All individual based models (IBMs) make use of known relationships (equations) between environmental factors and agents (individual blue crabs) that occur in the model. The key to a realistic individual based model is how well you can accurately describe these relationships. Consider this simplified diagram of a subset of factors that might influence the relationship between drought and commercial blue crab landings. Some of these relations will be positive (green arrows) while others will be negative (red arrows). Still other relationships will be cyclical or non-linear (black arrows). Single factors such as salinity may have many different pathways to influence crab abundance. A simple equation is unlikely to explain much variation in this relationship. Furthermore, this relationship is likely to change through time and space. So the value of the IBM approach to studying the effects of drought on crab abundance, it that it takes into consideration many different and often opposing relationships to produce a more realistic outcome.
The best way to describe these relationships of interest is to actually measure them in the field. During our four-year study of blue crabs in the ACE Basin NERR, we took lots of measures of environmental data, so we could construct better equations for the SCBCRABS model. For example, using data from the USGS gaging station at Givhans Ferry, SC (02175000) we were able to relate Edisto River Flow rates to season and construct a sine-curve equation that captures the change in average river flow by season. We also empirically measured salinity in response to spatial position in the estuary from the mouth of the river (station 1) to the northern boundary of the ACE Basin NERR (station 9). We then fit a logistic curve to these empirical observations so the model could predict realistic salinity levels at any location in model given the season and the current river flow.
Before running simulations using these complex equations, we evaluated how well our relationships compared to our field observations to see how well our model could match actual observations of salinity in the field. Our modeled salinities did an excellent job tracking the spatial, seasonal and annual variation in salinity actually measured during our four year field study.
The IBM is spatially-explicit which means each habitat patch in the model is given specific characteristics which can then influence the agents (individual blue crabs) in the model. This is accomplished by defining patch conditions in the set-up routine and updating patch conditions at each time step of the model. In the example above, the shades of yellow shown in the depiction of the habitat cells of the model represent a gradient of salinity from 35 psu salinity (brown) to 0 psu salinity (light yellow). You can also see that the salinity profile is slightly off-set for each of three simulated rivers in the model matching the observed difference in flow between the Combahee, Ashepoo and Edisto Rivers. The model keeps track of time on a weekly time step and thus the model knows which week during the annual cycle it is currently at. This allows to model to make use of that sine-curve of flow presented above to accurate influence the seasonal salinity profile for each habitat cell in the model. Similar relationships update each patch for temperature, dissolved oxygen and pH.
The next step is to add agents (individual blue crabs) to the model and let them move around the available habitat cells. In this model we only keep track of blue crabs once they have settled into the marsh and molted into their first benthic juvenile. Newly settled juvenile crabs (J1) are crabs with a 1 cm carapace width (CW). As they grow during the course of their life time they will molt to the next largest stage (J2, J3, J4...) increase in size in 1 cm CW increments. Juvenile in the model are red with darker shades representing older individuals. When crabs reach sexual maturity (stage 13) crabs become either M13 mature males (blue) or F13 mature females (green). They are not capable of participating in the reproductive part of the model subroutines. Movement of each crab stage assumes that they will move toward their preferred salinity. This was estimated from empirical observations of crab size and location from the four-year field study in the ACE Basin NERR. Since the salinity of habitat cells is constantly changing, the crabs in the model migrate upriver and downriver in a seasonal cycle similar to the seasonal migrations observed in the field. It is this movement of crabs that bring them into contact with commercial fishing pots, represented in the model as a long row of yellow habitat cells with white circles in them. When a crab encounters a crab pot, there is a chance that the crab will enter the pot and get caught (grey crabs). This allows us to fish for our model crabs in a fashion similar to how fishermen fish for crabs in the ACE Basin. The range and densities of crab pots in the model were derived from observed fishing effort seen during the four-year field study in the ACE Basin.
Finally, the model includes a series of subroutines that follow the steps an individual crab must go through during its lifetime. For example the first model subroutine adds new recruits (J1s) to the model based on the reproductive output of females from the previous turn of the model. Then the model allows each individual crab to move (Dispersal), avoid being killed (Survival), grow (Growth) and if ready, reproduce (Reproduction). The probability of accomplishing these challenges depends on the individual's stage, sex, age, disease condition as well as the patch conditions (temperature, salinity, dissolved oxygen, disease abundance, predator abundance). After every crab has been through these four subrountines, the model enters the next time step (one week interval), the patches are all updated, and the individual crabs go through the subroutines again. Once a crab is killed or caught in a crab trap, it is forever removed from the model. The relationships (equations) that link patch conditions such as salinity to crab effects such as predation or disease were estimated from empirical observations collected during the four-year field study in the ACE Basin NERR. Thus the model allow us to scale up many different effects that salinity has on individual crabs in a realistic fashion given that crabs are constantly on the move and salinity is constantly changing.
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