Globally, diversity and abundance of insect pollinators are declining. This  poses a threat for the integrity of natural ecosystems and for the production of  many crops. The enormity of the problem for agriculture becomes clear if one  considers that { by estimates from the Canadian Honey Council { the value of  honey bees to pollination of crops in Canada is at $2 billion annually. Both managed pollinators (e.g., honey bees, leafcutter bees, bumble bees) and wild pollinators (e.g., several native bees, flower flies, moths, etc.) are exposed to a range of stressors, including diseases, pesticide exposure, malnutrition, habitat loss and climate change.

These multi-faceted interactions are difficult to study in a reductionist approach by focusing on one aspect at a time. Moreover, as these systems are open and difficult to control, experimentation and observation alone are challenging. Mathematical modeling and statistical techniques have been developed over decades to describe disease propagation and relationships in ecological systems. A goal of this workshop is to assess the current state, and to develop a plan forward how such methods can be adapted and extended to become a valuable tool to study the multi-factorial aspects of plant pollinator relationships.

The workshop will focus on two main strands:

- Population and disease dynamics of pollinators. To a large extent this is based on ordinary differential equations, partial differential equations, functional differential equations, but also agent based models. This topic unites models that traditionally are considered a part of theoretical ecology with epidemiological models that are adapted to populations of pollinators. In many cases diseases are parasites (such as Nosema as a microsporidean parasite of the honeybee or bumble bees) or vectored by parasites (such as various honeybee viruses that are vectored by the ectoparasitic varroa mite), i.e. the disease itself needs to be described by population models. This leads to highly complex models in their own right that are coupled with aspects of further external stressors, such as certain management practices (in the case of managed pollinators such as honeybees) and environmental influences (e.g. exposure to pesticides). Accounting for the fact that seasonal variations are strong adds another level of complexity, as the standard, relatively well-developed theory of autonomous systems cannot be readily applied. Remedial strategies introduce questions of optimization and optimal control. Inter-colony interaction introduces aspects of metapopulation and network dynamics.

- Ecological aspects of pollination. At the heart of pollination are plant pollinator relationships. Which pollinator species visits which plant species how frequently, and how is this affected by environmental stressors, habitat fragmentation or (other) anthropogenic factors? How do factors affecting one pollinator species perturb the entire pollination network, which redundancies are built in, etc? In addition to wild pollinators, managed pollinators play a dominant role in agriculture. This raises questions of how managed pollinators affect the natural ecology, e.g. whether they interfere wild pollinators, etc. In the face of recent losses of honeybee colonies the question emerges which impacts this will have on pollination. Furthermore it is currently being explored to use managed pollinators as delivery platform for biocontrol agents that protect plants against diseases. These are complex questions of interaction, to which mathematical modeling can provide at least partial answers. This involves methods of graph theory, Bayesian and decision networks, computational and spatial statistics, partial differential equations, integro-difference equations, agent based modeling, etc. A key question of this workshop will be how mathematical models that come from so vastly different areas of mathematics can be brought together into a well-defined and well-posed hybrid modeling framework, and the formulation of interfaces.

The workshop will be smaller in size and duration than others in this Thematic Program and more narrowly focused. It will emphasise break-out sessions, discussion, and collaboration to identify a research program that brings together the current efforts underway in pollinator population and disease modeling, and in pollination ecology modeling. One objective of this workshop is to bring together scientists from different academic fields to establish a workgroup on modeling plant-pollinator relationships (as a work group of the International Commission on Plant Pollinator Relationships), potentially with follow-up workshops at NimBIOS, MBI, BIRS, etc.