cognitive ability affects connectivity in metapopulation: a simulation approach séverine...
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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 ?