The competition model with Holling type II competitive response to interfering time

Abstract

In Nature, species coexistence is much more frequent than what the classical competition model predicts, so that scientists look for mechanisms that explain such a coexistence. We revisit the classical competition model assuming that individuals invest time in competing individuals of the other species. This assumption extends the classical competition model (that becomes a particular case of the model presented) under the form of a Holling type II term, that we call competitive response to interfering time. The resulting model expands the outcomes allowed by the classical model by (i) enlarging the range of parameter values that allow coexistence scenarios and (ii) displaying dynamical scenarios not allowed by the classical model: namely, bi-stable conditional coexistence in favour of i (either species coexist or species i wins) or tri-stable conditional coexistence (either species coexist or any of them goes extinct), being exclusion in both cases due to priority effects. ARTICLE HISTORY

Network-level containment of single-species bioengineering

“…Finally, for convenience we set the carrying capacity to K i = 1. Along with the linear case, we will also consider Holling type II and type III functional responses [37][38][39] that incorporate two main forms of saturation functions (see the electronic supplementary material).…”

Multispecies models for population dynamics: Progress, challenges and future directions

“…predator-prey dynamics (Certain et al 2018). For example, functional responses can take different shapes depending on how a species searches, handles and processes prey, with potentially large effects on population dynamics (Spalinger & Hobbs 1992;Koen-Alonso 2007;Castillo-Alvino & Marvá 2020). Additionally, functional responses can vary between habitats and life stages, where a prey species might itself be an important competitor or even predator on young individuals of the predator species (Essington 2004), highlighting the importance of considering population structure.…”

Stability and bifurcation of a two competing prey-one predator system with anti-predator behavior

“…Recently, Castillo-Alvino and Marvá [15] revisited the classical two species Lotka-Volterra competition model considering the time spent in competition for the interacting species. They proposed the model by incorporating Holling type II competition response to interference time as follows:…”

“…It is assumed that a 1 ̸ = a 2 . In [15], the authors showed that the more time interfering with competition takes, the more likely coexistence and also obtained multi-stability scenarios. In the above study, the role of predator is not considered.…”

“…In view of the above, we have interested to study predatorprey interaction with anti-predator behavior along with competition between the prey species where each species invest time in competing individual of the other species. The competition term suggested in [15] is considered here. Here we consider two competing prey species which share a common predator.…”