Distance-dependent competition measures for eucalyptus plantations in Portugal

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Distance-dependent competition measures for

eucalyptus plantations in Portugal

Paula Soares, Margarida Tomé

To cite this version:

Original

article

Distance-dependent competition

measures

for

_{eucalyptus plantations}

in

_Portugal

Paula

Soares*

_Margarida

Tomé

Department

of

_{Forestry, Tapada}

da

_Ajuda,

1399 Lisboa Codex,

Portugal

(Received 17 March 1998;

_accepted

22

_February

₁₉₉₉₎

Abstract - Data from _permanent

_plots

and

_spacing

trials of

_Eucalyptus

globulus Labill. were used to

_{study distance-dependent}

com-petition

measures. The data were divided into three subsets

_representing

different _stages of stand

_development

and therefore different

levels of

_competition.

Different formulations of each _type of index were tested. The rules for the selection of

_competitors

as well as

the mathematical formulation of each index were considered in the

_analysis.

The linear

_relationship

between the dbh and the distance to which a tree can _{compete -} characteristic of the selection of

_competitors

based on the basal area factor - was not consistent over

time. Rules defined as

_{asymptotically}

restricted non-linear functions of tree size were

_designed

to overcome this

_problem.

The use of

a fixed number of

_competitors

was also tested. The evaluation of the

_{prediction ability}

of each index was based

_mainly

on its

perfor-mance in

_multiple

linear

_regression

functions for the

_prediction

of the tree basal area annual increment. The results showed the

supe-riority

of the indices based on the Richards’ function for

_{selecting competitors.}

This supremacy was more evident when trees in the lower diameter classes were not

_suppressed.

When the

_{asymmetric competition}

was evident the area

_potentially

available indices showed the best

_performance.

(© Inra/Elsevier, Paris.)

distance-dependent

indices / selection of

_competitors

/

_{prediction ability}

/ stand

_development

/

_{Eucalyptus globulus}

Labill. /

plantations

Résumé - Indices de

_{compétition dépendants}

_{de la distance pour}

_{plantations d’eucalyptus}

au

_Portugal.

Pour étudier des indices de

_{compétition dépendants}

des distances, on utilise des données des

_parcelles

_permanentes et d’essais

_{d’espacement}

d’Eucalyptus globulus

Labill. Les _données, divisées en trois sous-groupes,

_{représentent}

différentes

_étapes

de

_{développement}

du

peu-plement,

donc, différents niveaux de

_{compétition.}

Diverses formulations de

_chaque

_type d’indice de

_compétition

sont testées. Les

règles

pour la sélection des

compétiteurs

ainsi que la formulation

mathématique

de

chaque

indice sont testées dans cette

_analyse.

La relation linéaire établie entre le diamètre et la distance

_{jusqu’à laquelle chaque}

arbre _peut concurrencer _{n’est pas} consistante dans le

temps. Aussi, on _{propose des}

_règles

basées sur des fonctions non linéaires restreintes par une _asymptote

_supérieure.

L’utilisation d’un nombre fixe de

_{compétiteurs}

est aussi testé. L’évaluation de la

_capacité

de

_prédiction

de

_chaque

indice est basée sur sa

_performance

en fonction d’une

régression

multilinéaire pour la

prédiction

de l’accroissement annuel en surface terrière au niveau individuel. Les résultats mettent en évidence la

_{supériorité}

des indices de

_compétition

basés sur _{la fonction de Richard pour la sélection des}

compéti-teurs. Cette

_suprématie

est

_plus

évidente au moment où les arbres des classes de diamètre le

_plus

bas ne sont _pas

_supprimés

naturelle-ment.

_Lorsque

la

_{compétition asymétrique}

est évidente, les indices basés sur le

_polygone

de Voronoï montrent une meilleure

perfor-mance. _{(© Inra/Elsevier, Paris.)}

indices

_dépendants

de la distance / sélection des

_{compétiteurs}

/

_capacité

de

_prédiction

/

_{développement}

du

_peuplement

/

Eucalyptus globulus

Labill. /

_plantations

*

1.

Introduction

Competition

may be defined as an interaction between

individuals

_brought

about

_by

a shared

_requirement

for a resource in limited

_supply,

and

_leading

to a reduction in the

_survival,

_growth

and/or

_reproduction

of the individ-ual concerned

_[2].

The effect of

_competition

on

_growth

of individual trees has

_long

been studied in an _attempt to

predict

tree

_growth

as

_accurately

and

_precisely

as

possi-ble.

_{Distance-dependent competition}

indices are used to

predict

the

_performance

of focal individuals as a function

of the interference from a localised subset of other

_plants

[5].

These indices

_incorporate

in a mathematical

formu-lation the

number,

dimensions and location of certain

neighbours

that are selected as

_{competitors according}

to an

_empirical

rule.

_{Conceptually,}

one would _expect some

improvement

in

_precision

when

_comparing

models that

incorporate distance-dependent

measures as _regressors

against simpler

models that do not use them. However,

most of the

_comparisons

between

_{distance-dependent}

and

_{distance-independent}

individual tree

_growth

models do not report the

_expected

differences in

_prediction

abili-ty. One of the main reasons _{for this poor}

_efficiency

of

distance-dependent

competition

indices in

_explaining

tree

_growth

is the fact that the processes

controlling

inter-tree

_competition

are not well

_known,

_making

it

impossible

to

_{develop biologically}

consistent

competi-tion indices.

_Generally,

the

_competition

index

formula-tion

_{simply implies}

that

_competition

is _greater if the

sub-ject

tree has more

_neighbours

_(selected

with an

_empirical

rule),

if these

_neighbours

are

_larger

and if

_they

are close

[3, 7-9,

11, 14,

16, 23].

Depending

on the

_respective

for-mulation,

competition

indices

_implicitly

assume an

asymmetric

or

_symmetric

_partitioning

of

_plant

interfer-ence _processes into

_{neighbourhood}

effects and are then

used to

_{predict growth}

of trees

_growing

in stands of

dif-ferent ages

independently

of the _stage of stand

develop-ment.

_Competition

_{processes have been defined}

accord-ing

to two basic models:

_{symmetric/asymmetric}

and one-sided/two-sided

_competition

_{[4, 18, 31, 32].}

In two-sided

_competition

resources are shared

_(equally

or

pro-portionally

to

_{size) by}

all the trees while in one-sided

competition larger

trees are not affected

_by

smaller

neighbours

[4, 33].

When there is

_perfect

_sharing

relative

to size,

_competition

is

_symmetric

_[4].

In this

_study

one-sided

_competition

is considered as an extreme case of

asymmetric competition

and two-sided

_competition

is considered as

_being

_symmetric

or

_asymmetric

_according

to whether or not the

_sharing

of resources is

_proportional

to the size of the individuals.

Recently,

some indices have used crown measures,

therefore

_{reflecting competition}

for

_light

with some suc-cess

_[5,

_{14, 21, 22]. However,}

crown measures are not

always

available

and,

it has also been shown for some

species

that,

in the

_early

_stages of a

_stand,

_competition

for

_light

_may not be _present,

_although

the effects of

com-petition

for water and nutrients are evident.

_{Additionally,}

even when

_competition

for

_light

is the main factor

con-trolling

individual

_{plant growth,}

two-sided

_competition

for water and nutrients also controls

_{plant growth}

_[24].

The

_objective

_{of the research described in this paper}

was to select a

_competition

index for future use to model individual tree

_growth.

Some of the

_{existing competition}

indices were

_analysed

with

improvements being

pro-posed

when

_appropriate.

Particular attention was

_given

to the rules for the selection of

_competitors

in order to assess their

_importance

in the

_prediction

_ability

of the

indices in

_comparison

with the index formulation. It was also our

_objective

to test how the

_{prediction ability}

of

different

_competition

indices

(both

formulation and

rule)

depends

on the _stage of

_development

of the

stand,

i.e. if there is an overall best index

_applicable

_during

all the

life of the stand or not. The

_analysis

was based on data from

_eucalyptus

stands in

_{Portugal, managed}

in

planta-tions without

_thinnings

and without

_{density-dependent}

mortality,

in relation to which a detailed

_study

on the

changes

in structure,

variability

and relative

_growth

rate

pattern under different

_{intraspecific competition}

gradi-ents was available

[24].

2. Data

Eucalyptus globulus

is a

_{fast-growing species}

that was

introduced in

_Portugal

_{150 years ago. At present} it is the third most

_represented

forest

_species

in

_Portugal,

cover-ing

20.7 % of the total forestland and

_occupying

an area

of 3 358.8 x

10

3

ha

[10].

The success of

_eucalyptus

was a _{consequence, in part,} of

_good

environmental conditions in a substantial _part of the _country for

_{eucalyptus growth.}

In

fact,

eucalyptus species

are

_{highly productive}

even in

areas where

_drought

and nutrient stress occur in

_spite

of the fact that its

_productivity

is

_{strongly dependent}

on soil water and nutrient

_availability

_[13,

_19].

In

_Portugal,

eucalyptus plantations

are

_mainly

used

_by

the

_pulp

industry

and the trees are

_planted

at the final

_density

-thinning

and

_{pruning practices}

are not

_usually

carried

out. These stands are

_{intensively managed}

as a short

rotation

_coppice

_system

in which the first

_cycle

of

plant-ed

_seedlings

_(single

_stem)

is followed

_by

two or three

coppiced

stands,

with an _average

_{cutting cycle}

of 10-12 years.

Data from permanent

plots,

two

_spacing

trials and a

fertilisation and

_{irrigation experiment}

of

_Eucalyptus

globulus

Labill. in first

_rotation,

all located in the centre

cri-terion for the selection of these

_plots

was the

_availability

of tree co-ordinates or the

_possibility

of

_obtaining

them.

This data set includes ten

_plots

from the Alto do Vilão

spacing

trial with a _{range of densities between 500 and}

1667 trees

ha

-1

.

These

_plots

were used

_by

Tomé

[27]

in a

study involving

the evaluation of

_{distance-dependent}

competition

measures of different _types. The _permanent

plots

and the

_spacing

trials were remeasured at

approxi-mately

annual

intervals;

dbh of each tree, a

_sample

of

heights

and/or dominant

_height

were obtained in each measurement. Data about crown radius or

_height

of the base of the live crown were not available. Dbh and

height

of each tree were measured in the fertilisation and

irrigation experiment

at

_monthly

intervals

_during

the first

15

months,

every 2 months until the end of 1987 and

twice a _year thereafter. This

_experiment

was carried out at a 3 x 3-m

_spacing.

Table I _presents a _{summary of} the

_principal

variables that were

_gathered

in the 37

_plots

selected. An initial set of 54

_plots

was available but some of them were elimi-nated

_by

the use of the basal area factor

_(BAF)

1

m

2

ha

-1

as a rule to define the border trees in the calculation of the

_{distance-dependent}

indices. The border trees were selected for each remeasurement in _every

_plot

as a

func-tion of BAF = ₁ and the maximum diameter of _each

remeasurement. The

_{growth periods}

not

_{corresponding}

to 1 _year

_(or

_multiples

of

_that)

were eliminated as

euca-lyptus

is a

_species

characterised

_by

free

_growth

₁

_.

However, variations of 2 months were considered

acceptable.

After these eliminations there were 101

growth periods

available and a total number of

observa-tions at the tree level of 5 409.

1

free

_{growth -}

"involves

_elongation

of shoots

_by

simultaneous initiation and

_elongation

of new shoot _components as well as

expansion

of

_performed

_parts. Such

_plants,

which include

euca-lyptus,...,

continue to

_expand

their shoots late into the

sum-mer" [15].

Figure

I _presents the site index versus _{age and the} stand

_density

versus tree size

_graphics.

These

_provide

a

good

summary of the site and stand conditions represent-ed in the data base

_[30].

Site index was

_expressed

as the mean

_height

of the dominant trees

(100

largest

dbh trees

per

hectare)

at a base _{age of 10 years} and it was obtained

directly by interpolation

or estimated

_according

to Tomé

[28].

As can be seen

_{in figure}

11 there is a

_{representative}

range of sites and ages in the data set. The fertilisation and

_{irrigation experiment}

is well individualised

corre-sponding

to

_high

site indices and lower _{ages. Most} of the

plots

were monitored more than

_eight

times.

_Figure

1II shows that most of the

_plots,

_excluding

the

_spacing

trials,

had a similar

_{plantation density.}

In

_fact,

the

_pulp

compa-nies used the 3 x 3-m

_spacing

and small variations around

it

_during

the

_plantation

_period

under

_analysis

_{(table I).}

At

present there is a broader _{range of}

_spacings

and therefore

new

_plots

should be added to this database to obtain more

general

results. In the

_plots

used,

natural

_mortality

(self-thinning)

was not

found,

_reflecting

the

_{under-stocking}

of the

_{eucalyptus plantations}

in

_Portugal.

Two

_{plots, clearly}

shown

_{in figure}

1II,

are an

_exception,

with values of

mor-tality

of 23 % at 15 _{years and} 40 % at 25 _years.

3. Methods 3.1. Indices used

Most of the authors who

_{analysed existing}

competi-tion indices

_[e.g.

1, 3, 18, 29]

classified them into

dis-tance-weighted

size ratio

functions,

_{point density}

mea-sures, area

_overlap

indices and area

_potentially

available. These indices as well as the unilateral version of each

index and the modified version

developed by

Tomé and Burkhart

_[29]

were also

_analysed

_{(table II).}

The unilater-al as well as the modified indices reflect one-sided

usual area

_overlap

and

_{distance-weighted}

size ratio indices are

_typically

two-sided while the area

_potentially

available can be considered as

_assuming

a two-sided

asymmetric competition,

the level of _asymmetry

depend-ing

on the

_{weight given}

to the tree size in the definition of the area

_potentially

available.

One _aspect taken into consideration in the

_study

of

distance-dependent competition

measures is the

defini-tion of border trees. Two different

_approaches

can be

used:

₁₎

to simulate the border trees, which involves the reflection or translation of the trees inside the

_plot

to

form a border

_strip

with trees similar in size and distribu-tion with the

_plot;

₂₎

to define the border trees from the

trees on the

_plot

and close to the

_plot

limit. In the first

case,

approaches

based on the linear

_expansion

method can also be utilised

_[17].

In

_fact,

the use of these

simula-tion

_{methodologies}

on

_applications

of the

_competition

indices can be

_accepted

but when the

_objective

is the

comparison

of the

_{prediction ability}

of alternative indices these

_{methodologies}

_may bias the results. In that

case the measurement of real border trees should be

con-sidered.

_Accordingly,

in this

_study

the border trees were

selected from the trees inside the

_plots

so that _every

sub-ject

tree’s

_{possible neighbours}

had been measured.

3.2. Rules to select

_competitor

trees

To

_analyse

the influence of the rules to select

com-petitors

on the

_ability

of the index to

_{predict growth}

some traditional rules and new rules were tested. The

rules to select

_competitors

are

_usually

based on a fixed distance or a fixed number of trees, on

_overlap

areas or

on basal area

_factors,

_depending

on the

_type

of

competi-tion index used.

The area

_potentially

available index _represents the area of the smaller

_polygon

built with the

_{perpendiculars}

relative to the

_subject

tree and its

_neighbours,

and selects as

_competitors

the trees whose

_{perpendiculars}

contribute

to the definition of this

_polygon.

In this

_study

a

maxi-mum of 35 trees was used as

_potential

_competitors.

The tree basal area and its _square were tested

_(APA2

and

APA4,

respectively).

The APA4

_gives

a

_larger

propor-tion of space to

_bigger

trees than APA2.

The

_{distance-weighted}

size ratio functions and

_point

density

measures were calculated for BAF 1 and 4

m

2

ha

-1

.

BAF

1 is associated with a

_greater

number of

competitors

when

_compared

with BAF 4. From the two

modalities of

_{point density}

measures

_{presented by Spurr}

[26],

including

and

_excluding

the

_subject

tree, the second

was

_consistently

better in our data.

As crown measurements were not

_available,

the area

overlap

indices had to be calculated

_using

two

_empirical

definitions of radius of influence area

_(0.125

x

_dbh;

0.25

x

_dbh).

The first definition

_corresponds

_{approximately}

to a BAF of 4 and the second to a BAF of 1. The rules to select

_competitors

based on BAF define a linear

_positive

relationship

between the distance and the size of the tree. For

instance,

a tree with 40-cm

diameter,

for BAF =

1,

competes

until a distance of 20 m and is therefore associ-ated with a

_high

number of

_{competitors (figure}

_2I).

In

practice,

and in

_plantations,

it is not

_probable

that one tree has a

_strong

effect on the

_growth

of

_neighbours

that are 20 m _away

_(more

than six rows _apart for a 3 x 3-m

Each selected

_competitor

has its own contribution to

the value of the index and this contribution must

decrease when the distance increases or the size

decreas-es. New rules based on

_{asymptotically}

restricted non-lin-ear functions of tree size are

_proposed

in this _paper.

These rules are

specific

for the

_{distance-weighted}

size

ratio function indices and

_{point density}

measures both in

their traditional and modified formulations. The selected

functions were

_hyperbolic

and monomolecular and

Richards’ function _(see mathematical formulations in

figure

21,

II, III,

_{respectively).}

The monomolecular func-tion is a

particular

case of Richards’ function when m = 0. This selection was based on the

_graphical

form of

these functions in their

_integral

formulation and on the existence of a

_superior

_asymptote. Each of these

func-tions has two to three _parameters: one of them

_being

the

asymptote A and the others

(k,

m)

being shape

parame-ters

_(figure

2).

Based on the results of a

_{previous study}

by

Soares and Tomé

[25],

a value of 7 m for the asymp-tote was used. This distance is a function of tree size

and,

for the

_bigger

trees, it

_approaches

7 m. The

asymp-tote of 7 m was found to be the more

_appropriate

based on a

_{previous study}

in which different _asymptotes were

tested. This value refers

_only

to

_eucalyptus

trees in

plan-tation

(densities

ranging

from 1 000 to 1 600 trees _per

hectare).

Both functions were restricted to obtain null

co-ordinates in the

_origin.

Different values were tested for the m and k _parameters. A fixed number of

_competitors

(four

or

_eight)

were also tested.

The

_consistency

of the different rules that were

tested,

as well as the selection of the _parameters in the

asymp-totically

restricted non-linear functions of tree size

(test-ing

one value of _asymptote and several values for the k and m

_parameters),

was

_mainly

based on the number of

selected

_competitors

for a

particular

rule in different _age

classes.

3.3. Definition of

_stages

of stand

_development

The

_study

of evidence and

_intensity

of

_competition

present in the selected data at different moments in time was

_analysed.

For

that,

and based on

_{Perry [20],}

the data were

_initially

divided into three subsets

representing

dif-ferent

_competition

_stages of stand

_development:

1)

small

negative

and

_{significantly}

different from zero;

2)

RGR differs little _among social classes - correlation coeffi-cient not

_{significantly}

different from zero;

3)

trees in the lower diameter classes are

_{suppressed -}

correlation

coef-ficient between RGR and dbh

_positive

and

_{significantly}

different from zero.

The characterisation of the data subsets is

_presented

in table III. It was

_anticipated

that the two-sided oriented

indices would

_give

better

_predictions

for subset 1 while the unilateral or

_asymmetric

versions would be more

appropriate

to

_predict

_growth

in subsets 2 and 3.

3.4. Prediction

_ability

The

_growth

of individual trees on

_particular

sites is influenced

_by

a number of factors such as tree character-istics

_(size

and

_age),

_{microenvironment,}

_genetic

charac-teristics and

_competitive

status

_[29].

One of the most

important predictors

of how a tree _grows is its own size

[20]

because _past

_competitive

interactions are

_integrated

in current tree size and also because

_variability

is

intro-duced as a _consequence of

_genotypic

differences in

response to

_competition

and of environmental

hetero-geneity

[6].

Stand

_density

_expresses differences in tree

growth

among different

stands,

the relative dimension of the tree _expresses the dominance of a tree in relation to

other trees in the stand and

_competition

indices _express

local

_competition

_among a tree and its

_neighbours.

The

_study

of the

_prediction

_ability

of

distance-depen-dent indices was based both on:

-

simple

correlation of each index with tree basal area

growth

for each one of the data subsets

considered;

-

performance

in a

_multiple

linear

_{regression equation}

to

_predict

the annual increment of tree basal area where

variables

_{characterising}

the stand and the individual tree were

_present:

where

_i

_b

is the annual increment in tree basal area;

_S

_h,t

_,

represents a measure of site

_productivity

(site index);

TD

expresses tree initial characteristics

(diameter, dbh;

tree

basal area,

b);

RTD is a measure of the relative tree dimension

(ratio

between tree basal area and stand basal area, RBM; ratio between dbh and the

_quadratic

mean

dbh, RDM);

and SC expresses the

competition

at stand level

_(number

of trees _per

hectare,

N; basal area _per

hectare,

G; the inverse of each of these variables,

l/N,

l/G).

An all

_{possible regression algorithm}

was used to select the best model out of a

_large

set of tree and stand

variables

_representing

site

index,

initial tree

size,

stand

density

and relative tree size. The selection of the model was based on measures of

_multiple

linear

_regression

quality

and

_{prediction ability: adjusted R}

₂

_,

residual mean square

(RMS),

prediction

sum of _squares

(PRESS)

and sum of absolute

_prediction

errors

_(APRESS).

The

pres-ence of

_colinearity

in the models was

_{analysed through}

the values of the variance inflation factors

_(VIF).

This

study

was carried out

_separately

for each one of the data

4.

Results

and

discussion

4.1. Rules to select

_competitor

trees

Table

Iva,

b shows the number of observations obtained with six different rules to select

_competitors

in each one of the

_possible

combinations of ’number of selected

_{competitors/age’.}

To

_analyse

these tables the

stage

of stand

_development

_{represented by}

each one of the data subsets was considered. For rules based on

BAF = ₄

m

2

ha

-1

,

in

32 _% of the observations in age

class

]36, 60]

months no

_competitors

were selected

(table

IVa).

Based on the conclusions of

_previous

studies

[24],

considering

the age and the

development

of the

stand,

the non-existence of

_{competition relationships}

between trees was not

_expected

_{for these ages.} In

fact,

if the low number of selected

_{competitors by}

this rule for

older stands

_(maximum

of 12

_competitors)

seems

_logical

for

_planted

stands,

the

_high

_percentage

associated with

no

_competitors

in this _age class is not

_biologically

con-sistent. For BAF = 1

m

2

ha

-1

,

41

and 84 % of the

obser-vations in the _age classes

_{] 108, 132]}

and

_{]132, 216]}

months,

respectively,

were associated with a number of

competitors

superior

to 20 that seems too

_large

from a

biological standpoint.

On the selection of the

_parameters

for the new rules to

select

_competitors

in the classes of both no

_competitors

and age

greater

than 24 months as well as in the classes

of more than 20

_competitors,

a reduced or low number of

observations was

_required

_{(table IVb).}

_Accordingly,

the

following

parameter values were selected:

_hyperbolic

function k = 0.2 and

_0.3;

monomolecular function k = 10

and

15;

Richards’ function k = 15 and

30;

m = 1/2 and

4.2. Prediction

_ability

Table V

_presents

the linear tree basal area

_growth

models selected for the three

_stages

of stand

develop-ment considered. The best model with four variables was

similar for each one of the

_stages

of stand

_development

considered,

involving

site

_{index, dbh,}

RDM or RBM and

basal area _per hectare. In the latter _stages of stand devel-opment the RBM had a better contribution to the tree

basal area

_growth

model while in the other _stages the

RDM was

_superior.

This result _may be

_{justified by}

the fact

_that,

for

_eucalyptus

trees, the exponent in the

allo-metric

_relationship

between

_weight

and dbh increases with _age

_{[ 12].}

The RDM and _{RBM may both express,} at

different _{ages, the} ratio between the

_subject

tree biomass

and the tree of mean biomass.

The contribution of each

_competition

index to the tree

basal area

_growth

model is

_presented

in table VI. APA

indices were excluded from the

_analysis,

as

_they

are

quite

different both in the mathematical formulation and

in the way the

_competitors

are selected. The

_superiority

of the rules to select

_competitors

based on the Richards’

function is evident from this

table,

particularity

in the

modality

2

_(A

=

_7,

k = 30 and _m =

_9/10).

It is also

evi-dent that the contribution of a certain index formulation

(mathematical

expression

and selection

_rule)

is different for each

_stage

of stand

_development.

In the initial _stages

DR indices are

_{generally non-significant}

with the excep-tion of those defined

_by

the Richards’ function

_(namely

modality

2) and,

to a certain extent, BAF = 4. The AO

indices are

_{poorly significant}

for BAF = 1 and

non-sig-nificant for BAF = 4. The contribution of PD measures is

strong

superiority

of the Richards’

function,

in

_particular

if associated with the unilateral version.

_However,

the

expected superiority

of the unilateral or modified

ver-sions of the indices is not clear. Most of the tested indices are not

_significant

in the intermediate _stage of stand

_development.

An

_exception

is the DR indices

asso-ciated with the Richards’

function,

namely

in the modali-ty 2 with the unilateral and modified versions

_being

slightly superior

to the traditional one. This lack of

sig-nificance of

competition

indices in this intermediate stage may indicate that this data set

_joins

remeasure-ments that are not

_clearly

from the initial _stages of stand

development

nor show evidence effects of

_suppression

of small trees. Note that this is the smallest of the three

subsets. Later in stand

_development,

when there is

evi-dence of

_suppression

of small trees, the unilateral and modified versions of the DR indices associated with the

modality

of the Richards’ function were

_{clearly superior}

Finally,

the

_superiority

of the APA indices in the last

stage of stand

_development

is also evident with the APA indices

_showing

the

_{highest partial}

correlation in

multi-ple regression

with tree basal area

_growth.

Tomé and

Burkhart

_[29]

and Tomé

_[27]

with adult

_eucalyptus

stands have obtained identical results.

APA4,

which

gives

more

_weight

to

_larger

trees, shows greater F-values

reinforcing

the _{presence of}

_asymmetric

_competition

in

the data.

The

DRU,

based on Richards’ function with

asymp-tote 7, k = 30 and _m = 9/10 _presents the best contribution

when

_analysed

_{simultaneously}

in each subset and with

all the data. In

fact,

the contribution of the DRU to the tree basal area

_growth

model defined for all the data

(model

with four variables -

_S

_h,t

_,

_d,

G and

_RDM)

corre-sponded

to a

_partial

F of

_162.2,

the

_{highest partial}

F-value when all the data were considered as a whole

_(very

similar to the value of 161.5 obtained with

_APA4).

The correlation coefficients of some

_competition

indices with tree basal area

_growth

are

_presented

in table VII. The lack of

_{correspondence}

between the values of correlation coefficients and the contribution of each index to the tree basal area

_growth

model reinforces the scant information

_given

_by

the correlation coefficients when

_analysed

_per se. For

_instance,

in the last

_stage

of

stand

_development,

the PDU _presents the

_highest

absolute values but this

_type

of index has no

_significant

contribution to the tree basal area

_growth

model

_(table

VI).

This fact is a _{consequence of the}

_relationship

between some of the indices and the other variables

already

present

in the model

_{(colinearity).}

As

_expected,

all the indices

_{indicating competitive}

stress present

negative

correlation with

_growth,

while the APA indices

_{expressing competitive advantages}

show

positive

correlation.

_Analysing

the correlation between

competition

indices and tree basal area

_growth

over an

increased

_intensity

of

_{asymmetric competition -}

subset 1 to subset 3 - it can be observed that the correlation

coef-ficients are small in subset 1 and increase as the asym-metric

_competition

increases. This behaviour was not observed with the DRM and DD as well as with the APA

indices.

5. Conclusion

Indices based on

_{asymptotically}

restricted non-linear functions of tree size as rules for

_selecting

_competitor

trees

_present,

when

_compared

with the BAF

rule,

a

high-er contribution to

_multiple

linear

_regression

models. The

Richards’ function defined

_by

_asymptote 7 m and

_shape

form

_parameters

k = 30 and _m = 9/10 _{seems to} be

supremacy of the indices based on the Richards’ func-tions was observed for all _stages of stand

_development.

The DRU

indices,

based on the Richards’

function,

make a

_significant

contribution to the tree basal area

growth

model in all of the

_analysed

data subsets.

However,

later in stand

_development,

when there is evi-dence of

_suppression

of small trees, the APA4 seemed to

present

a better

_performance.

Acknowledgements:

Financial

_support

for this

pro-ject

was

_{provided by}

the

projects

AIR2-CT93-1678

’Improvement

of

_eucalyptus

_management. An

_integrated

approach:

breeding,

silviculture and economics’ and

PAMAF 4025 ’Influência do _compasso no crescimento e

produção

de

_plantações

de

_{Eucalyptus globulus}

Labill. e Pinus

_pinaster

Ait. em diferentes ambientes

_{ecológicos’.}

We

_{acknowledge unpublished}

data

_{provided by}

the

_pulp

company STORA CELBI.

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