Abstract
Predator–prey relationships are one of the most studied interactions in population ecology. However, little attention has been paid to the possibility of role exchange between species, despite firm field evidence of such phenomena in nature. In this paper, we build a mathematical model capable of reproducing the main phenomenological features of role reversal in a classical system and present results for both the temporal and spatio-temporal cases. We show that, depending on the choice of parameters, our role-reversal dynamical system exhibits excitable-like behaviour, generating waves of species' concentrations that propagate through space. Our findings fill a long-standing gap in modelling ecological interactions and can be applicable to better understanding ecological niche shifts and planning of sustainable ecosystems.
Highlights
Predator–prey interactions have been widely studied in the last hundred years, and their mathematical models are among the oldest established in ecology
The ranges of flow included in [18] were vast, matching conditions typical of benthic flows. By putting these findings together, we argue a reasonable model need not incorporate influences from shallow water currents and would assume whelks to move towards ‘bait’ at a speed roughly one order of magnitude smaller than that of lobsters
We have modelled a well-documented case of role-reversal in a predator–prey interaction, capturing the essential ecological factors within the study of Barkai & McQuaid [8], who did extraordinary fieldwork and meticulously reported this striking role-reversal phenomenon happening between whelks and lobsters in the Saldanha Bay
Summary
Predator–prey interactions have been widely studied in the last hundred years, and their mathematical models are among the oldest established in ecology. One of the classic ecological models, the Lotka–Volterra model, was independently proposed by Alfred J. Lotka and Vito Volterra in the first quarter of the 1900s. Lotka developed preliminary models with a focus on demography, but later refined his model while turning his attention to trophic interactions by using a plant species and a herbivorous animal as an example. Vito Volterra, on the other hand, is said to have developed his version of the model by analysing fishery patterns in the Adriatic Sea. The wide origins and scales of the questions that led to this classic model show its inherent flexibility and adaptability, a probable reason why Lotka–Volterra models remain popular to this day
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