Small pelagic fish lack clear stock-recruitment relationships. This is a problem because such relationships are taken to be the primary descriptors of density dependence, responsible for regulating population density. In this paper, we show that small pelagic fish species, anchovy (Engraulis spp, Engraulidae), living in a stochastic environment, can be strongly regulated without a stock-recruitment relationship emerging. This is done through numerical analysis of a size-spectrum model, in which fish grow by eating and die in part from being eaten, with the result that birth, growth and death are all density dependent. The model includes cannibalism, and growth-dependent larval mortality, both of which have been suggested as regulatory mechanisms in anchovy, together with growth and reproduction later in life. Despite the lack of a clear stock-recruitment relationship in the presence of stochasticity, signals of density dependence in the vital rates remain clear, suggesting that they might prove to be better indicators of density dependence than stock-recruitment relationships in small pelagic fish.

中文翻译：

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没有种群-招募关系的鱼类种群的调节：小型远洋鱼类的案例

小型中上层鱼类缺乏明确的种群-招募关系。这是一个问题，因为这种关系被认为是密度依赖的主要描述，负责调节人口密度。在本文中，我们表明，生活在随机环境中的小型远洋鱼类鳀鱼（鳀鱼科）可以受到严格监管，而不会出现种群招募关系。这是通过尺寸谱模型的数值分析完成的，其中鱼通过进食生长，部分因被吃而死亡，因此出生、生长和死亡都与密度有关。该模型包括自相残杀和依赖生长的幼虫死亡率，两者都被认为是凤尾鱼的调节机制，以及生命后期的生长和繁殖。