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François Munoz * , Pierre-Olivier Cheptou and Finn Kjellberg

Space is ecologically meaningful: about the spatial component of the ecological niche, with the help of spectral analysis. François Munoz * , Pierre-Olivier Cheptou and Finn Kjellberg Centre d’Ecologie Fonctionnelle et Evolutive, Montpellier, France. Theoretical background.

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François Munoz * , Pierre-Olivier Cheptou and Finn Kjellberg

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  1. Space is ecologically meaningful: about the spatial component of the ecological niche, with the help of spectral analysis François Munoz*, Pierre-Olivier Cheptou and Finn Kjellberg Centre d’Ecologie Fonctionnelle et Evolutive, Montpellier, France

  2. Theoretical background • Are current spatial species distributions ecologically meaningful ? What processes are involved ? (Legendre & Legendre 1998) Environmental Control Model: environment is dominating Biotic Control Model: population and community dynamics  networks: metapopulation, metacommunity Historical dynamics: historical events are dominating

  3. p=0.5 q=0.9 ECM: environment spatial structure • Local conditions may be more or less suitable to population survival • Elementary units = • habitat patches • Landscape lattice with binary habitat states • Static habitat state Parameters: habitat density p, habitat agregation q

  4. r=0.4 BCM: metapopulation dynamics • Model of the spatial dynamics of populations • Elementary units = • populations • local spatial scale • Landscape lattice with binary occupancy • Balance of extinction- colonization events at quasi-stationary state Parameter: ratio r = extinction / colonization

  5. 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 q • BCM  parameter r p=0.5 q=0.9 r=0.4 Black = unsuitable habitat Grey = suitable unoccupied White = suitable occupied

  6. BCM vs ECM: simulated metapopulations • Local time averaged occupancy probabilities p=0.5 q=0.9 r=0.4 Markov evolution process Estimation of quasi-stationary local occupancy probabilities  time averages on 0/1 occupancy states

  7. BCM vs ECM: simulated metapopulations Can we separate out p, q and r effects on the quasi-stationary populations spatial distribution ?

  8. PCNM 1 PCNM components on a 10x10 lattice PCNM 3 PCNM 10 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)

  9. ECM-BCM decoupling • Separation of spectral features by mean of PCA PCA on quasi-stationary spectra  {p,q,r} triplets 2 first PCs = 90% variation

  10. ECM-BCM decoupling • Separation of spectral features by mean of PCA High p (habitat density) Low p Habitat structure (Results with Fourier analysis)

  11. - + Fine scale Coarse scale ECM-BCM decoupling • Separation of spectral features by mean of PCA Second PC loadings

  12. ECM-BCM decoupling • Separation of spectral features by mean of PCA High r Low r Low colonization High colonization (Results with Fourier analysis) Metapopulation dynamics

  13. ECM-BCM decoupling • Separation of spectral features by mean of PCA First PC loadings + Emergent structure Fine scale Coarse scale PCA results are supported by both methods, and is robust regarding occupancy estimation

  14. 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

  15. 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

  16. Perspectives – Improving understanding • Analytical spectral model for inferences Spectral formulation of metapopulation models Expectations on spectral decoupling and individual spectra ECM: multilevel quality habitat landscape 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

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