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

2 S PATIAL T RANSITION M ODEL O F V EGETATION C HANGES Spatial dynamicsTemporal dynamics Spatial interactions between individual plants Resource supply and transport

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

4 C ELLULAR A UTOMATON WGW SW SGG either G or W or S

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

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

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

8 Resource-mediated direct competition

9 C 1 >C 2 Schematic diagram of resource uptake mechanism from overlapping depletion zone

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

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

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

14 SPATIALABUNDANCESSPATIALABUNDANCES Lower thresholdUpper threshold Resource input rate

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

18 Effects of fire and definition of resource-based neighborhood Post-fire habitat Pre-fire habitat Burned area Burn nbd. Semi-burn nbd. unburn nbd. The site specific neighborhood center at ‘x’ is defined as a physical space in which resource level is constant. x x ‘ 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’

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

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

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

23 Advantages…… 1.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