Adaptive foraging
Many pollinators can adjust their foraging behavior in response to resource availability (i.e. adaptive foraging) (Goulson 1999). When considering adaptive foraging, a pollinator’s foraging preference for a given floral host is related to the reward intake from that host relative to the average reward intake from all its plant hosts (Valdovinos et al. 2016). In other words, a plant with higher reward content on average will be more attractive to its pollinators than a plant with lower reward content. In the model, reward availability (and therefore reward intake) is determined by the number of pollinator visits per flower, with more visits resulting in greater reward depletion. When floral rewards are produced at a constant rate, or are produced only once at the time of flower opening, the average quantity of reward available per flower of the plant species a ,Qa , is directly linked to the average number of pollinator visits received per flower. Qa can therefore be expressed as a proportion of the maximal reward content, corresponding to
\begin{equation} Q_{a}=\frac{1}{1+\frac{\text{Vr}_{j}}{F_{a}}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (6)\nonumber \\ \end{equation}
where Vrj corresponds to the per flower pollinator visitation rate to plant a measured in the same unit as the reward production rate, Fa .Fa represents the product of the flower production rate and reward replenishment rate. The denominator ”1” corresponds to the initial reward content of a flower, such that previously unvisited flowers contain the maximal amount of reward. In many plant species, however, reward (mostly nectar) is replenished dynamically following pollinator visits (Castellanos et al. 2002; Juan & Ornelas 2004; Bobrowiec & Oliveira 2012; Ogilvie et al.2014; Ye et al. 2017). With dynamic replenishment, the reward replenishment rate is initially high following reward removal, but eventually plateau. When considering dynamic reward replenishment,Qa corresponds to
\begin{equation} Q_{a}=1-\left(1-F_{a}\right)^{\text{Vr}_{j}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (7)\nonumber \\ \end{equation}
where Fa is the initial replenishment rate after a pollinator visit, expressed as a proportion of the maximal reward content. Assuming that reward production is equal among plant species, the total number of visits to plant a by pollinator i is
\begin{equation} \text{Vt}_{\text{ij}}=V_{\text{i\ }}\bullet\ \frac{A_{a}\bullet Q_{a}}{\sum_{a=1}^{n}{A\bullet Q}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (8)\nonumber \\ \end{equation}
and the number of visits to the focal flower by pollinator i ,Vij is equal to Vtij /Aa .