Predicting availability to consumers of spatially and temporally variable resources

Ecological dynamics in many aquatic communities are strongly influenced by spatial and temporal variability of key limiting resources, and the extent to which consumers can locate and exploit concentrations of those resources. Intuitively, resource concentrations that are 'close' and 'long- lived' should typically be more available to consumers than 'distant' and 'ephemeral' resource concentrations. The speed and accuracy with which consumers can locate concentrations of their resources is in part determined by their movement characteristics and sensory constraints, which vary with taxon, life-history stage, physiological state, environmental conditions, and other factors. This has motivated detailed observation and modelling of individual-level foraging behaviors in a wide variety of taxa. However, our abilities to develop this intuitive concept of availability into empirically-based, quantitative predictions for consumer-resource interactions remain limited, largely due to the complexities of formulating and simulating spatially explicit models of consumer-resource interactions, and the difficulty of understanding how specific simulation results relate to broader ecological situations. This paper presents a non-dimensional index, the Frost number, that provides a simple prediction of availability to consumers of spatially and temporally varying resource concentrations. This index incorporates characteristics of both resource distributions and consumer movement behaviors. When Frost numbers characterizing consumer-resource interactions are much less than unity, resource concentrations are typically unavailable to consumers because travel time to reach them exceeds the longevity of the resource. Conversely, when Frost numbers are much greater than unity, resource longevity exceeds travel time so that resource concentrations are available. The Frost number may provide a preliminary identification of the length and time scales at which resources are available to consumers in complex ecological systems, even when detailed spatial observations and simulations are not available.