Type II functional response for continuous, physiologically structured models.

The goal of this work is to formulate a general Holling-type functional, or behavioral, response for continuous physiologically structured populations, where both the predator and the prey have physiological densities and certain rules apply to their interactions. The physiological variable can be, for example, a development stage, weight, age, or a characteristic length. The model leads to a Fredholm integral equation for the functional response, and, when inserted into population balance laws, it produces a coupled system of partial differential-integral equations for the two species, with a nonlocal integral term that arises from rules of interaction in the functional response.

An individual, stochastic model of growth incorporating state-dependent risk and random foraging and climate.

We model the effects of both stochastic and deterministic temperature variations on arthropod predator-prey systems. Specifically, we study the stochastic dynamics of arthropod predator-prey interactions under a vary ing temperature regime, and we develop an individual model of a prey under pressure from a predator, with vigilance (or foraging effort), search rates, at tack rates, and other predation parameters dependent on daily temperature variations. Simulations suggest that an increase in the daily average temperature may benefit both predator and prey.

Insect development under predation risk variable temperature, and variable food quality.

We model the development of an individual insect, a grasshopper, through its nymphal period as a function of a trade-off between prey vigilance and nutrient intake in a changing environment. Both temperature and food quality may be variable. We scale up to the population level using natural mortality and a predation risk that is mass, vigilance, and temperature dependent.

An index to measure the effects of temperature change on trophic interactions.

Experimental studies document the fact that environmental temperature changes can affect the timing of interactions in many consumer-resource systems through altered, or shifted, phenologies of the species involved. We develop a simple mathematical model that shows one method to measure, quantitatively, the magnitude of the shift. Under different temperature regimes we compute the intersection of two regions in a joint phenology space: the region where temporal interactions can occur and the region where particular-sized predators consume particular-sized prey.

Control of CNP homeostasis in herbivore consumers through differential assimilation.

Stoichiometric analysis recognizes that a herbivore is a mixture of multiple chemical elements, especially C, N, and P, that are fixed in various proportions. In the face of a variable quality food supply, herbivores must regulate ingested nutrients to maintain a homeostatic state. We develop a dynamic mathematical model, based on differential assimilation, that controls the C:N and C:P ratios in a herbivore within given tolerance ranges; the actual mathematical mechanism is to define the absorption coefficients to be dependent on these elemental ratios.

Location, time, and temperature dependence of digestion in simple animal tracts.

In this paper, we develop plug flow reactor models that simultaneously investigate how reaction and absorption, morphological differences, and temperature influence nutrient acquisition rates in simple, tubular animal guts. We present analytical solutions to the resulting reaction-advection equations that model these processes, and we obtain formulas giving the throughflow speed that maximizes the absorption rate. The model predicts that the optimal digestion speed increases as the ratio of the rate of enzyme breakdown to the rate of absorption increases.