space is ecologically meaningful: about the spatial component of the ecological niche, with the help...
TRANSCRIPT
Space is ecologically meaningful: about the spatial component of the ecological
niche, with the help of spectral analysis
François Munoz*, Pierre-Olivier Cheptouand Finn Kjellberg
Centre d’Ecologie Fonctionnelle et Evolutive, Montpellier, France
Theoretical background
Are current spatial species distributions ecologically meaningful ?
Environmental Control Model: environment is dominating
Biotic Control Model: population and community dynamics networks: metapopulation, metacommunity
What processes are involved ? (Legendre & Legendre 1998)
Historical dynamics: historical events are dominating
ECM: environment spatial structure
Local conditions may be more or less suitable to population survival
Parameters: habitat density p, habitat agregation q
• Elementary units = habitat patches
• Landscape lattice with binary habitat states
• Static habitat state
0 20 40 60 80 100
0
20
40
60
80
100
p5 q9p=0.5 q=0.9
BCM: metapopulation dynamics
Model of the spatial dynamics of populations
Parameter: ratio r = extinction / colonization
• Elementary units = populationslocal spatial scale
• Landscape lattice with binary occupancy
• Balance of extinction- colonization events at quasi-stationary state
0 20 40 60 80 100
0
20
40
60
80
100
r4r=0.4
BCM vs ECM: simulated metapopulations
ECM and BCM are likely to be involved together
Extinction / colonization dynamics in a spatially structured habitat
ECM parameters p qBCM parameter r
Black = unsuitable habitat
Grey = suitable unoccupied
White = suitable occupied
p=0.5 q=0.9 r=0.4
BCM vs ECM: simulated metapopulations
Local time averaged occupancy probabilities
Markov evolution process
Estimation of quasi-stationary local occupancy probabilities
time averages on 0/1 occupancy states
0 20 40 60 80 100
0
20
40
60
80
100
p5 q9 r4p=0.5 q=0.9 r=0.4
BCM vs ECM: simulated metapopulations
Can we separate out p, q and r effects on the quasi-stationary populations spatial
distribution ?
The legacy of spectral analysis
A widely used method for pattern analysis
Example of PCNM analysis(Borcard 2002)
Representing a spatial pattern by a combination of autocorrelated structures
Working on regular or irregular sampling schemes
Other spectral technique: Fourier analysis(regular sampling schemes)
0 2 4 6 8 10
0
2
4
6
8
10
PCNM 3
0 2 4 6 8 10
0
2
4
6
8
10
PCNM 10
0 2 4 6 8 10
0
2
4
6
8
10
PCNM 1
PCNM componentson a 10x10 lattice
ECM-BCM decouplingSeparation of spectral features by mean of PCA
PCA on quasi-stationary spectra {p,q,r} triplets
2 first PCs = 90% variation
ECM-BCM decouplingSeparation of spectral features by mean of PCA
High p (habitat density)Low p
(Results with Fourier analysis)
Habitatstructure
ECM-BCM decouplingSeparation of spectral features by mean of PCA
Fine scale Coarse scale
- +
Second PC loadings
ECM-BCM decouplingSeparation of spectral features by mean of PCA
High rLow r
Highcolonization
Lowcolonization
Metapopulation dynamics(Results with Fourier analysis)
+
ECM-BCM decouplingSeparation of spectral features by mean of PCA
PCA results are supported by both methods, and is robust regarding occupancy estimation
Emergent structure
Fine scale Coarse scale
First PC loadings
What about presence-absence data?
Losing one dimension
Spectra computed for 0/1 occupancy data at a given time
PCA one PC for 95% of explained variation
Variation of spatial structure over one dimension
Necessity of some knowledge about the spatial structure of the potentially suitable habitat
Conclusion – Relevance of spectral analysis
Spectral decoupling: when does it work ?
ECM: binary environmental control
BCM: r parameter is intrinsic to the species
Time averaged quasi-stationary occupancy probabilities
Why is spectral analysis a plus ?
Currently analyses of occupancy data are often:• ECM centered (GLM)• BCM centered (metapopulation model)
Coupling remains underestimated spectral analysis is more informative on spatial dynamics and allows decoupling
Perspectives – Improving understanding
Analytical spectral model for inferences
Spectral formulation of metapopulation models
Expectations on spectral decoupling and individual spectra
What about emergent structuring properties ?
Colonization-extinction of binary populations = Contact process
Self organization leads to cross-scale correlation
Expectation on the metapopulation emergent spatial structure
ECM: multilevel quality habitat landscape