Pest host expansion as a scale-free stepwise process across the host phylogeny

The present and future host ranges of pests have important implications for ecology, economics and health. Most multi-host pests have phylogenetically conserved host symbioses, but jumps to phylogenetically distant hosts are surprisingly common and can have large fitness consequences. We introduce a model representing host distributions as outcomes of random jumps across a host phylogeny, with jump probabilities proportional to a power function of phylogenetic distance, parallel to Lévy flights in foraging behaviour. Using machine learning, we fit our model to empirical data on insect and pathogen pests of North American trees and estimate the parameter controlling the distribution of jump distance. We find that non-native insect pests are more likely to make jumps to phylogenetically distant hosts than native insect pests, although we did not observe a similar distinction between non-native and native pathogens. Finally, we use estimated jump parameters to describe the risk of future host expansion across the phylogeny of North American trees.