Cognitive ability affects connectivity in metapopulation:

A simulation approach

Séverine Vuilleumier

The University of Queensland

Pop 2

Pop 1

Patch1

Patch 2

C12

C21

Context: spatially-explicit metapopulation model

Fragmented landscape

e2

e1

Landscape heterogeneities and structures / animal behavior

travel path and cost

iji j i i i

dpc p (1 p ) e p

dt

What is the influence of cognitive abilities on the connectivity in metapopulation ?

Question

What is the influence of cognitive abilities on the connectivity in metapopulation ?

Question

Simulation of interactions between individuals and landscape features during dispersal ?

Therefore, the model must contain ….

• the dispersal abilities and the behavioral traits of the animal

• landscape representation with its properties according to animal dispersal (visibility, attractiveness, cost, etc.)

Landscape model

Animal model

Assumptions

• Species are moving on the ground

• An individual moves across an unfamiliar landscape

• Searching behaviour is driven by finding a new habitat patch

• Animals are constrained by time, energy and mobility

• Animals use their environment to direct searching

The landscape : an irregular grid in shape and dimension

Landscape model

Cell

Frontier

Nodes

Cell

Allows all spatial representations, roads, habitat patches, etc.

Hedges

Tree

Rocks

Rivers

Bush

Fallen rocks

Trail

Quarry

Fruit tree

Vineyard

Lake

Inhabited area

Quarry

Swamp and bush

Swamp

Swamp and forest

Swamp and scattered forest

Cultivated land

Forest

Scattered forest

Hedges

Tree

Rocks

Rivers

Bush

Fallen rocks

Trail

Quarry

Fruit tree

Vineyard

Lake

Inhabited area

Quarry

Swamp and bush

Swamp

Swamp and forest

Swamp and scattered forest

Cultivated land

Forest

Scattered forest

First category roadSecond category road Third category roadFourth category roadFifth category roadSixth category roadHighway ASteamHedge AHighway BHedge BRailroad AFruit treeFourth category road BFourth category road CSixth category roadRailroad BFootbridgeTrain station

Landscape model: Illustration

(1) Blind Strategy (B) : no knowledge of the environment

(2) Near-Sighted Strategy (N) : use of the neighbouring environment to direct their movements

(3) Far-Sighted Strategy (F) : use of the neighbouring environment and visual scanning of the environment to find a new habitat patch

Animal cognitive abilities

Animal Model

While the individual has enough energy and has not reached a habitat patch, it goes on and chooses with the help of a pseudorandom number a new cell depending on :

Movement strategy algorithms

Animal Model

(i) the possibility to cross the frontier and the cell,

(ii) a probability (computed dynamically)

•Blind: depends on the frontier length.

•Near-sighted: depends on the attractiveness of neighboring cells and frontiers.

•Far-sighted: depends on the attractiveness of cells and frontiers and on the shortest way to a habitat patch that is in the perceptual range

Probabilities

Pn

P1

P2

P3

F3Fn

F2F1 Cell 2

Cell 1

Cell 3Cell n

?

…Pn

P1

P2

P3

F3Fn

F2F1 Cell 2

Cell 1

Cell 3Cell n

?

…

What is the influence of cognitive abilities on the connectivity in metapopulation ?

Question

1. The colonization probability from patch i to patch j (Pij, Pij <>Pji)

2. The overall exchange of individuals between two patches i and j , (Pij +Pji)

3. The balance at a given patch is the difference between flows in and out (Sum Pij – Sum Pji).

4. The ecological distance (The median value and standard deviation)

Measure of connectivity

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 2500 5000 7500 10000 12500 15000 17500 20000 22500 25000 27500 30000 32500 35000 37500 40000 42500 45000 47500 50000 More

Ecological distance between A and B

Nb

r. o

f in

div

idu

als

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency

Cumulative %

A

B1E

iE

nE

Each cell and frontier is characterized by:

the possibility to go through (barrier).

an ecological cost (in terms of distance),

an attractiveness

Simulations of Dispersal

Landscape model Test area: Rural area in Switzerland

13 habitat patches

From each habitat patches 50’000 individuals are dispersed for each strategy

The starting ecological energy level is “equal to 50 km”

Results:

Effect of cognitive strategies on connectivity

1. The colonization probability from patch i to patch j (Pij, Pij <>Pji)

2. The overall exchange of individuals between two patches i and j , (Pij +Pji)

3. The balance at a given patch is the difference between flows in and out (Sum Pij – Sum Pji).

4. The ecological distance (The median value and standard deviation)

In gray, values are between 0% and 1%, and in black, values are larger than 1%.

Blind strategy

Near-sighted strategy Far-sighted strategy

Overall exchange of individuals:Average number of connections by patch:

B: 10,6 (89%)

N: 4.1 (33%)

F: 5 (42%)

Average of colonization probability:

B: 37.1%

N: 18.7%

F: 38%

Results:

Effect of cognitive strategies on connectivity

1. The colonization probability from patch i to patch j (Pij, Pij <>Pji)

2. The overall exchange of individuals between two patches i and j , (Pij +Pji)

3. The balance at a given patch is the difference between flows in and out (Sum Pij – Sum Pji).

4. The ecological distance (The median value and standard deviation)

Balance at each patch

Results:

Effect of cognitive strategies on connectivity

1. The colonization probability from patch i to patch j (Pij, Pij <>Pji)

2. The overall exchange of individuals between two patches i and j , (Pij +Pji)

3. The balance at a given patch is the difference between flows in and out (Sum Pij – Sum Pji).

4. The ecological distance (The median value and standard deviation)

Results: Density probability of ecological distance (medians)

Blind Strategy

Near-sighted Strategy

Far-sighted Strategy

Median of ecological distances

 

Results

r2 : Spearman

10000 20000 30000 40000

Median of the ecological cost

0.0

0.1

0.2

0.3

succ

es p

roba

bilit

y

10000 20000 30000 40000 50000

Median of the ecological cost

0.00

0.24

0.48

succ

es p

roba

bilit

y

0 10000 20000 30000 40000

Median of the ecological cost

0.0

0.2

0.4

0.6

succ

es p

roba

bilit

yr2 = 0.828 r2 = 0.408 r2 = 0.419

Blind Near Far

Colonization probability - Median of ecological distances

Blind strategy : the smaller the value of ecological distance, the higher the chance to join them

Near and far-sighted strategy: high colonization probability can occur at large ecological distances

High probability of colonization is not related to shortest distance!

Co

lon

izat

ion

p

rob

abili

ty

Ecological distance

 

Results

2000 4000 6000 8000 100001200014000

Standard deviation

0.0

0.1

0.2

0.3

succ

es p

roba

bilit

y

5000 10000 15000

Standard deviation

0.0

0.1

0.2

0.3

0.4

0.5

succ

es p

roba

bilit

y

5000 10000 15000

Standard deviation

0.0

0.2

0.4

0.6

succ

es p

roba

bilit

y

Colonization probability - Standard deviation

r2 = 0.773 r2 = 0.270 r2 = 0.105

Blind Near Far

Blind strategy: high values of colonization probability are related to large variability of ecological distances - number of connections.

Near and Far-sighted strategies: High colonization probability can be found for any ecological distances – number of connections

Numerous connections do not mean high colonization success!

Co

lon

izat

ion

p

rob

abili

ty

Standard deviation

Discussion

Cognitive abilities seem to act on the spatial structure of populations

• lead to the genetic sub-structure of populations

• lead to the extinction of marginal populations

Benefits of individual strategy are not linked with benefits for population

It seems not possible to generalize, or even forecast responses of an individual to landscape heterogeneity and fragmentation

Institute of Environmental Science and Technology

Swiss Federal Institute of Technology of Lausanne

Dept. Ecology & Evolution,

University of Lausanne

Switzerland

Many thanks to

The metapopulation capacity of a fragmented landscape wk (Hanski &

Ovaskainen, 2000)

Measure at metapopulation level

i

ij

A : Area of patch i

d : Distance between patches i and j

1: Average migration distance

e et c: Constants

ijij

ij i

ii

j

dp (t)A p (t) 1 p (t) p (t)

dc e

e

t Ad ( )xp

ij i j

ij

exp( d )cA A for j iK

0 for j i

dpdiag(A) Kp diag(p)Kp ep

dt

��������������

wk : The leading eigenvalue of the matrix K, which measures the impact of

landscape structure for long-term persistence of a species.

Patch1

Patch 2

C12

C21

E2

E1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

Patch area

Me

tap

op

ula

tio

n c

ap

ac

ity

Random Near Local

0

0.005

0.01

0.015

0.02

0.025

0.03

0 10000 20000 30000 40000 50000

Nbr of dispersers

Co

lon

isa

tio

n p

rob

ab

ility P(col.) patch 1

P(col.) patch 2

P(col.) patch 3

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 10000 20000 30000 40000 50000

Dispersal distance

Co

lon

iza

tio

n p

rob

ab

ilit

yPatch 3 Patch 1

Patch 2(b) the assigned dispersal distances

Simulated colonization probability curve related to

(a) the number of dispersers

Blind

Local

Frequency of cells being crossed

Near

Density probability

Random Near Local

Median value of the distribution of ecological cost grouped by strategies

Den

sity

pro

babi

lity

Random strategy: the highest values of ecological distance

Random and Local strategy: single peak distribution of the median

This value defines the minimum distance that an individual has to cover in order to join other habitat patches quantification of a landscape to support population.

Local strategy: colonisation can appear at any level of ecological distance.

Density probability

Random Near Local

Minimum value of the distribution of ecological cost grouped by strategies

All strategies behave the same when patches are close. when the patches are spatially further, the minimum values of ecological cost depends on the strategy.

Den

sity

pro

babi

lity

Metapopulation capacity of a fragmented landscape (Hanski & Ovaskainen, 2000)

 

The leading eigenvalue of the matrix K is the metapopulation capacity of a fragmented landscape that measures the impact of landscape structure for long-term persistence of a species.

dpdiag(A) Kp diag(p)Kp ep

dt

�������������� ij i, j i j

ii

K C A A pour j i

K = 0 pour j=i

iij j j i i

j i i

dp (t) ec exp d A p (t) 1 p (t) ( ) p (t)

dt A

Equation 1

i

ij

A : Area of patch i

d : Distance between patches i and j

1: Average migration distance

e et c: Constants

We modify the colonisation probability by ij i, j

j i

c exp d C

The Metapopulation Capacity kw of a fragmented landscape corresponds to the leading eigenvalue of

the matrix K (landscape matrix, condensing the effects of habitat patch area and connectivity on

extinction and colonisation). It can be shown that an equilibrium solution with * 0ip for all i exists

if and only if k

ew

c, thus persistence depends on both the structure of the landscape, kw,and the

properties of the species (e/c).

Pop 2

Pop 1

Patch1

Patch 2

C12

C21

Context: spatially-explicit metapopulation model

Fragmented landscape

E2

E1

Colonization Extinction

Hanski and Gyllenberg (1997)

i

ij

A : Area of patch i

d : Distance between patches i and j

1: Average migration distance

e et c: Constants

iji j i i i

dpc p (1 p ) e p

dt i

jiji

j ii

ij

dp (t)A p (t) 1 p (t) p (t)

dc e

e

t Ad ( )xp

« Connectivity »

iji

iij

iij

j

c exp d A p (tdp (t)

1 p (t) p (t) d A

)t

e( )

Colonization Extinction

dpcp(1 p) ep

dt

Hanski’s spatially explicit metapopulation model

i

ij

A : Area of patch i

d : Distance between patches i and j

1: Average migration distance

e et c: Constants

Metapopulation capacity of a fragmented landscape (Hanski & Ovaskainen, 2000)

ij i j

ij

exp( d )A A for j iK

0 for j i

dpdiag(A) Kp diag(p)Kp ep

dt

��������������

 

The leading eigenvalue of the matrix K is the metapopulation capacity of a fragmented landscape that measures the impact of landscape structure for long-term persistence of a species.

     

both local and global aspects of dispersal

allows the simulation of various dispersal strategies, landscape uses, and dispersal cues,

quantification of colonisation probability and ecological distances,

spatial identification of paths,

contributes to a better understanding of factors that may have implications in dispersal processes

offers assistance to planners for management decisions.

The dispersal model

metapopulation assumptions

specific movement strategy and cues

the temporal scale

data

the dependency of the results on expert judgment.

General conclusions

Choosing procedure

RandomP1

P2

P3Pn F3Fn

F2F1

P1

P2

Pn

0

1

Additive probability

Fn

F2

F1

P: Probability

F: Associated frontier

?Cell 2

Cell 1

Cell 3Cell n

Habitat patchHabitat patch

Transition loop Dispersal model

Landscape model•Topological properties

•Typology

•….

Landscape model•Topological properties

•Typology

•….

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Dispersal modelLandscape model•Topological properties

•Typology

•….

Landscape model•Topological properties

•Typology

•….

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Habitat patchHabitat patch

Active entities

Active entities

Start

PathPath

Path

Recorder

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

PathPath

Path

Recorder

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

For i=1

add

Result

OutputPath generation Results

SelectionMessages exchange

Algorithm

11

Transition loop Dispersal model

Landscape model•Topological properties

•Typology

•….

Landscape model•Topological properties

•Typology

•….

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Habitat patchHabitat patch

List of suitable entities

List of suitable entities

Active entities

Active entities

Start

PathPath

Path

Recorder

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

PathPath

Path

Recorder

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

For i=1

Transition loops

Topological Relations

add

Result

OutputPath generation Results

SelectionMessages exchange

Algorithm

11

22

Transition loop Dispersal model

Landscape model•Topological properties

•Typology

•….

Landscape model•Topological properties

•Typology

•….

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Dispersal modelLandscape model•Topological properties

•Typology

•….

Landscape model•Topological properties

•Typology

•….

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Habitat patchHabitat patch

List of suitable entities

List of suitable entities

EntitieEntitie

Active entities

Active entities

Start

PathPath

Path

Recorder

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

PathPath

Path

Recorder

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

For i=1

Transition loops Choosing

procedure

TopopogicalRelations

add

Result

OutputPath generation Results

SelectionMessages exchange

Algorithm

11

22

33

Transition loop

Dispersal modelLandscape model•Topological properties

•Typology

•….

Landscape model•Topological properties

•Typology

•….

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Animal model•Movement type

•Choosing procedure

•Dispersal abilities

•…..

Habitat patchHabitat patch

List of suitable entities

List of suitable entities

EntitieEntitie

End

Active entities

Active entities

Start

PathPath

Path

Recorder

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

PathPath

Path

Recorder

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[ Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

[Spatial entity]1

[Spatial entity]2

…..

[Spatial entity]i

[Spatial entity]i+1

For i=1

Transition loops Choosing

procedure

Limitations testsLimitations tests

Topological Relations

add

Result

OutputPath generation Results

SelectionMessages exchange

Algorithm

11

22

3344

Transition loop

n

f 0 ii 0

E E E

t1

t2

t4

t3

t6

t5

t7t10

t8t9

t1t2

t4

t3

t6

t5

t7

t10

t8

t9

t11

t12

0E

fE

1E 2E

3E

4E

5E 6E

7E 8E

9E

10E11E

1E

2E

3E

4E

5E

6E

7E

8E9E

Test:

i i 1 iE E E 0

Distance écologique entre les patches

A

B1E

iE

nE

Patch1

Patch 2

C12

C21

E2

E1

Pn

P1

P2

P3

F3Fn

F2F1 Cell 2

Cell 1

Cell 3Cell n

?

…

: Virtual frontier

Hydrological network

Road network

Hedge

Forest

Inhabited areaActive cell

Cell 4

Cell 3

Cell 1

Cell 2

Linear features ?