  Apis mellifera plays a crucial role as pollinator of the majority of crops
linked to food production and thus its presence is currently fundamental to our
health and survival. The composition and configuration of the landscape in
which Apis mellifera lives will likely determine the well-being of the hives
and the pollination service that their members can provide to the crops. Here
we present a spatially explicit model that predicts the spatial distribution of
visits by Apis mellifera to crops, by simulating daily trips of honey bees, the
demographical dynamic of each hive and their honey production. This model goes
beyond existing approaches by including 1) a flower resource affected by the
feedback interaction between nectar extraction, pollination, blossoming and
repeated visits, 2) a pollinators dynamic that allows competition through short
term resource depletion, 3) a probabilistic approach of the foraging behavior,
modeling the fact that the pollinators have only partial knowledge of the
resource on their surroundings, and 4) the specific and systematic foraging
behavior and strategies of Apis mellifera at the moment of choosing foraging
sites, as opposed to those adopted by solitary and wild pollinators. With a
balance between simplicity and realism we show the importance of keeping a
minimal fraction of natural habitat in an agricultural landscape. We also
evaluate the effects of the landscape's structure on pollination, and
demonstrate that there exists an optimal size of natural habitat patches that
maximizes the pollination service for a fixed fraction of natural habitat.
