Vegetation dynamics: Land Use and Landscape Ecology

This is an adapted version of web site about a course on Environmental Modeling of Prof. Miguel Acevedo. The complete course can be found at http://www.geog.unt.edu/~acevedo/courses/5400/week9/lect09.htm

1.- Vegetation dynamics: individual-based models

References:

Swartzmann and Kaluzny textbook pages 129-133; 155-167
Lecture notes addendum (hand out). For remote use: available as Word Perfect 6.0 gapnotes.wpd in download\zelig
Urban, D.L. 1993. A User's Guide to ZELIG Version 2. Colorado State University, Department of Forest Sciences, Fort Collins, Colorado.
Urban D.L. and H.H. Shugart. 1992. Individual-based models of forest succession. In: D.C. Glenn-Lewin, R.K. Peet and T.T. Veblen (Editors). Plant Succession: Theory and Prediction. Chapman and Hall, New York. pp: 249-292.

Changes of species composition and biomass (ecosystem + community dynamics) is an emergent property of the dynamics of the individuals.

Examples:

Forest: JABOWA, ZELIG

Example, description of forest gap model:

The individual trees of each species can grow (i.e., change tree volume with time) or die.
The individuals are competing for light
V= D² H

V=Tree Volume
D= diameter, H=height

Dynamics:

dV/dt= volume growth rate (m3/yr)
dV/dt = G LA [ 1- DH/DmaxHmax]
G = maximum growth rate [ m3 wood per m2 leaf area/ yr]
LA = leaf area [m2]

Allometric factors:

Allometric relationship of diameter and height (two options)

H = h + a D - b D²
H = h ( 1- exp(cD)d)
h is "breast height" = 1.37 m = (or height at which diameter is usually measured)

Allometric relationship between LA and diameter LA = f D

Environmental limiting factors:

G = Gmax F(L) F(SM) F(T) F(N)
F(X) = limiting factor (between 0 and 1), due to environmental variable X
X can be L=light, SM= soil moisture, T=temperature, N= nutrients
The functions F(X) have parameters which depend on species type: shade-tolerance, drought-tolerance, cold-tolerance, etc.

Community dynamics feedbacks on environmental factors: As the trees grow: total basal area increases and crowding effects reduce growth: less light, more light attenuation by canopy (Beer's law), less nutrients, less water
Most individual-based forest models (JABOWA, FORET, ZELIG) use random establishment and mortality. Simulation uses Monte-Carlo method.
In the lab we will exercise:

a deterministic (does not explicitly include random establishment and mortality) and lumped (not based on individuals, but on averages) gap model using time zero adn applies to the Hubbard Brook watershed
zelig using preliminary Ray Roberts Lake area upland forest data

2.- Succession models: Semi-Markov and related models

Reference:

Swartzmann and Kaluzny textbook:

on Markov pages 32-33; p:64
on grassland succession pp:16-17, p:56-57, p: 64.

Acevedo, M.F. D.L. Urban and H.H. Shugart. 1996. Models of forest dynamics based on roles of tree species. Ecological Modelling. 87:267-284.

Another approach to vegetation dynamics and succession is to use Markov (we cover this last lecture), semi-Markov models and compartment models (also related to semi-Markov with exponential holding times).

In this approach, each cover type is a state variable

Markov:

Probability transition matrix: entries are probabilities of transition among several states at each time step.
Numerically done by iterating matrix
State variables represent occupancy probabilities or fraction of space occupied by each cover type at time t
Time-Zero has capabilities for doing markov simulations.
Mean and variance of state vector
Steady-state depends on probabilities.

Semi-Markov:

Transitions also depend on holding time in the source state.
Steady-state depends on probabilities and parameters of holding time density.
Simple holding time is gamma density
First -order gamma density is exponential
semi-Markov with expo holding time is the same as a continuous time Markov process
For semi-markov with gamma densities we can use program dynlayer
have to edit the input file, run the simulation and look at the output file.

Related to compartment models; make the transfer rates related to probabilities of transition

One example are grasses in prairie succession (textbook)
Each cover type is seen as a compartment and have transfer rates among compartments
There is SEEM model for this example (we will use in lab)
the model in seem includes interrupting succession every so many years by fire
that is a disturbance parameterized by frequency and intensity

Can be applied to the landscape level; see next section.

3.- Landscape dynamics: habitat changes

References:

Acevedo, M.F. D.L. Urban and M. Ablan. 1995. Transition and gap models of forest dynamics. Ecological Applications. 5(4):1040-1055.

The individual-based approach can be applied to landscape by making topographic position (elevation, slope and its aspect) and soils affect the environmental constraints (temp, precip, radiation). Each zelig plot corresponds to a homogeneous parcel of landscape. However, large areal extent requires very large computer storage and speed due to the great quantity of detail in indiv-based models.

The semi-Markov approach can be applied to the landscape level by making the parameters (probabilities and holding times) depend on elevation, slope and its aspect, soils, etc.

It is convenient to have a GIS manage all the info on topography and soils to parameterize the dynamical model, and to send model output to the GIS for spatial analysis.

For semi-markov use program MOSAIC which we have coupled to several GIS packages: ArcInfo, GRASS and IDRISI

To use MOSAIC have to edit the input file, run the simulation and look at the output file

Neighborhood effects:

In landscapes spatial structure could affect the dynamics
e.g. proximity of landscpe parcels with abundance of a cover type could affect dispersal and establishment patterns
Neighborhood effects are not implemented in MOSAIC
a variant named NHOOD which does more general semi-Markov models (not limited to gamma holding times)
nhood has a wndows user interface.

4.- GIS and Remote Sensing: Linkages to modeling

References: Proccedings of three NCGIA international conferences on integrating GIS and models

2nd: Goodchild M.F., L.T. Steyaert, B.O. Parks M.P. Crane, C.A. Johnston, D.R. Maidment and S. Glendinning. GIS and Environmental Modeling: Progress and Research Issues. GIS World, Fort Collins, Colorado.
3rd: Latest 1995 Santa Fe, New Mexico

Remote sensing images are linked to simulation models in various manners; for example,

parameterize models by identifying landscape conditions
evaluate model results
Info derived from remote sensing is made part of the GIS

A good deal of effort has gone into developing spatial hydrology

for example, linkages with the GRASS GIS

End of lecture outline. In the lab session we will be practicing these ideas.

Miguel F. Acevedo