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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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Random forest output overview. (A) Relationship between Variable Importance and interactivity (H-statistic) of parameters in Random Forest output. Blue line: RF model across all five parameters, AUC:0.998 ( $α_{g 1}$ = $α_{g 2}$ = $α_{F}$ = 0.1; $h_{2}$ = $h_{F}$ = 0.5). Red line: RF model with single stage herbivory ( $a_{2}$ = 0); AUC = 0.984 ( $α_{g 1}$ = $α_{g 2}$ = $α_{F}$ = 0.1; $h_{2}$ = $h_{F}$ =1). Shaded regions represent standard error. (B,C) Box and whisker plots detailing range of Variable Importance (B) and H-statistic (C) for each demographic rate in random forests run with set attack rates where $a_{2}$ and $a_{F}$ vary between 0.2 and 2.0 ( $α_{g 1}$ = $α_{g 2}$ = $α_{F}$ = 0.1; $h_{2}$ = $h_{F}$ = 0.5). Boxes represent the interquartile range with the horizontal line showing the median, the lower box showing the 25 percentile, and the upper box showing the 75 percentile. Upper and lower lines extending from the boxes show the most extreme values within 1.5 times the 75th and 25th percentile respectively. Outliers are shown as single dots. (D–F) Heatmaps showing changing importance for each demographic rate across different allocations of consumption across plant stages. Here we found consistently but only slightly better performance with mtry = 2.