Space is ecologically meaningful: about the spatial component of the ecological niche, with the help of spectral analysis François Munoz *, Pierre-Olivier.

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

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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

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8

10

PCNM 3

0 2 4 6 8 10

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PCNM 10

0 2 4 6 8 10

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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