Larger organisms commonly have seasonal migration patterns that allow them to utilize favourable seasonal resource and environmental conditions over large spatial areas. Such movements can be represented in Ecospace in two ways. First is a simple "Lagrangian" approach that does not require explicit simulation of movement; the idea here is to simply think of the whole Ecospace map as moving in space so as to remain centreed on the distribution of some dominant migratory species. Second is a more complex "Eulerian" approach, which does involve explicitly modelling changes in instantaneous rates of biomass flow among the Ecospace spatial cells, in some way that approximates at least the changing centre of distribution of the migratory species.
The Eulerian approach is implemented in Ecospace by allowing users to define a monthly sequence of "preferred" map cell positions (using the Migration dialog box accessible from the Ecospace Basemap form (Migration patterns are also defined on the Basemap form) and to define how spread out the migrating fish are likely to be around these preferred cells by setting north-south and east-west "concentration parameters" on the Ecospace Dispersal form.
The Migration dialogue box displays a map of the Ecospace region, with migratory species and months of the year listed. Preferred position for each month (and the annual trajectory of preferred positions) is set by simply clicking on this map - each such mouse click also triggers the interface to increment the entry month by 1, making it very simple to "sketch" the annual migration trajectory.
The mathematical method used in Ecospace to create migratory behaviour is quite simple. Spatial movement is represented in general in Ecospace as a set of instantaneous exchange rates across the boundaries of adjacent spatial cells. For migratory species, these exchange rates are simply multiplied by relative factors at each simulation time step, where the factors depend on distance from the preferred cell for that time step as shown in Figure 4.3. The function is reversed for movement across a northern cell boundary. A similar function is used for east-west movements with map column-preferred column as the independent variable.
The factor has no effect (multiplies movement rates by 1.0, so movement rates are similar in all directions) for cells near the preferred cell, and 'shuts down' movement away from the preferred cell for cells far from that preferred cell. Note that the base movement rates that are multiplied by the migration factors may not be the same in all directions to start with; these base rates can include advection effects and/or increased/oriented movement rates towards preferred habitat types. That is, migration effects can be combined with advection and orientation of movement toward preferred habitats; it was the desire to represent such combined effects that motivated the multiplicative factor formulation in the first place.
Figure 4.3 Relative movement rates; see text for details.
Tips for setting up migration in Ecospace
Unfortunately, there is no way to make the Ecospace migration simulations very simple to set up. Generally the user must do considerable numerical experimentation to find reasonable migration parameter values and a stable numerical solution scheme; these cannot be computed in advance since they depend on a variety of details about the spatial map grid and species movement characteristics. Here are a few key points to keep in mind while experimenting (by repeated simulations) with the migration interface: