Avi Bar Massada 1 , Gili Koniak 2 , Yohay Carmel 1 , Imanuel Noy Meir 2

1. Dynamics of the Mediterranean vegetation mosaic: modeling across spatial scales from simple to complex Avi Bar Massada1, Gili Koniak2, Yohay Carmel1, Imanuel Noy Meir2 1Technion – Israel Institute of Technology 2The Faculty of Agriculture, The Hebrew University of Jerusalem

2. Background • Thousands of years of human agro-pastoral activities converted the Mediterranean landscapes into spatially heterogeneous “Mosaics” • Land use changes in the recent decades transformed these landscapes into closed scrublands and woodlands, with lower biodiversity, lower scenic diversity, and increased fire risk.

3. How can we preserve mosaic landscapes? • Mainly through grazing, clearing, and burning, the traditional disturbances that created and maintained these landscapes. • How to manage for heterogeneity? Woody vegetation recovery is quick, thus a complex set of management practices is needed. • Long-term interactions between disturbance and vegetation dynamics are not fully understood, especially in complex systems as the Mediterranean region.

4. The modeling approach In order to understand and predict the spatiotemporal dynamics of Mediterranean vegetation under multiple disturbances, we are developing mathematical models across three spatial scales: patch, site and landscape. The models are constructed by successive approximations, from simple to complex, registering the changes in model behavior and realism at each stage

5. Hierarchical levels The models are being developed on three hierarchically nested spatial scales, incorporated into model structure with rising complexity: Landscape: a contiguous set of sites (>>100m2) that may differ in environment and disturbance history. Site: a group of neighboring patches (100m2) of uniform environment and disturbance history. Patch (cell): a unit area of 1m2, the size of an adult dwarf shrub.

6. Underlying mechanism: states and transitions theory (Westoby, Walker, and Noy-Meir 1989) Grazing effects Spontaneous transitions via colonization or expansion Disturbance related transitions (fire, clearing), or natural death

7. The basic model – Patch scale A state-and transition process between vegetation states at the patch level, described by a simple Markov model with constant transition probabilities. x=A,B,…,N Frequency of patches in vegetation state B at time t+1 Transition probability between state x and state B Frequency of patches in state x at time t

8. Intermediate model: patch + site scales This stage increases model complexity by: • Adding states. • Introducing non-constant transitions. • Adding a hierarchical level.

9. 1. Increasing model complexity: states The simple Markov model had one state variable – the vegetation state. Increasing complexity starts by adding variables. Now, each patch is characterized by 5 state variables: • The dominant vegetation state. • Height of the dominant. • Age of the dominant. • Identity of the colonizer vegetation state. • Age of the colonizer.

10. 2. Increasing model complexity: transitions In reality, transition probabilities aren’t constant, but depend on: • Residence time of a patch in a specific vegetation state, and of a colonizer growing below it. • Vegetation states of neighboring patches • Fire, clearing, and grazing events. The transition probabilities are turned into continuous transition functions

11. 3. Adding the site hierarchical level The probability of colonization from seeds depends on the percentage cover of all dominants in the site, plus a constant contribution from patches outside the site. Pcolonization = Psite + Plong

12. 3. Adding the site hierarchical level The probability of expansion has two forms: 1. Non-spatial explicit, depending on percentage cover 2. Spatial explicit: only one of its 8 nearest neighbors can expand into a patch.

13. Top model: patch + site + landscape scales • Different sites may have different disturbance histories. • The probability of colonization from seeds has now three components: • Pcolonization = Pshort + Pmedium + Plong

14. Validation at the site scale Model performance tested for a 10 years period – no disturbance.

15. Site scale model – undisturbed

16. Site scale model – intensive goat grazing

17. Goat grazing excluded after 30 years

18. Site scale model – intermediate goat and cattle grazing Possible equilibrium?

19. Landscape level initial simulations:Disturbance effects on landscape structure

20. Future research • Large scale simulations on actual landscapes. • Landscape structure studies: effects of disturbances, initial structure. • Management practices: which are better for mosaic conservation. • Addition of vegetation types: model generalization to other Mediterranean landscapes.

21. Thank you! • Many thanks to: • Prof. Avi Perevolotsky, Dr. Liat Hadar, and Sagie Sagiv of the Ramat Hanadiv Nature Park staff. • The research is generously supported by the ISF.