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 dEcologie 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 p=0.5 q=0.9

BCM: metapopulation dynamics Model of the spatial dynamics of populations Parameter: ratio r = extinction / colonization Elementary units = populations local spatial scale Landscape lattice with binary occupancy Balance of extinction- colonization events at quasi-stationary state r=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 q BCM 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 p=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) PCNM 3 PCNM 10 PCNM 1 PCNM components on a 10x10 lattice

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

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

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

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

+ ECM-BCM decoupling Separation 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