Modeling species distribution using species-environment relationships

Istituto di Ecologia ApplicataVia L.Spallanzani, 3200161 Rome ITALYemail: iea@mclink.it

Fabio Corsi

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

The information “space” • data are:

– fragmented– localised– on average, of modest

quality

Data availability

Extent

Qu

alit

y

Can we use them for broad scale planning?

The answer is a set of new questions

• Can we extrapolate existing knowledge to the entire continent?

• Under which assumptions?

• For which use?

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

Spatial Modeling

E1

EnE2

Geographic space Geographic spaceEnvironmental space

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EnE2

E1

EnE2

E1

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 )

Alternatives

Quantitative data Distribution

Semivariogram structure

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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– …..

“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

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

AvoidanceAvoidanceSelectionSelection

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

ObservationsObservations

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HabitatHabitatSuitabilitySuitability

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

The method (step 1)

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

• 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

The method (step 1)

x

x = f(x in blue cells)

Building the model (Step 2)

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

Locations

{Environmentalvariables

L1

L2

L3 Ln

E1E2En

L1 L2 L3 ...Ln

E11 E12 E13 E1n E21 E22 E23 E2n En1 En2 En3 Enn

Building the model (Step 2)

• Calculating the species “ecological signature”

L1 L2 L3 … Ln

E11 E12 E13 E1n E21 E22 E23 E2n En1 En2 En3 Enn

E1

EnE2

E2

E1

En

E1 / n = E1

E2 / n = E2

En / n = En

Building the model (Step 3)

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

Px

E1

EnE2

E2x

E1x

Enx

Px

E1x E2x

...

Enx

EcologicalDistance

The method (Step 3)• Species “ecological signature” calculated as

the vector of means and the variance-covariance matrix

L1 L2 L3…. Ln

E11 E12 E13 E1n E21 E22 E23 E2n En1 En2 En3 Enn

& VE1 CE1E2 CE1En CE2E1 VE2 CE2En CEnE1 CEnE2 VEn

mVector of means

SVariance-covariance

matrix

E1E2

...

En

The method (Step 3)

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

'-12xD m-xS m-x

D = Mahalanobis distance (environmental distance) at point x

x = vector of environmental variables measured in xm = vector of the meansS = variance-covariance matrix

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

Map production• The mean (m) and standard deviation (of the

Ecological Distance is calculated for the territories and locations

• The Ecological Distance surface is partitioned according to the following threshold:

– m, m + 1,m + 2, m + 4, m + 8, m + 16• First three classes account for more than 95% of

variability (assuming a normal distribution)

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

• Environmental suitability model for the Wolf

Results

Results

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1.2

0 55 109 164 218 273 327 382 436 491 545 600 655

Mahalanobis distance

Cum

ulat

ive

freq

uenc

y

log-normal distribution of dead wolves

environmental distance classes in the study area

• Cumulative frequency distributions

• Environmental suitability model for the Lynx

Results

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

Results

• Environmental suitability model for the Bear

Results

• Environmental suitability model for the Deer

Results

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

Species n

Species 2

Classification

Clustering

…

Classification• Map showing the result of the principal component analysis on the

suitability maps of the 3 species of large carnivores in the Alps

Alternatives

Quantitative data Distribution

Semivariogram structure

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