Holling Type I versus Holling Type II functional responses in Gram-negative bacteria

Abstract

We consider how the double-membrane structure of the cell envelope of Gram-negative bacteria affects its functional response, which is the mathematical relationship that expresses how the nutrient uptake flux depends on environmental conditions. We show that, under suitable conditions, the Holling Type I functional response is a plausible model, as opposed to the Holling Type II (rectangular hyperbolic, ‘Michaelis–Menten’) response that is the default model in much of the literature. We investigate both diffusion-limited and capacity-limited regimes. Furthermore, we reconcile our findings with the preponderance in the established literature of hyperbolic models for the growth response, which are generally assumed to be valid, for both Gram-negative and Gram-positive bacteria. Finally, we consider the phenomenon of dynamic adjustment of investment of molecular building blocks in cellular components, and show how this will affect the functional response as observed by the experimenter.

The Dynamics of Modified Leslie-Gower Predator-Prey Model Under the Influence of Nonlinear Harvesting and Fear Effect

“…𝑊 [𝐷 𝐹(𝐸 , 𝑘 * )(𝑈 , 𝑈 , 𝑈 )] = 6 − − + ( ) . Note that, condition (16) guarantees that 𝑊 [𝐷 𝐹(𝐸 , 𝑘 * )(𝑈 , 𝑈 , 𝑈 )] ≠ 0. Hence, a pitchfork bifurcation takes place, and the proof is complete.…”

“…The functional response is an essential part of the predator-prey model, which describes the change in prey number killed per individual predator per unit of time as a consequence of changes in prey density. The most commonly used functional response in the existing literature is a function of prey's density only (Holling I-III) [2,4,15,16], in which interfering among predators is not utilized whereas this will be common when predators contest for food. To address this important factor, functional responses (ratio-dependent [17], Beddington-DeAngelis [18], and Crowley-Martin [7] have been developed which do not rely just on the density of the prey but rather on the density of both prey and predator.…”

The Dynamics of Sokol-Howell Prey-Predator Model Involving Strong Allee Effect

“…In theoretical ecology, several known functional responses in the prey-predator system exist, which include Holling type-I, type-II, type-III, type-IV, Beddington-DeAngelis type, and ratio-dependent type, etc. Some authors investigated and introduced several open questions for the structured prey-predator models using different types of functional responses, [12,13,15,16]. In this paper, however, Sokol-Howell type of functional response [17] that is expressed as ( ) = 1 2 + 2 is used, which is simply a modified version of the Holling type III that is represented by ( ) = 1 2 + + 3 2 .…”

Allee Rate Effect in a Prey Model with a Holling Type II Functional Response

“…The predator-prey paradigm of the avenue effect on prey growth has also attracted considerable interest. [3,4,5,6,7,8,9]. Longxing Qi and Lijuan Gan also investigated Allee's effects on prey with shelter [10].…”