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. 2023 Mar 8;13:3881. doi: 10.1038/s41598-023-30313-8

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© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Interactive feature effects on model behavior. Across different herbivory allocations, partial dependence (PD) plots (A,C,E) show interactive effects between maturation rates on categorical simulation stability. Threshold plots (B,D,F) extend this analysis to include gradations of seed production rates. (A,B) Herbivory allocation $a_{F}$ = 1.0 and $a_{2}$ = 0.0. (A) Partial dependence plot shows probability of stability across all values of $r_{F}$ . (B) Threshold plot shows the location of the threshold between stable and unstable dynamics in { $g_{12}$ , $g_{2 F}$ } parameter space as a function of seed production levels ( $r_{F}$ ). (C,D) Herbivory allocation $a_{F}$ = 0.2 and $a_{2}$ = 1.0. (C) Partial dependence plot shows probability of stability across all values of $r_{F}$ . (D) Threshold plot shows the location of the threshold between stable and unstable dynamics in { $g_{12}$ , $g_{2 F}$ } parameter space as a function of seed production levels ( $r_{F}$ ). (E,F) Herbivory allocation $a_{F}$ = 1.0 and $a_{2}$ = 0.2. (E) Partial dependence plot shows probability of stability across all values of $r_{F}$ . (F) Threshold plot shows the location of the threshold between stable and unstable dynamics in { $g_{12}$ , $g_{2 F}$ } parameter space as a function of seed production levels ( $r_{F}$ ).