HexSim Networks

Overview

HexSim's grid-based landscape is the most general, and thus most powerful way in which space can be represented. However, there are some specific properties of networks, such as directionality and branching order, which are commonly used in network-based landscape ecology that could be built by the user with grid-based events, but are much more efficient as an explicit capacity of the HexSim platform.

HexSim developers have recently added the potential for users to specify a HexSim population of type “network”. Individuals in a “network” population live and move only on the network structure specified in the workspace, rather than across the full 2 dimensional landscape that is typical of a traditional HexSim scenario.

HexSim “network” population Events and Workspaces take full advantage of the topological properties of branching networks by assigning directionality (e.g., upstream, downstream), by being able to quickly search all of the segments “above” and “below” any segment on the network, and by specifying movement simply in terms of direction (binary) and a branch following rule.

When to Use HexSim Networks

If the spatial structure of the biology to be represented in a HexSim scenario has any network-like aspects, users should consider the option of using a “network” population.

In some cases, the choice of grid versus network is straightforward – wide ranging terrestrial species such as many ungulates that fully exploit the two-dimensional nature of their landscape; however, in other cases it may not be so clear at first glance. Stream dwelling fishes are an ideal candidate for the application of the network-based population structure, but only if the spatial domain is sufficiently network-like to override the fact that it is also two-dimensional.

Therefore, when developing a stream dwelling fish population scenario in HexSim, the user must first decide if large-scale, network-dominate structure is more important than fine scale spatial structure such as movement from the left to right river bank. If the network structure dominates and the fine scale (e.g., within reach) structure and movement can be ignored, then a network-based population and associated network-based events and tools would be the best option. If, on the other hand, the two dimensional nature of river habitat is necessary to represent, then a network of grid cells representing an aquatic habitat can be constructed within HexSim’s grid-based population environment such that both left-right movement within reaches and up- down-stream movement across the network are possible.

Networks naturally exist as spatially constrained domains for aquatic species, but for very large spatial extent simulations of terrestrial and voltine species, network-based populations may also be the most efficient option. For example, species with life cycles dominated by long distance migrations such as birds or insects operating on distinct fly-ways, or ungulates moving between summer-winter, wet-dry seasonal habitats could be represented as network populations, thereby simplifying the spatial representation of their domain to a network rather than to set of paths that sparsely cover a full 2-dimensional domain.

What Changes with Networks

Grid based populations operate on a 2-dimensional array of hexagons, while network based populations operate on a 1.x-dimensional network. The fractal dimensional property of networks means that there is only 1-dimensional movement possible (e.g., upstream-downstream in a stream network), while correspondingly in a grid-based population, 2-dimensional movement (e.g., north-south or east-west, and any direction that results from the combination of these two direction vectors) is possible.

Users familiar with the original HexSim construct – populations existing on a 2-dimensional grid of hexagons – will notice a number of changes to the User Interface now that Network populations are possible. Most notably, populations must now be specified as either “terrestrial” or “network”. HexSim simulations must include at least one population. When multiple populations are present, individuals from the different populations may interact with each other and they may compete for resources as long as they are of the same type.

A Practical Application of HexSim Networks

A network based population modeling framework that supports multiple populations interacting through their landscape is the perfect setting with which to develop restoration scenario planning and assessment templates for beaver based stream restoration. Developing restoration scenarios within a HexSim Network for beaver-based restoration of salmonid habitat first involves generating spatially explicit population life-cycle models of beaver and salmonid populations in a target watershed.

It is known how beaver and salmonid population demographic terms (e.g., capacity and survival) are affected by habitat quality and quantity and how beaver dam building alters stream habitat form and function. Therefore, the population life-cycle models need only be linked through the stream habitat properties (aka the networked landscape) to close the loop between beavers and fish. Stream habitat properties are functions of their geomorphic setting (elevation, gradient, stream power, sediment supply), but in the presence of beavers, are also a function of colony formation, duration and spatial extent of the colony. Beavers form their own habitat, and therefore change their own population dynamics through the dynamics of their footprint on the landscape. Stream rearing salmonids also benefit from beaver activity, so there is an interaction between habitat modification by beavers to support their own populations and the fish population dynamic response.

The basic biology of Beaver (Castor canadensis) that was captured by the example scenario centers around the family-group-based territories, or colonies, that beavers are known for. Beavers are highly territorial, scent marking and defending a section of a stream network or a lake edge that is suitable and sufficient foraging habitat to support the colony. Beaver colonies consist of a mated pair of adults and two cohorts of offspring. Beaver can reproduce annually, having 2-4 kits each year. Beavers don’t become sexually mature until their second year, remaining in their natal colony until they disperse to establish territories/colonies of their own. Thus, a colony typically consists of a breeding pair, ~2 kits of the year and ~2 kits from the year before. Beavers live for up to 9 years with a peak reproductive capacity at 6 to 7 years of age. When 2 year old beavers disperse from their natal colonies, they explore the river or lake network in search of unoccupied, suitable habitat in which to establish a breeding territory. Beavers are thought to form long-term stable breeding pairs, but if a breeding adult dies, it is possible for a new pair to be established with a dispersing individual. The population genetics of beaver are not well understood, but in other rodents, kin recognition is possible and the potential for mating is inversely related to the level of relatedness.

The scenario described above, developed for exploring HexSim population modeling in a network environment, was based on Bridge Creek - a tributary to the lower John Day River in central Oregon. The setting for Bridge Creek is arid sage-scrub steppe, and as such, much of the stream network has only intermittent flow. For the Beaver population model, the portion of the stream network occupied by beaver is the perennial flow portion of the entire stream network. The example model was set up based on various population dynamic conditions, such as pairing and breeding and physical factors, such as flood frequency, dam failure rates, and temperature conditions.