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A Stage-Structured Continuous-/Discrete-Time Population Model: Persistence and Spatial Spread

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Abstract

Population persistence and spatial propagation and their dependence on demography and dispersal are of great importance in spatial ecology. Many species with highly structured life cycles invade new habitats through the dispersal of organisms in their early life stages (e.g., seeds, larvae, etc.). We develop a stage-structured continuous/discrete-time hybrid model to describe the spatiotemporal dynamics of such species, in which a reaction-diffusion equation describes the random movement of dispersing individuals, while two difference equations describe the demography of sedentary individuals. We obtain a formula for the spreading speed of the population in terms of model parameters. We show that the spreading speed can be characterized as the slowest wave speed of a class of traveling wave solutions. We provide an explicit formula for the critical domain size that separates population persistence from extinction. By comparing our stage-structured model with a physically unstructured model, we find that the structured model reduces to the unstructured one in some special cases. Accordingly, the results about the spreading speed and the critical domain size for the unstructured model represent some special cases of those for the structured one. This highlights the significance of including stage structure in studying the spatial dynamics of species with complex life cycles.

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Acknowledgements

We thank Yu Jin (University of Nebraska-Lincoln) for helpful discussions. We are grateful to the anonymous referees for many insightful comments and suggestions that helped improve the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Minglong Wang & Qihua Huang

  2. School of Science, Tianjin University of Technology and Education, Tianjin, 300222, China

    Yuxiang Zhang

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  1. Minglong Wang
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Correspondence to Qihua Huang.

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The research of this author was partially supported by the National Natural Science Foundation of China (Nos. 11701415 and 11801400). The research of this author was partially supported by the National Natural Science Foundation of China (No. 11871060), the Venture and Innovation Support Program for Chongqing Overseas Returnees (No. 7820100158).

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Wang, M., Zhang, Y. & Huang, Q. A Stage-Structured Continuous-/Discrete-Time Population Model: Persistence and Spatial Spread. Bull Math Biol 84, 135 (2022). https://doi.org/10.1007/s11538-022-01090-8

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