Hump-shaped relationship between aggregation tendency and body size within fish populations

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.