FEC507.fm Page 145 Monday, March 5, 2001 10:06 AM
Functional
Ecology 2001
15, 145 –154
ESSAY REVIEW
Oxford,
Functional
FEC
Blackwell
0269-8463
Woody
507
2000
15
L.
Blackwell
Sackseedling
&
UK
Science,
P.
Science,
Ecology
J. Grubb
relative
Ltd
Ltd growth rate rank changes
Graphicraft Limited, Hong Kong
000
Why do species of woody seedlings change rank in relative
growth rate between low and high irradiance?
L. SACK† and P. J. GRUBB
Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK
Functional Ecology (2001) 15, 145 –154
Introduction
It is often assumed that if a plant species has a higher
relative growth rate (RGR) than another species in
deep shade, it will have a lower RGR at high irradiance
(Spurr & Barnes 1980; Thomas & Bazzaz 1999; Walter
1973). In other words, species change rank (crossover)
between low and high irradiance. This idea was suggested
chiefly by the finding that in deep shade the massbased net photosynthetic rates of the leaves of shade
plants exceed those of sun plants, while at high
irradiance the reverse is true (Björkman & Holmgren
1963; Boardman 1977; Givnish 1988). This finding has
been assumed to scale up to the level of whole-plant RGR
(Shugart 1984). In the past decade, however, a contrary
view concerning RGRs has emerged, the idea that if a
plant grows faster than another at high irradiance it will
also do so in the shade (Kitajima 1994; Poorter 1999).
According to this later view, light plays a role in maintaining the mixture of forest species only through the
well established trade-off between survival rate in deep
shade and RGR in bright light (Kitajima 1994, 1996).
Similar experimental studies of RGR responses to
irradiance for woody seedlings report surprisingly different results. Here we indicate why such disparate results
have been produced. We provide a simple analytical
approach to understanding why crossovers should occur
among particular species at particular stages of ontogeny. This approach is useful for understanding the
maintenance of forest species richness, as well as for
interpreting plant specialization in physiology and
morphology to contrasting irradiance regimes.
Conflicts among studies
We reconsider here seven studies (Table 1) that focused
on the dry-mass RGRs of five to 15 species of woody
seedlings from temperate or tropical systems, at two or
more irradiances (comprising at least understorey
shade, i.e. ≈2% daylight, and tree-fall gap irradiance, i.e.
10 – 25% daylight); in each study the species spanned a
© 2001 British
Ecological Society
†Author to whom correspondence should be addressed.
Present address: Harvard University, Department of Organismic and Evolutionary Biology, Biological Laboratories, 16
Divinity Ave, Cambridge, MA 02138, USA.
wide spectrum of shade tolerance/light demand. The
results can be summarized by the correlation coefficients
of RGRgap and RGRunderstorey calculated from the final
harvests of all species in each study (Kitajima 1994).
The extreme opposite results are shown in Fig. 1: an
almost complete positive correlation (Kitajima 1994),
and a nearly significant negative one (Agyeman, Swaine
& Thompson 1999). While most studies show an overall positive correlation, its strength varies (Table 1, iii).
How do such different patterns arise from the same
type of experiment? We suggest that a major cause is
the different methods used to grow seedlings, and the
harvest intervals chosen. For instance, we suppose that
harvesting seedlings after a short time will produce
rank retentions that would not be found in longer
studies, and that do not represent the relative performances of seedlings during longer periods of growth in
the wild. For example, while a certain small-seeded,
light-demanding species may grow more quickly than
a certain large-seeded shade-tolerator, both in deep shade
and at high irradiance immediately after emergence,
we suggest that the advantage in deep shade may well be
temporary. After a year or two (assuming it survives), it
may well be outranked in the shade by the shade-tolerator.
This is expected from what is known of seedling physiology. The small-seeded seedling will have an initial
burst of relative growth consistent with its initially
very high specific leaf area ( lamina area/lamina dry
mass, SLA), which gives it a relatively high leaf area
ratio (lamina area / plant dry mass, LAR; Grubb 1998a;
Grubb et al. 1996; Marañón & Grubb 1993; Wright &
Westoby 1999). As a result, it will have the superior
RGR at both gap and understorey irradiances. However as the seedlings grow larger, differences among
species’ SLAs diminish (Grubb et al. 1996; Veneklaas
& Poorter 1998), lose their correlation with seed size
(Grubb et al. 1996), and cease to be the chief determinant of RGR (Grubb et al. 1996), a point further
explained in the following section.
Once other factors influence RGR, the large-seeded
shade-tolerator may outrank the small-seeded lightdemander at understorey irradiance, although not at
gap irradiance (indicated by the trends of RGR over
time in Walters, Kruger & Reich 1993). A longer study
will therefore produce more rank changes between gap
and understorey irradiance than a shorter study. We
145
(i) Number of
species and life
form at maturity
(RF = rainforest)
‘Understorey’
‘Gap’
15 tropical RF trees
2
6, 10, 28,
44, 66
10 tropical RF trees
≈1·6
≈4·1, ≈46
Five temperate trees
2
8
13 tropical RF trees
2
23
10 tropical RF trees†
2·5
10, 37
Nine temperate shrubs,
one temperate tree
0·3, 1·6
11, 63
15 tropical RF trees
3
(ii) Irradiance (% daylight)
6, 12, 25,
50, 100
(iii) General acrossspecies correlation
between RGRs at
irradiances shown in
bold in (ii)
Negative trend
r = – 0·46;
P = 0·082
No pattern*
r = 0·12;
P = 0·74
No pattern
r = – 0·17;
P = 0·79
Positive correlation
r = 0·94;
P < 0·001
Positive correlation
r = 0·85;
P = 0·002
Positive correlation
r = 0·91;
P < 0·001
Positive correlation
r = 0·82
P < 0·001
(iv) Percentage of
species pairs’ CPs
occurring between
2 and 10% daylight
68
36
50
12
22
11
26
(v) Species pairs’ CPIs
(% daylight): 1st quartile/
median /3rd quartile
(vi) Fit of L
vs. R line: r
and P value
2·1
3·9
6·2
1·8
4·7
14
1·3
2·5
4·2
− 0·88
− 0·38
0·69
− 0·04
6·8
20
− 0·44
r = − 0·96;
P < 0·001
1·6
Agyeman et al. (1999)
r = − 0·91;
P < 0·001
1·6
Popma & Bongers (1988)
r = – 0·98;
P = 0·005
1·2
Walters & Reich (1996)
r = 0·34;
P = 0·25
− 0·40
0·11
1·6
0·43
1·9
9·2
(vii) Regression
coefficient of
L vs. R line (α )
Author/s
Kitajima (1994)
r = − 0·58;
P = 0·078
1·4
Osunkoya et al. (1994)‡
r = − 0·24
0·17
Grubb et al. (1996)
1·1
Poorter (1999)
P = 0·50
r = − 0·83;
P < 0·001
RGR = Dry mass relative growth rate; CPs = crossover-points; CPIs = crossover-point irradiances. See text for definitions of dark loss rate (L) and responsiveness (R).
*Positive correlation results if Cecropia obtusifolia is excluded from the analysis; then r = 0·81, P = 0·008.
†12 tree species were grown in this study, but for two species no data were available at the irradiances considered, due to high seedling mortality.
‡RGRs were read from a graph for those values that conflicted with those recalculated from raw data.
FEC507.fm Page 146 Monday, March 5, 2001 10:06 AM
146
L. Sack &
P. J. Grubb
© 2001 British
Ecological Society,
Functional Ecology,
15, 145 –154
Table 1. Results of seven studies focusing on growth of woody seedlings at low and high irradiance. Relative growth rates (RGRs) were recalculated from raw data, when these were provided, for greater accuracy
than reading values from graphs
FEC507.fm Page 147 Monday, March 5, 2001 10:06 AM
Very frequently the fit is significant (P < 0·05), even
when only three data points are available. We are concerned here only with the range of irradiance over which
species show increasing RGRs, and therefore we exclude
growth data for photoinhibitory irradiances or limitation, by nitrogen for example (for these studies we
excluded data for irradiances above 23% daylight). As
data are scarce, methods of less than ideal exactitude
must suffice; we fitted the function to only two data
points when the absence of other data made this
necessary. While the logarithmic function is adequate,
other models such as the Michaelis–Menten function
may have advantages when more data are available (see
sapling studies below).
A major advantage of using a two-parameter function
such as the logarithmic is that we can easily estimate the
irradiance at which the crossover of any two species’
RGR functions occurs, the crossover point irradiance
(CPI):
147
Woody seedling
relative growth rate
rank changes
– (LspeciesA – LspeciesB) ⁄ (RspeciesA – RspeciesB)
CPI = e
Fig. 1. Plots of RGRgap vs. RGRunderstorey from two contrasting
studies: (a) a study showing a strong positive correlation
(data from Kitajima 1994); (b) one showing a negative trend
(data from Agyeman et al. 1999).
can test this idea with the data from the seven studies
reviewed here. First, however, we need to take a step
beyond the correlation analysis described above, and
for each study to consider the crossovers of the individual
species pairs.
Crossover-point patterns
For each study, we fitted for each species a line representing dry mass relative growth (in g g–1 week–1) as a
logarithmic function of irradiance (% daylight), using
ordinary linear regression:
RGR = R × ln (irradiance + 1) + L
© 2001 British
Ecological Society,
Functional Ecology,
15, 145 –154
eqn 1
where R, the slope of the line, represents responsiveness to irradiance, and L, the y intercept, represents
the theoretical dark loss rate, the negative RGR in
complete darkness. We note that fitting the logarithmic
model sometimes results in positive L values; this occurs
because in some studies data are scarce for RGRs at
very low irradiance, where species respond strongly to
irradiance. As L is purely theoretical, and as even positive
values can be usefully compared with other species’ L
values, we have included them in the analysis. Excluding
the species with positive L values does not alter the
findings of our analysis. All statistics were performed
using  for Windows Release 12.
–1
eqn 2
Equation 2 emphasizes that just as any two non-parallel
lines must cross, any two species’ RGR functions must
cross over. Therefore two species must switch rank at a
particular irradiance if their R values differ. When the
difference between two species’ R values is small, relative
to the difference between their L values, the CPI may
become wholly theoretical, occurring above 100% or
below 0% daylight. Otherwise the CPI is likely to occur
between 0 and 100% daylight. The CPI may be calculated
for each species pair; it then allows prediction of which
of the pair grows more quickly at any irradiance. The
estimated R and L values may be used to calculate the
difference between the species’ RGRs at any irradiance.
We emphasize that R and L values are statistical
quantities, and are subject to uncertainty – largely due
to intraspecific variability in RGR response. For this
reason, any study that quotes studies’ R and L values,
or the derived CPI values, should also provide standard
errors or confidence intervals (Sokal & Rohlf 1995). We
do not offer here the parameters for prediction for any
particular species or species pair. Below, when we refer
to a species’ R value (or L value), we mean a central
value for the species. In the following analysis of CPIs
we are chiefly interested in comparing trends across
studies; for the statistics we use (median and interquartile
range) the standard errors of individual species’ values
are not needed.
Once the CPIs are calculated for each species pair,
the percentage occurring between understorey and gap
irradiances can be determined (Table 1, iv). When a
species pair’s CPI falls within this range, a rank-reversal
between understorey and gap irradiance results. The
percentage of species pairs’ CPIs that occurs between
understorey and gap irradiance provides a more complete quantification of rank reversals for each study
than is possible in a plot of RGRgap vs. RGRunderstorey (of
the type shown in Fig. 1), or in considering correlation
FEC507.fm Page 148 Monday, March 5, 2001 10:06 AM
148
L. Sack &
P. J. Grubb
Table 2. Methodology of the seven studies the results of which are summarized in Table 1
Author(s)
Pretreatment; (weighted
mean duration, weeks)
Agyeman et al. (1999)
2–6 weeks in 15% daylight,
depending on species; (4*)
Popma & Bongers
(1988)
Grown in ‘moderate shade’
until two post-cotelydonous
leaves developed (exc. two
species, grown in sunny
greenhouse); (4*)
≈7 weeks in 20% daylight
None
4 weeks in 37% daylight
2 weeks in 60 – 70% daylight
5 species transplanted from
wild – these planted in 3% light
and ‘gradually moved to higher
irradiance levels’; 10 species grown
from seed; pretreatment depending
on species, 2–36 weeks (15)
Walters & Reich (1996)
Kitajima (1994)
Osunkoya et al. (1994)
Grubb et al. (1996)
Poorter (1999)
Experimental growth
period, weeks (weighted
mean duration, weeks)
Seedling growth period,
weeks (pretreatment
period + experimental
growth period)
‘not exceeding’ 16 weeks for
‘fast-growing species’; 23 weeks
for ‘slower-growing’ species; (21*)
≈14 –39 weeks, depending
on species; (32)
25
≈13
8
≈61
≈16
≈12 to ≈28; (23)
20
8
65
18
38
36
*Value approximate; not enough information available for a true weighted mean.
© 2001 British
Ecological Society,
Functional Ecology,
15, 145 –154
coefficients. Ultimately the information is the same:
>50% indicates the emergence of a negative correlation
across species between these irradiances, that is, the plot
beginning to slope negatively. This analysis again highlights the disparity among the studies: the percentage of
species pairs crossing over between gap and understorey
irradiance ranges from 11 to 68%.
Just as species’ RGR functions change during ontogeny,
species pairs’ CPIs will change with time. We predict
that they will often increase, at least for many of those
species pairs comprising a small-seeded light-demander
and a large-seeded shade-tolerator. As we suggested
earlier, when RGRs are determined primarily by seed
size (through SLA), the light-demander will grow more
quickly at both gap and understorey irradiances, and
so the species pair’s CPI will at this stage be very low,
well below understorey irradiance. However, as the seedsize effect diminishes, the shade-tolerator will often outperform the light-demander at understorey irradiance; the
CPI will hence increase to a value above that irradiance.
We can test this hypothesis with the seven studies’ data.
However, as the studies included different sets of species,
we cannot compare their species pairs’ CPIs directly;
instead we compare their CPI summary statistics. Most
useful here are the median and interquartile range of
the species pairs’ CPIs (Table 1, v). The variability of
the studies’ medians is apparent. For the two studies
showing strongest general rank retention (Grubb et al.
1996; Kitajima 1994), most of the species pairs’ crossovers occur at <2% daylight; the other studies show a
range of higher median values. The studies used various
pretreatments and growth periods (Table 2). Confirming
our hypothesis, the range of CPI medians reflects the
range of seedling growth periods; for the seven studies,
Fig. 2. Median species pair crossover-point irradiance (CPI)
vs. seedling growth period (pretreatment + experimental
growth period) for the seven studies in Table 1.
median CPI is correlated strongly to experimental
duration (Fig. 2; r 2 = 0·73; P = 0·014). The longer the
study, the greater the irradiance at which its species tend
to change rank. The dispersion of the species pairs’ CPIs
also increases: studies’ interquartile ranges increase
linearly with seedling age (r 2 = 0·92; P < 0·001).
We note that the results of two other studies of species’
dry mass RGRs across irradiances (Boot 1996; Reich
et al. 1998a) are consistent with these trends: including
points for these species gives for the first trend r2 =
0·73 (P = 0·002), and for the second trend r2 = 0·90
(P < 0·001). We did not include these studies in the full
analysis because they did not match the criteria met
by the other seven studies – one covered too few species
(Boot 1996), and for the other the lowest irradiance
used was 5% daylight (Reich et al. 1998a).
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Woody seedling
relative growth rate
rank changes
The trends described above ensure that short studies
of species that vary in seed size produce low CPIs (<2%
daylight), with minimal scatter, while longer studies
produce crossover points scattering widely, with their
medians occurring between gap and understorey
irradiances. Most of the studies were long enough to
result in >20% of the crossover points occurring between
gap and understorey irradiance. This finding illustrates
the principle that very short studies do not adequately
represent the processes of long-term natural establishment, unless one can competently scale up. The finding
that median CPI increases stably with time suggests that
scaling up is possible.
This analysis is only roughly quantitative; we compare
studies of different species, grown in different locations,
in different ambient conditions. Further, many of the
studies used imperfect methodologies, including
problematic calculations of RGRs (e.g. weighing for
‘initial biomass’ of the ungerminated embryo-cumendosperm, or weighing young seedlings after removal
of cotyledons or still-attached seeds), pretreating
species differently, growing species for different lengths
of time and / or in differently sized pots, and fertilizing
and watering on an ad hoc basis. These are confounding influences, and future experiments will presumably
achieve greater rigour. The robust and systematic trends
we demonstrate suggest that once such rigour is achieved
in several long, multiple-harvest experiments on identical
groups of species, quantitative trends may emerge which
will allow prediction of rank reversals and rank retentions over different growth periods.
Morphological and physiological basis
© 2001 British
Ecological Society,
Functional Ecology,
15, 145 –154
Why should so many species pairs’ CPIs increase as
seedlings mature? We have suggested that seed size is a
major factor. Because most researchers select mainly
small-seeded light-demanders and large-seeded shadetolerators, this effect is common. For light-demanders
and shade-tolerators of similar seed size, we might
expect a smaller CPI shift. The importance of such
seed size effects on CPI shifts in nature requires study.
While seed size correlates strongly with shade tolerance
for certain species sets, for others there is only a weak
correlation, or none, as light demand is only one of a
host of potentially strong evolutionary influences on seed
traits (Grubb 1996; Grubb 1998b; Grubb & Metcalfe
1996). A completely different reason for the CPI shift
may be the fact that plants become increasingly potbound, chiefly due to increasing nutrient limitation
(cf. Ingestad 1982), but perhaps also to space limitation
(Cresswell & Causton 1988; McConnaughay & Bazzaz
1992). This issue also requires study.
Leaving such questions aside for the moment, we
can use the parameters of the species’ RGR to further
investigate the CPI shift. As described earlier, L and R
determine each species pair’s CPI by equation 2. We
ask to what degree this equation constrains the possible
CPI: is there a general relationship between L and R?
Fig. 3. L vs. R plot for the species in a single study (data from
Agyeman et al. 1999).
Classical theory suggests a negative correlation. For
leaves, mass-based dark respiration rate is positively
correlated across species with light compensation point
and maximum mass-based photosynthetic rate (Givnish
1988). If modelled logarithmically, this relation becomes
a negative L- vs. R-type correlation (with dark respiration
rate analogous to – L, and photosynthetic rate analogous to RGR). For whole plants, a species’ R value will
be determined not only by photosynthetic responsiveness, but also by morphology; and a species’ L value
will reflect not only dark respiration rate but also loss
of parts. Remarkably, there is a significant whole-plant
L vs. R correlation for four of the seven studies at
P < 0·05, and for a fifth at P = 0·078 ( Table 1, vi; Fig. 3).
The slopes of regression for each study vary greatly
(Table 1, vii); as expected (Sokal & Rohlf 1995) the
two studies with shallowest L vs. R slopes show no
correlation.
The L vs. R trade-off described is a new example of
a quantifiable trade-off between resource acquisitiveness and retentiveness (cf. Grime 1974). Mechanistically,
the species that increase their RGR most when given a
larger resource supply often pay a price in high respiration rate (Reich et al. 1998a; Reich et al. 1998b) and/
or short-lived parts (Walters & Reich 1999). The tradeoff has further relevance as a tool for investigating the
physiological and morphological bases for species pairs’
crossovers.
Firstly, for most studies the tightness of the line’s fit
(Figure 3) means that we can predict each species’ L
value from its R value from the regression:
L = −α R + β + ε i
eqn 3
where εi represents the error, the deviation of species i’s
L value from that predicted by the line. This equation
must constrain the CPI for each species pair, as it correlates
L and R, the parameters used for the CPI calculation.
The variation among the studies’ L vs. R slopes (α ;
Table 1, vii) indicates that a separate equation holds
for each study; therefore, a study’s α value can play a
major role in determining the CPI values of its species
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L. Sack &
P. J. Grubb
pairs. This is clarified if equation 3 is substituted into
equation 2:
α
– (εspeciesA – εspeciesB) ⁄ (RspeciesA – RspeciesB)
CPI = e ⁄ e
© 2001 British
Ecological Society,
Functional Ecology,
15, 145 –154
– 1 eqn 4
If there were no scatter about a study’s L vs. R regression
(and therefore for each species pair εspeciesA = εspeciesB = 0),
all the species’ RGR functions would cross over at eα – 1,
that is, the steeper the slope of the study’s L vs. R line, the
higher will be the study’s median CPI (studies’ median
CPIs and α values are positively correlated, r = 0·84,
P = 0·018).
That α should vary with median CPI across the
studies is not surprising. As we have seen, the studies
span a range of seedling growth periods: the enormous
differences in morphology among a group of young
seedlings of species originating from a wide range of seed
sizes, and the rapid changes in morphology of each
species during early ontogeny, will affect the slope of
the L vs. R line. Elucidation of the precise effects will
require explicit investigation; however, we suggest that
initially small α values can arise from the coincidence
of initially high SLA values for small-seeded lightdemanders and initially low SLA values for large-seeded
(epigeal) shade-tolerators, as described above. Because
of the morphological differences among seedlings, species
differing slightly in L may differ hugely in R during
early establishment.
For instance, suppose that during early establishment
one species has a marginally more negative L than
another, and therefore a marginally stronger irradiance
response, as a result of its gas-exchange properties. If
this species also has smaller seeds than the other (i.e. it
is a small-seeded light-demander), and so a higher
LAR, it can have a dramatically larger R (as R is related
both inversely to L, for physiological reasons, and positively to LAR). This ensures a shallow L vs. R slope
(Fig. 4a). The species with the more negative L may,
however, have larger seeds, and therefore have the lower
initial LAR (for instance, if it is a larger-seeded lightdemander). If this is the case, the species with the more
negative L may also have the smaller R. Such a plant
will produce scatter about the study’s L vs. R line,
weakening the slope further.
A shallow slope may also result when the shadetolerators are hypogeal species (i.e. their cotyledons
remain in the seed coat). Such species will probably take
longer than epigeal species to reach the stage of positive
RGR (Grubb 1998a). Hypogeal shade-tolerators in
the understorey will take a long time to catch up with
small-seeded epigeal light-demanders in dry mass and
leaf area: in effect, their LAR will remain zero for a
longer period. As a result, R is very small. This is another
mechanism by which two species differing marginally
in L can differ hugely in R (Fig. 4a).
At a given irradiance, the species’ LARs become more
uniform during growth (Grubb et al. 1996; Veneklaas
& Poorter 1998), and acclimate across irradiances
( Veneklaas & Poorter 1998). If we consider a group
Fig. 4. Schematic representation of the steepening of α, the
slope of the loss rate (L) vs. responsiveness (R) regression,
during early growth, from (a) to (b).
of species varying widely in seed size, as do the seven
studies, we are likely to find that over time the effect of
the impressive, initial divergence of the species’ LARs
at each irradiance will become weakened by species
differences in other traits that affect onward growth.
Morphology now confounds the L vs. R relationship
much less, and the L vs. R slope will steepen (α will
increase) (Fig. 4b).
From this stage on, possible major determinants of
species ranking in RGR include, in addition to LAR,
respiratory costs and leaf lifetime (especially in deep
shade; Agyeman et al. 1999; Seiwa & Kikuzawa 1991;
Walters & Reich 1999); net photosynthetic rates (StraussDebenedetti & Bazzaz 1996; Walters & Reich 2000a; but
see Beaudet et al. 2000); and whole-plant architecture
(King 1991; Kohyama & Grubb 1994; Kohyama & Hotta
1990). All these traits influence the unit leaf rate (dry
mass gain per lamina area, ULR), which is the other
component of RGR besides LAR (RGR = LAR × ULR;
Evans 1972). At high irradiance the fastest-growing
species will be those with highest ULRs and LARs. At
low irradiance the species’ ULRs, and not their LAR
values, often determine their relative performances
(Agyeman et al. 1999; Osunkoya et al. 1994; Popma &
Bongers 1988). In fact, at low irradiance LAR may show
a weak negative correlation with RGR (Agyeman et al.
1999; Popma & Bongers 1988), as it is those species
with highest LAR values (the light-demanders) that
eventually tend to have the lowest ULRs in the shade,
due to high respiratory costs and short leaf lifetimes
(Walters & Reich 1999).
These effects indicate the non-generality of the paradigm asserted by Veneklaas & Poorter (1998), that LAR
determines RGR differences at low irradiance, while
ULR determines differences at high irradiance. Such a
paradigm does not apply to very young seedlings, whose
RGR ranking at both low and high irradiance is determined by seed size-linked differences in SLA and
therefore LAR, as found by Kitajima (1994). The leaf
mass fraction (LMF), the other component of LAR,
generally does not drive RGR in young seedlings of
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Woody seedling
relative growth rate
rank changes
Table 3. Percentage (and proportion) of species pairs’ crossover points occurring between understorey and single treefall gap
conditions (2% and 10% daylight) in five studies
Percentage of species pairs’ CPs occurring between 2% and
10% daylight
Number of species and
life form at maturity
15 tropical rainforest trees
10 tropical rainforest trees
Five temperate trees
10 tropical rainforest trees
15 tropical rainforest trees
Total
P–P
P–NP
LD–ST
LD–LD
ST–ST
Author/s
68
(72 / 105)
36
(16/45)
50
(5/10)
22
(10/45)
26
(27 /105)
83
(5/6)
0
(0/1)
–
–
0
(0/1)
100
(3/3)
66
(29/44)
50
(8/16)
50
(2/4)
38
(6/16)
36
(13 / 36)
67
(12/18)
27
(4/15)
50
(2/4)
33
(2/6)
21
(7 / 34)
72
(26 / 36)
33
(1/3)
100
(1 / 1)
9
(2 / 22)
18
(4 / 22)
0
(0/1)
30
(3 /10)
0
(0 / 1)
–
–
0
(0 / 10)
Agyeman et al. (1999)
Popma & Bongers (1988)
Walters & Reich (1996)
Osunkoya et al. (1994)
Poorter (1999)
CPs = crossover-points. P – P = pairs of pioneers; P–NP = pioneers paired with non-pioneers; LD–ST = light-demanding
non-pioneers paired with shade-tolerating non-pioneers; LD –LD = pairs of light-demanding non-pioneers; ST–ST = pairs
of shade-tolerating non-pioneers.
© 2001 British
Ecological Society,
Functional Ecology,
15, 145 –154
woody species (Agyeman et al. 1999; Osunkoya et al.
1994; Reich et al. 1998a; Walters & Reich 1996). However, among certain sets of species the differences in LMF
may parallel and reinforce the larger, more important
differences in SLA (Reich et al. 1998a; Veneklaas &
Poorter 1998; Walters & Reich 1996). Once seed sizelinked differences in SLA (and LAR) have dissipated,
as we have seen, ULR begins to play a strong determining
role. This happens first for plants at high irradiance,
and later for plants in deep shade. Misunderstandings
occur when short studies are used as the basis of generalizations (Poorter 1999; Veneklaas & Poorter 1998); at
the end of such studies the plants at high irradiance
have emerged from the SLA-dominated first stage, while
those in deep shade have not. There is much evidence,
however, that woody seedlings in deep shade eventually
enter the second stage, in which ULR is the dominant
factor in species RGR differences (Agyeman et al. 1999;
Osunkoya et al. 1994; Popma & Bongers 1988).
Once the seedlings have entered this second stage, as
we have seen, the L vs. R slope steepens, and many of
the light-demanders that initially outranked shadetolerators in the shade will now be overtaken, in RGR
and then in whole-plant mass. Many species pairs’
CPIs shift upwards from below 2%, to between understorey and gap level irradiance.
light environment cannot maintain species richness
through species differences in RGR responses to light.
There are other ways in which light environment can
play a role: as mentioned in the Introduction, there is
ample evidence for a trade-off between survival rate in
deep shade and RGR at high irradiance for seedlings
and saplings (Grubb et al. 1996; Hubbell & Foster 1992;
Kitajima 1994; Kobe et al. 1995; Kobe 1996; Kobe 1999).
However, the results of short studies do not reflect
long-term processes in the field. When we consider the
five longest studies of the seven, >20% of the total
species pairs in each study show rank reversal in RGR
between gap and understorey irradiance (Table 1, iv).
Such changes to RGR hierarchies with changing resource
supply rates can potentially contribute importantly to
the maintenance of species richness (Latham 1992).
Sorting the species pairs into functional type categories
increases resolution. We have used convenient categories
following Whitmore (1999) (and stress that these categories are qualitative and defined arbitrarily): pioneer
(P); light-demanding non-pioneer (LD); and shadetolerating non-pioneer (ST). In general, for the five
studies in which >20% of species pairs’ CPIs occurred
between 2 and 10% daylight, substantial proportions
of species pairs of all combinations of functional types
have crossovers between 2 and 10% daylight (Table 3).
Maintenance of species richness
Studies on saplings
Contention surrounds the issue of whether species differences in seedling RGRs across irradiance regimes
contribute to the maintenance of forest species richness.
The contention has arisen in part from the seemingly
conflicting evidence in the seven studies, and in related
work (Kobe 1999; Walters & Reich 2000b). A result
from a very short study, such as that of Kitajima (1994),
will suggest that in nearly every case a plant that grows
most quickly at low irradiance also grows most quickly
at high irradiance, and so the forest’s heterogeneous
Do the median CPI and CPI interquartile range for a
group of seedlings increase linearly with seedling age over
the long term, as for the short term? At present the data
needed to answer this question are lacking. Unfortunately, analogous studies performed on groups of species
at the sapling stage have used different methodologies,
producing results not directly comparable with those of
seedling studies. Interspecific comparisons of saplings
have quantified radial and/or height RGR (Pacala,
Canham & Silander 1994; Wright et al. 1998; for this
FEC507.fm Page 152 Monday, March 5, 2001 10:06 AM
152
L. Sack &
P. J. Grubb
approach used on seedlings see Kobe 1999). This
approach has the potential to be admirably nondestructive, but it does not immediately permit estimation of whole-plant (mass-based) relative growth, as
height- or diameter-based allometries for a given species
are susceptible to ontogenetic drift and environmental
variation, not at present well understood (Henry &
Aarssen 1999; Kohyama & Grubb 1994).
In the several studies of sapling RGRs cited above,
data were gathered at many irradiances, and a Michaelis–
Menten (MM) response fitted to the increase of RGR
with irradiance. The MM model has been used to test
for a trade-off between ‘high-light growth’ and ‘low-light
growth’, where the former is defined as one parameter
of the model, the maximum RGR at high irradiance
(the asymptote of the MM line), and the latter is defined
as the second parameter, the estimated slope of the
growth function at zero irradiance, which indicates the
RGR forecast for very deep shade (Pacala et al. 1994).
These studies have demonstrated variously a weak
trade-off ( Pacala et al. 1994; Wright et al. 1998), or no
relationship ( Wright et al. 1998) between high- and lowlight growth, depending on the group of species tested.
Such findings do not imply a strict rank retention of
species’ RGRs across irradiances. For instance, in a
study of the radial RGRs of 10 species of saplings from
a wide range of natural light environments (Pacala
et al. 1994), 31% of species pairs crossed over between
2 and 10% daylight. The median CPI in this study is
8·2% daylight – a value exceeding any of those for the
seedling studies (Table 1, v), consistent with the finding for seedlings that median CPI for a group of species
pairs increases as plants grow. Further, it suggests that
the rise of the median CPI slows down by the sapling
stage.
Suggestions for new research
© 2001 British
Ecological Society,
Functional Ecology,
15, 145 –154
When designing an experiment, the length of the
seedling growth period and the initial sizes of seedlings
used must be considered. As the median CPI of a study’s
species pairs, and the CPI interquartile range, increase
as plants grow, the estimation of species pairs’ rank
reversals will be greatly affected. In future studies it
will be important to determine the length of time one
wishes to model in nature, and to grow species either
for that length of time, or for a shorter period, over which
time progressive harvests are made. RGRs calculated
from later harvest intervals will better represent longterm trends than RGRs calculated from early intervals.
Our analysis indicates that time- and/or size-based
trends may be quantitatively established, and natural
processes occurring over longer periods may be extrapolated realistically. This proposition assumes that as
species’ RGR functions change during ontogeny, the
changes are smooth. Long-term studies will be useful
in testing this assumption.
The L vs. R trade-off described above allows investigation of the morphological and physiological factors
underlying a species pair’s rank reversal or rank retention at a given irradiance. Further study of the slope of
this relationship, and how it relates to species choice
and length of study, may lead to the prediction of species’
relative performances at specific irradiances from physiological and morphological metrics.
The studies made so far collectively support the idea
that species differences in RGR across irradiance regimes
do constitute a basis for the maintenance of species
richness in forests. This evidence assumed that species’
RGRs, as determined from isolated plants in pot experiments, reflect their relative performance in natural
communities. This assumption requires detailed testing.
Not considered above, but potentially very important,
is interspecific variation in response to sunflecks as
opposed to the diffuse light experienced in all of the studies
we have analysed (Watling, Ball & Woodrow 1997).
Do species cross over in response to other resources?
The CPI approach can, in theory, be extended to determining crossovers in response to, for instance, low- and
high-nutrient supply rates. Such crossovers may also
change with time: one study reports that when five grass
species from contrasting sites were grown on nutrientpoor soil, the three species from primarily nutrient-rich
sites outperformed the two from nutrient-poor sites,
but only for one season – by the second season the ranking had switched (Ryser 1996). The eventual crossovers
were attributed to a trade-off between carbon assimilation rates and leaf longevity (Ryser 1996), the same
principle that we have argued is one basis for crossovers
in response to irradiance. In nutrient studies the principle has also been framed in terms of the assimilation
and loss rates of nitrogen, rather than carbon (Aerts &
van der Peijl 1993). If woody species cross over in RGR
predictably in response to multiple resources, and further,
their crossovers change predictably over time, the resulting patterns may determine an important part of forest
function.
Much work lies ahead. The final objective, however,
is undeniably compelling. With this research we move
toward a technical basis for the conservation and
management, even the gardening of forest systems, of
any type, at least at the small scale. Coincident with the
development of this knowledge – and of complementary knowledge also being actively sought (for
instance the understanding of seed dispersal patterns
and the roles of herbivores and pathogens) – will be
a minimum theoretical and empirical framework for
understanding how forests persist and function, from
the level of species physiology, to the co-existence of
dominant species, to succession.
Acknowledgements
We thank D. Burslem, D. Coomes, M. Swaine, E. Tanner
and J. Wright for their stimulating comments. Lawren Sack
thanks NSERC (Canada), the Cambridge Commonwealth Trust, and Cambridge University Department
of Plant Sciences (Frank Smart Fund) for scholarships.
FEC507.fm Page 153 Monday, March 5, 2001 10:06 AM
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Woody seedling
relative growth rate
rank changes
© 2001 British
Ecological Society,
Functional Ecology,
15, 145 –154
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Received 29 June 2000; accepted 10 November 2000