We lack an adaptive explanation for a striking phenomenon, that of bright colours displayed in autumn by the leaves of many deciduous trees. The usual explanation is that it is simply a non-adaptive secondary effect of leaf senescence. A game-theoretic model of biological signalling provides an adaptive hypothesis for autumn colours showing that they can be the result of a process of coevolution between insects and trees: if leaf colour acts as a warning indicator of the tree's vigour to autumn parasite insects, trees can gain advantage from the reduction of parasite load and insects can gain advantage from location of the most profitable hosts to lay their eggs. The results of the model are consistent with Zahavi's handicap principle. Possible explanations for the origin of the system and evidence from natural history are discussed.