Interannual temperature variability is a principal driver of low-frequency fluctuations in marine fish populations

Marine fish populations commonly exhibit low-frequency fluctuations in biomass that can cause catch volatility and thus endanger the food and economic security of dependent coastal societies. Such variability has been linked to fishing intensity, demographic processes and environmental variability, but our understanding of the underlying drivers remains poor for most fish stocks. Our study departs from previous findings showing that sea surface temperature (SST) is a significant driver of fish somatic growth variability and that life-history characteristics mediate population-level responses to environmental variability. We use autoregressive models to simulate how fish populations integrate SST variability over multiple years depending on fish life span and trophic position. We find that simulated SST-driven population dynamics can explain a significant portion of observed low-frequency variability in independent observations of fisheries landings around the globe. Predictive skill, however, decreases with increasing fishing pressure, likely due to demographic truncation. Using our modelling approach, we also show that increases in the mean and variance of SST could amplify biomass volatility and lessen its predictability in the future. Overall, biological integration of high-frequency SST variability represents a null hypothesis with which to explore the drivers of low-frequency population change across upper-trophic marine species.


SUPPLEMENTARY FIGURES 1-6 Figure S1 | Temporal autocorrelation in biomass estimates increases with fish maximum age in the North
Sea and Celtic Sea. First-order autocorrelation (i.e. lag 1) was determined in ICES abundance estimates, as recently compiled and standardized by Heessen, et al. 1 for the North and Celtic seas. We initially selected all species for which the North Sea and/or Celtic Sea represent a central part of their distributional range (i.e. no species that are only occasionally found in these areas) and for which no known issues with the assessment data where reported in Heessen, et al. 1 . This yielded biomass time series (most covering period 1984-2013) for 31 species in the Celtic Sea and 31 (most covering 1977-2013) species in the North Sea. However, for the North Sea, we excluded Atlantic cod (Gadus morhua) due to fishing-induced stock collapses in the time period analysed, and witch (Glyptocephalus cynoglossus) because of uncertainty in stock-specific longevity. For some species, the time period over which autocorrelation was calculated was shortened because of very low abundance in the first part of the time series (i.e. a period without temporal variability). Data on life-history traits were acquired from Heessen, et al. 1 and references therein, or from Froese and Pauly 2 . When data of the two regions are combined: r=0.38, p=0.003. Effect of trophic level p=0.08 for the North Sea, and p=0.12 for the Celtic Sea are not shown.
The data shown in the figure is included in Supplementary Data 3.
Part of the uncertainty around the temporal autocorrelationlife span relationships is likely due to the challenge of computing autocorrelation from times series of abundance estimates (e.g. because of measurement errors and time series length). The zero autocorrelation observed for some species could have at least three causes: (1) the temporal dynamics of a species' abundance may exhibit very little low-frequency variability and thus lack detectable temporal autocorrelation; (2) zero autocorrelation may reflect the potentially large sampling error in the stock assessment data for some species, which can create large "random" year-to-year fluctuation in the data that conceal low-frequency variability, and (3) the relatively short time span of the stock assessment data could also inhibit the detection of temporal autocorrelation. Also note that we set non-significant autocorrelations to a value of zero in these analyses and in Figure S1. This explains the lack of data points between zero and values of around 0.3. Arrows in top panel indicated fish species shown in Fig. 1.  Table S2 for model details.
The fish maximum age data are largely modelled estimates (e.g. based on the work of Taylor 3 ), with about 10% consisting of empirical data 2 . We tested to what extent the relationships shown here and in Table S2, would change when using only empirical data. We used the R package Rfishbase to extract empirical data on fish maximum age from the Fishbase database. This yielded results for 573 species globally; for each the source of the age information was available. We found that the correlation between modelled estimates and empirical observations of maximum age was significant (r=0.51, p<0.0001), and that a multiple regression using empirical data only provided similar results as those found with the larger dataset that also includes modelled estimates of maximum age. Although the estimate of the SST effect on fish maximum age was similar (-0.32 versus -0.24, when using the full dataset or empirical dataset, respectively), the estimated effect of trophic level dropped from 6.59 to 2.76 in the regression based on empirical data only. Next, we re-ran all analyses using the relationship between fish age, trophic level and SST based on empirical data only. We found that the results presented in our manuscript  are almost identical to those using the age relationships derived from the original dataset, with the exception of the spatial patterns found for trophic level 2 (Fig. 2b). A clear latitudinal increase in first-order autocorrelation disappears when using the age-TL-SST relationship based on empirical data only. However, closer inspection of the empirical dataset used, showed that age estimates are virtually absent for fish <30 cm. Thus, the lack of age data for small fish, which constitute the majority of species at low trophic levels and at low latitudes, likely resulted in an overestimation of the max age of fishes in tropical waters and at low trophic levels and hence explains the much lower effect of trophic level on maximum age and the change in the spatial pattern at TL 2. This interpretation is corroborated by the finding that the presence of a latitudinal change in first-order autocorrelation is supported to some extent by observational data (i.e. autocorrelation in timeseries of landings; Fig. S4). We therefore used the relationship between maximum age, SST and TL based on the dataset that also includes modelled data on maximum age in our analyses, given the restricted availability of empirical data on maximum age (in particular for small fish species).
Although we acknowledge there may be substantial uncertainty in the relationship presented in Fig S2 and Table S2, we stress that our goal was not to derive accurate estimates of fish age at a species level, which may be highly uncertain for many species. Instead, our main goal here was to derive an estimate of mean fish longevity at each trophic level per large marine ecosystem (LME), with each LME containing hundreds of species. Mean longevity estimates were subsequently used to parameterize autoregressive models, allowing the comparison of model predictions to the general patterns observed in fisheries landings at each LME (Fig. 3,4). Autoregressive models were based on annual NPP, and parameterized using the relationships among trophic level, temperature, and fish maximum age ( Fig. S2; Table S2). Autocorrelation in these analyses is likely lower compared to those presented in Figure 2 because of the considerably shorter time span of the data used (≤32 years).

Figure S5 | Correlation coefficients between SST-based models and observations surpass those expected by
change. We reran our global analyses 100 times using random data (grey bars) instead of SST (red bar) in our models. In all cases, the first principal component of the observational data (i.e. landings) in an LME was correlated to the first principal component of simulated populations across all 1° grids within the same LME (using random noise or SST). Next, the mean absolute correlation coefficient across all LMEs was taken for each trophic level and shown in the figure. The dashed line shows the overall mean correlation across all 100 runs with random data. Note that for each trophic level, the models using SST data instead of random data have overall correlations that are well above those that could be expected by chance (i.e. the grey bars).

Figure S6 | Relationship between stock status and the difference in mean first-order autocorrelation (AC)
of model predictions and of landings for each LME (observed -predicted). At higher level of exploitation, time series of landings generally contain a lower level of first-order autocorrelation than expected based on our model approach (but only significant at TL2). Left panel illustrates how fishing-induced age/size truncation may explain this divergence. Table S1. Review of published fish growth chronologies (based on increment rings in fish otoliths) and the main climate driver(s). These growth chronologies reveal extraordinarily strong correlations of individual fish growth to sea surface temperature (SST) across latitudes. The SST effect indicates the sign of the correlation with growth.

SUPPLEMENTARY TABLES 1-5
Map in top row shows location of studies, and if temperature effects on growth were found.