf with high SLA will capture more light per unit mass than a leaf with low SLA. Variation in SLA is of major importance when explaining differences between species in the increase of biomass per unit mass per day (relative growth rate [RGR]).”
“ A higher SLA can be the outcome of thinner leaves or leaves with a lower density.”
“ An alternative explanation for the observed differences in SLA is a difference in the amount or composition of cell wall material. Less deposition of secondary cell wall thickenings would lead to a lower leaf density.”
“ We found a negative relationship between ULR and SLA for all species … increased SLA may decrease nitrogen content and photosynthesis per unit area … Growing plants at low light also results in a higher SLA and a lower nitrogen content per unit leaf area.”
“ Up to 75% of the leaf organic nitrogen is present in the chloroplasts, most of it in the photosynthetic machinery. In a study comparing plants with different amounts of organic nitrogen content per area … higher SLA resulted in fewer photosynthetically active mesophyll cells per area.”
“ The purpose of our tool is to estimate all five parameters, including LAR, as mean values solely across one harvest-interval ( t 1 to t 2 ), with a standard error (s.e.) and 95% confidence limits attached to each estimate. The root-shoot allometric coefficient, and its s.e. and limits, are also derived for the same harvest-interval.”
RGR = LWF SLA x ULR x Hunt 2002
Simple Excel Worksheet “ The tool is liberally supplied with drop-down comments explaining and advising on each part of the procedure … In any or all of these dimensions, the units selected for the outputs may differ from those used for the inputs (the tool will perform the appropriate conversions).” Hunt 2002
“ Does it matter how far apart the harvests are spaced?
No … of course, the larger the time interval between harvests, the more the average values of the growth parameters will differ from the instantaneous values if the plants are not growing exponentially.”
“ Do there have to be equal numbers of plants at each harvest?
No, but sparse or unbalanced replication will adversely affect the statistical results.”
“ What are the lower and upper limits for numbers of replicate plants?
Two plants minimum per harvest; five plants minimum for both harvests combined (because the degrees of freedom for the allometric coefficient are n – 4); 100 plants maximum for both harvests combined.”
The tool will disregard any cases (i.e. rows or single plants) having one or more missing values (empty cells). Missing values will not be equated to zero. Cases can also be deleted temporarily to investigate the effect of eliminating potential data outliers.”
“ What if one whole variable is missing throughout?
Fill in this variable’s range with zeros. The calculations will process wherever possible, but will omit any parameters requiring the missing variable(s), e.g. without L A only RGR, LWF and the allometric coefficient will be calculated.”