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

W G W

S W

S G G

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 effectsof resource transport and supply. The American Naturalist 144: 954-977

(k)

7Huston 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

Low rate of resource input

Constant transport rate

Low rate of resource inputCompetitive 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 concentrationin rooting zone per unit volume and resource uptake from rooting zone per unitvolume.

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

Overlappingdepletion

zone

Overlappingdepletion

zone

Overlappingdepletion

zone

Overlappingdepletion

zone

Overlappingdepletion

zone

Higher resource capture efficiency

lower resource concentration in non-overlapping rooting zone

Less access to overlapping zone within the neighborhood of interactions

Non-overlappingdepletion zone

Non-overlappingdepletion zone

Non-overlappingdepletion zone

Non-overlappingdepletion zone

Non-overlappingdepletion zone

13

Resource-based invasion mechanism

Invasive plant trait

Nativeplant trait

Lowerthreshold

Upperthreshold

Range of variation of resource input rate

14

SPATIAL

ABUNDANCES

Lower threshold Upper 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 spatialextent 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 coexistingplant species.

A deterministic formula calculate that number; followingparameter values are required :a) resource input rate b) resource transport rate c) habitatresource concentration d) resource requirement of individual speciese) maximal rate of seeds production f) resource concentration at which the seeds production is half the maximum

17

Fire-induced successional processesHighest 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

Burnedarea

Burn nbd.

Semi-burnnbd.

unburnnbd.

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 basedon time of germination

Post-fire vegetation pattern

Early SuccessionEarly Succession Late SuccessionLate Succession

Semi-burn

Agent

Unburn-Agent

Burn-Agent

Germination

Establishment

Individual-basedmodel 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

Spatial Non-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