Phenologically explicit models for studying plant–pollinator interactions under climate change

Climate change is significantly influencing phenology. One potential effect is that historically interacting partners will respond to climate change at different rates, creating the potential for a phenological mismatch among previously synchronized interacting species, or even sexes of the same species. Focusing on plant demographics in a plant–pollinator interaction, we develop a hybrid dynamical model that uses a “non-autonomous” differential equation system (Zonneveld model) for within-season dynamics and discrete equations for season-to-season dynamics. Our model outlines how and when changes in the relative phenologies of an interacting species pair will alter the demographic outcome of the interaction. For our plant–pollinator system, we find that plant population growth rates are particularly sensitive to phenology mismatch when flowers are short-lived, when pollinators are short-lived, or when flowers and pollinators exhibit high levels of within-population synchrony in emergence or arrival dates. More generally, our aim is to introduce the use of hybrid dynamical models as a framework through which researchers can directly explore the demographic consequences of climatically driven phenological change.