Mathematical ecology on persistence of cross predation in fish communities

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Two morphological types ("righty" and "lefty") have been discovered in several fish species and are referred to as a typical example of antisymmetry. It has been suggested, first, that this dimorphism (called laterality) is inheritable ; second, that the frequencies of laterality in each species fluctuate around 0.5 ; and third, that predators mainly exploit prey of the opposite laterality ; that is, lefty and righty predators prey on righties and lefties, respectively. The latter is defined as "cross predation" ; the antonym "parallel predation" means predation within the same laterality. We hypothesized that cross predation drives alternation of the survival and reproductive advantages between two morphological types, leading to frequency-dependent selection that maintains the dimorphism. To investigate this, we constructed mathematical models of population dynamics of one prey/one predator systems and three-trophic-level systems with omnivory. Mathematical analysis and computer simulations explained the behavior of the laterality frequency in nature well, insofar as cross predation dominated over parallel predation. Furthermore, the simulations showed that when only one of the morphological types exists in a species, the other type can invade. This suggests that dimorphism is maintained in all interacting species.