1. Modeling species distribution using species-environment relationships Istituto di Ecologia Applicata Via L.Spallanzani, 32 00161 Rome ITALY email: iea@mclink.it Fabio Corsi

2. 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

3. The information “space” data are: –fragmented –localised –on average, of modest quality Can we use them for broad scale planning?

4. The answer is a set of new questions Can we extrapolate existing knowledge to the entire continent? Under which assumptions? For which use?

5. 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

6. Spatial Modeling E1 En E2 Geographic space Environmental space Feedback En E2 E1 En E2 E1

7. 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 )

8. Alternatives Quantitative data Distribution Semivariogram structure Feedback

9. 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 –…..

10. “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

11. 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 Avoidance Selection

12. 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 surfaceObservations 1 2 3 a bc............................5.7.2 12 31 7 60 20 50 F2 F1 HabitatSuitability

13. 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

14. The method (step 1) Environmental data pre-processed with map algebra to account for individuals awareness of the environment

15. 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)

16. Building the model (Step 2) Environmental characterisation of known species locations based on available environmental variables Locations { Environmental variables L1L1 L2L2 L3L3 LnLn E1 E2 En L 1 L 2 L 3...L n E1 1 E1 2 E1 3 E1 n E2 1 E2 2 E2 3 E2 n En 1 En 2 En 3 En n

17. Building the model (Step 2) Calculating the species “ecological signature” L 1 L 2 L 3 … L n E1 1 E1 2 E1 3 E1 n E2 1 E2 2 E2 3 E2 n En 1 En 2 En 3 En n E1 En E2 E1 En  E1 / n = E1  E2 / n = E2   En / n = En

18. Building the model (Step 3) Calculating the distance of each portion of the study area from the ecological signature in the environmental variables space PxPx E1 En E2 E2 x E1 x En x P x E1 x E2 x... En x Ecological Distance

19. The method (Step 3) Species “ecological signature” calculated as the vector of means and the variance- covariance matrix L 1 L 2 L 3…. L n E1 1 E1 2 E1 3 E1 n E2 1 E2 2 E2 3 E2 n En 1 En 2 En 3 En n & V E1 C E1E2 C E1En C E2E1 V E2 C E2En C EnE1 C EnE2 V En m Vector of means S Variance-covariance matrix E1 E2... En

20. 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

21. 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

22. 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)

23. 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

24. Environmental suitability model for the Wolf Results

25. log-normal distribution of dead wolves environmental distance classes in the study area Cumulative frequency distributions

26. Environmental suitability model for the Lynx Results

27. Environmental suitability model for the Lynx (boarder between France, Switzerland and Italy) Results

28. Environmental suitability model for the Bear Results

29. Environmental suitability model for the Deer Results

30. 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 …

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

32. Alternatives Quantitative data Distribution Semivariogram structure Feedback