Modelling the spatial structure of heterogeneous stands.

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Modelling the spatial structure of heterogeneous stands.

Example of sessile oak (Quercus petraea) – Scots- pine (Pinus sylvestris)) mixed stands of the

Orleans forest in France.

M.A. Ngo Bieng¹² C. Ginisty¹

F. Goreaud²

1 Research group « Forest ecosystem » (CEMAGREF Nogent / Vernisson, France).

2Laboratory of engineering for complex systems (CEMAGREF Clermont – Ferrand, France).

IUFRO 1. 14. 00 Research group conference. May 14-18, 2006. Rouyn-Noranda, Québec Canada Natural disturbance - Based silviculture – Managing for complexity

Agricultural and environmental engineering research

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Outline

I. Introduction

II. The Orleans forest

III. Spatial structure analysis

IV. Results : Oak and Scots pine mixed stands typology

V. Prospect: spatial structure modelling

VI. Conclusion

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I. Introduction I.1 Context

I.2 My PHD Project

I.3 Strategy

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I.1 Context

Introduction

Complex stands (

mixed and / or irregular)

Individual Based Model (IBM)

Growth modelling Description

Complex dynamics

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I.1 Context

For complex stands:

Introduction

Initial state Simulation

proceed

IBM

Description

(species, circumference, height)

Location

(local environment)

of each tree

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I.1 Context

For complex stands:

Introduction

Initial state Simulation

proceed IBM

Virtual stand

Stand level characteristics

Model of structure

Realistic

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I.2 My PHD Project

Build a realistic model of structure

Illustrate it on mixed stands sessile oak

(Quercus petraea) – Scots-pine (Pinus sylvestris) of the Orleans forest

Introduction

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I.3 Strategy (and aim of my presentation)

Study and characterize precisely the studied stand spatial structure

Identify spatial types

Build a model of structure for each types

(Reconstruction of real identified spatial types)

Introduction

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II. The Orleans forest

II.1 Presentation of the study site

II.2 Data collection

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II.1 Study site.

The Orleans forest

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II.1 Study site.

26 * 1 ha mapped plots

The Orleans forest

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II.2 Data collection

For each tree (C >=23cm)

distance angle

Species name Circumference Relative height

Theodolite Prism

The Orleans forest

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II.2 Data collection

26 maps of 1ha plots

The Orleans forest

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III. Spatial structure analysis

III.1 Specific spatial structure III.2 Intertype structure

III.3 One example

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Arrangement of trees in space

Spatial structure analysis

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III.1 specific spatial structure

random

Regularity Aggregation

0 100

L(r) = 0 Κ( r)= π r

²

0 100

L(r) < 0

0 100

L(r) >0

Spécific structure by L(r) function (Besag in Ripley, 1977)

L(r) = (K(r)/ π)

^1/2

– r

Spatial structure analysis

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III.1 specific spatial struture

Specific structure by L(r) function (Besag in Ripley, 1977)

L(r) = (K(r)/ π)

^1/2

– r

random regular clustered

-4 -3 -2 -1 0 1 2 3 4

10 20 30 40 50

L(r)

range r

Spatial structure analysis

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III.2 Intertype structure

Interaction structure by L

₁₂

(r) function

(Lotwick and Silvermann, 1982)

. L

₁₂

(r) = (K(r)/ π)

^1/2

– r

Repulsion Independence Attraction

0 50 100

L

₁₂

(r) < 0 L

₁₂

(r) = 0

Κ

₁₂

( r)= π r

²

L

₁₂

(r) >0

Spatial structure analysis

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III.3 one example

Defining sub-populations:

Other species

pines

oaks

100m

Spatial structure analysis

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III.3 one example.

L(r) for Scots pine

-4 -2 0 2 4 6 8

0 10 20 30 40 50

L(r) CSR CSR (a)

aggregation

L(r) for Oaks from the canopy

-4 -2 0 2 4 6 8

0 10 20 30 40 50

L(r) CSR CSR (b)

aggregation

L12(r) : Oaks canopy vs. Scots pine

-8 -6 -4 -2 0 2 4 6

0 10 20 30 40 50

L12(r) Pop. Ind.

Pop. Ind.

(d)

repulsion

Plot 5

0 25 50 75

-50 -25 0 25 50

canopy oaks canopy Plot 5

0 25 50 75

-50 -25 0 25 50

canopy oaks Plot 5

0 25 50 75

-50 -25 0 25 50

canopy pines

Spatial structure analysis

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IV. Results: stands typology IV. 1 General principle IV. 2 Canopy typology

IV.3 Understorey typology

Iv.4 Conclusion

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IV.1 General principle

Identification of detailed spatial characteristics of each 26 plots

aggregation \ Random\ regularity attraction \ independence\ repulsion

Separate canopy from understorey

Results

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IV.1 General principle

Typology: putting together plots with similar spatial characteristics

1- for canopy

Specific spatial structure of canopy oaks Specific spatial structure of canopy pines

Intertype structure canopy oaks-canopy pines Results

Plot 5

0 25 50 75

-50 -25 0 25 50

canopy oaks canopy Plot 5

0 25 50 75

-50 -25 0 25 50

canopy oaks

Plot 5

0 25 50 75

-50 -25 0 25 50

canopy pines

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IV.1 General principle

Typology: putting together plots with similar spatial characteristics

2- for understorey

Specific spatial structure of understorey oaks

Intertype structure understorey oaks-canopy oaks Intertype structure understorey oaks-canopy pines Results

Plot 5

0 25 50 75

-50 -25 0 25 50

understorey oaks

Plot 5

0 25 50 75

-50 -25 0 25 50

canopy oaks understorey oaks

Plot 5

0 25 50 75

-50 -25 0 25 50

canopy pines understorey oaks

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IV.2 Canopy typology

Results

Plot 3

0 25 50

-50 -25 0 25 50

canopy oaks canopy pines

(I) canopy pine

(oak in understorey)

(I) (II)

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IV.2 Canopy typology

Results

(II) (I)

(II) oak - pine canopy

Type 1 Type 2 Type 3 Type 4

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IV.2 Canopy typology

Results

Plot 5

0 25 50 75

-50 -25 0 25 50

canopy oaks canopy

Type 1:

- Strong aggregation for oaks and pines

- repulsion

(II)

(I)

^{Type 1} ^{Type 2} ^{Type 3} ^{Type 4}

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IV.2 Canopy typology

Results

Plot 2

0 25 50 75

-50 -25 0 25 50

Type 2:

- Aggregation for oak and pine (less)

- Repulsion (less)

(II)

(I)

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IV.2 Canopy typology

Results

Plot 17

0 25 50

-50 -25 0 25 50

Type 3:

- Random structure for oak and pine

- independence

(II)

(I)

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IV.2 Canopy typology

Results

Plot 13

0 25 50 75

-50 -25 0 25 50

(II)

(I)

Type 4:

- Random structure for oak; agregation for pine - Independence or slight

repulsion

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IV.3 Understorey typology

Results

(I) (II)

Plot 4

0 25 50 75

-50 -25 0 25 50

understorey oak

(I) aggregation for oaks

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IV.3 Understorey typology

Results

(I) (II)

Type 3

Type 4

plot 1

0 25 50 75

-50 -25 0 25 50

understorey oaks

Plot 1

0 25 50 75

-50 -25 0 25 50

(II) less aggregation for oaks Non significant attraction

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IV.3 Understorey typology

Results

(I) (II)

Plot 5

0 25 50 75

-50 -25 0 25 50

understorey oaks

Plot 5

0 25 50 75

-50 -25 0 25 50

(II) less aggregation for oaks Non significant repulsion

Type 3

Type 4

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IV.4 Conclusion

For canopy: a gradient

…to random

…to independence

From aggregation….

From repulsion

Results

Plot 5

0 25 50 75

-50 -25 0 25 50

canopy oaks canopy

Plot 17

0 25 50

-50 -25 0 25 50

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IV.4 Conclusion

For Understorey:

aggregation (at different level) is the most common structure

Few or no intertype relations not differing significantly from independence.

Results

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V. Prospect: Spatial structure modelling V.1 General principle

V.2 One example

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V.1 General principle

Average spatial characteristics for each identified type

Build of a model of spatial structure for each type

Prospect: spatial structure modelling

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V.2 One example (on canopy trees) Type 1:

Prospect: spatial structure modelling

-1 0 1 2 3 4 5 6 7 8 9

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Plot 5 Plot 16 Plot 10 Plot 1 Plot 11

-3 -2 -1 0 1 2 3 4 5 6 7

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

-7 -6 -5 -4 -3 -2 -1 0

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

L(r) for canopy oaks

L₁₂(r) between canopy oaks ans pines L(r) for canopy pines

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V.2 One example (on canopy trees) Type 1:Average spatial characteristics

Aggregated spatial pattern of canopy oaks Aggregated spatial pattern of canopy pines Repulsive Intertype structure between canopy oaks and canopy pines

Build of a model of spatial structure for type 1

Prospect: spatial structure modelling

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V.2 One example (on canopy trees) Build of a model of spatial structure for type 1

Aggregated spatial pattern of canopy pines

Reconctruction of spatial pattern by appropriate point processes (Diggle, 1983)

Prospect: spatial structure modelling

-3 -2 -1 0 1 2 3 4 5 6 7

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Plot 5 Plot 16 Plot 10 Plot 1 Plot 11

L(r) for canopy pines

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V.2 One example (on canopy trees) Build of a model of spatial structure for type 1

Aggregated spatial pattern of canopy pines

Reconctruction of spatial pattern by appropriate point processes

Parameters: - Number, radius and density of aggregates

Prospect: spatial structure modelling

Neyman Scott process

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V.2 One example (on canopy trees) Build of a model of spatial structure for type 1

Aggregated spatial pattern of canopy pines

Reconctruction of spatial pattern by appropriate point processes

Prospect: spatial structure modelling

Neyman Scott Process

1ha Plot simulated with a Neyman-Scott process

0 20 40 60 80 100

Scots pine (a)

-6 -4 -2 0 2 4 6 8 10

2 6 10 14 18 22 26 30 34 38 42 46 50

L(r)B simulated Lic- Lic+

Simulated pattern

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V.2 One example (on canopy trees) Build of a model of spatial structure for type 1

Aggregated spatial pattern of canopy oaks; intertype structure of repulsion

Reconctruction of spatial pattern by appropriate point processes

Prospect: spatial structure modelling

L(r) for canopy oaks

-1 0 1 2 3 4 5 6 7 8 9

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Plot 5 Plot 16 Plot 10 Plot 1 Plot 11

-7 -6 -5 -4 -3 -2 -1 0

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

L₁₂(r) canopy oaks / pines

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V.2 One example

Build of a model of spatial structure for type 1

Aggregated spatial pattern of canopy oaks; intertype structure of repulsion

Reconctruction of spatial pattern by appropriate point processes

Parameters: - Number of points, minimal distance to pine

Prospect: spatial structure modelling

Interspecific gibbs proccess

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V.2 One example

Build of a model of spatial structure for type 1

Aggregated spatial pattern of canopy oaks; intertype structure of repulsion

Reconctruction of spatial pattern by appropriate point processes (Diggle, 1983)

Prospect: spatial structure modelling

Interspecific gibbs proccess

1ha Plot simulated with a repulsive Gibbs process

0 20 40 60 80 100

Scots pine Oaks canopy

(a)

-12 -10 -8 -6 -4 -2 0 2 4 6

2 6 10 14 18 22 26 30 34 38 42 46 50 L12(r)

L12ic- L12ic+

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

2 6 10 14 18 22 26 30 34 38 42 46 50

L(r)A Simulated Lic- Lic+

Simulated pattern

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VI. Conclusion

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Build of a typology of oak- Scots pine mixed stands

A typology based on spatial structure

5 canopy and 3 understorey spatial types identified

Conclusion

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For each types

Spatial characteristics

(individual description and local environment)

that can be simulated

Stand level characteristics

⁽

tree density, presence or absence of species in the understorey, basal area,

diameter classes, few inter-tree distances)

Conclusion

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Conclusion

Virtual stand Experimental plots

Spatial structure analysis

Typology

^Point

process

For any stand

Results with IBM

simulation

Stand level characteristics

Inter-tree distance

Diameter classes Basal area

Tree density

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