Optimal gut size of small birds and its dependence on environmental and physiological parameters

•We present an optimal foraging model of small birds that includes both fat reserves and gut contents as state variables.•There exists a unique gut size that maximises a bird's chances of survival.•The optimal gut size depends on the meal size, food availability, and, to a lesser extent, the rate of digestion.•In rich environments, the optimal gut size exactly equals the meal size. Most optimal foraging models assume that the foraging behaviour of small birds depends on a single state variable, their energy reserves in the form of stored fat. Here, we include a second state variable—the contents of the bird's gut—to investigate how a bird should optimise its gut size to minimise its long-term mortality, depending on the availability of food, the size of meal and the bird's digestive constraints. Our results show that (1) the current level of fat is never less important than gut contents in determining the bird's survival; (2) there exists a unique optimal gut size, which is determined by a trade-off between the energetic gains and costs of maintaining a large digestive system; (3) the optimal gut size increases as the bird's digestive cycle becomes slower, allowing the bird to store undigested food; (4) the critical environmental factor for determining the optimal gut size is the mass of food found in a successful foraging effort (“meal size”). We find that when the environment is harsh, it is optimal for the bird to maintain a gut that is larger than the size of a meal. However, the optimal size of the gut in rich environments exactly matches the meal size (i.e. the mass of food that the optimal gut can carry is exactly the mass of food that can be obtained in a successful foraging attempt).