A distribution with high spatial variability may impair the bet-hedging capacity of a population, threatening population sustainability. Although the association between aggregation and life history traits of a species (e.g. body size) has been documented, the relationship between aggregation and size within a population has rarely been explored. As selective over-fishing may induce size truncation in the targeted stocks, it is critical to understand if such a truncation also undermines the distribution patterns of the population. In this study, we examined if and how the ‘aggregation tendency' varies among different size classes of a population. Aggregation tendency was quantified as the exponent b of Taylor's power law (V = a × M^b), which measures the change in spatial variance (V) with the mean abundance (M) of a population. We estimated b by size class for each of the nine commercially important fish species in the North Sea, using ICES survey data from 1991 to 2015. Our study found that the relationship between b and body size within a population is hump-shaped, with a peak slightly larger than the 50% mature length of the species. This result indicates larger adults in a population tend to distribute less heterogeneously when abundance increases, suggesting that larger size classes play a critical role in reducing the variability of population distribution. Our findings highlight the importance of considering the combined effects of fishing-induced size truncation and changes in aggregation patterns in fishery management. That is, maintaining the size and spatial structure for the target stocks of selective fisheries is critical for the sustainability of the populations.

中文翻译：

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鱼群内聚集趋势与体型之间的驼峰状关系

具有高空间变异性的分布可能会削弱人口的对冲能力，从而威胁到人口的可持续性。尽管已记录了物种聚集与生活史特征（例如体型）之间的关联，但很少探索种群内聚集与大小之间的关系。由于选择性过度捕捞可能会导致目标种群的大小截断，因此了解这种截断是否也会破坏种群的分布模式至关重要。在这项研究中，我们检查了“聚集趋势”是否以及如何在人口的不同规模等级之间变化。聚集趋势被量化为泰勒幂律的指数b ( V  =  a × M ^b)，它衡量空间方差 ( V ) 与总体平均丰度 ( M ) 的变化。我们估计b的尺寸级别为每个在北海的九个重要商业价值的鱼类品种，使用ICES调查数据从1991年到2015年，我们的研究发现之间的关系b种群内体型呈驼峰状，峰值略大于该物种50%的成熟长度。这一结果表明，当丰度增加时，人口中较大的成年人往往分布不均匀，这表明较大的规模等级在减少人口分布的变异性方面起着关键作用。我们的研究结果强调了在渔业管理中考虑捕捞引起的尺寸截断和聚集模式变化的综合影响的重要性。也就是说，保持选择性渔业目标种群的规模和空间结构对于种群的可持续性至关重要。