Landscape modeling efforts for N-Biocomplexity program

1. Landscape modeling effortsfor N-Biocomplexity program Amit Chakraborty & Bai-Lian Li University of California, Riverside

2. SPATIAL TRANSITION MODEL OF VEGETATION CHANGES Spatial dynamics Temporal dynamics Spatial interactions between individual plants Resource supply and transport

3. Habin Li and F. Reynolds (1997) Scale in Remote sensing and GIS. p.211-230

4. CELLULAR AUTOMATON either G or W or S

5. Rules of Automaton AUTOMATON MECHANISMS OR PROCESSES Automaton without interference Resource-mediated competition Automaton under species invasion Resource-based invasion mechanism Automaton after fire-disturbance Fire-induced successional processes

6. Resource-mediated Indirect Competition (k) Huston M.A. and DeAngelis D.L. (1994) Competition and coexistence: the effects of resource transport and supply. The American Naturalist 144: 954-977

7. Huston M.A. and DeAngelis D.L. (1994) Competition and coexistence: the effects of resource transport and supply. The American Naturalist 144: 954-977

8. Resource-mediated direct competition

9. C1>C2 Schematic diagram of resource uptake mechanism from overlapping depletion zone

10. Constant transport rate Low rate of resource input Overlapping depletion zone Non-overlapping depletion zone Low rate of resource input Competitive equilibrium

11. Which plant will occupy the overlapping zone? The plant has lowest resource concentration in its non-overlapping depletion zone will occupy an overlapping zone at equilibrium by depleting the resource concentration to its lowest. What plant trait confers the competitive superiority? • Higher resource capture efficiency; defined by a ratio of resource concentration • in rooting zone per unit volume and resource uptake from rooting zone per unit • volume. • 2. Lower resource concentration in non-overlapping rooting zone • 3. Less access to overlapping zone within the neighborhood of interactions. • Above three are the measure of competitive superiority and • it confers the variation of R* at equilibrium

12. Higher resource capture efficiency lower resource concentration in non-overlapping rooting zone Less access to overlapping zone within the neighborhood of interactions Overlapping depletion zone Non-overlapping depletion zone Overlapping depletion zone Non-overlapping depletion zone Overlapping depletion zone Non-overlapping depletion zone Overlapping depletion zone Overlapping depletion zone Non-overlapping depletion zone Non-overlapping depletion zone

13. Resource-based invasion mechanism Invasive plant trait Native plant trait Range of variation of resource input rate Lower threshold Upper threshold

14. S P A T I A L A B U N D A N C E S Resource input rate Lower threshold Upper threshold

15. Relative physiological characters of an invasive species 1. Higher maximal seeds production 2. Lower resource requirement for seeds production 3. Lower mortality rate The invasive species is not necessarily to be a best resource competitor

16. Limit to coexisting plant species • Spatially homogenous competitive environment is one in which • species’ competitive ranking do not change within the spatial • extent of the landscape being considered • In this environment species spatially coexist because of competition- • colonization trade-off; an appropriate species trait allows spatial coexistence • of several plant species. • The resource input rate defines the limit to the number of that coexisting • plant species. • A deterministic formula calculate that number; following • parameter values are required : • resource input rate b) resource transport rate c) habitat • resource concentration d) resource requirement of individual species • e) maximal rate of seeds production f) resource concentration at which the • seeds production is half the maximum

17. Highest level: general causes of succession Site availability Differential species availability Differential species performance Intermediate level: Contributing processes or conditions Fire-disturbance Seeds pool Germination, establishment Stochastic environmental stress Competition Colonization Lower level: Defining factors Resource level Temperature Site history Fire-induced successional processes

18. Pre-fire habitat Burn nbd. Burned area x Semi-burn nbd. x unburn nbd. The site specific neighborhood center at ‘x’ is defined as a physical space in which resource level is constant. ‘Burn neighborhood centered at ‘x’’ is completely empty. ‘Semi-burn neighborhood centered at ‘x’’ consists of some occupied sites and some empty sites and the center ‘x’ is empty. ‘Unburn neighborhood centered at ‘x’’ does not contain any fire affected sites and have an individual occupy the center ‘x’ Post-fire habitat Effects of fire and definition of resource-based neighborhood

19. Agents: Burn agent x Semi-burn agent x Unburn agent

20. Simulation scheme Post-fire vegetation pattern Burn- Agent Semi- burn Agent Unburn- Agent Germination Early Succession Late Succession Establishment Species ranking based on time of germination Competition-colonization tradeoff Colonization Germination R*-rule Temperature Establishment Colonization rate Natural vegetation dynamics Seeds pool before fire Resource utilization rate Species rank based on resource requirement Individual-based model with Moore’s neighborhood where state transition calculated by discrete-time Markov chain Temperature Available seeds pool

21. Simulation Steps… Step-1:Classify post-fire habitat based on the definition of site-specific neighborhood Step-2: Creating three agents corresponding three different nbd. Step-3: The ‘burn agent’ locates all burn neighborhoods and the ‘semi-burn agent’ locates all semi-burn neighborhoods in the post-fire habitat. The ‘burn agent’ and ‘semi-burn agent’ act till the early successional individual at target-cell is replaced by late successional individual. Step-4: The ‘unburn agent’ controls natural vegetation dynamics in the portion of the habitat which is not fire affected.

22. Information needed Spatial Non-spatial Post-fire soil temperature Habitat information Post-fire N level Total number of species in the habitat. It depends on pre-fire habitat history. Pre-fire vegetation pattern Life-span of each species. Post-fire vegetation pattern Colonization rate of each species. Life-time N-consumption of each species

23. Advantages…… • The model includes post-fire successional processes, i.e. process based. • 2.The model is relatively simple and easy to run because less number of data are needed to get series of vegetation patterns correspond to different successional stages. • 3.The model has predictable potentiality. • 4.The model could be used to determine grassland or shrubland • conditions by defining successional indices.

24. Thanks