Predicting pathogen spillover requires counting spillover events and aligning such counts with process-related covariates for each spillover event. How can we connect our analysis of spillover counts to simple, mechanistic models of pathogens jumping from reservoir hosts to recipient hosts? We illustrate how the pathways to pathogen spillover can be represented as a directed graph connecting reservoir hosts and recipient hosts and the number of spillover events modelled as a percolation of infectious units along that graph. Percolation models of pathogen spillover formalize popular intuition and management concepts for pathogen spillover, such as the inextricably multilevel nature of cross-species transmission, the impact of covariance between processes such as pathogen shedding and human susceptibility on spillover risk, and the assumptions under which the effect of a management intervention targeting one process, such as persistence of vectors, will translate to an equal effect on the overall spillover risk. Percolation models also link statistical analysis of spillover event datasets with a mechanistic model of spillover. Linear models, one might construct for process-specific parameters, such as the log-rate of shedding from one of several alternative reservoirs, yield a nonlinear model of the log-rate of spillover. The resulting nonlinearity is approximately piecewise linear with major impacts on statistical inferences of the importance of process-specific covariates such as vector density. We recommend that statistical analysis of spillover datasets use piecewise linear models, such as generalized additive models, regression clustering or ensembles of linear models, to capture the piecewise linearity expected from percolation models. We discuss the implications of our findings for predictions of spillover risk beyond the range of observed covariates, a major challenge of forecasting spillover risk in the Anthropocene. This article is part of the theme issue 'Dynamic and integrative approaches to understanding pathogen spillover'.
Keywords: generalized linear model; multilevel model; percolation; probability; regression; spillover.