Movement rules for individual-based models of stream fish

Spatially explicit individual-based models (IBMs) use movement rules to determine when an animal departs its current location and to determine its movement destination; these rules are therefore critical to accurate simulations. Movement rules typically define some measure of how an individual’s expected fitness varies among locations, under the assumption that animals make movement decisions at least in part to increase their fitness. Recent research shows that many fish move quickly in response to changes in physical and biological conditions, so movement rules should allow fish to rapidly select the best location that is accessible. The theory that a fish’s fitness is maximized by minimizing the ratio of mortality risk to food intake is not applicable to typical IBM movement decisions and can cause serious errors in common situations. Instead, we developed fitness measures from unified foraging theory that are theoretically and computationally compatible with individual-based fish models. One such fitness measure causes a fish to select habitat that maximizes its expected probability of survival over a specified time horizon, considering both starvation and other risks. This fitness measure is dependent on the fish’s current state, making fish with low energy reserves more willing to accept risks in exchange for higher food intake. Another new measure represents the expectation of reaching reproductive maturity by multiplying expected survival by a factor indicating how close to the size of first reproduction the fish grows within the time horizon. One of the primary benefits of the individual-based approach is avoiding the need for simplifying assumptions; this benefit is best realized by basing movement decisions on such simple, direct measures of fitness as expected survival and expected reproductive maturity.