Modeling species distribution using speciesenvironment relationships

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Modeling species distribution using
species-environment relationships

• Fabio Corsi

Istituto di Ecologia Applicata Via L.Spallanzani,
32 00161 Rome ITALY email iea_at_mclink.it
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Conservation Needs

• Broad scale planning (eventually global)
• Metapopulation approach
• Identification of core areas and corridors
• .
• Which imply
• Detailed knowledge on actual species distribution
• Extensive data on species ecology and biology
• Spatially explicit predicting tools

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The information space

• data are
• fragmented
• localised
• on average, of modest quality

Can we use them for broad scale planning?
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The answer is a set of new questions

• Can we extrapolate existing knowledge to the
  entire continent?
• Under which assumptions?
• For which use?

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Can we extrapolate existing knowledge to the
entire continent?

• Yes, using modeling techniques which
• enable to extrapolate from limited data new
  information
• are cost effective
• produce updateable distributions
• define a repeatable approach

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Spatial Modeling
Geographic space
Geographic space
Environmental space
En
En
E2
E2
E1
E1
E1
En
E2
Feedback
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Under which assumptions?

• Species distribution is influenced by available
  environmental data (e.g. test for randomness of
  point data Mantel test)
• Local variations of these relationships
  throughout the study area can be neglected (e.g.
  stratification)
• Available data are sufficient to define
  species-environment relationships (field
  validation, sensitivity analysis, hope and fate ?)

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Alternatives
Interpolation
Quantitative data
Distribution
Semivariogram structure
Feedback
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For which use?

• Application of results include, but are not
  limited to
• Identify potential/critical corridors
• Predict areas of major conflicts
• Assessment of conservation scenarios and
  management options on a cost/benefit basis
  (zoning system)
• Include spatial elements in a PHVA
• ..

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Blotch distribution

• The polygon defining the distribution range of
  the species as interpreted by the specialist
  based on her/his knowledge
• The environmental requirements of the species are
  synthesized directly into the drawing itself

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Deterministic overlay

• The analysis of the environmental space is
  synthesized by the expert knowledge (deductive
  approach based on known ecological preferences)
• Simple overlay of environmental variables layers
• The goal is to describe the distribution within
  the blotch perimeter, showing the areas of
  expected occurrence.
• Mostly categorical models of suitability

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Statistical overlay

• Formal analysis of the environmental space
  defined by the available variables
• Result of previous analysis control the overlay
  process.
• The goal is to describe the variation of
  suitability within the blotch
• Continuous suitability rank surface

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Examples

• Models developed at regional scale for the large
  Italian carnivores and major ungulate species
• Available data
• Extent of Occurrence of each species
• known territories and point locations from
  previous studies (e.g. radio tracking, direct
  investigations etc.)
• land cover maps, digital terrain model,
  population densities, ungulates distributions,
  protected areas, sheep and goats densities

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The method (step 1)

• Environmental data pre-processed with map algebra
  to account for individuals awareness of the
  environment

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The method (step 1)

• Surface of the circular window is equal to the
  average size of the territories and/or home range

• To each cell of the study area is assigned a
  value which is a function of the surrounding
  cells

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Building the model (Step 2)

• Environmental characterisation of known species
  locations based on available environmental
  variables

L1
L1 L2 L3 ...Ln
L3
Ln
Locations
E11 E12 E13 E1n
L2
E21 E22 E23 E2n
En1 En2 En3 Enn

E1 E2 En
Environmental variables
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Building the model (Step 2)

• Calculating the species ecological signature

E1
S E1 / n E1 S E2 / n E2 ... S En / n En
L1 L2 L3 Ln
E11 E12 E13 E1n
E21 E22 E23 E2n
En1 En2 En3 Enn
En
E2
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Building the model (Step 3)

• Calculating the distance of each portion of the
  study area from the ecological signature in the
  environmental variables space

E1
Px
Px E1x E2x ... Enx
Ecological Distance
E1x
E2x
Enx
En
E2
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The method (Step 3)

• Species ecological signature calculated as the
  vector of means and the variance-covariance matrix

S Variance-covariance matrix
m Vector of means
L1 L2 L3. Ln
E11 E12 E13 E1n
E1 E2 ... En
E21 E22 E23 E2n

En1 En2 En3 Enn
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The method (Step 3)

• Using the above definition of ecological
  signature, distances can be calculated using the
  Mahalanobis Distance

D Mahalanobis distance (environmental distance)
at point x x vector of environmental
variables measured in x m vector of the means S
variance-covariance matrix
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Mahalanobis distance

• takes into account not only the average value but
  also its variance and the covariance of the
  variables measured
• accounts for ranges of acceptability (variance)
  of the measured variables
• compensates for interactions (covariance) between
  variables
• dimensionless
• if the variables are normally distributed, can be
  readily converted to probabilities using the ?2
  density function

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Map production

• The mean (m) and standard deviation (s) of the
  Ecological Distance is calculated for the
  territories and locations
• The Ecological Distance surface is partitioned
  according to the following threshold
• m, m 1s ,m 2s, m 4s, m 8s, m 16s
• First three classes account for more than 95 of
  variability (assuming a normal distribution)

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The Extent of Occurrence

• Accounts for variables that influence the species
  distribution but cannot easily be included in the
  analysis, such as
• historical constraints
• behavioural patters
• Mapped results are interpreted as expected within
  the EO and potential outside the EO

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Results

• Environmental suitability model for the Wolf

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Results

• Cumulative frequency distributions

log-normal distribution of dead wolves
environmental distance classes in the study area
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Results

• Environmental suitability model for the Lynx

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Results

• Environmental suitability model for the Lynx
• (boarder between France, Switzerland and Italy)

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Results

• Environmental suitability model for the Bear

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Results

• Environmental suitability model for the Deer

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Towards a model for biodiversity

• Biodiversity distribution models may derive from
• deterministic overlay of suitability models
• the analysis of the environmental suitability
  space

Species 1
Classification
Clustering
Species n

Species 2
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Classification

• Map showing the result of the principal component
  analysis on the suitability maps of the 3 species
  of large carnivores in the Alps

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Alternatives
Interpolation
Quantitative data
Distribution
Semivariogram structure
Feedback