Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to equilibrium. With the help of the causal ordering algorithm, one can construct graphical representations of dynamical systems that represent the causal relations between the variables and the conditional independences in the equilibrium distribution. We apply these tools to formulate sufficient graphical conditions for identifying perfect adaptation from a set of first-order differential equations. Furthermore, we give sufficient conditions to test for the presence of perfect adaptation in experimental equilibrium data. We apply this method to a simple model for a protein signalling pathway and test its predictions both in simulations and using real-world protein expression data. We demonstrate that perfect adaptation can lead to misleading orientation of edges in the output of causal discovery algorithms.

翻译：动力系统中的完美适应是指，当一个或多个变量对外部刺激的持续变化产生初始瞬态响应后，随着系统收敛至平衡态，这些变量恢复到其原始值的现象。借助因果排序算法，可以构建动力系统的图形表示，以展示变量间的因果关系以及平衡分布中的条件独立性。我们运用这些工具，从一组一阶微分方程中给出了识别完美适应的充分图形条件。此外，我们还提出了在实验平衡数据中检验完美适应存在的充分条件。我们将该方法应用于一个简单的蛋白质信号通路模型，并通过数值模拟及真实蛋白质表达数据验证了其预测结果。我们证明，完美适应可能导致因果发现算法输出的边方向产生误导性判断。