ORIGINAL PAPER

Tree shape plasticity in relation to crown exposure

Degi Harja • Gregoire Vincent • Rachmat Mulia •

Meine van Noordwijk

Received: 16 November 2011 / Revised: 10 February 2012 / Accepted: 18 February 2012 / Published online: 2 March 2012

� Springer-Verlag 2012

Abstract Trees outside closed forest stands differ in the

relation between stem diameter, height and crown volume

from trees that grew with neighbours close by. Whether

this plasticity in tree shape varies between species in

relation to their light requirement is unknown. We pur-

posefully sampled 528 trees ranging 5–100 cm diameter at

breast height growing in a range of light conditions. Across

ten broad-leaved species observed in Sumatra or Kali-

mantan, a generic relationship was found between light

exposure of the crown and a light-dependent al parameter

that modifies the height–diameter allometric equation

(H = alDb) from those for closed stands. In our results,

vertical stretching is well predicted by light availability. In

fully open conditions, trees are on average 31% shorter for

the same diameter than under (partial) shade. Most of the

stretching response occurs in all species as soon as some

degree of lateral shading occurs. The response, however,

varies by species (8–44% reduction) in a way apparently

unrelated to species’ successional status. Crown volume

varied less than stem height in its relationship with stem

diameter across all light conditions tested. The scaling of

crown volume with stem diameter, however, differed

markedly between tree species.

Keywords Tree height � Crown shape � Humid tropics �Wood density � Allometry

Introduction

Competition for light and space between neighbouring

trees plays a central role in shaping forest structure and

dynamics (King et al. 2005; Kohyama 1994). The spatial

arrangement of a tree’s foliage relative to its competing

neighbours controls the outcome of the competition for

light (Weiner 1990). The pattern of leaf display over time

and space also drives biomass allocation rules between

photosynthetic leaves and structural components to support

them mechanically and in terms of water transport (Niklas

1994; Weiner 2004).

Tree shape plasticity in response to light availability

reflects changes in growth-allocation rules that probably

have strong adaptive significance (Vincent and Harja 2008;

Weiner 2004). There is, however, little quantitative infor-

mation available regarding the degree of plastic response of

the allometric relations between tree overall dimensions

(stem diameter, stem height, crown depth, crown width) to

various light regimes. How this plasticity may relate to

ecological strategies and vary across species is also poorly

documented.

Known responses to environment involving changes in

growth allocation include modification of the height–

diameter relationship and modification of relative crown

radius and height. Several factors affecting within-species

variation of the stem height–diameter relationship have

been identified and are briefly reviewed below.

1. The proximate (physiological), direct effect of the light

regime on slenderness (height/dbh ratio) is ascribed to

Communicated by R. Matyssek.

D. Harja (&) � R. Mulia � M. van Noordwijk

Southeast Asia Regional Program, World Agroforestry

Centre (ICRAF), Jalan CIFOR, Situ Gede,

Sindang Barang, Bogor 16115, Jawa Barat, Indonesia

e-mail: d.harja@cgiar.org

G. Vincent

Unite Mixte de Recherche AMAP,

Institut de Recherche pour le Developpement (IRD),

TA A-51/PS2, 34398 Montpellier Cedex 5, France

123

Trees (2012) 26:1275–1285

DOI 10.1007/s00468-012-0703-x

the phytochrome-mediated perception of far-red radi-

ation (700–800 nm wavelength) scattered from the

leaves of neighbours, which provides early warning of

shading and triggers the change in the growth-alloca-

tion characteristic of the shade-avoidance response

(increased allocation in height). This response has

been clearly established at sapling stage (Gilbert et al.

2001; Ballare 1999) and most probably affects a tree’s

entire growth. The functional interpretation and selec-

tive advantage (ultimate cause) of the response

requires understanding of the immediate trade-offs:

every unit of internal resources can be invested in

diameter increment or height growth of the main stem,

and/or in branches and leaf formation. The payoff in

terms of light capture clearly depends on the alloca-

tions made by neighbours and competitors.

2. Competition in a stand (as measured through basal area

at stand level) has long been known to affect growth in

diameter more than growth in height. This observation

is at the heart of the site fertility index concept

developed by European foresters in the eighteenth

century and defined as the dominant height of a stand

at a given age (Skovsgaard and Vanclay 2008). The

stability of height growth for a range of planting

density—and resulting basal areas—is well illustrated

by Zeide and Vanderschaaf (2002), who studied shade-

intolerant Pinus taeda. As a consequence, trees tend to

be slender in denser stands. The extent to which the

response is light dependent or rather reflects priority

rules in growth allocation independent of light status

is, however, unclear. At individual level, the same

observation holds as the competitive status of a tree

within a stand (as captured by crown depth, for

example) is typically negatively correlated to its

slenderness coefficient. This was reported for shade-

intolerant silver birch (Betula pendula) (Ilomaki et al.

2003) as well as semi-tolerant ash (LeGoff and

Ottorini 1996) and shade-intolerant P. taeda (Naidu

et al. 1998).

3. Site fertility (height/age) was found to be positively

correlated to slenderness (height/dbh ratio) in planta-

tion of Callitris sp. in Australia (Vanclay and Henry

1988) and in five species of mixed boreal forest

covering a wide range of shade tolerance (Wang et al.

1998). The generality of this relation was questioned

by Geoff Wang (1998), who found no such relation in

his study on white spruce (Picea glauca Voss, a late

successional species of intermediate tolerance to shade

according to Burns and Honkala 1990). To reconcile

those conflicting results, the following hypothesis may

be put forward. Fertility needs not to have a monotonic

effect on slenderness: extremely poor soil may bear

lank trees with an underdeveloped crown because

height growth (primary growth) may have strict

precedence over diameter growth (secondary growth)

and crown development may be severely reduced

under low fertility. Trees with stunted crowns will also

experience lower mechanical stress (lower weight,

lower wind resistance) compatible with more slender

stems. On the other end of the fertility spectrum,

stronger competition (for light and/or belowground

resources or mere space) may result in an increased

height/diameter growth-allocation ratio and, hence,

increased slenderness. So, depending on the fertility

gradient explored the relation with slenderness may be

positive, negative or non-monotonic.

4. Wind-exposed edge Sitka spruce [Picea sitchensis

(Bong.) Trautv. & C.A.Mey.] trees were found to grow

shorter and more tapered than more sheltered trees

(Bruchert and Gardiner 2006). Site differences in

height–dbh relationship in Pinus radiata D. Don have

also been related to local wind regimes in New

Zealand (Watt et al. 2010).

5. Topography: Dipterocarp trees growing on steep

slopes (Robert and Moravie 2003) were found to be

shorter and more tapered, possibly reflecting stronger

mechanical constraints and correlative butt swelling

due to more demanding anchorage or tension wood

developed to compensate for early leaning (Loehle

1997) or merely better access to light (less shading

from down-slope neighbours).

As already mentioned, plasticity in crown vertical

extension (crown depth) has been reported in various

contexts (see also Williams et al. 1999, who examined

crown morphology of conifer saplings under varying can-

opy openness) and this plasticity is typically more pro-

nounced in light-demanding species (Jack and Long 1991).

Contrasting with crown depth (length), it has been noted

for plasticity in many species both in natural and plantation

forests that the species-specific relation between crown

lateral extension and stem diameter (either measured at

breast height or preferably below crown) was hardly

affected by competitive status (Bohlman and O’Brien

2006; Dawkins 1963; Hemery et al. 2005; Pryor 1988).

From this brief review, it appears that the shape of a tree

is affected by its local environment and that factors

accounting for this plasticity may be confounded (local

competitive status and local fertility or exposure to

mechanical stress associated with topography or wind

regime). Furthermore, the plasticity in response to crowd-

ing seems to vary between species. Shade-tolerant species

may be expected to be less responsive to crowding both in

precocity and extent of response in as much as light is the

dominant factor governing the response (Gilbert et al.

2001).

1276 Trees (2012) 26:1275–1285

123

In the present study, we analyse height–diameter–crown

extension data of 10 tree species growing in a wide range

of light conditions in the humid tropics of Indonesia,

ranging from isolated trees on field boundaries through

half-open types of agroforestry to closed (agro)forest

conditions and aim to answer the following questions:

1. To what extent are height–diameter and crown

volume–stem diameter relationships affected by access

to light across a range of species?

2. How much of the response is species dependent?

3. Is the species effect related to light preference or other

ecological characteristics of the species?

Materials and methods

Study sites and species

A collection of 528 trees from 10 tropical species of

diverse successional status were purposefully sampled in

contrasting environments across the lowlands of Sumatra

and Kalimantan (Indonesia): isolated trees growing in the

open, co-dominant trees in (agro)forest stands and over-

topped trees in the (agro)forest understory.

The species studied were common agroforest species in

Sumatra and Kalimantan and were predominantly light-

demanding species but included some late successional

species and one understorey species. A brief description of

each species follows (the local Indonesian name is in

parentheses). Species are tentatively arranged in three

shade-tolerance groups, namely intolerant, intermediate,

and tolerant. This classification is based on the scantly

available published information and the authors’ expertise

and considers both seedling/sapling tolerance as well as

adult stages sensitivity to canopy closure.

Intolerant

• Albizia falcataria (L.) Fosberg (Sengon). Synonym:

Paraserianthes falcataria, Albizia moluccana, Ade-

nanthera falcataria. This is a medium-to-large tree, up

to 40 m tall; with a spreading flat crown. It is a strongly

light-demanding species (Agroforestry Tree Database,

ICRAF).

• Acacia mangium Willd (Akasia) is a single-stemmed,

evergreen tree that grows 25–35 m in height. A pioneer

species, it is also light demanding (Agroforestry Tree

Database, ICRAF).

• Alstonia scholaris (L.) R.Br (Pulai) is a medium-to-

large tree, up to about 40 m high. It is found not only in

secondary as well as primary forest but also in open

grasslands. It has light wood, a fast growth rate

(Agroforestry Tree Database, ICRAF), the best growth

of seedlings is achieved in the open (Vincent 2006) and

the best germination occurs in full sunlight (Jøker

2000). It is classified as shade intolerant.

• Fagraea fragrans Roxb. (Tembesu) is a medium-sized

or occasionally large tree up to 25–55 m tall. It occurs

in light primary and secondary forest. It is classified as

a light-demanding species (Agroforestry Tree Data-

base, ICRAF).

Intermediate

• Schima wallichii (DC.) Korth (Seru) is an evergreen,

medium-to-large tree growing to 47 m in height. It is

particularly common in disturbed and secondary for-

ests, scrub and grassland. Its light requirement is,

however, considered as moderate and is explicitly

mentioned as being less than that of Fagraea fragrans

(Agroforestry Tree Database, ICRAF).

• Hevea brasiliensis (Willd. ex A. Juss.) Muell. Arg

(Karet) is a large tree native to the forests of Amazonia

but cultivated widely throughout the humid tropics as a

source of latex for commercial rubber production. The

species can be classified as intermediate as it germi-

nates readily in the shade but tolerates full sunlight

even at seedling stage (Vincent 2006).

• Archidendron jiringa (Jack.) I. C. Nielsen (Jengkol)

grows up to 24 m tall. It is fast growing and found in

primary and secondary rainforest. Specific information

on light requirements is lacking but the species is

abundant in young fallows after shifting cultivation

(Lawrence et al. 2005). It is therefore classified as

intermediate.

• Shorea stenoptera Burck. (Tengkawang) is a dominant

or emergent tree with height reaching 60 m. Given its

rapid growth, relatively light wood within the meranti

group and early fruiting (Weinland 1998), it is consid-

ered intermediate, notwithstanding its shade tolerance

at seedling stage.

Tolerant

• Durio zibethinus L. (Durian) is a medium-to-large

buttressed tree up to 45 m tall. Under natural conditions

its early development occurs in the shaded understorey

and the adult tree reaches the top canopy. Seedlings

require shading to survive and develop vigorously

(Vincent 2006).

• Lansium domesticum Corr. (Duku) is a small-to-

medium tree. An understorey specialist, it is adapted

to shade. Its seedlings do not, physiologically, adapt

readily to very open conditions (Vincent 2001, 2006).

Trees (2012) 26:1275–1285 1277

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Tree sampling and measurement

Individual trees from 5 cm diameter at breast height were

sampled according to a stratified design (Table 1). The three

strata/social statuses were defined as: (a) an ‘‘isolated’’ tree

growing alone or with a few other trees scattered in an open

area (roadside, grassland, garden); (b) overtopped/sup-

pressed trees growing in a stand, clearly over-shaded by

competitors but with no significant restriction to crown lat-

eral expansion; and (c) co-dominant trees growing in a stand

i.e. with no competitor over-shading them.

Most of the trees growing in stands were measured in

mixed agroforest plots except for Albizia and Acacia,

which were measured in monocultural stands.

Variables measured for individual trees were: stem

diameter (measured at breast height) (D), tree height (H),

crown width and crown depth. Crown width was defined as

the average of the largest extension of the crown projection

in two perpendicular directions. Crown depth was defined

as the length of crown from crown base to the top of the

tree. The base of the crown was defined as the height of the

lowest foliage, which was most often very close to the

height of first branching. Tree height and crown base height

were measured using a Carl-Leiss Altimeter and a standard

measuring tape was used for diameter and crown width

measurement.

For each tree we also recorded the crown position (CP)

index sensu (Dawkins 1966), which is an index of how

much light a crown receives. This index is commonly used

as a growth predictor (Aasamaa and Sober 2001; Vincent

et al. 2002, 2011). The CP scale was defined following

Alder and Synnott (1992):

• Emergent = 5, crown exposed vertically and free from

lateral competition at least within 90� inverted crown

subtended by the crown base

• Full overhead light = 4, crown plan fully exposed

vertically but adjacent to other crowns of equal or

greater height within the 90� cone

• Some overhead light = 3, crown partially exposed

vertically but partly vertically shaded by other crowns

• Some side light = 2, crown plant entirely vertically

shaded but exposed to some direct light due to a gap or

edge of overhead canopy

• No direct light = 1, crown plant entirely shaded

vertically and laterally.

We also recorded all trees with D [ 5 cm in the immediate

neighbourhood of each target tree. The neighbourhood was

defined by a circular plot centred on the target tree with radius

equal to the maximum between two distances r1 and r2, where

r1 was the width of the target tree crown and r2 was the dis-

tance to the furthest tree in contact with target tree. Local

crowding indices were then computed in the following way.

When r1 [ r2 the local basal area was the sum of all cross-

sectional areas of individual trees divided by plot area. If

r2 [ r1 then the furthest tree (which determined the plot

radius) was counted as half inside and half outside the plot and,

hence, given a weight of 0.5 for both when computing basal

area. This varying neighbourhood size was adopted to ensure

that neighbourhood size would be consistent with target tree

size while not neglecting the case of large competitors not

included in a radius limited to crown width, which is a com-

mon situation in uneven-aged stands. In the remainder of the

text, the log of the ratio of the sum of cross-sectional areas of

all neighbouring stems (excluding the target tree) to the

neighbourhood area is referred to as the local crowding index.

Crown volume was derived from crown depth and

crown width measurements assuming a half ellipsoid shape

(Vhalf) of the crown with half major axis equal to crown

depth (a) and minor axis equal to crown radius (b):

Vhalf ¼2

3pab2 ð1Þ

Statistical analysis

A series of general linear models was tested to explore the

relative importance of the local aboveground environment

Table 1 Frequency table of

data per tree species and social

status group; stem diameter

range per species

Species Isolated Understorey Co-dominant Total Diameter (cm)

Albizia falcataria 9 0 27 36 17–73

Alstonia scholaris 19 13 16 48 6–79

Pithecelobium jiringa 26 7 10 43 8–41

Shorea stenoptera 10 16 67 93 5–124

Acacia mangium 28 1 20 49 5–47

Durio zibethinus 19 10 13 42 6–73

Hevea brasiliensis 34 16 15 65 5–60

Schima wallichii 12 13 18 43 5–51

Fagraea fragrans 22 10 22 54 5–66

Lansium domesticum 18 9 28 55 6–75

Total 197 95 236 528

1278 Trees (2012) 26:1275–1285

123

(i.e. social status) and species’ identity (or some proxy of

species’ identity) and their possible interaction in shaping

the allometric equations examined.

Models were fitted either on the whole set of species or

on a subset of eight species adequately sampled in all types

of aboveground environments (Table 1).

The general form of the models tested was:

Log Hð Þ � Log Dð Þ � Social Status � Species ið Þ ð2Þ

Log crown volumeð Þ � Log Dð Þ � Social Status

� Species iið Þ ð3Þ

where 9 indicates that all direct and interaction terms were

included.

We further examined crown dimension (crown depth

and crown width) from which crown volume was derived.

Models used had the following form:

Log crown depthð Þ� Log Hð Þ � Social Status

� Species iiið Þ ð4Þ

Log crown widthð Þ�Log Dð Þ � Social Status

� Species ivð Þ ð5Þ

Log(H) was used rather than log(D) in predicting log(crown

depth) as it provided better predictions (lower AIC).

For each model we ran a step() function in order to

select the best model starting with the most complete

model including all predictors and interactions. Akaike

Information Criterion (AIC) was used to select among the

various models tested. AIC is defined as 2k - 2ln(L) where

k is the number of parameters in the model, and L is the

maximized value of the likelihood function for the esti-

mated model (Akaike 1974).

We evaluated the models above after replacing social

status by crown position index or local crowding index. To

help interpret differences in AIC when comparing non-nes-

ted models, we compared the likelihood of the models (M).

The likelihood of model i (conditional to the data) was

computed as (Burnham and Anderson 2002):

LðMi=dataÞ� exp � 1

2DiðAICÞ

� �ð6Þ

where Di AICð Þ ¼ AIC� AICmin, AICmin is the AIC of the

best model and *reads ‘‘is proportional to’’.

When comparing any pair of models (i, j) we reported

the ‘‘evidence ratio’’, which is simply defined as the rela-

tive likelihood of one model to the other:

LðMi=dataÞLðMj=dataÞ ð7Þ

Tree dimensions (H, D, crown volume, crown width and

crown depth) were systematically log transformed to

improve normality of residuals, which was checked using

Shapiro–Wilk statistic. This allowed meaningful testing for

significance of effects.

However to avoid bias involved by back-transforming

log-transformed data (Beauchamp and Olson 1973; Sprugel

1983), we used a non-linear regression (nls( ) function) to

adjust an individual species’ model and compare coeffi-

cients across species and environments. The H–D relation

was modelled with a power function H = a 9 Db (Niklas

1994).

Finally, we used generalized additive models (GAM)

(Hastie and Tibshirani 1990) to explore the species-specific

shape of the response of tree change in slenderness with

decreasing access to light. GAM is a generalized linear

model in which part of the linear predictor is specified as a

sum of smooth functions of predictor variables. We used

spline regression to model the CP effect implementing the

following model in R (GAM package) for each species:

Log Hð Þ�Log Dð Þ þ s CP; df ¼ 2ð Þ vð Þ ð8Þ

where df is the equivalent degrees of freedom of the spline

smoother.

All the statistical analyses were conducted with R sta-

tistical software and programming language (http://cran.

rproject.org).

Results

We first restricted the analysis to the eight species ade-

quately sampled in all three environments i.e. excluding

Acacia mangium and Albizia falcataria, which were not

sampled in the understorey (Table 1).

As expected, there was a tight relation between social

status and CP (Table 2). Similarly, the local crowding

index decreased with increasing CP index (Fig. 1,

r2 = 0.40***).

The best models of tree height and crown volume both

included all predictors and all their interactions. However,

the contribution of the various predictors to deviance

reduction differed significantly between the two models

(Table 3). Log(D) alone captured almost 61% of deviance

in log(H) and more than 78% of deviance in log(crown

volume). Social status captured 14% of the deviance in

log(H) but only 2% of the deviance in log(crown volume).

Species’ identity accounted for about the same amount of

deviance in both models i.e., respectively, 6 and 7% (not

taking into account the interaction terms).

The contribution of social status to prediction of

log(crown_width) was small, accounting for less than 1.4%

of the deviance reduction, and much smaller than its con-

tribution to log(crown_depth), which accounted for 7.6%

of the deviance reduction (Table 4).

Trees (2012) 26:1275–1285 1279

123

When understorey and co-dominant social statuses

were collapsed into a single category, the AIC of the

full model predicting log(H) was marginally increased

(AIC2groups = 2,187; AIC3groups = 2,185, evidence ratio =

0.37), reflecting the similar degree of vertical stretching

occurring in trees growing in stands whether overshadowed

or co-dominant (Fig. 2). For log(crown volume) the evidence

ratio was slightly more strong in favour of three groups

(AIC2groups = 611; AIC3groups = 606, evidence ratio = 0.06)

but still not decisively so.

GAM modelling (formula (v), Fig. 3) revealed that for

most species (7 out of 10) the increase in slenderness with

decreasing CP was non-linear and that most of the response

occurred as trees changed from CP 5 to CP 4, indicating

that co-dominant trees (mostly CP 3 and CP 4, Table 2)

and understorey trees (mostly CP 1 and CP 2, Table 2)

differed much less than trees in stands (CP 1 to CP 4)

versus isolated trees (mostly CP 5, Table 2). Some species,

however, showed a more progressive response (e.g. Lan-

sium domesticum).

Understorey and co-dominant trees were grouped into a

single category for subsequent analyses in which we

compared the height–diameter relationship of trees grow-

ing isolated to the height–diameter relationship of trees

growing in stands. When records of all 10 species were

pooled, regression lines of log-transformed data were

almost parallel (Fig. 2), suggesting that the two popula-

tions differed in terms of the linear coefficient a rather than

the scaling exponent b of the original H = aDb relation).

We tested the above hypothesis at species’ level by

comparing a model in which parameters a and b (of the

H = aDb relation) would be the same across environments

against two models allowing either a alone or a and b to be

Table 2 Cross tabulation of social status and crown position index

(CP) in full data set (10 species, 528 trees)

CP Social status Total

Isolated Understorey Co-dominant

1 0 49 3 52

2 0 36 20 56

3 0 9 114 123

4 16 1 87 104

5 181 0 12 193

Total 196 94 234 620

Fig. 1 Box plot of sum of basal area (log transformed from m2 ha-1)

of competitors in neighbourhood per CP class of each target tree

(n = 528)

Table 3 Deviance structure of the best linear model (minimum AIC)

predicting various tree dimensions from tree log D (log of diameter at

breast height), species identity and social status (SS)

Predictor Residual deviance (terms added

sequentially, first to last) (%)

Log of

height

Log of crown

volume

Log D 39.4 21.8

SS 25.4 21.6

Species 19.3 14.1

Log D 9 SS 19.3 14.0

Log D 9 Species 17.1 13.6

SS 9 Species 15.8 12.9

Log D 9 SS 9 Species 14.7 12.5

Fig. 2 Scatter plot of height and diameter of trees growing either

isolated (crosses) or in stands (open circles understorey trees, filledcircles co-dominant trees); 528 trees from 10 species were pooled.

Note the log scale on x and y axis

1280 Trees (2012) 26:1275–1285

123

adjusted per subgroup (isolated trees or trees in stands)

using non-linear regression. For six out of 10 species the

best model (i.e. with the lowest AIC) was obtained when

allowing the scaling parameter to vary between subgroups

while keeping the power coefficient constant at species

level (Table 5). When species were pooled, allowing both

parameters a and b to be adjusted per group was marginally

preferable than setting the power exponent b equal across

groups (Table 5).

The plasticity of the height–diameter relationship (the

percentage increase in height due to shading) differed

across species (last column, Table 6). However, there was

no obvious relation between this plasticity and species’

light requirements. In particular, early successional Alsto-

nia scholaris showed low plasticity in the H–D relation-

Table 4 Deviance structure of the best linear model (minimum AIC)

predicting crown dimensions from species identity, social status (SS)

and tree log H (log of tree height for crown depth) or log D (log of

diameter at breast height, for crown width)

Predictor Residual deviance (terms added

sequentially, first to last) (%)

Log of

crown depth

Log of

crown width

Log H (or Log D) 42 24.7

SS 34.4 23.3

Species 29.9 14.1

Log H (Log D) 9 SS 27.4 –

Log H (Log D) 9 Species 24.4 –

SS 9 Species – 13.2

Fig. 3 Effect of CP on logHeight estimated per species using spline regressor (GAM). Dashed lines represent upper and lower point wise twice-

standard error curves. NS, asterisk and double asterisk are significance values (Fisher test) comparing a spline smoother to the linear effect

Trees (2012) 26:1275–1285 1281

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ship, Fagraea fragrans (also classified as light demanding)

had the lowest plasticity, while Lansium domesticum (the

most shade-tolerant species) was amongst the most plastic.

Similarly, the two species showing the most progressive

response to change in CP index, Lansium domesticum and

Acacia mangium (Fig. 3), belonged to the two extreme

light requirement groups represented in this study.

Finally, light preference was introduced as a three-level

factor (intolerant, intermediate, tolerant) in replacement of

species’ identity to predict height from diameter. It per-

formed poorly (evidence ratio of model using light pref-

erence to reference model was 5.0 9 10-22).

The local crowding index was tested in models (i), (ii),

(iii) and (iv). The local crowding index was always a

poorer predictor of crown shape than CP (data not shown).

For instance, the evidence ratio of model predicting

log(H) using log(crowding_index) instead of CP [as in the

reference model (i)] was 3.0 9 10-16, indicating that CP

was clearly a better predictor of slenderness than local

crowding.

Discussion

We found the height–diameter relationship to be much

affected by social status for all species examined while the

crown volume–diameter relationship was not. The response

was found to be species dependent but successional status

was not a good predictor of the differential response.

Some degree of plasticity in the height–diameter rela-

tionship with the light environment and some degree of

variability between species was expected (Cabanettes et al.

1998; Gilbert et al. 2001; Vincent and Harja 2008; Wil-

liams et al. 1999). The magnitude of the response and the

variability across species were less predictable and were

found to be large (Table 6; Fig. 3). The lack of relation

between the degree of plasticity of slenderness and species’

light preference was also unexpected and seems at odds

with theoretical arguments and previous findings (see

‘‘Introduction’’). Two reasons why this may be the case can

be suggested.

1. The observed change in allometry in response to

crowding may be a response to competition for

belowground resources and space as well as for light.

So part of the response may be unrelated to species’

light requirements: under more stringent competition,

height growth is maintained while stem diameter and

crown volume is reduced. Strong colinearity between

the local crowding index and the CP index (Fig. 1)

suggests that distinguishing both competition effects is

not possible with the present dataset. The poorer

predictive power of local crowding may simply reflect

suboptimal characterisation of global competition by

the index used. Crowding has been successfully distin-

guished from shading in analyses by Canham et al.

(2004) but their approach requires data on diameter

increments. Heineman et al. (2011), on the other hand,

has shown the importance of belowground resources to

allometric plasticity, where trees growing on fertile soil

tend to be less slender (regardless the species’ light

preferences). This conforms with the crowding index

effect in colinearity with CP, where less competitive

neighbours may result in less slender trees. Further

study could include more comprehensive data on

belowground competition related to root architecture.

2. Another reason why no relation was found between

light requirements and plasticity may be that there is

no such relation. Arguably, even a shade-tolerant

species tree would benefit from early signalling of the

presence of a close competitor in its neighbourhood

and from the capacity to develop a morphological

Table 5 Akaike Information

Criterion (AIC) of a series of

increasingly complex allometric

model of tree height

Models are adjusted for each

species allowing none, one or

both of the parameters of the

basic model to vary according to

tree local environment (open

area or stand)

The italic values are the relative

lowest AIC value within the

models for each species

Species AIC mod1 AIC mod2 AIC mod3

H = aDb H = a1Db (if isolated) H = a1Db1 (if isolated)

H = a2Db (if in stand) H = a2Db2 (if in stand)

Albizia falcataria 226.8 191.8 189.8

Alstonia scholaris 209.6 197.3 194.6

Pithecelobium jiringa 295.1 255.6 256.9

Shorea stenoptera 491.0 461.2 463.2

Acacia mangium 200.2 160.1 158.2

Durio zibethinus 230.2 166.4 168.3

Hevea brasiliensis 259.0 258.0 250.7

Schima wallichii 232.0 184.3 186.3

Fagraea fragrans 246.5 194.6 196.3

Lansium domesticum 318.9 288.1 290.0

All species pooled 2,933.9 2,675.6 2,674.6

1282 Trees (2012) 26:1275–1285

123

response allowing itself to maintain its leaf area (to

achieve resource preemption) through increased height

growth. Shade-tolerant and light-demanding species

may differ more in terms of sensitivity to shading than

in terms of plasticity (the amplitude of the response).

Our data set is ill suited to detect such possible

relations between species’ light requirements and

sensitivity to crowding. Even the CP index, which

provides a more direct estimate of light availability

than social status, is probably too crude for that

purpose. For instance, co-dominant trees under differ-

ent planting densities would all score a 4, irrespective

of the planting density and the correlative difference in

light availability. Furthermore, an identical CP index

at one point in time does not preclude the existence of

fairly different past light conditions.

Despite significant inter-specific variation in the degree

of plasticity in the height–diameter relationship, there is a

common trend of increasing height when light exposure is

reduced and this reaction seems to affect similarly trees in

the understorey and co-dominant trees (Fig. 2). In most

cases, this change can be parsimoniously modelled by

allowing the linear coefficient a of the standard height–

diameter relationship to vary according to tree environ-

ment, either open or closed (Table 6).

Species differed significantly in the power exponent

value relating stem diameter to stem height, even under

similar constant light environments (Table 6, b0 parame-

ter). Such differences lend support to other studies (Makela

and Valentine 2006; Muller-Landau et al. 2006) that

challenge the existence of a universally valid allometric

parameter between stem diameter and stem height as pre-

dicted by the metabolic theory of allometric scaling in trees

(Enquist and Niklas 2002).

Various shifts in growth allocation between height

growth and diameter increment during tree life can be

expected (Niklas 1995; Osunkoya et al. 2007). It is likely

that the same applies to the species studied here, making

the reality somewhat more complex than what was por-

trayed. For example, when top canopy trees finally reach

the upper canopy they tend to invest more in diameter

growth than height (Aiba and Nakashizuka 2009; Collinet

1997; Henry and Aarssen 1999). A similar change in

growth allocation may also happen in understorey trees that

grow to their final height and still grow in diameter for

some time after (Osunkoya et al. 2007). Most of the trees

sampled in stands were sampled in agroforest plots and

were less than 70 years old. Consequently, few of the trees

sampled would have reached the so-called ‘‘liberation

point’’ (Collinet 1997) where growth in height is much

reduced and growth in diameter strongly favoured.

Plasticity of crown volume in relation to light exposure

appears to be significantly less than the plasticity observed

in the height–diameter relationship (Table 3). This can be

related to the fact that enhanced growth in height triggered

by lateral shading is usually paralleled by a reduction in

crown depth while crown lateral extent seems largely

unaffected by light status (Table 4). The stability between

crown diameter and stem diameter (measured at breast

height or below crown) has previously been noted for many

species both in natural and plantation forests, tropical and

temperate (Bohlman and O’Brien 2006; Dawkins 1963;

Hemery et al. 2005; Pryor 1988). A tight relation between

stem diameter and crown volume makes sense both from a

hydraulic point of view (stable ratio between transpiring

leaf surface and xylem conducting section) and a

mechanical point of view (larger heavier crowns requiring

thicker stem base). Consistent with previous findings (see

Table 6 Parameter estimates of the allometric function H = aDb, where a is allowed to vary between groups (isolated a0 or trees in stands a1) or not

Species a and b are common across groups a is adjusted per group, b is common across groups Plasticity

indexa b Adj. r2 a0 a1 b0 Adj. r2

Albizia falcataria 9.87 (3.36) 0.23 (0.09) 0.13 3.54 (0.94) 5.77 (1.34) 0.42 (0.07) 0.68 0.39

Alstonia scholaris 1.60 (0.26) 0.62 (0.05) 0.72 1.36 (0.20) 1.6 (0.23) 0.64 (0.04) 0.86 0.15

Pithecelobium jiringa 6.26 (2.30) 0.17 (0.12) 0.03 2.3 (0.44) 4.13 (0.72) 0.42 (0.06) 0.79 0.44

Shorea stenoptera 3.18 (0.32) 0.49 (0.03) 0.80 2.26 (0.24) 3.11 (0.27) 0.51 (0.02) 0.85 0.27

Acacia mangium 3.45 (0.58) 0.38 (0.05) 0.52 2.09 (0.26) 2.95 (0.32) 0.5 (0.04) 0.81 0.29

Durio zibethinus 2.04 (0.55) 0.61 (0.07) 0.66 1.08 (0.16) 1.73 (0.23) 0.73 (0.04) 0.90 0.38

Hevea brasiliensis 4.92 (0.73) 0.33 (0.05) 0.46 2.98 (0.43) 3.92 (0.48) 0.46 (0.04) 0.68 0.25

Schima wallichii 3.72 (0.73) 0.43 (0.06) 0.51 1.79 (0.24) 2.99 (0.33) 0.56 (0.04) 0.84 0.4

Fagraea fragrans 3.42 (0.45) 0.45 (0.04) 0.72 3.2 (0.44) 3.49 (0.45) 0.45 (0.04) 0.73 0.08

Lansium domesticum 3.22 (0.73) 0.44 (0.06) 0.51 1.90 (0.33) 2.8 (0.45) 0.51 (0.05) 0.77 0.38

All species pooled 2.81 (0.19) 0.51 (0.02) 0.58 2.09 (0.11) 2.98 (0.15) 0.53 (0.01) 0.74 0.30

Standard error of parameters in brackets Plasticity Index is computed as 1 - (a0/a1)

The bold value is plasticity index for all species in general

Trees (2012) 26:1275–1285 1283

123

‘‘Introduction’’), crown depth was found to be more

responsive to light availability (Table 4).

Our results suggest that the current use of allometric

equations that were developed for closed stands for trees

growing in more open conditions, as is common in land-

scape-level carbon stock assessments (Hairiah et al. 2011),

contains a risk of considerable overestimate of tree biomass

and carbon stocks, unless empirical equations and field data

incorporate an indicator of crowding.

Conclusion

In all species examined, the aboveground environment

strongly affected some of the allometric scaling rules and,

most significantly, the height–diameter relation. Once

diameter was accounted for, two-thirds of the remaining

deviance in height was accounted for by social status

(isolated, co-dominant or suppressed) alone, i.e., regardless

of the species. Conversely, crown volume was found to be

fairly stable at species level: three-quarters of the reduction

in residual deviance in crown volume (once corrected for

stem diameter) was accounted for by the species’ factor

alone and only modestly affected by the aboveground local

environment.

This plasticity in height–diameter relationships varied

between species but was not related to successional status

in a systematic way. Stability of the crown volume–stem

diameter relation at species’ level probably reflects some

biophysical constraint, possibly the hydraulic supply/

demand ratio, which limits the range of variation to be

expected within species. Vertical stretching was similar in

co-dominant and understorey trees.

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