Relative Growth RateRelative Growth RatePresentation by Zach Jarou Presentation by Zach Jarou

Literature ReviewedLiterature Reviewed

Blackman, V.H. 1919. The compound interest law and Blackman, V.H. 1919. The compound interest law and plant growth. plant growth. Annals of Botany Annals of Botany 33, 353-360.33, 353-360.

H. Lambers et al., H. Lambers et al., Plant Physiological Ecology,Plant Physiological Ecology, Second Second edition, DOI: 10.1007/978-0-387-78341-3_7, © edition, DOI: 10.1007/978-0-387-78341-3_7, © Springer Science+Business Media, LLC 2008Springer Science+Business Media, LLC 2008

Danny Tholen, Laurentius A.C.J. Voesenek, and Hendrik Danny Tholen, Laurentius A.C.J. Voesenek, and Hendrik Poorter. 2004. “Ethylene Insensitivity Does Not Poorter. 2004. “Ethylene Insensitivity Does Not Increase Leaf Area or Relative Growth Rate in Increase Leaf Area or Relative Growth Rate in Arabidopsis, Arabidopsis, Nicotiana tabacumNicotiana tabacum, and, and Petunia x Petunia x hybridahybrida.” .” Plant PhysiologyPlant Physiology (134), 1803-1812. (134), 1803-1812.

Hunt et al. 2002. A Modern Tool for Classical Plant Hunt et al. 2002. A Modern Tool for Classical Plant Growth Analysis. Growth Analysis. Annals of Botany Annals of Botany 90, 485-488.90, 485-488.

Cellular Basis of GrowthCellular Basis of Growth

““Growth is the increment in dry mass, volume, Growth is the increment in dry mass, volume, length, or area that results from the division, length, or area that results from the division, expansion, and differentiation of cells.” expansion, and differentiation of cells.”

““Cell division cannot cause an increase in volume, Cell division cannot cause an increase in volume, however, and therefore does not drive growth however, and therefore does not drive growth itself. Rather, it proves the structural framework itself. Rather, it proves the structural framework for subsequent cell expansion (Green 1976).”for subsequent cell expansion (Green 1976).”

““In addition, growth requires cell elongation and In addition, growth requires cell elongation and the deposition of mass in the cytoplasm and cell the deposition of mass in the cytoplasm and cell walls which determine the increment in volume or walls which determine the increment in volume or mass.” mass.”

Lambers 2008

Intro to Growth AnalysisIntro to Growth Analysis

““Plant growth analysis is an explanatory, Plant growth analysis is an explanatory, holistic and integrative approach to holistic and integrative approach to interpreting plant form and function.” interpreting plant form and function.”

““It uses simple primary data in the form of It uses simple primary data in the form of weights, areas, volumes and contents of plant weights, areas, volumes and contents of plant components to investigate processes within components to investigate processes within and involving the whole plant.”and involving the whole plant.”

Hunt 2002

Keeping it in ContextKeeping it in Context

““Increment in dry mass may not, however, coincide Increment in dry mass may not, however, coincide with changes in each of these components of with changes in each of these components of growth. growth. For example, leaves often expand and roots elongate For example, leaves often expand and roots elongate

at night, when the entire plant is decreasing in dry at night, when the entire plant is decreasing in dry mass because of carbon use in respiration. mass because of carbon use in respiration.

On the other hand, a tuber may gain dry mass with On the other hand, a tuber may gain dry mass with out concomitant change in volume, as starch out concomitant change in volume, as starch accumulates.” accumulates.”

““Discussion of ‘growth’ therefore requires careful Discussion of ‘growth’ therefore requires careful attention to context and the role of different attention to context and the role of different processes at different times.“processes at different times.“

Lambers 2008

First ThoughtsFirst Thoughts

““In many phenomena of nature we find In many phenomena of nature we find processes in which the rate of change of some processes in which the rate of change of some quantity is proportional to the quantity itself.”quantity is proportional to the quantity itself.”

““It is clear that in the case of an ordinary plant It is clear that in the case of an ordinary plant the leaf area will increase as growth proceeds, the leaf area will increase as growth proceeds, and with increasing leaf area the rate of and with increasing leaf area the rate of production of material by assimilation will also production of material by assimilation will also increase; this again will lead to still more rapid increase; this again will lead to still more rapid growth, and thus to a greater leaf area and a growth, and thus to a greater leaf area and a greater production of assimilating material, and greater production of assimilating material, and so on.”so on.”

Blackman 1919

Blackman’s EquationBlackman’s Equation

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W1 =W0ert

“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

Blackman SummaryBlackman Summary

““The growth of an annual plant, at least in its The growth of an annual plant, at least in its early stages, follows approximately the early stages, follows approximately the ‘compound interest law’ … The plant is ‘compound interest law’ … The plant is continually unfolding its leaves and increasing its continually unfolding its leaves and increasing its assimilating power. Successive increases in the assimilating power. Successive increases in the weight of the plant cannot therefore be treated as weight of the plant cannot therefore be treated as a discontinuous geometric series, as if the new a discontinuous geometric series, as if the new material (interest) were added at the end of daily material (interest) were added at the end of daily or weekly periods.”or weekly periods.”

““A small difference in the “efficiency indices” of A small difference in the “efficiency indices” of two plants (resulting, for example, from a slightly two plants (resulting, for example, from a slightly greater rate of assimilation or a more economical greater rate of assimilation or a more economical distribution of material between leaves and axis) distribution of material between leaves and axis) may lead to a large difference in final weight.” may lead to a large difference in final weight.”

Blackman 1919

Ultimate Dry Weight Ultimate Dry Weight DeterminantsDeterminants

““In the case of an annual plant, the ultimate dry In the case of an annual plant, the ultimate dry weight attained will depend on:weight attained will depend on:

(1) the weight of the seed, since that determines (1) the weight of the seed, since that determines the size of the seedling at the time that the size of the seedling at the time that accumulation of new material beginsaccumulation of new material begins

(2) on the rate at which the material present is (2) on the rate at which the material present is employed to produce new material, i.e. the employed to produce new material, i.e. the percentage increase of dry weight per day or percentage increase of dry weight per day or week or other periodweek or other period

(3) the time during which the plant is increasing in (3) the time during which the plant is increasing in weight.”weight.”

Blackman 1919

Physiological Basis?Physiological Basis?

““It would be of great interest to determine to what It would be of great interest to determine to what these differences in efficiency are due. They may be these differences in efficiency are due. They may be the result of differences in the rate of assimilation per the result of differences in the rate of assimilation per unit area of leaf surface, or differences in the rate of unit area of leaf surface, or differences in the rate of respiration, of differences in the thickness of the respiration, of differences in the thickness of the leaves, or of differences in the distribution of material leaves, or of differences in the distribution of material to leaves on the one hand and to the axis on the other. to leaves on the one hand and to the axis on the other.

The larger the proportion of new material that the The larger the proportion of new material that the plant can utilize in leaf production the greater, other plant can utilize in leaf production the greater, other things being equal, should be its efficiency.”things being equal, should be its efficiency.”

“ “The fall in efficiency after the first few weeks of The fall in efficiency after the first few weeks of growth may perhaps be correlated with the growth may perhaps be correlated with the mechanical relations connected with larger size. A mechanical relations connected with larger size. A doubling of the leaf area would require a stem of more doubling of the leaf area would require a stem of more than twice the weight to attain equal strength.”than twice the weight to attain equal strength.”

Blackman 1919

Types of AnalysesTypes of Analyses

““Different growth analyses can be carried out, Different growth analyses can be carried out, depending on what is considered a key factor for depending on what is considered a key factor for growth (Lambers et al. 1989). Leaf area and net growth (Lambers et al. 1989). Leaf area and net assimilation rate are most commonly treated as the assimilation rate are most commonly treated as the “driving variables” … however, we can also consider “driving variables” … however, we can also consider the plant’s nutrient concentration and nutrient the plant’s nutrient concentration and nutrient productivity …”productivity …”

““We first concentrate on the plant’s leaf area as the We first concentrate on the plant’s leaf area as the driving variable for the relative growth rate (RGR, the driving variable for the relative growth rate (RGR, the rate of increase in plant mass per unit of plant mass rate of increase in plant mass per unit of plant mass already present) (Evans 1972). According to this already present) (Evans 1972). According to this approach, RGR is factored into two components: the approach, RGR is factored into two components: the leaf area ratio (LAR), which is the amount of leaf area leaf area ratio (LAR), which is the amount of leaf area per unit total plant mass, and the net assimilation rate per unit total plant mass, and the net assimilation rate (NAR), which is the rate of increase in plant mass per (NAR), which is the rate of increase in plant mass per unit leaf area …”unit leaf area …”

Lambers 2008RGR = LAR x NAR

Types of AnalysesTypes of Analyses

Lambers 2008

LAR ComponentsLAR Components

“ “LAR is the product of the LAR is the product of the specific leaf area (SLA), which is the amount of specific leaf area (SLA), which is the amount of

leaf area per unit leaf mass, and the leaf area per unit leaf mass, and the leaf mass ration (LMR), which is the fraction of leaf mass ration (LMR), which is the fraction of

the total plant biomass allocated to leaves.”the total plant biomass allocated to leaves.”

Lambers 2008

LAR = SLA x LMR

NAR ComponentsNAR Components

“ “The NAR, which is the rate of dry mass gain per unit leaf 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 area, is largely the net result of the rate of carbon gain in photosynthesis per unit leaf area (A) and that of carbon photosynthesis per unit leaf area (A) and that of carbon use in respiration of leaves, stems, and roots (LR, SR, and use in respiration of leaves, stems, and roots (LR, SR, and RR) which, in this case, is also expressed per unit leaf RR) which, in this case, is also expressed per unit leaf area. If these physiological processes are expressed in area. If these physiological processes are expressed in moles of carbon, the net balance of photosynthesis and moles of carbon, the net balance of photosynthesis and respiration has to be divided by the carbon concentration respiration has to be divided by the carbon concentration of the newly formed material, [C], to obtain the increase in of the newly formed material, [C], to obtain the increase in dry mass.”dry mass.”

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NAR =Aa − LRa −

SR× SMR

LAR−RR× RMR

LAR[C]

Lambers 2008

Underlying ProcessesUnderlying Processes

““Although the net assimilation rate is Although the net assimilation rate is relatively easy to estimate from harvest data, relatively easy to estimate from harvest data, it is not really an appropriate parameter to it is not really an appropriate parameter to gain insight into the relation between gain insight into the relation between physiology & growth. Rather, we should physiology & growth. Rather, we should concentration on the underlying processes: concentration on the underlying processes: photosynthesis, respiration, and allocation.”photosynthesis, respiration, and allocation.”

Lambers 2008

Underlying ProcessesUnderlying Processes

““Plant species characteristic of favorable Plant species characteristic of favorable environments often have inherently higher environments often have inherently higher maximum relative growth rates (RGRmaximum relative growth rates (RGRmaxmax) than do ) than do species from less favorable environments…species from less favorable environments…

High RGR could be associated with High RGR could be associated with a high NAR (reflecting high photosynthesis and/or a high NAR (reflecting high photosynthesis and/or

low whole-plant respiration)low whole-plant respiration) a high SLA (i.e., high leaf area per unit leaf mass)a high SLA (i.e., high leaf area per unit leaf mass) and/or a high LMR (high allocation to leaf mass).and/or a high LMR (high allocation to leaf mass).

Which of these traits is most strongly correlated Which of these traits is most strongly correlated with a high RGR?”with a high RGR?”

LAR Variation LAR Variation (SLA & LMR)(SLA & LMR)

“ “Low SLA values decrease the amount of leaf area Low SLA values decrease the amount of leaf area available for light interception and hence available for light interception and hence photosynthetic carbon gain, therefore reducing RGR.”photosynthetic carbon gain, therefore reducing RGR.”

““Numerous surveys of herbaceous CNumerous surveys of herbaceous C33 species show species show significant positive correlations of RGR with LAR, LMR, significant positive correlations of RGR with LAR, LMR, and SLA, but not with NAR … and SLA, but not with NAR …

When comparing more productive cultivars of tree When comparing more productive cultivars of tree species with less productive ones, SLA, rather than species with less productive ones, SLA, rather than photosynthesis, is the main factor that accounts for photosynthesis, is the main factor that accounts for variation in RGR (Ceulemans 1989). variation in RGR (Ceulemans 1989).

In addition, leaf and twig architecture of the more In addition, leaf and twig architecture of the more productive trees is such that more of the light is productive trees is such that more of the light is harvested throughout the entire day (Leverenz 1992).”harvested throughout the entire day (Leverenz 1992).”

Lambers 2008

LAR VariationLAR Variation

Lambers 2008

NAR VariationNAR Variation

“ “In a broad comparison of herbaceous species, there is In a broad comparison of herbaceous species, there is no clear trend of NAR with RGR. Rate of photosynthesis no clear trend of NAR with RGR. Rate of photosynthesis per unit leaf area also shows no correlation with RGR… per unit leaf area also shows no correlation with RGR…

Slow-growing species, however, use relatively more of Slow-growing species, however, use relatively more of their carbon for respiration, especially in their roots, their carbon for respiration, especially in their roots, whereas fast-growing species invest a relatively greater whereas fast-growing species invest a relatively greater proportion of assimilated carbon in new growth, proportion of assimilated carbon in new growth, especially leaf growth.”especially leaf growth.”

“ “Fast-growing species allocate relatively less to their Fast-growing species allocate relatively less to their stems, both in terms of biomass and N, when compared stems, both in terms of biomass and N, when compared with slower-growing ones. Similarly, high-yielding crop with slower-growing ones. Similarly, high-yielding crop varieties generally have a low allocation to stems (Evans varieties generally have a low allocation to stems (Evans 1980). A high allocation to stem growth reflects a 1980). A high allocation to stem growth reflects a diversion of resources from growth to storage…” diversion of resources from growth to storage…”

Lambers 2008

NAR VariationNAR 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.”

RGR 2.0 (Used as a RGR 2.0 (Used as a Tool)Tool)

““On two time points, leaf number, leaf area, and the On two time points, leaf number, leaf area, and the dry and fresh mass of roots, stem and leaves of each dry and fresh mass of roots, stem and leaves of each plant were measured. From these measurements, the plant were measured. From these measurements, the following growth parameters can be calculated. The following growth parameters can be calculated. The net dry biomass increase per unit dry mass per day is net dry biomass increase per unit dry mass per day is the RGR (mg gthe RGR (mg g-1 -1 dd-1-1). RGR was calculated using the ). RGR was calculated using the classical approach (Hunt, 1982):classical approach (Hunt, 1982):

where where MM1 1 and and MM22 is the plant dry mass at time is the plant dry mass at time tt11 and and tt22, , respectively. RGR can be factorized into three respectively. RGR can be factorized into three components (Evans, 1972).” components (Evans, 1972).”

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RGR =ln(M2 )− ln(M1)

t2 − t1

Tholen 2004

RGR 2.0RGR 2.0

““The first component is the leaf area per leaf The first component is the leaf area per leaf dry mass or SLA (mdry mass or SLA (m22 kg kg-1-1). The second is the ). The second is the fraction of total biomass allocated to the fraction of total biomass allocated to the leaves or LMF (g gleaves or LMF (g g-1-1). The third is the increase ). The third is the increase of biomass per unit leaf area per day or ULR of biomass per unit leaf area per day or ULR (g m(g m-2-2 d d-1-1). The formula for RGR then ). The formula for RGR then becomes:” becomes:”

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RGR = SLA× LMF×ULRTholen 2004

ULR replaces NARULR replaces NAR

““The third factor is the increase in biomass per unit The third factor is the increase in biomass per unit leaf area per day and is called the unit leaf rate (ULR). leaf area per day and is called the unit leaf rate (ULR). ULR is driven by the carbon fixation in the process of ULR is driven by the carbon fixation in the process of photosynthesis. A part of the carbon fixated is respired photosynthesis. A part of the carbon fixated is respired by shoots and roots, providing energy for biosynthesis by shoots and roots, providing energy for biosynthesis and maintenance; the remaining carbon being and maintenance; the remaining carbon being incorporated into the biomass of the plant. incorporated into the biomass of the plant.

In contrast with SLA, variation in ULR appears to be of In contrast with SLA, variation in ULR appears to be of minor importance for explaining differences in RGR minor importance for explaining differences in RGR between species.between species.

It has been shown previously that a decrease of the It has been shown previously that a decrease of the ULR due to environmental factors such as low light or ULR due to environmental factors such as low light or COCO2 2 levels can be compensated by an increase in SLA.”levels can be compensated by an increase in SLA.”

Tholen 2004

Calculating ULRCalculating ULR

ULR can be calculated from plant mass and ULR can be calculated from plant mass and leaf area on two time points:leaf area on two time points:

€

ULR =ln(A2 )− ln(A1)

A2 − A1

×M2 − M1

t2 − t1

Tholen 2004

Calculating ULRCalculating ULR

ULR can also be calculated from ULR can also be calculated from measurements of gas exchange and carbon measurements of gas exchange and carbon concentration:concentration:

€

ULR =PSA × FCI

[C]

Tholen 2004

The ULR depends on (1) photosynthesis per unit leaf area (PSA; 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).

SLA RevistedSLA Revisted

““The SLA is calculated as the leaf area divided by the leaf 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 The SLA is also the reciprocal product of leaf thickness (m) and leaf density (kg mleaf density (kg m-3-3). Leaf density is dependent on the amount of ). Leaf density is dependent on the amount of air space inside the leaf tissue (leaf porosity) and the amount of air space inside the leaf tissue (leaf porosity) and the amount of water per dry mass (leaf water content).” water per dry mass (leaf water content).”

““Leaves vary in SLA, which affects the amount of Leaves vary in SLA, which affects the amount of photosynthetically active radiation captured per unit of mass. photosynthetically active radiation captured per unit of mass. For example, a leaf with high SLA will capture more light per unit 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 mass than a leaf with low SLA. Variation in SLA is of major importance when explaining differences between species in the importance when explaining differences between species in the increase of biomass per unit mass per day (relative growth rate increase of biomass per unit mass per day (relative growth rate [RGR]).”[RGR]).”

““A higher SLA can be the outcome of thinner leaves or leaves A higher SLA can be the outcome of thinner leaves or leaves with a lower density.”with a lower density.”

““An alternative explanation for the observed differences in SLA An alternative explanation for the observed differences in SLA is a difference in the amount or composition of cell wall material. is a difference in the amount or composition of cell wall material. Less deposition of secondary cell wall thickenings would lead to Less deposition of secondary cell wall thickenings would lead to a lower leaf density.”a lower leaf density.”

Tholen 2004

SLA & ULRSLA & ULR

“ “We found a negative relationship between ULR and We found a negative relationship between ULR and SLA for all species … increased SLA may decrease SLA for all species … increased SLA may decrease nitrogen content and photosynthesis per unit area … nitrogen content and photosynthesis per unit area … Growing plants at low light also results in a higher Growing plants at low light also results in a higher SLA and a lower nitrogen content per unit leaf area.” SLA and a lower nitrogen content per unit leaf area.”

““Up to 75% of the leaf organic nitrogen is present in Up to 75% of the leaf organic nitrogen is present in the chloroplasts, most of it in the photosynthetic the chloroplasts, most of it in the photosynthetic machinery. In a study comparing plants with different machinery. In a study comparing plants with different amounts of organic nitrogen content per area … amounts of organic nitrogen content per area … higher SLA resulted in fewer photosynthetically higher SLA resulted in fewer photosynthetically active mesophyll cells per area.”active mesophyll cells per area.”

Tholen 2004

Growth Analysis ToolGrowth Analysis Tool

““The purpose of our tool is to estimate all five The purpose of our tool is to estimate all five parameters, including LAR, as mean values parameters, including LAR, as mean values solely across one harvest-interval (solely across one harvest-interval (tt11 to t to t22), ), with a standard error (s.e.) and 95% with a standard error (s.e.) and 95% confidence limits attached to each estimate. confidence limits attached to each estimate. The root-shoot allometric coefficient, and its The root-shoot allometric coefficient, and its s.e. and limits, are also derived for the same s.e. and limits, are also derived for the same harvest-interval.”harvest-interval.”

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1

W

⎛

⎝ ⎜

⎞

⎠ ⎟δW

δT

⎛

⎝ ⎜

⎞

⎠ ⎟=

1

LA

⎛

⎝ ⎜

⎞

⎠ ⎟δW

δt

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⎝ ⎜

⎞

⎠ ⎟×LALW

×LWW

RGR = LWFSLA xULR x Hunt 2002

Simple Excel WorksheetSimple 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

FAQsFAQs

““Does it matter how far apart the harvests are spaced?Does it matter how far apart the harvests are spaced? No … of course, the larger the time interval between No … of course, the larger the time interval between

harvests, the more the average values of the growth harvests, the more the average values of the growth parameters will differ from the instantaneous values if the parameters will differ from the instantaneous values if the plants are not growing exponentially.”plants are not growing exponentially.”

“ “Do there have to be equal numbers of plants at each Do there have to be equal numbers of plants at each harvest? harvest? No, but sparse or unbalanced replication will adversely affect No, but sparse or unbalanced replication will adversely affect

the statistical results.” the statistical results.”

““What are the lower and upper limits for numbers of What are the lower and upper limits for numbers of replicate plants? replicate plants? Two plants minimum per harvest; five plants minimum for Two plants minimum per harvest; five plants minimum for

both harvests combined (because the degrees of freedom for both harvests combined (because the degrees of freedom for the allometric coefficient are the allometric coefficient are nn – 4); 100 plants maximum for – 4); 100 plants maximum for both harvests combined.”both harvests combined.”

Hunt 2002

FAQsFAQs

“ “What if a variable contains missing values? What if a variable contains missing values? The tool will disregard any cases (i.e. rows or single The tool will disregard any cases (i.e. rows or single

plants) having one or more missing values (empty plants) having one or more missing values (empty cells). Missing values will not be equated to zero. cells). Missing values will not be equated to zero. Cases can also be deleted temporarily to investigate Cases can also be deleted temporarily to investigate the effect of eliminating potential data outliers.”the effect of eliminating potential data outliers.”

““What if one whole variable is missing throughout? What if one whole variable is missing throughout? Fill in this variable’s range with zeros. The Fill in this variable’s range with zeros. The

calculations will process wherever possible, but will calculations will process wherever possible, but will omit any parameters requiring the missing omit any parameters requiring the missing variable(s), e.g. without Lvariable(s), e.g. without LAA only RGR, LWF and the only RGR, LWF and the allometric coefficient will be calculated.”allometric coefficient will be calculated.”

Hunt 2002

Questions?Questions?