SEARCH: Spatially explicit animal response to composition of habitat
Purdue University, Department of Forestry and Natural Resources, 715 West State Street, West Lafayette, IN 47907, USA
Spatially explicit population models (SEPMs) show promise as tools for conservation, but have been criticized as being behaviorally minimalist. Behavior is important because it influences patterns of animal movement, is temporally dynamic, and can vary at fine spatial and temporal scales. To investigate questions related to underlying behavioral mechanisms that occur at fine scales, we present a SEPM that allows researchers to simulate animal dispersal across complex, realistic landscapes while modeling a range of search processes and habitat selection rules. SEARCH can be used to simulate the spatially explicit response of medium and wide-ranging, solitary animals to habitat composition over multiple successive dispersal seasons, at fine temporal resolutions, on temporally dynamic, high-resolution landscapes. Within SEARCH, animals move across a vector-based landscape of four GIS layers, with values assigned to each point in space on each layer to reflect animals’ response habitat characteristics (e.g., movement sinuosity and energy use). Dynamic landscapes can be simulated in SEARCH to reflect changes in habitat quality and/or spatial arrangement by replacing any combination of the landscape maps at times and dates scheduled by the user. Animals in SEARCH are parameterized by the user to reflect behavior, energetics, and home range requirements and baseline landscape and animal parameter values can be modified by the user to reflect variability caused by gender, activity mode, behavioral mode, time of day, and date. Dispersing animals retain memory of habitat suitability and occupancy and query their memory in combination with user-parameterized selection rules to locate and delineate home ranges. As SEARCH can be run for multiple years, stochastic reproduction is modeled and resident females reproduce annually, giving birth to a user-parameterized number of young. Output at the individual-level includes the animal location, energetics data, risk of predation, movement parameters at each time step, and shapefiles depicting the area perceived during dispersal. At the population-level, shapefiles depicting the arrangement of home ranges is produced and population demographics (e.g., age structure) can be constructed from individual-level data. To illustrate SEARCH’s capabilities we use a reintroduced American marten (Martes americana) population in the Chequamegon-Nicolet National Forest (CNNF), Wisconsin as a hypothetical study system. We first explored the theory that fishers (Martes pennanti) constrict marten populations by predation and competitive exclusion by testing the sensitivity of marten population expansion to increased predation and reduced food availability. We then explored the relative effects of forest management plans on marten population expansion by simulating marten dispersal on CNNF landscapes across a range of even-aged management scenarios. Results suggest that marten populations are constricted by fisher predation, competition with fishers, and forest management that increases the proportion of even-aged stands in the CNNF. These hypothetical case-studies demonstrate the capabilities of SEARCH for investigation of questions related to basic and applied science. SEARCH’s numerous fine-scale inputs and range of behavioral parameters gives it the flexibility to be a useful tool for investigating behavioral mechanisms for numerous solitary animals.
Spatially explicit population models (SEPMs) offer researchers an ability to study landscape-level processes and responses to habitat change, such as management strategies or natural disturbance (Pulliam et al. 1992, Turner et al. 1994, Pulliam and Dunning 1995). They specify the location of each object on landscape maps using idealized (South 1999, Wiegland et al. 1999) or realistic landscapes that can be created using geographic information systems (GIS; Turner et al. 1994, Liu et al. 1995). Such specification of the spatial arrangement of habitat is critical for understanding the ecology of the species being studied as well as system processes because wildlife populations are mobile (Turner et al. 1995, Mladenoff 2004).
Unfortunately, the scope of many studies that employ SEPMs are often limited because many SEPMs consider simplified, static landscapes and coarse spatial and temporal resolutions (Wiegland et al. 1999, Kramer-Schadt et al. 2004) rather than complex, realistic, temporally dynamic landscapes at fine resolutions. This is important because animals’ response to habitat can vary at fine spatial and temporal scales (CITE) and habitat-use can change daily or seasonally (Wolf 1978).
The scope of many SEPMs is also limited because they exclude behavior (South 1999). Behavior influences patterns of animal movement and incorporating behavior into SEPMs would yield a greater understanding of the mechanisms that underlie animal movement. For instance, modeling of decision rules that underlie habitat selection would allow researchers to investigate the interaction of management scenarios and behavior on landscape permeability and lead to new questions or approaches to unanswered questions. [Find something to cite here]
Many SEPMs are further constrained because they are species-specific, reducing their flexibility (Liu et al. 1995, Railsback and Harvey 2002, but see Gardner and Gustafson 2004). Adding flexibility allows researchers to avoid the often labor-intensive task of model development, allows researchers to use models in different systems, and facilitates model evolution (Mladenoff 2004). It also allows researcher to simulate different species’ responses to potential management scenarios or disturbance regimes and creates a common structure from which to begin discussions. Increased model flexibility has been a goal of several widely-used forest models (LANDIS, Mladenoff 2004; JABOWA, CITE), but has been lacking from animal dispersal models (but see Gardner and Gustafson 2004).
We present a SEPM that simulates animal dispersal across complex, realistic landscapes while modeling a range of search processes and habitat selection rules. It allows researchers to investigate questions related to underlying mechanisms that occur at finer scales than other simulations [are there any others that do this?], such as resource selection. We model the spatially explicit animal response to composition of habitat (SEARCH) over multiple successive dispersal seasons, at fine temporal and spatial resolution using temporally dynamic, GIS-based landscape maps. SEARCH allows for increased flexibility as the user defines multiple animal, spatial, and temporal parameters. To illustrate its use for study of solitary carnivores, we present an example of SEARCH’s application to an American marten (Martes americana) dataset.
SEARCH simulates animal dispersal on GIS-based landscapes to investigate the sensitivity of dispersal patterns to variability in habitat quality, habitat arrangement, and animal physiological and behavioral parameters. SEARCH builds on findings from field studies of animal demographics, behavior, and physiology to identify population dispersal patterns that emerge from the movement of individuals. It may be parameterized for numerous species and employs dynamic landscapes to simulate habitat change. It was coded in the C# language (CITE Visual Studio; CITE), employs a graphic user interface (GUI) to prompt the user to input maps and animal parameters, and is available at: http://ranchdelux.com.
Process overview and scheduling. THIS NARRATIVE IS KEY, AND NEEDS MORE
Within SEARCH, animals move across a GIS-based landscape composed of four maps, with values assigned to each polygon in each map to reflect habitat characteristics (Table 1; Figure 2). The landscape is populated by residents or is unpopulated to reflect the system under study. Each of the landscape maps are queried at each time step for a user-defined dispersal period and number of years (Figure 1). At each time step, animal location, energy level, behavioral mode, memory, and activity state, and activity mode is updated. Animals employ a behavioral rule using landscape values and user-input values to simulate habitat selection.
To simulate a dynamic landscape, the user can schedule the replacement of any combination of the four maps at selected times and dates. This can be done to reflect changes in habitat quality and/or spatial arrangement.
Animals are parameterized by the user to reflect behavior, energetics, and space requirements (Table 3). Baseline landscape map values and animal parameter values can be modified by the user to reflect variability caused by gender, activity mode, behavioral mode, time of day, and date (Table 2).
Once a user-defined number of steps taken or number of suitable sites is traversed, animals select a home range center from areas searched during dispersal, move to the selected home range center, and attempt to establish a home range. Animals become residents once a home range is established, but die if a home range is not established during the dispersal period. In the period between dispersal periods, the inter-dispersal period, residents are subject to random mortality and females stochastically give birth to young which disperse the following dispersal season.
State variables and scales
Within SEARCH temporal resolution is represented as a discrete time step. The user defines the time step length (≥ 5 minutes), dispersal period (≥ 1 d), and the extent of simulation runs, which may range one or multiple years. The inter-dispersal period composes the remainder of the year, when dispersal does not occur.
Scales employed by SEARCH are the resolution and extent of user-input vector-based GIS maps. User-defined values are assigned to each GIS map classification and characterize the following state variables: correlated random walk movement parameters, the probability of acquiring prey, the probability of being depredated, the suitability for home range establishment, and occupancy status (Table 1).
Individual animals are characterized by the following state variables: identification number, gender, dispersal mode, behavioral mode, energy level, and location (Table 3). Population characteristics can also be derived from model output including: age structure, sex ratio, and mortality rates.
Patterns emerge at the population-level based-on movements of individuals. They develop from the interaction of animal parameter values, behavioral rules, stochasticity, and landscape map values. Emergent patterns include: habitat selection, dispersal paths, dispersal speeds and directions, home range locations, population growth and spatial expansion rates, mortality rates, and mortality locations.
Adaptation and Prediction.
Simulated animals to choose from alternative behaviors. For example, individuals select habitat during dispersal by comparing the probability of predation and prey acquisition at their current location with adjacent locations and also evaluate landscape values when selecting a location to center a home range. Also, animal activity mode may change based-on a user-defined energy threshold and behavior of active animals can be effected by their perceived risk of predation.
Interaction and Sensing.
Interaction between individuals is implied because animals of the same gender cannot establish overlapping home ranges. Additionally, users may employ one of two criteria to trigger selection of a home range center. This allows the user to compare the success of populations that select home ranges using the different criteria.
Animals respond to map polygon values assigned for: suitability for home range establishment and occupancy status, probability of predation, and probability of acquiring prey. They respond to these values according to their: gender, social status (resident or disperser), energy level, behavioral mode, activity state, activity mode, and if they are at a heightened risk of predation.
Animal movement is a correlated random walk sampled from a wrapped Cauchy distribution (CITE), with sinuosity based on user-defined map polygon values. Stochasticity is also incorporated when dispersing individuals select habitat, after comparing the quality of their current location with locations into which they may cross.
Home range establishment uses a random set of points within a user-defined distance (±SD) from the home range center point. Mortality due to predation and prey acquisition during dispersal is based on the GIS classification in which an animal is located, its current behavioral mode, and a random number draw. Mortality and female natality during the inter-dispersal period is probabilistic and irrespective of habitat type. Dispersing animals in the years following initialization begin at random points within the female parent’s home range.
Note: I am missing behavioral mode changes due to perceived risk of predation.
Data output for individuals includes: habitat and individual state variables, location, date, and time during each time step. GIS maps that depict each animal movement path, home range, and perception of its travel path are also produced. Population-level maps are produced at user-defined intervals that depict home range and dispersal path arrangement. Additional population-level responses, such as sex ratio or population age structure, can be extrapolated from individual output.
Need to be careful throughout: residents vs. dispersers is an important distinction
Modifiers. The user modifies animal parameter values by multiplying them by a real number to reflect variation caused by gender, activity mode, behavioral mode, time of day, and date (Table 2). Temporal modifiers are used to alter parameters at times during the 24-hour period and dates scheduled by the user. For example, perception distance may be decreased at night.
Landscape. The user assigns values to map polygons that dispersing animals respond to (Table 1). A dynamic landscape can be simulated by scheduling the input of maps that have different values or spatial arrangement. These alternate maps are scheduled in a sequence of dates or times to reflect habitat management or disturbance. The user also assigns temporal parameters, including dispersal season dates and time step resolution (Table 3).
Home ranges. Two options are available to prompt selection of a home range center: (1) A minimum number of time steps occurred; or (2) A minimum number of suitable and unoccupied points were sampled by the dispersing animal. These minimum values are input by the user. Home range establishment requirements are also input by the user, including the minimum area for a home range and the mean distance (±SD) from the center point that will be used to create the home range (Table 3).
Energy. Energy parameters are defined by the user, including the initial energy within each animal and the minimum energy-level per animal below which mortality occurs due to starvation (Table 3). Energy is reduced at each time step due to the GIS classification the animal is in and gained if a prey item is acquired.
Activity states. Active, dispersing animals move across the landscape while resting animals do not. Temporal parameters reflect daily mean periods of activity or rest, after a user-defined daily start time. Variability among individuals is simulated by including a standard deviation measure with each mean.
Activity modes. Active, dispersing animals are either searching for habitat to establish a home range or foraging for prey. Variation of animal response to location because of activity mode is influenced by modifiers (Table 2). For example, the user may increase the probability of capturing prey when foraging versus searching. The default activity mode is searching but changes to foraging if the animal’s energy-level drops below a user-defined threshold.
Behavioral modes. Active animals may exhibit different behavior because of a perceived risk of mortality. Animals are active in a mode that is risky or safe. Similar to activity mode, variation of animal response to habitat because of behavioral mode is influenced by modifiers (Table 2). For example, the user can increase the probability of predation for animals in risky behavior mode and reduce that probability when in safe mode.
Default animal activity is risky but may change to safe if the animal perceives a heightened risk of mortality. This is simulated when a number drawn from an even distribution (r) falls between (PD + Ms) and (PD + Mr), where PD is the probability of depredation for the current location, Ms is input by the user to modify the minimum value at which the animal will change to safe behavior, and Mr is input by the user to modify the minimum value at which the animal will return to risky behavior. The animal will return to risky behavior at subsequent steps if: r > (PD + Mr). [If r equals PD + Mx? Check code.]
Perception and memory. Memory in SEARCH is the area perceived during dispersal: a function of perception distance and the path traversed during dispersal. Perception distance is the distance at which animals perceive key habitat elements (Zollner and Lima 1997). In SEARCH, perception distance is the radius (m) from each point along an individual’s travel path and habitat suitability and occupancy are the key habitat elements perceived by animals. Habitat suitability and occupancy are defined by a user input habitat map that is updated at each time step. Perception distance is user-defined and can be altered using modifiers to reflect differences caused by time of day or season. For example, the user can reduce nighttime animal perception distance relative to daytime perception distance. A circle with a radius of this distance is produced at each point along the line-segment connecting the animal’s travel path. The animal’s memory is the total area within these circles for all time steps. If a polygon is visited multiple times, the most recent status of the key habitat elements is recorded as memory. This assumes that animal’s retain a complete memory of habitat suitability and occupancy during dispersal.
Inter-dispersal periods. The inter-dispersal period is defined as the period between user-defined dispersal period p and p + 1. Resident animals are subject to a user-defined mortality probability during this period. Additionally, a user defined proportion of randomly selected females give birth to a user-defined mean (±SD) number of young. Young begin dispersal in the subsequent season at a random point drawn from a uniform distribution within the female’s home range.
One of three scenarios initialize the simulation: (1) Animals disperse from locations defined by an input map; (2) Dispersal begins at a random point within a random number of randomly selected female home ranges from an input map; or (3) A combination of these. In all 3 scenarios, the landscape map may be populated by existing home ranges. Scenario 2 requres this +++++ Scenario 1 most closely simulates a reintroduction, while scenario 2 simulates dispersal from young of a resident population. Combining the scenarios allows the user to simulate a reintroduction in areas where residents occur.
The landscape at initialization is defined by the user-input maps. ADD MORE+++++++
At initialization a memory map is created for each animal that is updated at each time step. The memory map records the area perceived at all points during dispersal. It simulates an animal’s memory of the dispersal season, and is queried during home range establishment to identify optimal sites for home range establishment.
Question: In the previous draft you point out that this may be redundant; do you have suggestions as to how I might mention it here and above, while not being redundant. I did my best to not re-state details here, but I feel it is appropriate to mention it in both sections. MAYBE COMBINE IT HERE?
Crossing. During dispersal, animals choose between the GIS landscape classification they are moving toward and remaining in their current location (Table 1). This choice uses landscape map values to calculate the probability that an animal will cross into a different habitat type using: p = n/c, where p equals the percent chance of selecting the new classification, n equals the user-defined rank of the new location, and c equals the rank of the current location. A random number (r) is generated from a uniform distribution. The animal will move into the new habitat if p > r. If p < r the animal will reflect 180º at the boundary and continue in the current habitat type for the remainder of the time step.
Home range selection and establishment. To select a home range center, each animal queries its memory map to evaluate potential home range centers. A decision matrix is then employed that incorporates the probability of acquiring food (PA) or probability of depredation (PD) at each point, weighted by a proximity factor. PA or 1-PD is multiplied by a proximity factor equaling the distance from the point to its current location (d). The user may modify d using a root factor: , where n is a value input by the user. This allows the user to modify the impact of d on home range center point selection. Movement in subsequent time steps will be directed to the point of the highest value, where attempts at home range establishment will occur. This assumes that home range center selection is based upon prey availability, predation risk, and proximity, and not other factors, such as habitat structure , or proximity to disturbance.
NEED TO ADD COMBO VALUE – FROM EMAIL TRAFFIC +++++++
Home range establishment attempts occur within 1 time step when the selected point is within the animal’s perceptual range. To simulate exploration around the home range center, 30 points are randomly selected from a user-defined gender-specific mean (±SD) distance from the home range center point, if it is unoccupied by an animal of the same gender. At that point a 100% minimum convex polygon (MCP) is calculated using the suitable, unoccupied points (n ≥ 3). If the area within the MCP is not ≥ the minimum home range size required for animals of its gender, 30 additional points are randomly selected and a MCP is generated using all suitable points including suitable points from the first draw. This is repeated until a MCP of suitable size is generated or until 10 unsuccessful attempts are made. If an acceptable MCP is defined, it delineates the home range boundary for that individual. Once the MCP is defined, points within its bounds are occupied and home range establishment using those points by animals of the same gender is prohibited. If 10 unsuccessful attempts are made or if an animal arrives at a home range center point occupied by another animal of the same gender that animal queries its memory map, recalculates the decision matrix, and redirects its movement toward the highest ranking remaining home range center point where the process is repeated. Only animals that establish home ranges during dispersal survive to subsequent years.
Example of a generalized dataset
SEARCH allows users to simulate the dispersal of multiple species and is most appropriate for medium or wide-ranging, solitary carnivores. We present an example of how SEARCH may be parameterized to simulate the dispersal of a mesocarnivore, using the American marten (Martes americana) as a study system. Martens were extirpated from Wisconsin during its settlement in the late 19th and early 20th centuries and reintroduction efforts have been largely unsuccessful (Williams et al. 2006). The marten is the only mammal listed as endangered in Wisconsin (CITE) and understanding the effects of habitat composition and configuration on marten dispersal is important for management of the remaining populations and for identification of areas suitable for future introductions.
Parameter estimates, modifiers, and map scheduling
Landscape and animal parameter values (Table X) were collected from published marten field studies from throughout the marten range and ongoing studies in Wisconsin. Landscape maps are from the from the USDA Stands coverage for Wisconsin (CITE) [Add details of what it classifies and where it comes from].
Modifiers were applied to +++. Support the use of modifiers in text [or add to the Table if possible]. For example, if males have a XX% greater chance of being depredated, this can be cited and modified and reflected in the Table.
Different maps were scheduled to reflect: reduced food availability during winter, reduced food availability during nighttime hours, ADD +++
ü Review the info in this section to verify that it covers all parameters (either in text or tables)
Refer to figure 4 (?) – 4 maps depicting some outputs.
Look at Mladenoff 2004 as he warns-against using a lot of parameters… should this be handled up-front, in the Intro.?
Model not validated…