Suboptimal foraging theory: How inaccurate predictions and approximations can make better models of adaptive behavior

Optimal foraging theory (OFT) is based on the ecological concept that organisms select behaviors that convey future fitness, and on the mathematical concept of optimization: finding the alternative that provides the best value of a fitness measure. As implemented in, e.g., state-based dynamic modeling, OFT is powerful for one key problem of modern ecology: modeling behavior as a tradeoff among competing fitness elements such as growth, risk avoidance, and reproductive output. However, OFT is not useful for other modern problems such as representing feedbacks within systems of interacting, unique individuals: when we need to model foraging by each of many individuals that interact competitively or synergistically, optimization is impractical or impossible-there are no optimal behaviors. For such problems we can, however, still use the concept of future fitness to model behavior, by replacing optimization with less precise (but perhaps more realistic) techniques for ranking alternatives. Instead of simplifying the systems we model until we can find "optimal" behavior, we can use theory based on inaccurate predictions, coarse approximations, and updating to produce good behavior in more complex and realistic contexts. This "state- and prediction-based theory" (SPT) can, for example, produce realistic foraging decisions by each of many unique, interacting individuals when growth rates and predation risks vary over space and time. Because SPT lets us address more natural complexity and more realistic problems, it is more easily tested against more kinds of observation and more useful in management ecology. A simple foraging model illustrates how SPT readily accommodates complexities that make optimization intractable. Other models use SPT to represent contingent decisions (whether to feed or hide, in what patch) that are tradeoffs between growth and predation risk, when both growth and risk vary among hundreds of patches, vary unpredictably over time, depend on characteristics of the individuals, are subject to feedbacks from competition, and change over the daily light cycle. Modern ecology demands theory for tradeoff behaviors in complex contexts that produce feedbacks; when optimization is infeasible, we should not be afraid to use approximate fitness-seeking methods instead.

Contingent trade-off decisions with feedbacks in cyclical environments: testing alternative theories

Many animals make contingent decisions, such as when and where to feed, as trade-offs between growth and risk when these vary not only with activity and location but also 1) in cycles such as the daily light cycle and 2) with feedbacks due to competition. Theory can assume an individual decides whether and where to feed, at any point in the light cycle and under any new conditions, by predicting future conditions and maximizing an approximate measure of future fitness. We develop four such theories for stream trout and evaluate them by their ability to reproduce, in an individual-based model, seven patterns observed in real trout. The patterns concern how feeding in four circadian phases—dawn, day, dusk, and night—varies with predation risk, food availability, temperature, trout density, physical habitat, day length, and circadian cycles in food availability. We found that theory must consider the full circadian cycle: decisions at one phase must consider what happens in other phases. Three theories that do so could reproduce almost all the patterns, and their ability to let individuals adapt decisions over time produced higher average fitness than any fixed behavior cycle. Because individuals could adapt by selecting among habitat patches as well as activity, multiple behaviors produced similar fitness. Our most successful theories base selection of habitat and activity at each phase on memory of survival probabilities and growth rates experienced 1) in the three previous phases of the current day or 2) in each phase of several previous days.