What is the relationship between nature and the unnatural order and Duncan's murder in Macbeth?
Well when discussing unnatural order, you must consider the cultural expectations of the noblemen and their relationship to the king and the cultural views on the king's connection to God.
If you also consider the affect that Duncan's death has on the natural world: the horses behaving wildly and eating each other and the owls shrieking at the hour of his death. These natural world happenings indicate that Duncan's murder will affect more than just the citizens' lives.
Macbeth is expected to be loyal as Duncan's servant and as his host. Macbeth does not follow those societal expectations and instead he kills the man he must be loyal and faithful to. This act will undermine the Great Chain of Being because the king is supposed to be chosen by God to act as king. By killing the king, he is disrupting this natural order.
The witches in Macbeth profess that "fair is foul and foul is fair" creating the idea that the natural order is somehow disrupted. This motif is carried throughout the play while the unnatural order deepens as Macbeth's greed and hunger for power deepens. Nature, a symbol of the natural order, helps highlight the unnatural order changes. It is only with Macbeth's final resolution to fight to the end that he receives partial redemption, thus the natural order can be restored.
Essentially, your question relates to the Medieval and Tudor/Elizabethan concepts of the 'chain of being' and the 'divine right of kings' and to how, if these are 'disordered' by any 'unatural' act or deed, even nature goes into a great upheaval. It might be useful to read the following links then relate them to the answers given.