Succession and Seed Dispersal

Succession is a non-spatial, site level process. In LANDIS, it is assumed that detailed, individual tree information and within-stand processes can be simplified, allowing large scale questions such as spatial pattern, species distribution, and disturbances to be adequately addressed. Succession at each site is a competitive process driven by species life history attributes. These are longevity, age of sexual maturity, shade tolerance class, fire tolerance class, minimum age of vegetative reproduction (sprouting), sprouting probability, and effective and maximum seeding distance based on 10 year interval. In contrast to most gap models, which track individual trees (Botkin et al. 1972, Botkin . 1993, Pastor and Post 1985, Shugart 1984, 1997, Urban et al. 1993), LANDIS tracks the presence and absence of species age cohorts. Therefore, succession dynamics is simplified and simulated as birth, growth, and death processes acting on species age cohorts. This approach is similar to a polygon-based landscape model, LANDSIM (Roberts 1996). During a single LANDIS iteration birth, death, and growth routines are performed on species age cohorts and random background mortality is simulated.

Birth, establishment, growth, and death

In succession, several parameters are treated as categorical inputs rather than modeled explicitly; these include species shade tolerant class and fire tolerant class. Other parameters are treated as numerical inputs, including a species' effective and maximum dispersal distance.

Birth adds the presence of the youngest age cohort (1-10) to a species. When seed dispersal is simulated for a given site, a uniform random number from 0 to 1 is drawn to check against an establishment coefficient to decide if seed can establish. A species establishment coefficient is a number ranging from 0 to 1 that expresses the species' relative ability to grow on different site categories or land types. Coefficients are differentiated based on relative responses of species to soil moisture, climate, and nutrients and are not themselves modeled within LANDIS. They can be estimated empirically or derived from a gap model with ecosystem-process drivers (He et al. 1999b). A species can establish only when its establishment coefficient is greater than the random number drawn. Therefore, species with high establishment coefficients have a higher probability of establishment.

Growth increases all species age cohorts by 10 years, and death deterministically removes the species age cohort when it reaches the longevity of the species. Random background mortality simulates tree mortality as it approaches its longevity, but not the mortality caused by disturbance and harvest.

Vegetative reproduction

Vegetative reproduction may occur following the death of a species age cohort. The process of vegetative reproduction is simulated stochastically based on the species' sprouting probability. Minimum sprouting age is used to determine the age at which species can resprout in this version of LANDIS. When checking for the sprouting of a species on a given site, a uniform random number from 0 to 1 is drawn to check against the species reproduction probability to decide if the species can reproduce. If the species can reproduce, the establishment process described in section 9.5.1.1 will determine if such reproduction is successful by checking again with the species sprouting probability.

Competition

A species' competitive ability is determined based upon simple logical rules by the combination of life history attributes and land type suitability (Mladenoff and He 1999). Shade - intolerant species (species with lower shade - tolerance class) cannot establish on a site where more shade tolerant and mature species are present. On the other hand, the most shade - tolerant species are delayed in being able to occupy an open site until specified years of shade creation are met. A s hade-checking algorithm defines shade by the most shade - tolerant species cohort present that is also sexually mature. Species cohorts younger than the minimum seed-producing age are ignored in this shade-checking algorithm. This was implemented as a surrogate for crown closure. Without disturbance, shade - tolerant species will tend to dominate the landscape if other attributes are not highly limiting and land types ( reflected as species establishment coefficients ) are generally suitable.

Seed dispersal

Seed dispersal is modeled as a function of species effective and maximum seeding distances. The effective seed - dispersal distance is the distance at 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 1999b) based on the literature for various tree species. Seed - dispersal probability ( P ) between the effective (ED) and maximum seeding distance (MD) follows a negative exponential distribution:

( 1 )

where x is a given distance from the seed source (MD > x > ED), m is the maximum seeding distance, and b is an adjustable coefficient ( b >0) (b=1 in the current version of LANDIS), which can change the shape of the exponential curve corresponding to various seed - dispersal patterns when information is available. If x £ ED, we set P =0.95, indicating that the probability of seed dispersing within its own effective seeding distance is very high, while if x ³ MD, we set P =0.001, indicating that the probability of seed dispersing beyond its own maximum seeding distance is very low (He and Mladenoff 1999b).



Other types of seed dispersal that are implemented include no dispersal (no cell receives seed), uniform dispersal (all cells receive seed from all species), and neighboring dispersal (seed only disperse to the neighboring cell).

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