Space is ecologically meaningful: about the spatial component of the ecological niche, with the help...
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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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Fran ois 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

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


Ecm environment spatial structure

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


Bcm metapopulation dynamics

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


Bcm vs ecm simulated metapopulations

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


Bcm vs ecm simulated metapopulations1

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


Bcm vs ecm simulated metapopulations2

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

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)


Ecm bcm decoupling

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 decoupling1

ECM-BCM decoupling

  • Separation of spectral features by mean of PCA

High p (habitat density)

Low p

Habitat

structure

(Results with Fourier analysis)


Ecm bcm decoupling2

-

+

Fine scale

Coarse scale

ECM-BCM decoupling

  • Separation of spectral features by mean of PCA

Second PC loadings


Ecm bcm decoupling3

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


Ecm bcm decoupling4

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


What about presence absence data

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

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

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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