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. 2018 May 15;16:53. doi: 10.1186/s12915-018-0519-2

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© Szathmáry et al. 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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Fig. 6 — Numerical example for a 2 × 2 Leslie matrix (see Additional file 1 for details). a Maximum family long-term growth rate (fitness), b optimal level of backward help (y*), c average number of offspring at y*, and d offspring survival at y* all as a function of b (effectiveness of backward help) and a₂₁ (effectiveness of forward help on offspring survival). Parameters: α₂ = 6, ω₁ = 0.45, ω₂ = 0.62, ω₃ = 0.25, d = 0.3, h = 1, c = 0.2, 0.6, 1, and a₁₂ = 10