A Physiologically Based Tritrophic Perspective on Bottom‐Up‐Top‐Down Regulation of Populations

Abstract

A general tritrophic model of intermediate complexity representing the dynamics of trophic level biomass and numbers is presented. The rudiments of the behavior and physiology of resource acquisition and conversion are incorporated as functional and numerical response models. The tritrophic model is used to examine the effects of trophic position on bottom—up—top—down regulation of populations in theory and in practice. The zero growth isoclines of the interacting populations are used to examine the dynamics of the tritrophic system. The herbivore (M2) and predator (M3) but not the plant (M1) isoclines can be solved explicitly. The plant and herbivore isoclines have two forms that depend on whether the proportion of the trophic level available to its consumer (i.e., its apparency) is greater than or less than its potential per unit biomass population growth rate. Rough estimates of the parameters of these inequalities may be deduced from our knowledge of the search biology of the species and known size to growth rate relationships. The model shows clearly that bottom—up regulation sets the upper limit for trophic—level growth and top—down regulation determines the level of realized growth. The model explains the paradoxes of enrichment and of biological control that arise from the standard Lotka—Volterra models, and its qualitative predictions compare well to the general conclusions of intensive studies on biological control of the cassava mealybug on cassava by an exotic parasitoid. However, discrepancies that were found caution against unconsidered extrapolation of theoretical predictions to specific situations. The model qualitatively defines the dynamics required of a successful weed biological control agent, of a stable fresh water algal—arthropod herbivore—vertebrate predator system, and of a marine phytoplankton—krill—whale system. The utility of the model is its generality and its basis in quantifiable biology.

Fine-scale ecological and economic assessment of climate change on olive in the Mediterranean Basin reveals winners and losers

“…The PBDM approach explicitly captures the mechanistic weather-driven biology and trophic dynamics in a realistic manner, while keeping model complexity to a minimum. This occurs by applying the same dynamics model and process submodels at all trophic levels (25,26).…”

“…The underlying assumption of the models is that all organisms in all trophic levels, including the economic one, are consumers that have similar resource acquisition (inputs) and allocation (outputs) priorities (25,36,37). Based on analogies, the dynamics of olive and olive fly were captured using the same resource acquisition and birth-death rate submodels imbedded in an age-mass structured population model (PBDM) (SI Appendix, Mathematical Structure of the Olive/Olive Fly Model).…”

Geographic Distribution and Relative Abundance of the Invasive Glassy-Winged Sharpshooter: Effects of Temperature and Egg Parasitoids

“…similarly convex (see Gutierrez et al 1994;Rochat and Gutierrez 2001). The simplest form for T is convex symmetrical (eqn.…”

A regional analysis of weather mediated competition between a parasitoid and a coccinellid predator of oleander scale

“…the transition time through the delay model) varies with temperature T (i.e. (T(t) = (t)), but it may also vary with nutrition (food supply/demand) and other environmental variables (Gutierrez 1992, Gutierrez et al 1994. 1 The simplest developmental rate model is the linear or degree-day (dd) model in which development accrues above a lower thermal threshold (de Candolle 1855).…”

“…If we normalize these functions, the resulting indices may be viewed as measures of the temperature related stress the population is experiencing at time t (Gutierrez et al 1994, Rochat & Gutierrez 2001. The physiological indices, 1 (T) 0, may be captured by a simple, albeit symmetrical, form with subscripts for growth or fecundity ( = g, f ) and survivorship ( =lx = 1-) (eqn.…”