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An evolutionary approach by second derivatives of the population growth rate of Castilleja tenuiflora, a hemiparasitic plant with and without hosts

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Abstract

The first partial derivatives of λ with respect to demographic parameters quantify linear responses of population growth to vital rate perturbations, but sensitivity itself is situational and can show non-linear responses. We use the second derivative of λ with respect to the demographic parameters to explore this type of responses in a population of a root hemiparasite (Castilleja tenuiflora). For plants growing with and without hosts, population transition matrices were built for the 2016–2018 period, and sensitivities and elasticities together with pure derivatives of the Hessian matrix were calculated, together with the second derivatives to survival and fecundity. We transformed the Hessian matrix to a logarithmic scale to avoid values with no biological meaning. Germination showed high sensitivity values, while permanence of individuals with dry aerial tissue that re-sprout had the highest elasticity. Negative values on the second derivative and on the logarithmic representation were obtained for germination with and without hosts in both years. Survival and fecundity have a similar behaviour in both conditions and periods, with negative values for survival for the first category and no negative values for fecundity. High negative values of the second derivative of the transition from seed to seedling indicate an evolutionary stable strategy and imply seeds are important to the permanence of C. tenuiflora population. A stochastic analysis of the second derivative of the transition from seed to seedling was performed with a Gamma distribution analysis, and showed negative values in all cases, corroborating this result.

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Acknowledgements

Luisa A. Granados Hernández was supported by Consejo Nacional de Ciencias y Tecnología (CONACyT) with scholarship 432340, as well as by the Department of Ecology and Natural Resources, Facultad de Ciencias (UNAM), and the Programa de Apoyo a Estudintes de Posgrado (PAEP/UNAM). We appreciate the insight of María C. Mandujano and Uzmar Gómez, and thank Pedro Mendoza-Hernández, Mariana Hernández-Apolinar, Israel Solano-Zavaleta, and Marco Romero-Romero for technical support.

Funding

Luisa A. Granados-Hernádez received support from Consejo Nacional de Ciencia y Tecnología (Conacyt) for her graduate (Master’s in Science) studies with scholarship 432340, as well as by the Programa de Apoyo a Estudiantes de Posgrado (PAEP/UNAM).

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  1. Departamento de Ecología y Recursos Naturales, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Luisa A. Granados-Hernández & Irene Pisanty

  2. Departamento de Ecología, Universidad de Alicante, Alicante, Spain

    José Raventós

  3. Department of Botany and Plant Sciences, University of California, Riverside, Riverside, CA, USA

    Exequiel Ezcurra

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  1. Luisa A. Granados-Hernández
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  4. Exequiel Ezcurra
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IP conceived the project, participated in field and laboratory data collection and in their analysis, LAG-H collected field and laboratory data and executed the data analysis, JR and EE proposed and executed the numerical and evolutionary approaches. All authors contributed equally to the main text.

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Correspondence to Irene Pisanty.

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Granados-Hernández, L.A., Pisanty, I., Raventós, J. et al. An evolutionary approach by second derivatives of the population growth rate of Castilleja tenuiflora, a hemiparasitic plant with and without hosts. Evol Ecol 37, 457–476 (2023). https://doi.org/10.1007/s10682-022-10224-2

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