Xavier Girardet

Laboratoire ThéMA UMR 6049

UBFC / CNRS

Besançon

Modél i sat ion des réseaux

écologiques en écologie

du paysage :

l es graphes paysagers

Séminaire Atelier 8 /

ISIG, « Graphes et

réseaux en géographie »

De la mise sous cloche.. …aux réseaux écologiques

20001900 2010

De la mise sous cloche.. …aux réseaux écologiques

L’émergence d’une discipline

20001900 2010

1970 1980 1990

De la mise sous cloche.. …aux réseaux écologiques

L’émergence d’une discipline

Les graphes paysagers

20001900 2010

1970 1980 1990

2001 2006 2008 2012

From landscape structures to landscape networks

Artistic movement: focus on the nature

Protection of aesthetics landscape

1. De la mise sous cloche.. …aux réseaux écologiques

From landscape structures to landscape networks

Protection of spectacular landscape

1. De la mise sous cloche.. …aux réseaux écologiques

From landscape structures to landscape networks

Protection of flora and fauna

In 1995, Germany had

5,314 nature reserves

1. De la mise sous cloche.. …aux réseaux écologiques

From landscape structures to landscape networks

Protection of flora and fauna

1. De la mise sous cloche.. …aux réseaux écologiques

From landscape structures to landscape networks

Networks of ecosystems

1. De la mise sous cloche.. …aux réseaux écologiques

From landscape structures to landscape networks

Ecological networks

1. De la mise sous cloche.. …aux réseaux écologiques

From landscape structures to landscape networks

Ecological networks

1. De la mise sous cloche.. …aux réseaux écologiques

From landscape structures to landscape networks

- Ecological networks- Landscape connectivity

Structural connectivity Functional connectivity

Landscape networks

1. De la mise sous cloche.. …aux réseaux écologiques

What is landscape ecology ?

LandscapeEcology

Broad Extents

K. McGarigal

2. L’émergence d’une discipline

What is landscape ecology ?

3 fundamental principles

1. The effect of spatial heterogeneity on ecological processes

2. The role of humans

3. A broad spatial scale: the landscape

2. L’émergence d’une discipline

The effect of spatial heterogeneity on ecological processes

MacArthur & Wilson (1967): The Theory of Island Biogeography

2. L’émergence d’une discipline

The effect of spatial heterogeneity on ecological processes

Forman & Godron (1986) : Landscape mosaic model

2. L’émergence d’une discipline

The effect of spatial heterogeneity on ecological processes

Metapopulation models: the first step to landscape connectivity

2. L’émergence d’une discipline

The role of humans

Forman (1995): Landscape fragmentation

2. L’émergence d’une discipline

A broad spatial scale: the landscape

Delcourt & Delcourt (1988) and Allen & Starr (1988):The hierarchical theory. Space and time are linked !

2. L’émergence d’une discipline

What is a landscape graph ?

Function

Reality

Model

3. Les graphes paysagers

3. Landscape graphs : origins

3. Landscape graphs : the sequel

3. Landscape graphs : the prequel

3. Intégration dans les scenarios de gestion et d’aménagement

Construction des graphes paysagers

Construction

des graphes

paysagers

Graph construction: identification of habitat patches and links

Landscape map

Suitable elements Barrier elementsOptimal habitat

Friction for speciesmovements

Minimum patch area

LANDSCAPE GRAPH

Construction des graphes paysagers

Mapping landscape

Input data

Landscape map in raster format

Categories defined accordingto a species/landscaperelation

Usually: cost value (friction) for each landscape category

Construction des graphes paysagers

Defining habitat patches

Patches = graph nodes

o Minimum patch area

o Connexity

o Capacity

Construction des graphes paysagers

Defining habitat patches

Patches = graph nodes

o Minimum patch area

o Connexity

4-connexity 8-connexity

Cell adjacent to the orange one

Focal cell

1

3

4-connexity=> 3 patches

8-connexity=> 1 patch

2 1

1

1

Construction des graphes paysagers

Defining habitat patches

Patches = graph nodes

o Minimum patch area

o Connexity

o Capacity

capacity = intrinsic quality of the patch as an indicator of its demographic potential

Function of the isotropicneighbourhood

Area of the habitat patch

Suitable elements Unfavourable elementsHabitat patches

Function of the anisotropicneighbourhood

Construction des graphes paysagers

Defining links

Voronoipolygon

Construction des graphes paysagers

Defining links

Topology- Complete- Planar

Direction

Distance- Euclidean distance- Least-cost distance

Threshold

Construction des graphes paysagers

Defining links

Topology- Complete- Planar

Direction

Distance- Euclidean distance- Least-cost distance

Threshold

Construction des graphes paysagers

Defining links

Topology- Complete- Planar

Direction

Distance- Euclidean distance- Least-cost distance

Threshold

Construction des graphes paysagers

Defining links

Topology- Complete- Planar

Direction

Distance- Euclidean distance- Least-cost distance

Threshold

Construction des graphes paysagers

Defining links

Topology- Planar- Complete

Direction

Distance- Euclidean distance- Least-cost distance

Threshold

Construction des graphes paysagers

Defining links

Topology- Planar- Complete

Direction

Distance- Euclidean distance- Least-cost distance

Threshold

Construction des graphes paysagers

Defining links

Topology- Planar- Complete

Direction

Distance- Euclidean distance- Least-cost distance

Threshold

Construction des graphes paysagers

Defining links

Topology- Planar- Complete

Direction

Distance- Euclidean distance- Least-cost distance

Threshold

Construction des graphes paysagers

Defining links

Land-use categories Function Cost

1 Ponds Habitat 1

2 Water Suitable 10

3 Built-up areas and infrastructures Unfavourable 1000

4 Forests Suitable 10

5 Wetlands Suitable 10

6 Croplands Unfavourable 1000

7 Grasslands Suitable 10

8 TGV line Unfavourable 2000

Construction des graphes paysagers

Defining links

Graph threshold

only links shorter than the threshold distance are kept.

(maximum dispersal distance of a given species)

Construction des graphes paysagers

Computing connectivity metrics

Several levels:

localcomponentglobal

Many metrics in graph theory…Rayfield B, Fortin MJ, Fall A, 2011. Connectivity for conservation: a framework to classify network measures. Ecology 92: 847-858.

Construction des graphes paysagers

Computing connectivity metrics

Sum of capacity of patches connected to the patch i

i

… weighted according to the minimum distance to the focal patch

=> indicator of the potential dispersion from/to the patch i

Similar to the degree index

i i

Construction des graphes paysagers

Computing connectivity metrics

Sum of the shortest paths through the focal patch i.

i

weighted both by the capacity of the twoend patches and by the distance betweenthem.

=> frequency of use of the patch i

Construction des graphes paysagers