Design Objectives
LANDIS is designed to simulate large landscape (10³ - 10⁷ ha) over long time span (10¹-10³ years) with reasonable simulation time (minutes to a few hours). It is recognized at such broad scales, available input data may be coarse and parameters poorly estimated. Thus, the designed level of detail incorporated in LANDIS is generally consistent with available data and knowledge at these scales. LANDIS is designed to provide species level dynamics of succession and dispersal as well as the interaction of multiple disturbances including fire, windthrow, and harvest.

LANDIS is not designed to predict the specific time or place that individual events will occur. Rather, it is a cause-response type of scenario model that simulates landscape patterns over time in response to the combined and interactive outcomes of succession and disturbance. It can provide managers with guidance about management practices that can mitigate current or anticipated problems on the forest landscape, and provide a better understanding of long-term, cumulative effects that may result from the combination of natural disturbances and management practices.

LANDIS Structure
In LANDIS, a landscape is organized as a grid of cells (or sites), with vegetation information stored as attributes for each cell (Fig. 1).

Figure 1. LANDIS structure

Cell size (site) can be varied from 10-1,000 m depending on the research scale. At each cell or site, the model tracks a matrix containing a list of species by rows and the 10-year age cohorts by columns. The model does not track individual trees. This differs from most forest stand simulation models that track individual trees. A species presence/absence approach provides a simple data structure that allows LANDIS to simulate large landscapes and avoid false precision of predicting species abundance measures with inadequate input data or parameter information.

LANDIS stratifies a heterogeneous landscape into land types (also called ecoregions for broad scale studies). Land types are generated from GIS layers of climate, soil, or terrain attributes (slope, aspect, and landscape position). Land types are also scalable depending on the research scales. It is assumed that a single land type contains a somewhat uniform suite of ecological conditions, resulting in similar species establishment patterns and fire disturbance characteristics, including ignition frequency, fire cycle (mean fire return interval), and fuel decomposition rates (He and Mladenoff, 1999a).

Fire
Fire disturbance is an important landscape process. Fires appear to be stochastic for a single site, but have repeated patterns in terms of ignition, location, size, and shape at landscape scales. It has long been noted that some areas are more fire-prone than others are. The differences are often represented by using mean fire-return intervals; the mean number of years for fire to recur on a given area. Depending on their extent, large landscapes can be stratified into ecoregions, relatively homogeneous sub-areas that are characterized by different climate, topography, and soils with relatively similar fire characteristics. Similar to the approaches used in other studies, in LANDIS the mean fire return interval is used to calculate fire probability using the following equation:

p = B lf MI^-(e+2) (1)

where P is the fire probability of a cell, MI is the mean fire return interval of a given ecoregion on which the cell resides, B is the fire probability coefficient designed for model calibration (B=MI by default), and lf is the number of years since last fire on that cell. With the above distribution, P varies among ecoregions with MIs, and it can be further altered by lf recorded for each single cell. For example, if fire burns a given cell in a given time step, lf of the cell is reset to 0, and P for that cell is calculated as 0 during that time step. This eliminates the possibility of cells being burned twice in the same time step regardless of how short MI is.
Another important feature of fire disturbance is fire size, defined from the following equation integrating random factors and the mean fire size:

S = A (10.0)^r MS (2)

where S is the fire size, is the mean fire size, A is the fire disturbance size coefficient designed for model calibration (A=0.34 by default), and r is a normalized random number (He and Mladenoff 1999a). Under similar mean fire return interval, one can have very different fire regimes ranging from small, frequent fires to large, infrequent fires, which are defined by S distribution (Fig. 2).

Figure 2. Fire size follows log-normal distribution with small fire occurring more frequently than large fires.

Each land type or ecoregion is assumed to have a unique combination of MI and MS. Fire intensity is determined by the quantity of fuel, which is derived from the time since last fire recorded for each cell. A fire of given intensity interacts with individual species and age cohorts in terms of species fire tolerance and age susceptibility. Fire is a bottom-up disturbance, and fires of increasing intensity affect younger age classes first. The interactions of fire with species fire tolerance and age susceptibility that has been explicitly defined in He and Mladenoff (1999a) (e.g., Fig. 3).

Figure 3. Fire intensity vs. fire tolerance (species classes) and susceptibility (age classes). Each individual bar represents the removal range of species of a given age class under fire intensity class three.

Wind
Windthrow disturbance follows a similar approach as fire, except that windthrow is a top-down disturbance, where species susceptibility increases with age and size (Mladenoff and He 1999). The time since a windthrow event can also influence the potential fire intensity class, depending on decomposition dynamics of the particular ecoregion. Interactions between these two disturbances can be interesting and complex. Generally, windthrow becomes more important on land types with long-lived species, and where fire frequency is low.

Harvest
The LANDIS harvest module simulates forest-harvesting activities based upon management area and stand boundaries (Gustafson et al., 2000). These maps are predefined and are only used by the LANDIS harvest and fuel modules. Harvest activities are specified through rules relative to spatial, temporal, and species age-cohort information tracked in LANDIS. The spatial component determines where harvest activities occur and may be used to enforce stand boundary and adjacency constraints. The temporal component determines the timing (rotations) and manner (single vs. multiple-entry treatments) of harvest activities. The species age-cohort component allows specification of the species and age cohorts removed by the harvest activities. For example, a clearcut removes all species and all ages, whereas a selection harvest typically removes only a few species and age cohorts. The ability to use a combination of spatial, temporal, species, and age information to specify harvest action independently allows a great variety of harvest prescriptions to be simulated (Gustafson et al., 2000).

Seed Dispersal
Seed dispersal is modeled as a function of species effective and maximum seeding distances. The effective seed dispersal distance is that for which seed has the highest probability (e.g., P>0.95) of reaching a site. The maximum seed dispersal distance is that distance beyond which a seed has near zero probability (e.g., P<0.001) of reaching. These distances have been parameterized for common tree species in northern Wisconsin (Mladenoff and He 1999), based on the literature for various tree species (e.g., Loehle 1988, Burns and Honkala 1990). Seed dispersal probability (P) between the effective (ED) and maximum seeding distance (MD) follows a negative exponential distribution:

$P\; =\; e-b\{x/MD\}$(3)

Figure 4. The negative exponential distribution of tree species seeding probability in relation to distance from available seed sources. ED- species effective seeding distance, MD- species maximum seeding distance. Other functions can also be used.

Seedling Establishment
When seed successfully arrives at a given site, the light condition checking procedure determines whether seedlings are allowed to establish based on the shade tolerance rank of the seeding species relative to the species already occurring on the site. When light conditions are favorable to a species, the site condition checking procedure determines if the species can establish (Mladenoff and He 1999). The environmental conditions of a site, such as soil nutrient and water availability, may favor certain species over others. The species establishment coefficient, a number from 0-1, is introduced in LANDIS as a relative scaling of how environmental conditions favor various species (Mladenoff and others 1996). These factors are not mechanistically simulated. Rather, they are assigned probabilities that can be derived empirically or from the simulation results of an ecosystem process model (He et al. 1999b)

Succession
Succession is a competitive process driven by species life history parameters in LANDIS. It is comprised of a set of logical rules primarily using the combination of shade tolerance, seeding ability, longevity, vegetative reproduction capability, and the suitability of the land type (Mladenoff and He, 1999). These rules are used to simulate species birth, growth and death at 10-year intervals. For example, shade intolerant species cannot establish on a site where species with greater shade tolerance are present. On the other hand, the most shade tolerant species are unable to occupy an open site. Without disturbance, shade tolerant species will dominate the landscape given that other attributes (e.g., dispersal distances) are not highly limiting and the environmental conditions are otherwise suitable.

Key References
Gustafson, E. J., S. R. Shifley, D. J. Mladenoff, K. K. Nimerfro, and H. S. He. 2000. Spatial simulation of forest succession and harvesting using LANDIS. Canadian Journal of Forest Research 30: 32-43.
He, H. S., D. J. Mladenoff,, K. K. Nimerfro, and E. J. Gustafson. 2003. LANDIS, a spatially explicit model of forest landscape disturbance, management, and succession--LANDIS 3.7 users' guide. Department of Forestry, University of Missouri-Columbia, Columbia, MO, USA.
He, H. S., and D. J. Mladenoff. 1999a. Spatially explicit and stochastic simulation of forest landscape fire disturbance and succession. Ecology 80: 81-99.
He, H. S., and D. J. Mladenoff. 1999b. Effects of seed dispersal in the simulation of long-term forest landscape change. Ecosystems 2:308-319.
He, H. S., D. J. Mladenoff, and J. Boeder. 1999a. Object-oriented design of LANDIS, a spatially explicit and stochastic landscape model. Ecological Modelling 119: 1-19.
He, H. S., D. J. Mladenoff, and T. R. Crow. 1999b. Linking an ecosystem model and a landscape model to study individual species response to climate change. Ecological Modelling 112: 213-233.
Mladenoff, J. D., G. E. Host, J. Beoder, and T. R. Crow, 1996. LANDIS : a spatial model of forest landscape disturbance succession, and management. in GIS and Environmental Modeling : Progress and Research Issues, Goodchild M. F. et al. Ed. GIS World Inc.
Mladenoff, D. J., and H. S. He. 1999. Design and behavior of LANDIS, an object-oriented model of forest landscape disturbance and succession. In D. J. Mladenoff and W. L. Baker (editors), Advances in spatial modeling of forest landscape change: approaches and applications. Cambridge University Press, Cambridge, UK.

Acknowledgement

LANDIS Structure and Design:
David J. Mladenoff (1,3) Hong S. He (1,2) and Joel B. Boeder (3) 

LANDIS 3.0 Program Implementation:
Hong S. He (1,2) and Kevin K. Nimerfro (4)

LANDIS Harvest Module Design:
Eric Gustafson (4), Kevin K. Nimerfro (4), Stephen R. Shifley (4), David J. Mladenoff (1), Hong S. He (1), and Patrick A. Zollner (4)

LANDIS Arcview Interface Implementation:
Jason F. McKeefry (1), Chuang-chang Chiang (1), and Hong S. He (1)

LANDIS Java Interface Implementation:
Barry DeZonia1

Institutions of the above individuals at which they made contributions to LANDIS (V1.0-V3.7)

1. University of Wisconsin-Madison

2. University of Missouri-Columbia

3. University of Minnesota-Duluth

4. USDA Forest Service North Central Research Station

Funding Supports for LANDIS 3.x Development

The following individuals also made contributions to LANDIS development.
Thomas Crow (USFS North Central Research Station), Robert Cumming (University of Wisconsin-Stephen Point), William Dijak (USFS North Central Research Station), Christopher Heim (University of Minnesota-Duluth), Dave Larsen (University of Missouri-Columbia), Wei Li (University of Missouri-Columbia), Brian Miranda (USFS North Central Research Station), Robert Scheller (University of Wisconsin-Madison), Bo Shang (University of Missouri-Columbia), Brian Sturtevant (USFS North Central Research Station), Jian Yang (University of Missouri-Columbia).

Contact
Dr. David J. Mladenoff
Department of Forest Ecology & Management, University of Wisconsin-Madison, 1630 Linden Drive, Madison, WI 53705

Dr. Hong S. He
School of Natural Resources, University of Missouri-Columbia, 203 ABNR Building, Columbia, MO 65211

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