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Peer-reviewedCC BY 4.0PLOS Ecosystems

Combining branching processes and Allee effects into an integral projection model to assess invasion risk

  • James P. Peirce1
  • Cynthia S. Tam2
  • Joseph J. Parkos3
  • Grace L. Loppnow4
  • Mark W. Fritts5
  • Alison A. Coulter6
  • Richard A. Erickson7
7 affiliations
  1. 1Mathematics & Statistics Department, University of Wisconsin - La Crosse, La Crosse, Wisconsin, United States of America
  2. 2River Studies Center, University of Wisconsin - La Crosse, La Crosse, Wisconsin, United States of America
  3. 3U.S. Geological Survey, Ecosystems Mission Area, Reston, Virginia, United States of America
  4. 4Kaskaskia Biological Station, Illinois Natural History Survey, Prairie Research Institute, University of Illinois at Urbana-Champaign, Sullivan, Illinois, United States of America
  5. 5Minnesota Department of Natural Resources, St. Paul, Minnesota, United States of America
  6. 6U.S. Fish and Wildlife Service, La Crosse Fish and Wildlife Conservation Office, Onalaska, Wisconsin, United States of America
  7. 7Department of Natural Resource Management, South Dakota State, Brookings, South Dakota, United States of America
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Abstract

Invasive species threaten both ecological systems and economies. Successful establishment is governed partly by demographic stochasticity, where random individual-level variation can significantly influence invasion dynamics. A critical factor is the Allee effect, which describes reduced population growth at low densities, potentially serving as a barrier to persistence. Size-dependent growth and survival further shape outcomes based on the size distribution of individuals within the population. To address these complexities, we developed a population-level model integrating an Integral Projection Model (IPM) for the expected size distribution with an Allee effect for recruitment dynamics and a branching process to account for demographic stochasticity. We applied this framework to Silver Carp (Hypophthalmichthys molitrix), a species established in the Upper Mississippi River system that poses significant risk of expanding into the Great Lakes. Our analysis compared temporal dynamics and population-size distributions under hypothetical introduction scenarios for large adult and smaller subadult fish. In both cases, initial population size relative to the Allee threshold was a critical determinant of establishment probability, with introductions below the threshold requiring stochastic growth across a critical biomass boundary before self-sustaining dynamics could take hold. Sensitivity analysis further indicated that per-spawner recruitment played a compounding role in invasion risk: higher recruitment rates reduced the critical introduction size for establishment and compressed the time to self-sustaining population size, jointly broadening the window of invasion risk. These findings highlight the framework’s potential for invasion assessments and offer insights into how Allee effects, size structure, and recruitment rates interact to govern establishment outcomes, while underscoring the need for species-specific parameter estimates before quantitative outputs can guide management decisions. Author summary: Invasive species can cause lasting ecological and economic damage, yet many introduced populations disappear before becoming established. Understanding why some succeed while others fail is therefore important for preventing future invasions. Small populations face particular challenges, since chance differences in survival and reproduction can determine their fate, and population growth is often difficult when too few individuals are present. We developed a model that tracks how the sizes of individuals in a population change over time while accounting for reduced growth at low population sizes and the role of chance. We applied it to silver carp, an invasive fish already established in parts of the Upper Mississippi River system and considered a potential threat to the Great Lakes. Across the scenarios we examined, the strongest predictor of establishment was whether the introduced population started above a critical population level. Populations that produced more offspring per spawner also established more easily and more quickly. Our approach may help assess invasion risk, though reliable predictions for any given species will require species-specific measurements before the results can guide management.

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Cite

BibTeXRIS
BibTeX
@article{peirce2026combining,
  title = {{Combining branching processes and Allee effects into an integral projection model to assess invasion risk}},
  author = {James P. Peirce and Cynthia S. Tam and Joseph J. Parkos and Grace L. Loppnow and Mark W. Fritts and Alison A. Coulter and Richard A. Erickson},
  journal = {PLOS Ecosystems},
  year = {2026},
  month = sep,
  doi = {10.1371/journal.pesy.0000022},
  url = {https://doi.org/10.1371/journal.pesy.0000022},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Combining branching processes and Allee effects into an integral projection model to assess invasion risk
AU  - James P. Peirce
AU  - Cynthia S. Tam
AU  - Joseph J. Parkos
AU  - Grace L. Loppnow
AU  - Mark W. Fritts
AU  - Alison A. Coulter
AU  - Richard A. Erickson
PY  - 2026
DA  - 2026/09/08
JO  - PLOS Ecosystems
DO  - 10.1371/journal.pesy.0000022
UR  - https://doi.org/10.1371/journal.pesy.0000022
AB  - Invasive species threaten both ecological systems and economies. Successful establishment is governed partly by demographic stochasticity, where random individual-level variation can significantly influence invasion dynamics. A critical factor is the Allee effect, which describes reduced population growth at low densities, potentially serving as a barrier to persistence. Size-dependent growth and survival further shape outcomes based on the size distribution of individuals within the population. To address these complexities, we developed a population-level model integrating an Integral Projection Model (IPM) for the expected size distribution with an Allee effect for recruitment dynamics and a branching process to account for demographic stochasticity. We applied this framework to Silver Carp (Hypophthalmichthys molitrix), a species established in the Upper Mississippi River system that poses significant risk of expanding into the Great Lakes. Our analysis compared temporal dynamics and population-size distributions under hypothetical introduction scenarios for large adult and smaller subadult fish. In both cases, initial population size relative to the Allee threshold was a critical determinant of establishment probability, with introductions below the threshold requiring stochastic growth across a critical biomass boundary before self-sustaining dynamics could take hold. Sensitivity analysis further indicated that per-spawner recruitment played a compounding role in invasion risk: higher recruitment rates reduced the critical introduction size for establishment and compressed the time to self-sustaining population size, jointly broadening the window of invasion risk. These findings highlight the framework’s potential for invasion assessments and offer insights into how Allee effects, size structure, and recruitment rates interact to govern establishment outcomes, while underscoring the need for species-specific parameter estimates before quantitative outputs can guide management decisions. Author summary: Invasive species can cause lasting ecological and economic damage, yet many introduced populations disappear before becoming established. Understanding why some succeed while others fail is therefore important for preventing future invasions. Small populations face particular challenges, since chance differences in survival and reproduction can determine their fate, and population growth is often difficult when too few individuals are present. We developed a model that tracks how the sizes of individuals in a population change over time while accounting for reduced growth at low population sizes and the role of chance. We applied it to silver carp, an invasive fish already established in parts of the Upper Mississippi River system and considered a potential threat to the Great Lakes. Across the scenarios we examined, the strongest predictor of establishment was whether the introduced population started above a critical population level. Populations that produced more offspring per spawner also established more easily and more quickly. Our approach may help assess invasion risk, though reliable predictions for any given species will require species-specific measurements before the results can guide management.
SN  - 3070-8141
ER  -