Biological disturbances, such as insect and disease outbreaks, are critically important agents of forest change that cause tree mortality at scales ranging from individual trees of a single SPP to entire regions. The BDA module is designed to simulate tree mortality following major outbreaks of insects and/or disease, where major outbreaks are defined as those significant enough to influence forest succession, fire disturbance, or harvest disturbance at landscape scales.
Figure 1.- BDA flow diagram.
Biological disturbances in LANDIS are probabilistic at the site (i.e., cell) scale, where each site is assigned a probability value called biological disturbance probability (BDP) and compared with a uniform random number to determine whether the site is disturbed or not. Disturbance causes species- and cohort-specific mortality in the cell. In the simplest case, BDP equals Site Resource Dominance, a number that ranges from 0 (no host) to 1 (most preferred host) based on the tree species and age cohorts present on the site. Four additional optional factors may also modify BDP: 1) environmental and/or other disturbance-related stress (Site Resource Modifiers); 2) the abundance of host in the neighborhood surrounding the site (Neighborhood Resource Dominance); 3) user-defined temporal functions (e.g., cyclic, random, or chronic) that affect the temporal pattern of disturbances across the entire spatial domain of the simulation (Regional Outbreak Status); and 4) spatial epidemic zones defined via simulated dispersal of a BDA through a heterogeneous landscape (Dispersal). The above combinations of optional factors allow the BDA module to accommodate several types of destructive insect and disease species, and more than one BDA may be simulated concurrently to examine their interactions.
More detail on the BDA module and its behavior can be found in Sturtevant et al. (2004). However, several key terms were modified from this publication to be consistent with the terminology of other natural disturbance modules in LANDIS 4.0. In this users guide, we use the term BDP for site vulnerability, all references to “vulnerability” or “susceptibility” been changed to either tolerance class (for species) or susceptibility class (for species age cohort). The rank order of these two classes is also consistent with the design of the other disturbance modules. Finally, all references to the “severity” class of a disturbance have been changed to “intensity” class.
Site resource dominance (SRD) indicates the relative quantity/quality of food resources on a given site and is a combined function of tree species composition and the age cohorts present on that site. The relative resource value of a given species cohort is defined by its host preference class, where preferred host = 1.0, secondary host = 0.66, minor host = 0.33, and nonhost = 0. The BDA module compares a look-up table with the species cohort list generated by LANDIS to calculate SRD using one of two methods: 1) the maximum host preference class present, and 2) an average resource value of all tree species present, where the resource value of each species is represented by the cohort with the oldest host preference.
Site resource modifiers are optional parameters used to adjust SRD to reflect variation in the quality of food resources introduced by both site environment (i.e., land type) and recent disturbance. Both land type modifiers (LTMs) and disturbance modifiers (DMs) can range between -1 and +1, and will be added to the SRD value of all active sites where host species are present. LTMs are assumed to be constant for the entire simulation, while DMs decline linearly with the time since last disturbance. Disturbances that may affect a given BDA include fire and wind. Disturbance effects from another BDA and user-specified harvest prescriptions are currently not implemented. SRD is then modified by LTM and the sum of all DMs:
SRDm = SRD + LTM + (DMwind + DMfire + ...) (8)
The user should calibrate the above modifiers to reflect the relative influence of species composition/age structure, the abiotic environment, and recent disturbance. For example, an LTM value of 0.33 is equal to a full step increase in disturbance intensity above that calculated using species composition alone.
Several recent studies suggest that the landscape context of a site also influences the probability and intensity of disturbance (Cappuccino et al. 1998; Radeloff et al. 2000). A neighborhood effect is modeled in LANDIS as the mean SRDm of each cell within a user-defined radius R , using one of three radial distance weighting functions listed in increasing order of local dominance: uniform, linear, and Gaussian (Orr 1996; see Sturtevant et al. 2004). Neighborhood resource dominance (NRD) is calculated for all sites containing host species (i.e., SRD > 0). An optional subsampling procedure calculates the NRD for every other site, and the NRD of the remaining sites are estimated by the mean NRD of adjacent sites in the four cardinal directions. For large neighborhoods, this subsampling routine can increase the processing speed of the BDA by over 40% (Sturtevant et al. 2004).
Several simple temporal patterns may be simulated in the BDA module to represent general outbreak trends for the entire study landscape. Temporal patterns in a given BDA are assumed constant for the length of the simulation, and are defined by a suite of temporal disturbance functions that define the landscape scale intensity of the BDA at a given time step, termed Regional Outbreak Status (ROS). ROS units are integer classes ranging from 0 (no outbreak) to 3 (intense outbreak). The time to the next outbreak is calculated following each outbreak event using either a uniform or a normal random function. Though the actual time periods between outbreaks will be constrained by the time step of LANDIS (currently set at 10 years), the random outbreak functions may be used to vary the outbreak interval so that the average interval between outbreaks observed during the length of the simulation approximates that expected by the user.
The magnitude of simulated regional outbreak severities is controlled by the MinROS and MaxROS parameters. MinROS defines the “background” outbreak activity that will occur in each time step. Outbreak type (“TempType” in the BDA parameter file) determines whether outbreaks are binary (either MinROS or MaxROS; TempType = “pulse”) or if the ROS can range between those values (TempType = “variable pulse”). For the variable pulse outbreak type, the ROS value is randomly selected for each outbreak event from the range between MinROS+1 and MaxROS.
Both the probability that a site is disturbed by a given BDA and the intensity of that disturbance are controlled by biological disturbance probability (BDP). BDP is defined by the following equation:
BDP = a × ((SRDm + (NRD × NW) / (1 + NW)) × (ROS / 3) (9)
where a. is a user-defined calibration parameter (by default, a should = 1); SRDm = the species and age composition of the site (SRD), optionally modified by land type and/or past disturbance (Equation 8); NRD = the mean SRDm of sites within the neighborhood surrounding a site; NW = Neighborhood Weight, a parameter designed to define the relative importance between site and neighborhood resources; and ROS = Regional Outbreak Status.
Some epidemics occur at spatial scales smaller than the typical simulation area of LANDIS. Accounting for BDA dispersal and spread will be necessary for these cases. The BDA dispersal procedure defines smaller spatial zones within the modeled landscape where insect disturbance may occur within a given time step. Within these restricted spatial zones, the BDA operates exactly the same as if the outbreak were synchronous. Note that the dispersal procedures for the BDA module are still under development, but there are some preliminary dispersal procedures available in LANDIS 4.0.
Epicenters are defined as central sites from which a BDA may disperse. There are three types of epicenters: 1) initial epicenters–sites randomly selected at time(t) = 0 to initiate new outbreak zones in the first time step; 2) seed epicenters–sites randomly selected at each time step an outbreak occurs to initiate new outbreak zones outside the outbreak zone defined at time t - 1 during the simulation; and 3) outbreak zone epicenters–sites randomly selected from within the last outbreak zone (i.e., time = t - 1) to continue the spread of an outbreak in consecutive time steps. The BDA module will randomly select epicenters from a subset of sites that are above user-specified threshold site vulnerability. Initial epicenters can be selected anywhere in the landscape where sites meet this criterion; seed and outbreak zone epicenters are selected from outside and inside (respectively) the outbreak zone defined at time t - 1.
The number of initial epicenters is a simple user-defined parameter. The following negative exponential equation determines how many new epicenters will be generated both inside and outside existing outbreak zones:
Yi = Ai × exp(-ci Xi) (10)
Here, Ai = the number of qualified potential epicenter sites (i.e., the number of sites either inside or outside the last outbreak zone where BDP > the epidemic threshold), Xi = the current number of selected epicenters of a given type, and Yi = the number of remaining sites that can be checked. Coefficient ci. is a user-defined parameter that controls statistically how many new epicenters may be generated for either seed epicenter or outbreak zone epicenter type. The number of epicenters will decrease with increasing c.
Outbreak zones are defined using dispersal routines that spread from an epicenter to a circular boundary with a radius defined by the annual dispersal distance of a BDA, multiplied by the number of years in a time step (i.e., 10). An outbreak zone either automatically expands to this maximum limit (termed “regular dispersal”) or occurs as a percolation process through a binary landscape, where it may only spread through sites containing host tree species. Ability to spread over nonhost cells is defined by a user-defined neighborhood rule (sensu Gardner 1999) termed a “structuring element” in the BDA Module. Available structuring elements include 4, 8, 12, and 24 nearest neighbors (fig. 1).
Figure 1.- Available structuring elements.
The dispersal routines will attempt to spread each epicenter to its maximum dispersal distance using the neighborhood rule defined by the user. An outbreak zone from a given epicenter with may overlap one created from a nearby epicenter. The cumulative area of all zones created during the time step defines the spatial extent over which the BDA may disturb sites during that time step.