Day T
Department of Zoology, University of British Columbia, Vancouver, Canada.
Evolution. 2000 Jun;54(3):715-30. doi: 10.1111/j.0014-3820.2000.tb00074.x.
Models of Fisher's runaway process show that if there is a cost to female preference, no preference or male trait exaggeration will evolve. Surprisingly, this is true no matter how small the cost, which reveals that these models of Fisher's process are structurally unstable (Bulmer 1989). Here a model of Fisher's runaway process is presented to demonstrate that costly female preference evolves very easily when space is explicitly included in the model. The only requirement is that the optimal male phenotype changes across the species' range. The model shows that the spatial average of the female preference and male trait reach an evolutionary equilibrium that is identical to those of nonspatial models, but that the preference and male trait can deviate greatly from these averages at any point in space. For example, if random mating results in the lowest cost to females, then at equilibrium the spatial average preference will be zero. Nevertheless, there will be some locations at which females prefer males with larger ornaments and others where they prefer males with smaller ornaments. Results also show that the structural instability of nonspatial models of Fisher's process is less of a problem in spatial models. In particular, many of the main qualitative features of cost-free spatial models of Fisher's process remain valid even when there are small costs of female preference. Finally, the model shows that abrupt changes in the optimal male phenotype across space can result in an amplification of this pattern when preference has a small cost, but it can also result in a pattern similar to reproductive character displacement. Which of these occurs depends on the magnitude of the cost of female preference. This suggests that some patterns of reproductive character displacement in nature might be explained simply by sexual selection rather than by hybrid dysgenesis and reinforcement.
费希尔失控选择过程模型表明，如果雌性偏好存在代价，那么偏好或雄性性状夸张都不会进化。令人惊讶的是，无论代价多小，情况都是如此，这表明这些费希尔过程模型在结构上是不稳定的（布尔默，1989）。本文提出了一个费希尔失控选择过程模型，以证明当模型中明确纳入空间因素时，代价高昂的雌性偏好很容易进化。唯一的要求是最优雄性表型在物种分布范围内会发生变化。该模型表明，雌性偏好和雄性性状的空间平均值会达到一个进化平衡点，这与非空间模型的平衡点相同，但在空间中的任何一点，偏好和雄性性状可能会与这些平均值有很大偏差。例如，如果随机交配导致雌性代价最低，那么在平衡点处，空间平均偏好将为零。然而，会有一些地点的雌性偏好具有较大装饰的雄性，而在其他地点她们则偏好较小装饰的雄性。结果还表明，费希尔过程的非空间模型的结构不稳定性在空间模型中不那么成问题。特别是，即使雌性偏好存在小代价，费希尔过程的无代价空间模型的许多主要定性特征仍然有效。最后，该模型表明，当偏好有小代价时，最优雄性表型在空间上的突然变化会导致这种模式的放大，但也可能导致一种类似于生殖性状替换的模式。具体出现哪种情况取决于雌性偏好代价的大小。这表明自然界中一些生殖性状替换模式可能仅仅由性选择来解释，而不是由杂种不育和强化来解释。
