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.

The raw cpue data, maturation stage, and fishing mortality data were downloaded from the DATRAS (https://datras.ices.dk/Data_products/Download/Download_Data_public.aspx). The temperature data was download from the ICES website (https://ocean.ices.dk/HydChem/HydChem.aspx?plot=yes). The life history traits data was extracted from Thorp et al.'s (2015) study. 

Using R code (https://github.com/ruo-yu-Pan/Hump-shaped-relationship_Aggregation-tendency_vs_bodysize), we processed the raw data, calculated the size-based Taylor's exponents, and investigated the effect of body size and temperature on the size-based Taylor's exponents within the population.

The data used and the outcome in the estimation of size-based Taylor's power law and the relationship between aggregation tendency and body size in the North Sea.

SizeAggregTend_data.zip