Overview

Least-cost path accounts for the affects of landscape structure on movement by depicting the relative resistance of different land-cover types or land uses encountered during species' movements. In other words, each land-use characteristic thought to influence movements is assigned a friction value, which approximates how much that feature impedes or facilitates movement (Adriaensen et al. 2003). The minimum cumulative cost between resource patches based on the resistance surface is known as the least-cost path (Adriaensen et al. 2003).The least-cost path can be associated landscape connectivity through a two step process; 1) calculate the least-cost distance from a source over a cost surface and 2) perform a connectivity analysis with the least-cost surface. Within GIS there are two options for connectivity analysis. The first option is to estimate the least-cost path which requires a set of possible destinations to calculate the back link in the cost distance analysis. The other, more computational option to estimate connectivity is to run a corridor analysis where a second cost-distance is calculated from the destination. This surface is then combined with cost distance from the source and destination at a set threshold value.

Data Requirements

This approach requires two types of data:

• Spatial distribution of habitat patches
• Resistance surface containing friction values representing how environmental features influence movement ability

The most important step when creating a resistance surface for this method is estimating biologically relevant friction values (Adriaensen et al. 2003). Due to the lack of detailed information about dispersal and movement behavior, friction values for most species are usually defined subjectively based on expert opinion, or are converted from species habitat preferences during common daily activities, and therefore not representative of dispersal behavior (Schultz and Crone 2001, Schadt et al. 2002).

Strengths

Due to the limited data requirements it is relatively easy to calculate least-cost path between habitat patches with minimal animal movement data.

Weaknesses/Assumptions

Friction values derived from these routine movements may not accurately depict an individual's reaction to landscape features outside their habitat because behavior may differ during dispersal through non-habitat (Palomares et al. 2000). Studies rarely validate friction values and resistance surface derived from expert opinion or daily activities with independent movement data. Therefore, surfaces are not confirmed in relation to observed movements. Resistance surfaces require continuous land-cover maps spanning large spatial extents.

The least-cost distance approach has two improbable assumptions:

1. Individuals have complete knowledge of their surroundings
2. • Individual select the global optimum least-cost path between patches

Capacity Needed (construct and run model)

Least-cost path can be calculated in GIS software.

Overview

Circuit theory models assume that species movements are analogous to electrical current flowing over a landscape composed of conductors with various amounts of resistance, represented by a raster dataset. Circuit theory models can be considered an efficient analytical equivalent to simple individual-based models known as "biased random walk" models (McRae et al. 2008), and allow dispersal corridors and "pinch points", where animal movements are constricted to only a few possible paths, to be mapped quickly and effectively. This model also allows the investigator to quantify the relative strength of connections between all habitat patches, based on their distance and the quality of intervening habitat.

Data Requirements

Circuit theory models require two inputs:

• A raster where valued cells represent occurrences of the focal species
• A raster of resistances that represent the relative impermeability of different landscape features to dispersing organisms

Strengths

Every grid cell in a landscape receives a relative movement ability estimate in Circuit theory models. One is able to identify pinch-points and landscape corridors a species has a high likelihood of passing through when moving between patches (McRae et al. 2008).

Weaknesses/Assumptions

The modeling outcome is based on resistance surface supplied by the investigator. Therefore, there will always be uncertainty in selecting biologically relevant friction values for the resistance surface and appropriate cell resolution. Edges of maps (i.e., landscape features data) limit estimation of the potential movement route. Movement is assumed to occur with the same ease in forward and backward directions. Therefore, species movements influenced by directional features like elevation or water currents may not be appropriate for this approach (McRae et al. 2008).

Circuit theory models are restricted to Markovian random walks with no "memory" between steps. This framework cannot incorporate correlated random walks, changes in movement behavior with time, or mortality rates that increase with an organism's age (McRae et al. 2008). Barriers to movement need to be identified and delineated.

Capacity Needed (construct and run model)

The investigator will have to know basic GIS processing to prepare grids. The model can be processed in freely available software Circuitscape.

Overview

Graph network models are able to summarize the spatial relationship between points of interest and estimate the optimal flow patterns or connectivity through a network (West 1996). A graph network data structure is a set of nodes (points) connected to some degree by links or edges. Nodes in the graph networks are typically denoted as habitat patches and edges usually represent the movement ability between pairs of patches. Potential connections between habitat patches exist if the focal species movement ability is greater than the edge's distance. Once a network is created, several network-level and patch-level graph metrics can be calculated to evaluate the topology of the network and centrality or juxtaposition of each habitat patch.

For many habitat connectivity studies, the flow of individuals between habitat patches is estimated for a wide range of distinct edge threshold distances (Bunn et al. 2000, e.g., Urban and Keitt 2001). Habitat patches within the threshold distance are defined as connected while patches beyond the distance threshold are defined as disconnected (Keitt et al. 1997, Minor and Urban 2008). This approach evaluates connectivity to movement ability and can reveal a sharp transition between connected and disconnected landscapes (Urban and Keitt 2001). This sharp transition is then compared to a fixed distance that represents typical or maximum dispersal distance and that is based on literature review (Roshier et al. 2001, e.g., Lookingbill et al. 2010).

Data Requirements

The only data required to create the simplest graph networks for landscape connectivity model is the location of habitat patches. The simplest graph networks are based solely on the spatial distribution of the habitat patches and assume that connectivity is only a function of distance between patches. More complex network models account for varying ability to move through the environment (Calabrese and Fagan 2004, Minor and Urban 2007). These more complex models replace the Euclidean distance matrix that is populated with all pairwise combination of habitat patches with least-cost distances. The distance matrix is then converted into a directed or unidirected graph network.

Strengths

Graph networks are able to incorporate spatial arrangement of habitat patches and attributes of the habitat patch (Keitt et al. 1997, Bunn et al. 2000, Urban and Keitt 2001). Graph networks do not require knowledge of behavior, fecundity, or mortality parameters. However, as data on a species become available they can be incorporated and used to create an ecologically rich graph model. For example, as mark-recapture data become more available for a species the estimated probability of long-distance dispersal events can be included in graph network model.

Weaknesses/Assumptions

Habitat patches need to be identified and delineated and are simplified into a single point with little or no habitat quality information. Therefore, gradient of habitat quality within a patch is usually not represented in graph networks.

Capacity Needed (construct and run model)

Graph networks can be created within R software with separate packages such as igraph, network, or sna. Free software called Pajek is also available to download.

Overview

Agent-based model (also known as individual-based models) is a spatially-explicit simulation modeling approach that attempts to capture the variation among individual movements in order to understand landscape-level movement behavior. Individuals are discrete agents with various properties that change during the life cycle (e.g., age, weight, and reproductive status) (Grimm and Railsback 2005). For every time step (e.g., year or season) dynamic movement behavior for each agent or individual is governed by local rules (Johnson et al. 1992). As a result each individual has a unique history of interactions with its environment and other agents (DeAngelis and Mooij 2005).

Random walk in a homogeneous environment is one of the simplest agent-based models. This model assumes that step directions are random and independent of each other and movement from a source is similar to diffusion model (Turchin 1998). The investigator can increase the complexity of the model by correlating species movements with heterogeneous environments. This is accomplished by adjusting the probability of moving into a cell based on the species preference/ability to traverse through that land-cover feature and a correlation between previous step and the next step can be adjusted for each land-cover to mimic straight or curved movements.

Data Requirements

Detailed individual-level movement data (e.g., radio-telemetry) throughout various land-cover types are required to accurately parameterize species movements (Belisle and Desrochers 2002). When modeling movements in different environments, continuous raster of all environmental data are required.

Strengths

Very flexible modeling approach where many different types of information regarding species biology, environmental interactions, and intra/inter species interactions can be incorporated into the model. Once the simulation model is constructed, it can be easily altered to account for different behavior rules between species or landscape features. This approach allows models constructed with movement data from a short temporal scale to represent the population or system at wider temporal scale.

Weaknesses/Assumptions

This approach can be data intensive. Many movement studies are needed to inform the local rules needed to mimic a species movement behavior. Each movement decision is based on the immediate surrounding cells. Therefore, this approach is very sensitive to the raster resolution selected by the modeler. The simulated patterns are rarely compared with independent movement data to determine closeness of fit between model predictions and observed movements.

Capacity Needed (construct and run model)

This approach requires a high skill level in computer programming.