Joron Mathieu, Iwasa Yoh
Institut des Sciences de l'Evolution, Université de Montpellier, Place Eugène Bataillon, 34095 Montpellier Cedex 05, France.
J Theor Biol. 2005 Nov 7;237(1):87-103. doi: 10.1016/j.jtbi.2005.04.005.
Strong positive density-dependence should lead to a loss of diversity, but warning-colour and Müllerian mimicry systems show extraordinary levels of diversity. Here, we propose an analytical model to explore the dynamics of two forms of a Müllerian mimic in a heterogeneous environment with two alternative model species. Two connected populations of a dimorphic, chemically defended mimic are allowed to evolve and disperse. The proportions of the respective model species vary spatially. We use a nonlinear approximation of Müller's number-dependent equations to model a situation where the mortality for either form of the mimic decreases hyberbolically when its local density increases. A first non-spatial analysis confirms that the positive density-dependence makes coexistence of mimetic forms unstable in a single isolated patch, but shows that mimicry of the rarer model can be stable once established. The two-patch analysis shows that when models have different abundance in different places, local mimetic diversity in the mimic is maintained only if spatial heterogeneity is strong, or, more interestingly, if the mimic is not too strongly distasteful. Therefore, mildly toxic species can become polymorphic in a wider range of ecological settings. Spatial dynamics thus reveal a region of Müllerian polymorphism separating classical Batesian polymorphism and Müllerian monomorphism along the mimic's palatability spectrum. Such polymorphism-palatability relationship in a spatial environment provides a parsimonious hypothesis accounting for the observed Müllerian polymorphism that does not require quasi-Batesian dynamics. While the stability of coexistence depends on all factors, only the migration rate and strength of selection appear to affect the level of diversity at the polymorphic equilibrium. Local adaptation is predicted in most polymorphic cases. These results are in very good accordance with recent empirical findings on the polymorphic butterflies Heliconius numata and H. cydno.
强烈的正密度依赖应该会导致多样性的丧失，但警戒色和缪勒拟态系统却展现出了极高的多样性水平。在此，我们提出一个分析模型，以探究在具有两种替代模型物种的异质环境中，一种缪勒拟态的两种形态的动态变化。允许一个具有双态、化学防御的拟态的两个相连种群进行进化和扩散。各个模型物种的比例在空间上有所不同。我们使用缪勒数量依赖方程的非线性近似来模拟这样一种情况：当拟态的任何一种形态的局部密度增加时，其死亡率会呈双曲线下降。首次非空间分析证实，正密度依赖使得拟态形态在单个孤立斑块中难以共存，但表明一旦建立，对较稀有模型的拟态可以是稳定的。双斑块分析表明，当模型在不同地方具有不同丰度时，只有当空间异质性很强，或者更有趣的是，当拟态的难吃程度不是太强时，拟态中的局部拟态多样性才能得以维持。因此，轻度有毒的物种在更广泛的生态环境中可以变得多态。空间动态因此揭示了一个缪勒多态区域，它沿着拟态的适口性谱将经典的贝茨多态和缪勒单态区分开来。在空间环境中的这种多态 - 适口性关系提供了一个简洁的假设，解释了观察到的缪勒多态现象，而无需准贝茨动态。虽然共存的稳定性取决于所有因素，但似乎只有迁移率和选择强度会影响多态平衡时的多样性水平。在大多数多态情况下预计会出现局部适应。这些结果与最近关于多态蝴蝶娜美透翅蝶和赛德透翅蝶的实证研究结果非常吻合。
