Yingli Pan

Conflicts of Interest The authors declare no conflicts of interest. Data Availability Statement The data that support the findings of this study are available in the Survival package of R. https://archive.ics.uci.edu/dataset/880/support2. References 1, , and , “A Rank-Based Approach to Estimating Monotone Individualized Two Treatment Regimes,” Computational Statistics and Data Analysis 151 (2020): 107015.

Conflicts of Interest The authors declare no conflicts of interest. References 1, , , et al., “Report of the AAPOR Task Force on Non-Probability Sampling,” Journal of Survey Statistics and Methodology 1, no. 2 (2013): 90–143. 2 and , “Estimation With Non-Probability Surveys and the Question of External Validity,” Proceedings of Statistics Canada Symposium (2014): 1–8.

How to characterize the rate of accelerating propagation in recursive systems is a challenging topic though it has attracted great attention of theoretical and empirical ecologists. In this paper, we determine the sharp rate of accelerating propagation for a unimodal recursive system with a heavy-tailed dispersal kernel through tracking of level sets of solutions with compactly supported initial data.