Relative Growth Rate (RGR) - Plant Physiology

1. Relative Growth RateRelative Growth Rate
Presentation by Zach Jarou Presentation by Zach Jarou

2. Literature ReviewedLiterature Reviewed
Blackman, V.H. 1919. The compound interest law and plant Blackman, V.H. 1919. The compound interest law and plant
growth. 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 edition, Second edition,
DOI: 10.1007/978-0-387-78341-3_7, © Springer DOI: 10.1007/978-0-387-78341-3_7, © Springer
Science+Business Media, LLC 2008Science+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 Increase Leaf Poorter. 2004. “Ethylene Insensitivity Does Not Increase Leaf
Area or Relative Growth Rate in Arabidopsis, Area or Relative Growth Rate in Arabidopsis, Nicotiana Nicotiana
tabacumtabacum, and, and Petunia x hybrida Petunia x hybrida.” .” Plant PhysiologyPlant Physiology (134), (134),
1803-1812.1803-1812.
Hunt et al. 2002. A Modern Tool for Classical Plant Growth Hunt et al. 2002. A Modern Tool for Classical Plant Growth
Analysis. Analysis. Annals of Botany Annals of Botany 90, 485-488.90, 485-488.

3. Cellular Basis of GrowthCellular Basis of Growth
““Growth is the increment in dry mass, volume, length, or Growth is the increment in dry mass, volume, length, or
area that results from the division, expansion, and area that results from the division, expansion, and
differentiation of cells.” 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 itself. however, and therefore does not drive growth itself.
Rather, it proves the structural framework for Rather, it proves the structural framework for
subsequent cell expansion (Green 1976).”subsequent cell expansion (Green 1976).”
““In addition, growth requires cell elongation and the In addition, growth requires cell elongation and the
deposition of mass in the cytoplasm and cell walls which deposition of mass in the cytoplasm and cell walls which
determine the increment in volume or mass.” determine the increment in volume or mass.”
Lambers 2008

4. Intro to Growth AnalysisIntro to Growth Analysis
““Plant growth analysis is an explanatory, holistic Plant growth analysis is an explanatory, holistic
and integrative approach to interpreting plant form and integrative approach to interpreting plant form
and function.” and function.”
““It uses simple primary data in the form of weights, It uses simple primary data in the form of weights,
areas, volumes and contents of plant components to areas, volumes and contents of plant components to
investigate processes within and involving the investigate processes within and involving the
whole plant.”whole plant.”
Hunt 2002

5. Keeping it in ContextKeeping it in Context
““Increment in dry mass may not, however, coincide with Increment in dry mass may not, however, coincide with
changes in each of these components of growth. changes in each of these components of growth.
For example, leaves often expand and roots elongate at For example, leaves often expand and roots elongate at
night, when the entire plant is decreasing in dry mass night, when the entire plant is decreasing in dry mass
because of carbon use in respiration. because of carbon use in respiration.
On the other hand, a tuber may gain dry mass with out On the other hand, a tuber may gain dry mass with out
concomitant change in volume, as starch accumulates.” concomitant change in volume, as starch accumulates.”
““Discussion of ‘growth’ therefore requires careful Discussion of ‘growth’ therefore requires careful
attention to context and the role of different processes at attention to context and the role of different processes at
different times.“different times.“
Lambers 2008

6. First ThoughtsFirst Thoughts
““In many phenomena of nature we find processes in In many phenomena of nature we find processes in
which the rate of change of some quantity is which the rate of change of some quantity is
proportional to the quantity itself.”proportional to the quantity itself.”
““It is clear that in the case of an ordinary plant the It is clear that in the case of an ordinary plant the
leaf area will increase as growth proceeds, and with leaf area will increase as growth proceeds, and with
increasing leaf area the rate of production of increasing leaf area the rate of production of
material by assimilation will also increase; this again material by assimilation will also increase; this again
will lead to still more rapid growth, and thus to a will lead to still more rapid growth, and thus to a
greater leaf area and a greater production of greater leaf area and a greater production of
assimilating material, and so on.”assimilating material, and so on.”
Blackman 1919

7. Blackman’s EquationBlackman’s Equation
 
W
1
=W
0
e
rt
“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

8. Blackman SummaryBlackman Summary
““The growth of an annual plant, at least in its early The growth of an annual plant, at least in its early
stages, follows approximately the ‘compound interest stages, follows approximately the ‘compound interest
law’ … The plant is continually unfolding its leaves and law’ … The plant is continually unfolding its leaves and
increasing its assimilating power. Successive increases in increasing its assimilating power. Successive increases in
the weight of the plant cannot therefore be treated as a the weight of the plant cannot therefore be treated as a
discontinuous geometric series, as if the new material discontinuous geometric series, as if the new material
(interest) were added at the end of daily or weekly (interest) were added at the end of daily or weekly
periods.”periods.”
““A small difference in the “efficiency indices” of two A small difference in the “efficiency indices” of two
plants (resulting, for example, from a slightly greater rate plants (resulting, for example, from a slightly greater rate
of assimilation or a more economical distribution of of assimilation or a more economical distribution of
material between leaves and axis) may lead to a large material between leaves and axis) may lead to a large
difference in final weight.” difference in final weight.”
Blackman 1919

9. Ultimate Dry Weight Ultimate Dry Weight
DeterminantsDeterminants
““In the case of an annual plant, the ultimate dry weight In the case of an annual plant, the ultimate dry weight
attained will depend on:attained will depend on:
(1) the weight of the seed, since that determines the size (1) the weight of the seed, since that determines the size
of the seedling at the time that accumulation of new of the seedling at the time that accumulation of new
material beginsmaterial begins
(2) on the rate at which the material present is employed (2) on the rate at which the material present is employed
to produce new material, i.e. the percentage increase of to produce new material, i.e. the percentage increase of
dry weight per day or week or other perioddry weight per day or week 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

10. Physiological Basis?Physiological Basis?
““It would be of great interest to determine to what these It would be of great interest to determine to what these
differences in efficiency are due. They may be the result of differences in efficiency are due. They may be the result of
differences in the rate of assimilation per unit area of leaf differences in the rate of assimilation per unit area of leaf
surface, or differences in the rate of respiration, of differences surface, or differences in the rate of respiration, of differences
in the thickness of the leaves, or of differences in the in the thickness of the leaves, or of differences in the
distribution of material to leaves on the one hand and to the distribution of material to leaves on the one hand and to the
axis on the other. axis on the other.
The larger the proportion of new material that the plant can The larger the proportion of new material that the plant can
utilize in leaf production the greater, other things being equal, utilize in leaf production the greater, other things being equal,
should be its efficiency.”should be its efficiency.”
 “ “The fall in efficiency after the first few weeks of growth may The fall in efficiency after the first few weeks of growth may
perhaps be correlated with the mechanical relations connected perhaps be correlated with the mechanical relations connected
with larger size. A doubling of the leaf area would require a with larger size. A doubling of the leaf area would require a
stem of more than twice the weight to attain equal strength.”stem of more than twice the weight to attain equal strength.”
Blackman 1919

11. Types of AnalysesTypes of Analyses
““Different growth analyses can be carried out, depending on Different growth analyses can be carried out, depending on
what is considered a key factor for growth (Lambers et al. what is considered a key factor for growth (Lambers et al.
1989). Leaf area and net assimilation rate are most commonly 1989). Leaf area and net assimilation rate are most commonly
treated as the “driving variables” … however, we can also treated as the “driving variables” … however, we can also
consider the plant’s nutrient concentration and nutrient consider the plant’s nutrient concentration and nutrient
productivity …”productivity …”
““We first concentrate on the plant’s leaf area as the driving We first concentrate on the plant’s leaf area as the driving
variable for the relative growth rate (RGR, the rate of increase variable for the relative growth rate (RGR, the rate of increase
in plant mass per unit of plant mass already present) (Evans in plant mass per unit of plant mass already present) (Evans
1972). According to this approach, RGR is factored into two 1972). According to this approach, RGR is factored into two
components: the leaf area ratio (LAR), which is the amount of components: the leaf area ratio (LAR), which is the amount of
leaf area per unit total plant mass, and the net assimilation rate 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 (NAR), which is the rate of increase in plant mass per unit leaf
area …”area …”
Lambers 2008
RGR = LAR x NAR

12. Types of AnalysesTypes of Analyses
Lambers 2008

13. LAR ComponentsLAR Components
 “ “LAR is the product of the LAR is the product of the
specific leaf area (SLA), which is the amount of leaf specific leaf area (SLA), which is the amount of leaf
area per unit leaf mass, and the area per unit leaf mass, and the
leaf mass ration (LMR), which is the fraction of the leaf mass ration (LMR), which is the fraction of the
total plant biomass allocated to leaves.”total plant biomass allocated to leaves.”
Lambers 2008
LAR = SLA x LMR

14. 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 use in photosynthesis per unit leaf area (A) and that of carbon use in
respiration of leaves, stems, and roots (LR, SR, and RR) which, respiration of leaves, stems, and roots (LR, SR, and RR) which,
in this case, is also expressed per unit leaf area. If these in this case, is also expressed per unit leaf area. If these
physiological processes are expressed in moles of carbon, the physiological processes are expressed in moles of carbon, the
net balance of photosynthesis and respiration has to be net balance of photosynthesis and respiration has to be
divided by the carbon concentration of the newly formed divided by the carbon concentration of the newly formed
material, [C], to obtain the increase in dry mass.”material, [C], to obtain the increase in dry mass.”
 
NAR=
A
a
-LR
a
-
SR´SMR
LAR
-
RR´RMR
LAR
[C]
Lambers 2008

15. Underlying ProcessesUnderlying Processes
““Although the net assimilation rate is relatively easy Although the net assimilation rate is relatively easy
to estimate from harvest data, it is not really an to estimate from harvest data, it is not really an
appropriate parameter to gain insight into the appropriate parameter to gain insight into the
relation between physiology & growth. Rather, we relation between physiology & growth. Rather, we
should concentration on the underlying processes: should concentration on the underlying processes:
photosynthesis, respiration, and allocation.”photosynthesis, respiration, and allocation.”
Lambers 2008

16. Underlying ProcessesUnderlying Processes
““Plant species characteristic of favorable environments Plant species characteristic of favorable environments
often have inherently higher maximum relative growth often have inherently higher maximum relative growth
rates (RGRrates (RGR
maxmax) than do species from less favorable ) than do species from less favorable
environments…environments…
High RGR could be associated with High RGR could be associated with
a high NAR (reflecting high photosynthesis and/or low a high NAR (reflecting high photosynthesis and/or low
whole-plant respiration)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 with a Which of these traits is most strongly correlated with a
high RGR?”high RGR?”

17. LAR Variation LAR Variation
(SLA & LMR)(SLA & LMR)
 “ “Low SLA values decrease the amount of leaf area available Low SLA values decrease the amount of leaf area available
for light interception and hence photosynthetic carbon gain, for light interception and hence photosynthetic carbon gain,
therefore reducing RGR.”therefore reducing RGR.”
““Numerous surveys of herbaceous CNumerous surveys of herbaceous C
33 species show significant species show significant
positive correlations of RGR with LAR, LMR, and SLA, but positive correlations of RGR with LAR, LMR, and SLA, but
not with NAR … not with NAR …
When comparing more productive cultivars of tree species When comparing more productive cultivars of tree species
with less productive ones, SLA, rather than photosynthesis, is with less productive ones, SLA, rather than photosynthesis, is
the main factor that accounts for variation in RGR (Ceulemans the main factor that accounts for variation in RGR (Ceulemans
1989). 1989).
In addition, leaf and twig architecture of the more productive In addition, leaf and twig architecture of the more productive
trees is such that more of the light is harvested throughout the trees is such that more of the light is harvested throughout the
entire day (Leverenz 1992).”entire day (Leverenz 1992).”
Lambers 2008

18. LAR VariationLAR Variation
Lambers 2008

19. NAR VariationNAR Variation
 “ “In a broad comparison of herbaceous species, there is no In a broad comparison of herbaceous species, there is no
clear trend of NAR with RGR. Rate of photosynthesis per unit clear trend of NAR with RGR. Rate of photosynthesis per unit
leaf area also shows no correlation with RGR… leaf area also shows no correlation with RGR…
Slow-growing species, however, use relatively more of their Slow-growing species, however, use relatively more of their
carbon for respiration, especially in their roots, whereas fast-carbon for respiration, especially in their roots, whereas fast-
growing species invest a relatively greater proportion of growing species invest a relatively greater proportion of
assimilated carbon in new growth, especially leaf growth.”assimilated carbon in new growth, especially leaf growth.”
 “ “Fast-growing species allocate relatively less to their stems, Fast-growing species allocate relatively less to their stems,
both in terms of biomass and N, when compared with slower-both in terms of biomass and N, when compared with slower-
growing ones. Similarly, high-yielding crop varieties generally growing ones. Similarly, high-yielding crop varieties generally
have a low allocation to stems (Evans 1980). A high allocation have a low allocation to stems (Evans 1980). A high allocation
to stem growth reflects a diversion of resources from growth to stem growth reflects a diversion of resources from growth
to storage…” to storage…”
Lambers 2008

20. 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.”

21. RGR 2.0 (Used as a Tool)RGR 2.0 (Used as a Tool)
““On two time points, leaf number, leaf area, and the dry and On two time points, leaf number, leaf area, and the dry and
fresh mass of roots, stem and leaves of each plant were fresh mass of roots, stem and leaves of each plant were
measured. From these measurements, the following growth measured. From these measurements, the following growth
parameters can be calculated. The net dry biomass increase parameters can be calculated. The net dry biomass increase
per unit dry mass per day is the RGR (mg gper unit dry mass per day is the RGR (mg g
-1 -1
dd
-1-1
). RGR was ). RGR was
calculated using the classical approach (Hunt, 1982):calculated using the classical approach (Hunt, 1982):
where where MM
1 1 and and MM
22 is the plant dry mass at time is the plant dry mass at time tt
11 and and tt
22, ,
respectively. RGR can be factorized into three components respectively. RGR can be factorized into three components
(Evans, 1972).” (Evans, 1972).”
 
RGR=
ln(M
2)-ln(M
1)
t
2-t
1
Tholen 2004

22. RGR 2.0RGR 2.0
““The first component is the leaf area per leaf dry The first component is the leaf area per leaf dry
mass or SLA (mmass or SLA (m
22
kg kg
-1-1
). The second is the fraction of ). The second is the fraction of
total biomass allocated to the leaves or LMF (g gtotal biomass allocated to the leaves or LMF (g g
-1-1
). ).
The third is the increase of biomass per unit leaf The third is the increase of biomass per unit leaf
area per day or ULR (g marea per day or ULR (g m
-2-2
d d
-1-1
). The formula for ). The formula for
RGR then becomes:” RGR then becomes:”
 
RGR=SLA´LMF´ULR
Tholen 2004

23. ULR replaces NARULR replaces NAR
““The third factor is the increase in biomass per unit leaf area 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 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 fixation in the process of photosynthesis. A part of
the carbon fixated is respired by shoots and roots, providing the carbon fixated is respired by shoots and roots, providing
energy for biosynthesis and maintenance; the remaining energy for biosynthesis and maintenance; the remaining
carbon being incorporated into the biomass of the plant. carbon being incorporated into the biomass of the plant.
In contrast with SLA, variation in ULR appears to be of minor In contrast with SLA, variation in ULR appears to be of minor
importance for explaining differences in RGR between species.importance for explaining differences in RGR between species.
It has been shown previously that a decrease of the ULR due It has been shown previously that a decrease of the ULR due
to environmental factors such as low light or COto environmental factors such as low light or CO
2 2 levels can be levels can be
compensated by an increase in SLA.”compensated by an increase in SLA.”
Tholen 2004

24. Calculating ULRCalculating ULR
ULR can be calculated from plant mass and leaf area ULR can be calculated from plant mass and leaf area
on two time points:on two time points:
 
ULR=
ln(A
2
)-ln(A
1
)
A
2
-A
1
´
M
2
-M
1
t
2
-t
1
Tholen 2004

25. Calculating ULRCalculating ULR
ULR can also be calculated from measurements of ULR can also be calculated from measurements of
gas exchange and carbon concentration:gas exchange and carbon concentration:
 
ULR=
PS
A
´FCI
[C]
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).

26. SLA RevistedSLA Revisted
““The SLA is calculated as the leaf area divided by the leaf mass. The SLA 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 is also the reciprocal product of leaf thickness (m) and leaf density (kg
mm
-3-3
). Leaf density is dependent on the amount of air space inside the leaf ). 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 tissue (leaf porosity) and the amount of water per dry mass (leaf water
content).” content).”
““Leaves vary in SLA, which affects the amount of photosynthetically Leaves vary in SLA, which affects the amount of photosynthetically
active radiation captured per unit of mass. For example, a leaf with high 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. SLA will capture more light per unit mass than a leaf with low SLA.
Variation in SLA is of major importance when explaining differences Variation in SLA is of major importance when explaining differences
between species in the increase of biomass per unit mass per day (relative between species in the increase of biomass per unit mass per day (relative
growth rate [RGR]).”growth rate [RGR]).”
““A higher SLA can be the outcome of thinner leaves or leaves with a A higher SLA can be the outcome of thinner leaves or leaves with a
lower density.”lower density.”
““An alternative explanation for the observed differences in SLA is a An alternative explanation for the observed differences in SLA is a
difference in the amount or composition of cell wall material. Less difference in the amount or composition of cell wall material. Less
deposition of secondary cell wall thickenings would lead to a lower leaf deposition of secondary cell wall thickenings would lead to a lower leaf
density.”density.”
Tholen 2004

27. 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 SLA Growing plants at low light also results in a higher SLA
and a lower nitrogen content per unit leaf area.” and a lower nitrogen content per unit leaf area.”
““Up to 75% of the leaf organic nitrogen is present in the Up to 75% of the leaf organic nitrogen is present in the
chloroplasts, most of it in the photosynthetic machinery. chloroplasts, most of it in the photosynthetic machinery.
In a study comparing plants with different amounts of In a study comparing plants with different amounts of
organic nitrogen content per area … higher SLA resulted organic nitrogen content per area … higher SLA resulted
in fewer photosynthetically active mesophyll cells per in fewer photosynthetically active mesophyll cells per
area.”area.”
Tholen 2004

28. 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 solely parameters, including LAR, as mean values solely
across one harvest-interval (across one harvest-interval (tt
11 to t to t
22), with a standard ), with a standard
error (s.e.) and 95% confidence limits attached to error (s.e.) and 95% confidence limits attached to
each estimate. The root-shoot allometric coefficient, each estimate. The root-shoot allometric coefficient,
and its s.e. and limits, are also derived for the same and its s.e. and limits, are also derived for the same
harvest-interval.”harvest-interval.”
 
1
W
æ
è
ç
ö
ø
÷
dW
dT
æ
è
ç
ö
ø
÷ =
1
L
A
æ
è
ç
ö
ø
÷
dW
dt
æ
è
ç
ö
ø
÷ ´
L
A
L
W
´
L
W
W
RGR = LWFSLA xULR x Hunt 2002

29. 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

30. 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 harvests, the No … of course, the larger the time interval between harvests, the
more the average values of the growth parameters will differ from the more the average values of the growth parameters will differ from the
instantaneous values if the plants are not growing exponentially.”instantaneous values if the plants are not growing exponentially.”
 “ “Do there have to be equal numbers of plants at each harvest? Do there have to be equal numbers of plants at each harvest?
No, but sparse or unbalanced replication will adversely affect the No, but sparse or unbalanced replication will adversely affect the
statistical results.” statistical results.”
““What are the lower and upper limits for numbers of replicate What are the lower and upper limits for numbers of replicate
plants? plants?
Two plants minimum per harvest; five plants minimum for both Two plants minimum per harvest; five plants minimum for both
harvests combined (because the degrees of freedom for the allometric harvests combined (because the degrees of freedom for the allometric
coefficient are coefficient are nn – 4); 100 plants maximum for both harvests – 4); 100 plants maximum for both harvests
combined.”combined.”
Hunt 2002

31. 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 plants) The tool will disregard any cases (i.e. rows or single plants)
having one or more missing values (empty cells). Missing having one or more missing values (empty cells). Missing
values will not be equated to zero. Cases can also be values will not be equated to zero. Cases can also be
deleted temporarily to investigate the effect of eliminating deleted temporarily to investigate the effect of eliminating
potential data outliers.”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 calculations will Fill in this variable’s range with zeros. The calculations will
process wherever possible, but will omit any parameters process wherever possible, but will omit any parameters
requiring the missing variable(s), e.g. without Lrequiring the missing variable(s), e.g. without L
AA only RGR, only RGR,
LWF and the allometric coefficient will be calculated.”LWF and the allometric coefficient will be calculated.”
Hunt 2002

32. Questions?Questions?