A generalized Holling type II model for the interaction between dextral-sinistral snails and Pareas snakes

• Published in: Applied Mathematical Modelling Vol. 73; pp. 459 - 472
• Main Authors: Alonso Izquierdo, A., González León, M.A., de la Torre Mayado, M.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.09.2019; Elsevier BV
• Subjects: Asymmetry; Evolution; Generalized Holling’s functional response; Mathematical models; Mollusks; Mutation; Parameters; Predator–prey model; Snail chirality; Snails; Snakes; Stability; Stability analysis; Generalized Holling’s functional response; Stability; Snail chirality; Predator–prey model
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.04.005

•A novel Holling type II model for one predator and two preys in mutual competence is constructed.•The interaction between dextral snail-eating specialized snakes and the two chiral variants of snails is realistically described.•The predator efficiency hunting the prey variants is the crucial parameter that essentially determines the model dynamics.•The abundance of experimental results allows unveiling the fate of the involved populations in realistic scenarios. Pareas snakes possess outstanding asymmetry in the mandibular tooth number, which has probably been caused by its evolution to improve the feeding on the predominant dextral snails. Gene mutation can generate chiral inversion on the snail body. A sinistral snail population can thrive in this ecological context. The interactions between dextral/sinistral snails and Pareas snakes are modeled in this paper by using a new generalized functional response of Holling type II. Distinct Pareas species show different bilateral asymmetry degrees. This parameter plays an essential role in the model and determines the evolution of the populations. Stability of the solutions is analyzed for different regimes in the space of parameters.