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 .