Population dynamical modeling of the invasive spotted lanternfly with stage-age-structured PDEs

Abstract: Invasive pest establishment is a pervasive threat to global ecosystems, agriculture, and public health, and one that is increasing as climate change intensifies. One pest of significant concern is the spotted lanternfly (SLF, Lycorma delicatula), a voracious feeder of over 100 plants, including grape, apple, hop, and other important crops. In the eight years since its introduction into southeastern Pennsylvania, SLF’s presence has proven harmful to farms and vineyards in its establishment area, which now includes 11 states. Predicting its population dynamical behavior in diverse climates is essential to the planning of effective interception and mitigation strategies. Here, we compute the SLF reproductive number (R_0) using a stage-age-structured system of PDEs representing the dynamics of a single population. To do this, we first develop a novel moving mesh method for computing solutions that captures age-advection accurately at coarse numerical discretizations. We then regard the dominant eigenvalue of a one-year numerical solution operator as a proxy for R_0. Using temperature-dependent rates of development, fecundity, and mortality fitted to emerging data, we compute R_0 as a function of the parameters that define temperature patterns. We quantify assumptions sufficient to give rise to the low-rank structure of the solution operator in part of the parameter domain. We discuss the establishment potential across the United States predicted by our parameter sweeps, address implications for control implementation, and preview future work.

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