Efficient random searches are essential to the survival of foragers searching for sparsely distributed targets. Lévy walks have been found to optimize the search over a wide range of constraints. When targets are distributed within patches, generating a spatial memory over the detected targets can be beneficial towards optimizing the search efficiency. Because foragers have limited memory, storing each target location separately is unrealistic. Instead, we propose incrementally learning a spatial distribution in favour of memorizing target locations. We demonstrate that an ensemble of Gaussian mixture models is a suitable candidate for such a spatial distribution. Using this, a hybrid foraging strategy is proposed, which interchanges random searches with informed movement. Informed movement results in displacements towards target locations, and is more likely to occur if the learned spatial distribution is correct. We show that, depending on the strength of the memory effects, foragers optimize search efficiencies by continuous revisitation of non-destructive targets. However, this negatively affects both the target and patch diversity, indicating that memory does not necessarily optimize multi-objective searches. Hence, the benefits of memory depend on the specific goals of the forager. Furthermore, through analysis of the distribution over walking distances of the forager, we show that memory changes the underlying walk characteristics. Specifically, the forager resorts to Brownian motion instead of Lévy walks, due to truncation of the long straight line displacements resulting from memory effects. This study provides a framework that opens up new avenues for investigating memory effects on foraging in sparse environments.
Keywords: Levy walk; heterogeneous environments; optimal foraging; random search; spatial memory.