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Spatial distribution models for foraging bumble bees and their application to enhance crop pollination services Capera Aragones, Pau


Bumble bees provide valuable pollination services to crops around the world. However, their populations are declining in intensively farmed landscapes. Understanding the dispersal behaviour of these bees is a key step in determining how agricultural landscapes can best be enhanced to prevent this decline. In my work, I develop mathematical models to predict the spatial distribution of foraging bumble bees. In Chapters 2 and 3, I develop a partial integro-differential equation model to predict the spatial distribution of foraging bumble bees in dynamic heterogeneous landscapes. My model considers the division of the foraging population into subpopulations with different movement modes, the effects of resource-dependent switching rates between movement modes, resource depletion, central-place foraging behaviour, memory, and the effect of the balance between nutrition and energy needs. I use the model to investigate how crop pollination services are affected by the characteristics of wildflower enhancements adjacent to crops. My model predicts the location, the pollen/nectar composition, and the wildflower density of patches that most benefit crop pollination services. The results lead to the establishment of a strategy – a spatial landscape design – that maximizes crop pollination services. My results suggest wildflowers planted in the far edge of the crop with respect to the nest site, and with pollen/nectar composition significantly different from crop flowers, is the best strategy. In Chapter 4, I use the Maximum Entropy Principle to predict equilibrium forager spatial distributions. My approach is a novel application of this universal principle, commonly used to predict distributions of non-living agents. In addition, it is a new and simple framework that can easily be used to incorporate mechanisms such as optimality of a foraging strategy or the depletion of resource, into correlative spatial distribution models. More generally, the models I develop provide important insights into spatial ecology, and constitute frameworks to predict the consequences of forager distributions on the environment and the population of foragers. Although the models developed here are applied to foraging bumble bees, the models can also be adapted to a broad range of species found in nature.

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