Mitchener W Garrett
Department of Mathematics, College of Charleston, Robert Scott Small Building, Room 339, Charleston, SC 29424, USA.
Bull Math Biol. 2007 Apr;69(3):1093-118. doi: 10.1007/s11538-006-9165-x. Epub 2007 Jan 30.
We investigate a model of language evolution, based on population game dynamics with learning. First, we examine the case of two genetic variants of universal grammar (UG), the heart of the human language faculty, assuming each admits two possible grammars. The dynamics are driven by a communication game. We prove using dynamical systems techniques that if the payoff matrix obeys certain constraints, then the two UGs are stable against invasion by each other, that is, they are evolutionarily stable. Then, we prove a similar theorem for an arbitrary number of disjoint UGs. In both theorems, the constraints are independent of the learning process. Intuitively, if a mutation in UG results in grammars that are incompatible with the established languages, then the mutation will die out because mutants will be unable to communicate and therefore unable to realize any potential benefit of the mutation. An example for which these theorems do not apply shows that compatible mutations may or may not be able to invade, depending on the population's history and the learning process. These results suggest that the genetic history of language is constrained by the need for compatibility and that mutations in the language faculty may have died out or taken over due more to historical accident than to any straightforward notion of relative fitness.
我们研究一种基于带有学习机制的种群博弈动力学的语言进化模型。首先，我们考察人类语言官能核心——普遍语法（UG）的两种基因变体的情况，假设每种变体都有两种可能的语法。动力学由一个交流博弈驱动。我们运用动力系统技术证明，如果收益矩阵服从某些约束条件，那么这两种UG对彼此的入侵是稳定的，也就是说，它们在进化上是稳定的。然后，我们针对任意数量不相交的UG证明了一个类似的定理。在这两个定理中，约束条件都与学习过程无关。直观地说，如果UG中的一个突变导致语法与已确立的语言不兼容，那么这个突变将会消失，因为突变体将无法交流，从而无法实现该突变的任何潜在益处。一个这些定理不适用的例子表明，兼容的突变可能能够入侵，也可能无法入侵，这取决于种群的历史和学习过程。这些结果表明，语言的遗传历史受到兼容性需求的限制，并且语言官能中的突变可能更多地是由于历史偶然而非任何直接的相对适应性概念而消失或占据主导地位。
