Unifying the spatial epidemiology and molecular evolution of emerging epidemics

Abstract

We introduce a conceptual bridge between the previously unlinked fields of phylogenetics and mathematical spatial ecology, which enables the spatial parameters of an emerging epidemic to be directly estimated from sampled pathogen genome sequences. By using phylogenetic history to correct for spatial autocorrelation, we illustrate how a fundamental spatial variable, the diffusion coefficient, can be estimated using robust nonparametric statistics, and how heterogeneity in dispersal can be readily quantified. We apply this framework to the spread of the West Nile virus across North America, an important recent instance of spatial invasion by an emerging infectious disease. We demonstrate that the dispersal of West Nile virus is greater and far more variable than previously measured, such that its dissemination was critically determined by rare, long-range movements that are unlikely to be discerned during field observations. Our results indicate that, by ignoring this heterogeneity, previous models of the epidemic have substantially overestimated its basic reproductive number. More generally, our approach demonstrates that easily obtainable genetic data can be used to measure the spatial dynamics of natural populations that are otherwise difficult or costly to quantify.

Fig. 1.

(A and B) The link between spatial ecology and phylogenetics. Filled circles represent viral sequences whose locations and dates of sampling are known. Squares represent unsampled ancestral infections whose locations and dates are estimated. The black squares in A and B denote the epidemic’s origin in space and time, respectively. (A) Colored arrows indicate the direction and distance d_i of the movement trajectory defined by each lineage. Thin colored lines show the random walk undertaken by each lineage. (B) The phylogeny resulting from the spatial infection process in A. Colored lines in B show the duration t_i of each lineage. Diffusivity can be inferred by combining the information in A and B. Diffusivity is low for lineages with long and winding paths that do not lead far (e.g., green), and is high for lineages that quickly move large distances (e.g., purple). (C) Maximum clade credibility phylogeny of the North American WNV epidemic, estimated from whole genomes under the best-fitting dispersal model (Table 1). Posterior probabilities of branching events are indicated by red (P > 0.95) and yellow (P > 0.85) circles. Blue bars show the 95% HPD credible intervals of the estimated dates of well-supported nodes. See Fig. S1 for full annotation.

Fig. 2.

The reconstructed spatiotemporal diffusion of WNV in North America, shown at annual intervals from mid-1999 onwards (A–H). White circles indicate isolate sampling locations. Black lines show a spatial projection of a representative phylogeny, with each node being mapped to its known (external node) or estimated (internal node) location. In each panel colored clouds represent statistical uncertainty in the estimated locations of WNV lineages (95% HPD regions) (42).

Fig. 3.

Characteristics of the North American WNV invasion estimated from viral genomes. Plots A and C were estimated under a homogenous dispersal model; plots B and D under the best-fitting heterogeneous model (Table 1). Plots A and B show the reconstructed epidemic wavefront. For each point in time, the black line is the estimated distance from the epidemic wavefront to its estimated origin: the gradient of this line is thus the invasion velocity. Gray lines indicate the 95% credible regions of the estimated wavefront position. Plots C and D show kernel density estimates of the diffusion coefficient (D) parameters. The horizontal axis shows the estimated mean D among lineages; the vertical axis shows the coefficient of variation of D among lineages. The three contours show, in shades of decreasing darkness, the 50%, 75%, and 95% HPD regions via kernel density estimation.