William Wolesensky

Natural History of Mass-action in Predator-prey Models: A Case Study from Wolf Spiders and Grasshoppers

Abstract Mass-action models of predator-prey interactions assume that predators encounter prey according to their relative densities as scaled by functional responses, although models seldom specify critical natural history and behavioral mechanisms that ensure that encounters actually occur. As a case study of this assumption, we assess the hypothesis that daily and seasonal activity and microhabitat use by wandering wolf spiders (Lycosidae: Schizocosa) searching for four common grasshopper species (Orthoptera: Acrididae) are coincident under natural conditions. There was great overlap in seasonal phenology and use of microhabitats between spiders and grasshoppers. Grasshoppers that were suitably sized (10–20 mm in length) as prey for spiders were relatively abundant from late spring through summer in this grassland. Three of the four common grasshopper species used microhabitat in a similar way, but differed from a fourth common species, Phoetaliotes nebrascensis. However, when they were active, spiders were about equally distributed between open microhabitats on the ground and up in the vegetation so that all grasshopper species were at risk. In response to temperature, spiders were active for only a portion of the day during which grasshoppers were also active so that the actual daily “window-of-opportunity” for capture each day was much smaller than expected. Spiders were more likely to be active during the early morning and evening, while grasshoppers were active during all daylight hours, most likely because of differences in thermal preferences. Schizocosa and their grasshopper prey are largely coincident in time and space except for overlap in daily activity which, presumably, reflects differences in thermal preferences. Consequently, overlap in daily time budgets that ensure actual encounter was reduced about 50%. The significance of this difference to the inclusion of simple mass-action dynamics in predator-prey models requires further consideration, but may be important.

Chemical reactor models of optimal digestion efficiency with constant foraging costs

Abstract We develop quantitative optimization criteria for transient digestion processes in simple animal tracts that can be modeled by a semi-batch reactor or plug flow reactor. Specifically, we determine the residence time that optimizes the average net energy intake over the total residence time. The net energy is measured by the total energy intake, less the cost of foraging and digestion. Precise values for optimal residence times are presented for different chemical kinetics of substrate breakdown and of absorption. Both first-order kinetics and Michaelis–Menten kinetics are examined and compared, and it is determined how these residence times vary with foraging costs.

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. The general model is, typically, analytically intractable, but specialization to a structured prey-unstructured predator model leads to some analytic results that reveal interesting and unexpected dynamics caused by the presence of size-dependent handling times in the functional response. In this case, steady-states are shown to exist over long times, similar to the stable age-structure solutions for the McKendick-von Foerster model with exponential growth rates determined by the Euler-Lotka equation. But, for type II responses, there are early transient oscillations in the number of births that bifurcate in a few generations into either the decaying or growing steady-state. The bifurcation parameter is the initial level of prey. This special case is applied to a problem of the biological control of a structured pest population (e.g., aphids) by a predator (e.g., lady beetles).

Mathematical model of consumer homeostasis control in plant-herbivore dynamics

Consumers must regulate the elemental composition of body tissue at ratios that differfrom those of their food. This problem of elemental homeostasis is especially acute for herbivores for which elemental composition of food does not equal that of the consumer and changes widely throughout the lifespan. We extend work of Sterner [1] and Frost and Elser [2] using a dynamic model of homeostatic control within tolerance limits by consumers feeding on unbalanced diets based on nonlinear assimilation as a primary mechanism. Differential assimilation provides a suitable, if incomplete, mechanism for homeostasis where the limiting element defines the accumulation trajectory of nutrients incorporated into the consumer.

Weather Affects Grasshopper Population Dynamics in Continental Grassland Over Annual and Decadal Periods

ABSTRACT Understanding the complex dynamics of insect herbivores requires consideration of both exogenous and endogenous factors at multiple temporal scales. This problem is difficult due to differences in population responses among closely related taxa. Increased understanding of dynamic relationships between exogenous and endogenous factors will facilitate forecasting and suggest nodes in the life cycle of economically important species susceptible to intervention by managers. This study uses an information-theoretic approach to examine the contributions of weather and density to model population densities and growth rates of nine common grasshopper species from continental U.S. grassland over 25 years. In general, grass-feeding species and total grass-feeders as a functional group were most closely associated with weather during the year before hatching. Increased variability in prior growing season precipitation was associated with increased densities of Mermiria bivittata, Opeia obscura, Phoetaliotes nebrascensis, and the grass-feeding guild. Melanoplus sanguinipes densities tended to be smaller following warm fall seasons, while Amphitoruns coloradus declined during the positive phase of the North Atlantic Oscillation or after warmer than average winters. Population growth rate dynamics of all grouped species combinations were best explained by models including variability in precipitation during the prior year growing season. Large-scale Pacific Decadal Oscillation (PDO) patterns were also associated with growth rate dynamics of the mixed-feeding species group. Density showed a negative relationship with population growth rates of five species. This study indicates the importance of parental and diapause environmental conditions and the utility of incorporating long-term, readily obtained decadal weather indices for forecasting grasshopper densities and identifying critical years with regard to grasshopper management—at least to the degree that the past will continue to predict the future as global climates change.