To detect the recent genetic history of Northern cod, we used the linkage-based method implemented in LinkNe (29) to estimate effective population size (Ne). We calculated Ne across a 150-year period in the 330 Northern cod samples from Newfoundland and Labrador. We separated LG1 homozygous inverted, heterozygous (n = 153), and LG1 homozygous noninverted individuals based on PC score. Before Ne estimation, we filtered genome-wide SNP datasets for these individuals to remove SNPs within the LG1 and LG12 rearrangements identified within Northern cod, resulting in a final dataset of 6270 SNPs. These regions were removed as selection and reduced recombination within rearrangements may skew LD inference of historical Ne. For each group, we calculated Ne separately in LinkNe in bins of 0.05 Morgans for all SNPs with minor allele frequency values greater than 0.05. We binned Ne estimates into generations calculated from recombination rate, assuming a mean generation time of 6 years (13). We assigned a contemporary sampling date of 2010, corresponding to an intermediate estimate of sampling dates from all Northern cod samples. To compare changes in effective population size between groups that exhibited large differences in Ne, we calculated relative Ne by scaling Ne values within each group by the maximum observed Ne for that group. We then plotted relative Ne estimates as proportions against estimates of cod abundance measured from 1983 to 2004 and historical reconstructions of stock biomass from 1850 to 2004 (11).

We also estimated Ne using a bin size of 0.01 to identify both finer-scale and long-term demographic variation. We found similar estimates of contemporary Ne, and again uncovered similar patterns of 20th-century expansion and decline to those identified using a bin size of 0.05 (fig. S4), but found that absolute values of historical Ne at intermediate time points varied from those found using the larger bin size (table S3). Simulations by Hollenbeck et al. (29) indicate that the detection of demographic changes over longer time periods will be limited by the number of genomic markers available, and previous analyses have suggested that long-term estimates may be affected by mutation over extended time frames (60), which may bias LD estimates of effective size. Our estimates with smaller bin sizes are thus expected to exhibit lower precision than those obtained from a larger sample of markers and likely account for the discrepancy in absolute values of Ne observed between intermediate time frames with different bin size parameters.

To account for the possibility of an observed decline in LG1 homozygous inverted individuals driven by small sample size (n = 41), we generated 10 subsamples of 41 LG1 homozygous noninverted individuals and conducted replicate effective size estimation. We observed similar starting effective sizes across replicates (mean, Ne = 2577.449, SD = 170.1235) and identified expansions coinciding with stock recovery in all 10 samples. We did not observe patterns of decline matching the pattern observed in the sample of homozygous inverted individuals, indicating that this decline is likely not an artifact of small sample size (fig. S5). We identified a recent, post-1980 decline across 3 of the 10 subsamples, which could indicate spatial heterogeneity in recent decline patterns across LG1 homozygous noninverted Northern cod samples (fig. S5). To test this hypothesis, we split LG1 homozygous noninverted, LG1 homozygous inverted, and heterozygous groups into population groups corresponding to coastal Labrador samples, offshore samples, and samples from coastal Newfoundland. We then conducted LinkNe analysis on these samples, revealing a recent decline of LG1 homozygous noninverted and heterozygous individuals within the coastal Labrador grouping (fig. S3). Together, these results indicate that small sample sizes have likely not produced false signals of decline and demonstrate potential spatial variation in cod stock decline across Newfoundland and Labrador.

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