Mathematical ecology on persistence of cross predation in fish communities

两种形态类型（“右”和“左”）在一些鱼类中被发现，被称为反对称的典型例子。有人提出，首先，这种二态性（称为侧性）是可遗传的；其次，每个物种的侧性频率在0.5左右波动；第三，捕食者主要捕食另一侧的猎物；也就是说，左撇子和右撇子捕食者分别捕食右撇子和左撇子。后者被定义为“交叉捕食”；“平行捕食”的反义词是指在同一侧边捕食。我们假设交叉捕食驱动了两种形态类型之间生存和繁殖优势的交替，导致了维持二态性的频率依赖选择。为此，本文建立了单食/单食系统和杂食性三营养系统种群动态的数学模型。数学分析和计算机模拟很好地解释了自然界中横向频率的行为，因为交叉捕食比平行捕食占优势。此外，模拟表明，当一个物种中只有一种形态类型存在时，另一种形态类型可以入侵。这表明在所有相互作用的物种中都保持着二态性。

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.