Differential equation model for central-place foragers with memory: implications for bumble bee crop pollination

How nutrition and energy needs affect bumble bee pollination services: A mathematical model

“…In our earlier work (Capera-Aragones et al, 2021), we showed that adding intermediate wildflower quantities in a location such that the crop is between the nest site and the wildflowers lead to the largest increase in crop pollination services. In the present paper, in addition to the location and quantity of wildflowers, we investigated the effects of the pollen and nectar composition of the wildflower patch (differentiation or type) relative to the crop and the effects of the density of the wildflower background (matrix) in the landscape.…”

“…In the same paper, it is shown that dividing the population into two sub-populations provides a better fit to organism movement data than models in which the population is considered homogeneous. Based on Tyson et al (2011), Capera-Aragones et al (2021) recently developed a mathematical model for wild bees, in which the foraging population is split into three different interacting sub-populations: Harvesting bees ( H ): those individuals that are collecting floral resources on the landscape and moving randomly from one flower to another (by diffusion). Scouting bees with memory ( S ): those bees that have knowledge of the landscape and use directed flight (advection) to move efficiently over larger distances, from one patch of flowers to another, or from the nest to a patch of flowers. These bees can be identified as exploiters if we follow the notation used in the empirical work done by Woodgate et al (2016). Scouting bees without memory ( Sn ): those bees that do not have knowledge of the landscape and use directed flights (advection) as well as diffusion to explore the landscape and find new patches of flowers.…”

“…One of the key contributions in Capera-Aragones et al (2021) is the inclusion of memory effects in a spatial differential equation model for bee foraging. Memory is an important tool used by bees to improve their foraging efficiency.…”

“…That is, those bees with knowledge of the landscape are less likely to use direct motion (advection) on a random direction, and more likely to use the direct motion towards those locations where they remember finding resources. By contrast to other recent approaches such Shi et al (2019a,b) and Oliveira and Berbert (2020), in this work we use the one developed in Capera-Aragones et al (2021).…”

“…The main difference and contribution of this paper with respect to the model in Capera Aragones et al (2021) is the division of food into two different variables: pollen and nectar, with the consequent division of the bee population into two: pollen foragers and nectar foragers. This division means that the new model doubles the number of sub-populations.…”