The Trivers-Willard hypothesis (TWH) states that parents in good condition preferentially produce the sex with a higher variation in reproductive success, whereas parents in bad condition favour the opposite sex. Theorists distinguish two variants of the TWH: (a) a biased sex-ratio at birth and (b) biased parental investment after birth. It has been argued before that the conditions stated by Trivers and Willard (good condition is inherited and affects reproductive success more strongly for one of the sexes) are sufficient for the sex-ratio version but insufficient for the investment version of the TWH. However, it has not yet been investigated how these conditions affect parental investment in high and low quality parents, depending on the life-cycle of a species. The present study aims to fill this gap by introducing a multi-stage matrix population model with nonlinear mating to describe the effects of parental investment after birth on the reproductive values of male and female individuals. Using methods from adaptive dynamics and evolutionary invasion analysis, evolutionary trajectories and evolutionarily stable strategies are derived for different parameterizations of the model. Simulation results demonstrate that the conditions given by Trivers and Willard produce a general bias of parental investment towards the sex with higher variance in reproductive value. This bias is stronger for low-quality parents than for high-quality parents and matches the expected marginal offspring reproductive values for parental investment.

中文翻译：

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父母投资是否有Trivers-Willard效应？使用具有非线性匹配的矩阵总体模型对演化稳定策略进行建模。

Trivers-Willard假设（TWH）指出，处于良好状态的父母会优先选择具有较高生殖成功变异性的性别，而处于不良状态的父母则会偏爱异性。理论家区分了TWH的两个变体：（a）出生时的性别比有偏差，（b）出生后的父母对父母的投资有偏差。以前有人认为，特里弗斯和威拉德所说的条件（良好的条件是遗传的，并且对其中一种性别的生殖成功影响更大）对于性别比例而言是足够的，但对于TWH的投资而言则不足。然而，尚未研究这些条件如何影响父母对高品质和低品质父母的投资，具体取决于物种的生命周期。本研究旨在通过引入具有非线性交配的多阶段矩阵人口模型来填补这一空白，以描述出生后父母的投资对男性和女性个体生殖价值的影响。使用来自自适应动力学和进化入侵分析的方法，针对模型的不同参数化导出了进化轨迹和进化稳定策略。模拟结果表明，特里弗斯（Trivers）和威拉德（Willard）给出的条件会导致父母对性别的生育投资普遍偏向，其生殖价值具有较高的差异。对于低质量的父母，这种偏见要比对高质量的父母更强，并且与父母投资的预期边际后代生殖价值相符。