Cognitive ability affects connectivity in metapopulation: A simulation approach Séverine Vuilleumier The University of Queensland

Pop 2 Pop 1 Patch1 Patch 2 C 12 C 21 Context: spatially-explicit metapopulation model Fragmented landscape e2e2 e1e1 Landscape heterogeneities and structures / animal behavior travel path and cost

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.

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

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

1.The colonization probability from patch i to patch j (P ij, P ij <>P ji ) 2.The overall exchange of individuals between two patches i and j, (P ij +P ji ) 3.The balance at a given patch is the difference between flows in and out (Sum P ij – Sum P ji ). 4.The ecological distance (The median value and standard deviation) Measure of connectivity

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 (P ij, P ij <>P ji ) 2.The overall exchange of individuals between two patches i and j, (P ij +P ji ) 3.The balance at a given patch is the difference between flows in and out (Sum P ij – Sum P ji ). 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 (P ij, P ij <>P ji ) 2.The overall exchange of individuals between two patches i and j, (P ij +P ji ) 3.The balance at a given patch is the difference between flows in and out (Sum P ij – Sum P ji ). 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 (P ij, P ij <>P ji ) 2.The overall exchange of individuals between two patches i and j, (P ij +P ji ) 3.The balance at a given patch is the difference between flows in and out (Sum P ij – Sum P ji ). 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 r 2 : Spearman r 2 = 0.828r 2 = 0.408r 2 = BlindNearFar 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! Colonization probability Ecological distance

Results Colonization probability - Standard deviation r 2 = 0.773r 2 = r 2 = BlindNearFar 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! Colonization probability 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 w k (Hanski & Ovaskainen, 2000) Measure at metapopulation level w k : The leading eigenvalue of the matrix K, which measures the impact of landscape structure for long-term persistence of a species.

(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 RandomNearLocal Median value of the distribution of ecological cost grouped by strategies Density probability 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 RandomNearLocal 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. Density probability

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. Equation 1 We modify the colonisation probability by

Pop 2 Pop 1 Patch1 Patch 2 C 12 C 21 Context: spatially-explicit metapopulation model Fragmented landscape E2E2 E1E1 ColonizationExtinction Hanski and Gyllenberg (1997) « Connectivity »

Colonization Extinction Hanski’s spatially explicit metapopulation model 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.

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 Random P1 P2 P3Pn F3 Fn F2 F1 P1P1 P2P2 PnPn 0 1 Additive probability FnFn F2F2 F1F1 P: Probability F: Associated frontier ? Cell 2 Cell 1 Cell 3 Cell n

Habitat 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 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 patch Active entities Active entities Start Path Recorder [Spatial entity] 1 2 ….. [Spatial entity] i [Spatial entity] i+1 [Spatial entity] 1 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 2 ….. [Spatial entity] i i+1 [Spatial entity] 1 2 ….. [Spatial entity] i i+1 Path Recorder [Spatial entity] 1 2 ….. [Spatial entity] i [Spatial entity] i+1 [Spatial entity] 1 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 2 ….. [Spatial entity] i i+1 [Spatial entity] 1 2 ….. [Spatial entity] i i+1 For i=1 add 1 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 patch List of suitable entities List of suitable entities Active entities Active entities Start Path Recorder [Spatial entity] 1 2 ….. [Spatial entity] i [Spatial entity] i+1 [Spatial entity] 1 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 2 ….. [Spatial entity] i i+1 [Spatial entity] 1 2 ….. [Spatial entity] i i+1 Path Recorder [Spatial entity] 1 2 ….. [Spatial entity] i [Spatial entity] i+1 [Spatial entity] 1 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 2 ….. [Spatial entity] i i+1 [Spatial entity] 1 2 ….. [Spatial entity] i i+1 For i=1 Transition loops Topological Relations add 1 2 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 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 patch List of suitable entities List of suitable entities Entitie Active entities Active entities Start Path Recorder [Spatial entity] 1 2 ….. [Spatial entity] i [Spatial entity] i+1 [Spatial entity] 1 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 2 ….. [Spatial entity] i i+1 [Spatial entity] 1 2 ….. [Spatial entity] i i+1 Path Recorder [Spatial entity] 1 2 ….. [Spatial entity] i [Spatial entity] i+1 [Spatial entity] 1 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 2 ….. [Spatial entity] i i+1 [Spatial entity] 1 2 ….. [Spatial entity] i i+1 For i=1 Transition loops Choosing procedure Topopogical Relations add 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 patch List of suitable entities List of suitable entities Entitie End Active entities Active entities Start Path Recorder [Spatial entity] 1 2 ….. [Spatial entity] i [Spatial entity] i+1 [Spatial entity] 1 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 2 ….. [Spatial entity] i i+1 [Spatial entity] 1 2 ….. [Spatial entity] i i+1 Path Recorder [Spatial entity] 1 2 ….. [Spatial entity] i [Spatial entity] i+1 [Spatial entity] 1 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 2 ….. [Spatial entity] i i+1 [Spatial entity] 1 2 ….. [Spatial entity] i i+1 For i=1 Transition loops Choosing procedure Limitations tests Topological Relations add Transition loop

t1 t2 t4 t3 t6 t5 t7 t10 t8 t9 t1 t2 t4 t3 t6 t5 t7 t10 t8 t9 t11 t12 Test: Distance écologique entre les patches

A B

Patch1 Patch 2 C 12 C 21 E2E2 E1E1

Pn P1 P2 P3 F3 Fn F2 F1 Cell 2 Cell 1 Cell 3 Cell n ? …

: Virtual frontier Hydrological network Road network Hedge Forest Inhabited area Active cell Cell 4 Cell 3 Cell 1 Cell 2 Linear features ?