What constitutes a discrete morphological character versus character state has been long discussed in the systematics literature but the consensus on this issue is still missing. Different methods of classifying organismal features into characters and character states can dramatically affect the results of phylogenetic analyses. Here, I show that, in the framework of Markov models, the modular structure of the gene regulatory network (GRN) underlying trait development, and the hierarchical nature of GRN evolution, essentially remove the distinction between morphological character and character state, thus endowing the character and character state with an invariant property with respect to each other. This property allows the states of one character to be represented as several individual characters and vice versa. In practice, this means that a phenotype can be encoded using a set of characters or just one complex character with numerous states. The representation of a phenotype using one complex character can be implemented in Markov models of trait evolution by properly structuring transition rate matrix.

中文翻译：

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形态特征和特征状态的不变性：来自基因调控网络的见解

什么构成离散形态特征与特征状态在系统学文献中已经讨论了很长时间，但仍然缺乏对这个问题的共识。将生物特征分类为特征和特征状态的不同方法会极大地影响系统发育分析的结果。在这里，我表明，在马尔可夫模型的框架中，基因调控网络（GRN）的潜在性状发展的模块化结构，以及 GRN 进化的层次性质，从根本上消除了形态特征和特征状态之间的区别，从而赋予了字符和字符状态彼此具有不变的属性。此属性允许将一个字符的状态表示为多个单独的字符，反之亦然。在实践中，这意味着可以使用一组字符或仅一个具有多种状态的复杂字符对表型进行编码。使用一个复杂字符的表型表示可以通过正确构建转换率矩阵在性状进化的马尔可夫模型中实现。