In 1948, Angus Bateman presented experiments and concepts that remain influential and debated in sexual selection. The Bateman gradient relates reproductive success to mate number, and Bateman presented this as the cause of intra-masculine selection. A deeper causal level was subsequently asserted: that the ultimate cause of sex differences in Bateman gradients is the sex difference in gamete numbers, an argument that remains controversial and without mathematical backup. Here I develop models showing how asymmetry in gamete numbers alone can generate steeper Bateman gradients in males. This conclusion remains when the further asymmetry of internal fertilisation is added to the model and fertilisation is efficient. Strong gamete limitation can push Bateman gradients towards equality under external fertilisation and reverse them under internal fertilisation. Thus, this study provides a mathematical formalisation of Bateman’s brief verbal claim, while demonstrating that the link between gamete number and Bateman gradients is not inevitable nor trivial.

1948 年，安格斯·贝特曼提出了在性选择中仍然具有影响力和争论的实验和概念。贝特曼梯度将繁殖成功与配偶数量联系起来，贝特曼将此视为男性内部选择的原因。随后断言了更深层次的因果关系：贝特曼梯度中性别差异的最终原因是配子数的性别差异，这一论点仍然存在争议且没有数学支持。在这里，我开发了模型，展示了配子数量的不对称如何在雄性中产生更陡峭的贝特曼梯度。当内部受精的进一步不对称性被添加到模型中并且受精是有效的时，这个结论仍然存在。强配子限制可以推动贝特曼梯度在外部受精下趋向平等，并在内部受精下逆转它们。因此，这项研究提供了贝特曼简短口头声明的数学形式化，同时证明配子数和贝特曼梯度之间的联系并非不可避免也不是微不足道的。