Single-species distribution models.

As density-independent predictors in the species distribution models, we used water temperature (bottom temperature for cod, and mean pelagic temperature from 50–200 m depth for capelin), bottom depth, sun height, survey day, and year. The temperature variables were allocated to each trawl station from the nearest CTD measurement from the same survey. The bottom depth was that measured at the beginning of trawling. Sun height was included to account for sampling variation associated with diurnal vertical migrations, and was calculated from the day of the year, geographical position, and sampling time. Survey day was expressed relative to the earliest day of the season (autumn, winter) across the study period when sampling took place, and was included to account for the quasi-synoptic coverage and inter-annual differences in timing of sampling in relation to the migrations of cod and capelin. The geographical coordinates x,y were projected stereographically with centre in the middle of our study area at 75° N and 35° E, and expressed in deviation from this centre in nautical miles. Finally, we included the annual total stock biomasses [27] of each species as covariates to test for potential density-dependent effects on species distributions. As the capelin stock assessment is done on data from the autumn survey, we used the capelin stock biomass from the previous year in the winter models of capelin distribution.

All data points containing missing values in any covariate were removed. To avoid large outliers in the covariates, we also limited the data to include bottom temperatures in the range -2 to +7.5°C, and depths of 50–500 m, which contained the bulk of observations in both seasons, leaving 3994 observations for analysis in winter, and 4644 observations in autumn. Calculation of variance inflation factors indicated that the correlations between covariates were not a cause for concern (values < 3, [36]), except for the correlation between year and stock biomasses. We therefore used stock biomass only.

Since the Barents Sea contains many islands and complex coastlines, we applied the soap film smoother in the GAMs (for details, see S1 Appendix). All analyses were done in R version 3.4.1 for Windows [37], using the packages mgcv [38, 39] for GAM fitting, and ggplot2 [40], cowplot [41] and itsadug [42] for visualisation.

The response variables in the models were local cod and capelin densities. Due to the large amount of acoustic data and the application of the soap film smoother, convergence of the capelin models was problematic. We therefore chose to include only acoustic registrations adjacent to the bottom trawl stations, using distance weighted interpolation of the area backscatter (NASC) within a 15 nmi (28 km) radius with weights of the form w_i = (1 + d_i)^-1, where d_i is the Euclidian distance between the acoustic sampling points and the station [43]. This did not lead to any loss of information relevant to our objectives, as initial runs using the finer resolution data gave similar response-covariate relationships.

For each season and component (immature cod, mature cod, acoustic capelin, trawl capelin), we fitted separate distribution models with the untransformed species density D_(x,y),t in position x,y in year t as the response, conditional on other environmental covariates, using a GAM with Tweedie distribution and the default log-link. The variance of the Tweedie distribution is related to the mean by a power function (Eq 1): (1) While a p of 0, 1 or 2 corresponds to the familiar Gaussian, Poisson and Gamma distributions, respectively, for 1 < p < 2, the Tweedie distribution is a compound Poisson–gamma distribution with mass at zero, appropriate for our data. This is also the range where automatic estimation of the power parameter during fitting is implemented in mgcv [44]. Firstly, we fit models with basic smooth term predictors to establish baselines for comparison with more complex formulations, and to evaluate the overall (across-space) relationships between covariates and response (habitat model Eq 2): (2) Here s_1-6 are smooth functions of geographical position, stock biomass, depth, sun height, temperature, and survey day, respectively, α is the global intercept and ε_(x,y),t is the error term whose variance is related to the mean according to Eq 1 under the Tweedie distribution. To avoid overfitting the smooth functions, we constrained their level of wiggliness by limiting the maximum number of basis dimensions (“knots”) to 5 on the univariate smooths and 20 on the two-dimensional smooth of geographical position. Thereafter, we systematically increased model complexity, ending up with seven candidate models describing the distribution of each component. These models included different combinations of the covariates in Eq 2 and spatially variant terms of stock biomass, temperature, and survey day. Spatially variant terms test for linear effects of a variable, but the effect is also allowed to vary smoothly in space so that there may be a positive effect in one part of the study area, and a negative effect in another [45]. The most complex candidate models were on the form: (3) Where each product of geographical position and a covariate represents a spatially variant term. The models contained either a regular smooth or a spatially variant term of the same covariate.

From the candidate models, one model for each component was selected for overlap calculations based on minimisation of the Akaike Information Criterion (AIC) and maximisation of deviance explained after backwards elimination of non-significant predictors. The relationships between response and covariates were assessed by examining their robustness across model formulations, i.e., if the relationships were stable or varied, where the latter could indicate that the predictor captured residual variation in the model rather than a meaningful pattern. The models were visually inspected for residual correlation using the R-functions pacf (temporal correlation) and variog (spatial correlation, library geoR, [46]). None of the model residuals showed temporal autocorrelation, but the residuals of the capelin models using acoustic data were spatially autocorrelated. Since this may cause an underestimation of confidence intervals, we performed a wild bootstrap [47] on the capelin habitat models. The wild bootstrap followed the same steps implemented by Llope et al. [48] to model phytoplankton distribution in the North Sea. Specifically, year was treated as a sample unit, and all scaled residuals within a year were randomly switched in sign. The new residuals were added to the model predictions to fit a new GAM. The operation was repeated 1000 times to estimate mean and confidence intervals for each covariate response. However, the bootstrapped mean effects and confidence intervals were similar to those observed in the models (S2 Appendix). We therefore concluded that accounting for the residual autocorrelation would not alter our conclusions, and kept the original model formulations.

For cod, we also fit separate habitat models that included local capelin density as predictor (extended habitat models). These models were used for inference only, not for calculation of overlap.

Quantifying overlap.

To calculate overlap, the best candidate distribution model for each component was used to predict species density on a 35 x 35 nmi (65 x 65 km) regular grid of the study area with covariate values corresponding to the nearest observation from the central point of the grid cell in year t. The grid resolution was the same as the standard inter-station distance of the survey with the coarsest station grid (the ecosystem survey). By using a standard grid, the seasons and years could be compared, despite variation in survey design and execution. Grid cells containing fewer than 5 (autumn) or 8 (winter) observations across the study period, as well as cells falling outside the sampled area in year t, were eliminated from the grid. In this way, we only predicted on locations where the models had been given a reasonable amount of data. The overlap O_(x,y),t in position (grid cell) x,y in year t was then calculated for each combination of components, using the formula: (4) Where and are the predicted capelin and cod densities in the grid cell, and and are the maximum predicted densities in the same year and season. With this formulation, the overlap can range from 0 to 1, where 0 means that one or both species are absent from the grid cell, and 1 means that both species are present in their maximum predicted densities in that year and season. Note that the index is symmetric with respect to species. Thus, our overlap index gave spatially explicit information about how well cod and capelin densities matched in a given year and season. The correlation (Kendall’s rank correlation tau) between the predicted cod and capelin densities across the grid was also calculated for comparison with the spatially explicit overlap formulation. The overlap between all capelin and cod component combinations (autumn: 2, winter :4) were mapped for each year and season.

Finally, the mean overlap across the grid and the extent of the overlap (n grid cells with overlap > 0.001 divided by the total number of grid cells) were calculated for each year, season and cod-capelin component combination to get an overview of the temporal dimension of the overlap, i.e., the between-year variation in how well cod and capelin densities matched.

Factors affecting species distributions in autumn.

The estimated relationships between local densities and depth and temperature from the habitat models in autumn (Table 1) are shown in Fig 3. Capelin did not associate strongly with bottom depth, but occurred in lower than average densities in the deepest areas (Fig 3A). The relationship between temperature and capelin density was bimodal: higher capelin densities were found in sub-zero waters, and in temperatures of around 5°C (Fig 3B). However, the confidence intervals for depth and temperature were relatively wide, and the bootstrapped confidence intervals resulted in non-significant p-values (S2 Appendix).

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Fig 3. Autumn GAM smooth functions from the habitat models.

Non-linear regression between local densities of A-B) capelin, C-D) immature cod, and F-G) mature cod and the density-independent covariates depth (m) and temperature (°C). The effect of local capelin density (log₁₀[NASC+1]) from the extended habitat models on E) immature cod density and H) mature cod density is also shown. The plot shows the (centered) log local species density as a function of each covariate when accounting for the other covariate effects. The horizontal line at y = 0 represents a neutral contribution of the covariate to the response. The grey bands represent ± 2 standard errors around the smooth estimate.

https://doi.org/10.1371/journal.pone.0205921.g003

Capelin was mainly restricted to the central-northern parts of the Barents Sea, with a core distribution area east of Svalbard (Fig 4A). For capelin, an increase in stock biomass lead to an expansion of the core distribution area towards the north and south, as well as density increases in the core area and farther east (Fig 4A and 4B). This effect was significant across all models. Including a spatially variant effect of temperature further improved model fit, as increased temperature in the north-eastern area was associated with higher local capelin densities (Fig 5A). The final model for capelin in autumn explained 74.5% of the deviance and included, in addition to the effects described above, a locally linear effect of survey day (Table 1, S3 Appendix).

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Fig 4. Predicted autumn distributions.

Autumn distributions of A-B) capelin, C-D) immature cod, and E-F) mature cod, as predicted from the best candidate model for each component (Table 1). The different columns show the partial effects of stock biomass when the other model predictors were set to their across-year mean values at each location; the left column shows species distributions at low stock biomass (capelin: 0.628, cod: 1.63 million tonnes, measured in 2004), and the right at high stock biomass (capelin: 3.96, cod: 4.38 million tonnes, measured in 2013). The contour lines indicate local species density on the log-link scale, and the colours range from blue at low density to yellow at high density.

https://doi.org/10.1371/journal.pone.0205921.g004

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Fig 5. Spatially variant effect of temperature on local cod and capelin densities.

The contour lines show how the slope of the linear regression between local species density and mean pelagic temperature (capelin) or bottom temperature (cod) from the best candidate models vary in space for A) acoustically estimated capelin in autumn, B) immature cod in autumn, C) mature cod in autumn, D) acoustically estimated capelin in winter, E) trawl-caught capelin in winter, F) immature cod in winter, and G) mature cod in winter. Blue colours indicate negative slopes, and pink colours indicate positive slopes.

https://doi.org/10.1371/journal.pone.0205921.g005

Immature cod occurred in areas with slightly shallower bottom depths compared to mature cod (Fig 3C and 3F). Peak densities of both components fell within the range 150–200 m. Less than average cod densities were found in temperatures below 1°C, but above that any effect of temperature on mature cod was generally weak and variable (Fig 3G), while immature cod associated more strongly with water masses of intermediate temperature (2–5°C, Fig 3D). Including local capelin density as a predictor of local cod density, we found a positive association, though the effect was more variable for immature than mature cod at high capelin densities (Fig 3E and 3H). Including capelin gave a modest improvement in model fit compared to the basic habitat models (1–2% increase in deviance explained, Table 1). Both immature and mature cod were found throughout the study area, with density maxima both in central-northern and south-eastern Barents Sea (Fig 4C and 4E). The distributions of mature and immature cod were similar, but the highest mature cod densities occurred slightly east of the immature cod density maximum in the north. The spatially variant effect of cod stock biomass on cod density was significant across model formulations for both immature and mature cod. As stock biomass increased, the main density increases for both components occurred in the north/north-eastern part of the study area (Fig 4C–4F). Including a spatially variant effect of bottom temperature further improved model fit (Table 1). Here, an increase in density of both components coincided with increasing bottom temperatures in the north-easternmost corner of the study area (Fig 5B and 5C). Finally, spatially variant effects of survey day were also retained in the final models for cod in autumn, which explained 62.5% and 58.6% of the deviance for immature and mature cod, respectively (Table 1, S3 Appendix).

For all autumn models, the effect size of stock biomass was larger than that of temperature as judged by the difference in AIC between the habitat models and the candidate models with the respective spatially variant term (Table 1).

Factors affecting species distributions in winter.

The estimated relationships between local species densities and depth and temperature from the habitat models in winter (Table 1) are shown in Fig 6. Higher than average densities of acoustic capelin were found in shallow areas and in the deepest areas, though variability in the response was high at large depths (Fig 6A, see also S2 Appendix; depth was non-significant after the wild bootstrap). Trawl capelin occupied the shallow part of the depth range (Fig 6C), but note that in the best candidate models, depth was non-significant for both capelin components (Table 1). The acoustic capelin was strongly and positively associated with the coldest waters (< 2°C, Fig 6B), reflecting the northern distribution, while the highest trawl catches of capelin coincided with the lowest and highest temperatures, but not those in between (Fig 6D). However, the number of observations at these temperature extremes were relatively few, and there was high variability in the response.

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Fig 6. Winter GAM smooth functions from the habitat models.

Non-linear regression between local densities of A-B) capelin sampled acoustically, C-D) capelin sampled with demersal trawl, F-G) immature cod, J-K) mature cod, and depth (m) and temperature (°C). The effect of local acoustic (log₁₀[NASC+1]) and trawl capelin (log₁₀[ind x nmi^-2+1]) densities from the extended habitat models are shown for H-I) immature cod and L-M) mature cod. The plot shows the (centered) log local species density as a function of the covariate when accounting for the other covariate effects. The horizontal line at 0 corresponds to a neutral contribution of the covariate to the response. The grey bands illustrate ± 2 standard errors around the smooth estimate. Panel E) shows probability density distributions of capelin length in demersal trawl hauls south and north of 74°. The distributions were calculated from the catch numbers of capelin in each 1 cm-length group using R base function “density” with default settings. Capelin matures at approximately 14 cm [23].

https://doi.org/10.1371/journal.pone.0205921.g006

Partly different geographic distributions were evident from the two sampling methods; the main concentrations of capelin sampled acoustically were found in the central Barents Sea (Fig 7A and 7B), while high densities were caught in the demersal trawl around Svalbard, but also in an area extending across the central areas down to the Norwegian/Russian coasts (Fig 7C and 7D). Smaller individuals dominated the demersal trawl catch in the north, while larger individuals dominated in hauls from the south (Fig 6E). Comparatively lower densities of capelin were measured acoustically along the coast (Fig 7A).

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Fig 7. Predicted winter distributions.

Winter distributions of A-B) acoustically estimated capelin, C-D) trawl-caught capelin, E-F) immature cod, and G-H) mature cod from the best candidate model for each component (Table 1). The different columns show the partial effects of stock biomass when the other model predictors were set to their across-year mean values in each location; the left column shows species distributions at low stock biomass (capelin: 0.628, cod: 1.63 million tonnes, measured in 2004), and the right at high stock biomass (capelin: 3.96, cod: 4.38 million tonnes, measured in 2013). The contour lines indicate local species density on the log-link scale, and the colours range from blue at low density to yellow at high density.

https://doi.org/10.1371/journal.pone.0205921.g007

The best models for capelin (both acoustics and trawl) in winter included spatially variant effects of temperature (Table 1). For acoustic capelin, there were negative effects of temperature in the central Barents Sea and along the eastern Norwegian/Russian coasts (Fig 5D), while for trawl capelin, local density decreased with temperature in the north, and increased with temperature in the south (Fig 5E). The effect size of temperature was larger than that of biomass for acoustic capelin, while the biomass effect was larger for trawl capelin (Table 1). The final models explained 67.3% and 39.6% of the deviance for acoustic and trawl capelin, respectively, and also included spatially variant effects of survey day (S3 Appendix) and capelin biomass (Fig 7A–7D).

In winter, immature and mature cod were associated with similar depths as in autumn, that is between 150–200 m (Fig 6F and 6J), while they occupied a narrower and warmer range of temperatures in winter (approx. 2–6°C Fig 6G and 6K). The overall association between acoustic capelin and both immature and mature cod was weak in winter (Fig 6H and 6L). Immature cod had a negative association with trawl capelin (Fig 6I), while mature cod was positively associated with the highest trawl capelin densities (Fig 6M). However, including capelin (either trawl or acoustics) as a predictor contributed little to improving model fits, or even reduced the explained deviance (Table 1).

Cod was found throughout the study area, with density peaks of immature cod in the western- and easternmost areas (Fig 7E) while mature cod occurred in higher densities closer to the Norwegian coast (Fig 7G). Stock biomass was important for explaining variation in the local density of both cod components; the areas of high immature cod density in the east expanded as stock biomass increased (Fig 7E and 7F), while mature cod density increased with stock biomass throughout most of the surveyed area (Fig 7G and 7H). Increased local temperature was associated with an increase in immature cod density in the north and east, and a weak decrease in density in the south-west (Fig 5F). Temperature had a small positive effect on mature cod density in the north (Fig 5G). The effect size of stock biomass was larger than that of temperature for both components (Table 1). The final models for immature and mature cod in winter also included spatially variant effects of survey day (S3 Appendix), and explained 55.5% and 57.4% of the deviance, respectively (Table 1).

Cod-capelin overlap in autumn.

Capelin was distributed in a comparatively smaller area than cod, mainly restricted to the central-northern parts of the Barents Sea (Fig 4). The main overlap area between cod and capelin coincided with the main distribution area of capelin in all years (Fig 8A, S3 Appendix). The mean overlap was higher between mature cod and capelin compared to the immature cod and capelin overlap in the beginning of the time series, but became similar towards the end as the overlap between immature cod and capelin increased (Fig 9, upper left panel). The overlap between immature cod and capelin was low when both stocks were at a relatively low level (2004), high when both stocks were at a high level (2013) and remained high as the cod stock remained at a high level and the capelin stock had collapsed (2015, Fig 8A, upper panel). There were less clear temporal trends in the overlap between mature cod and capelin (Fig 8A, lower panel). The overlap extent (number of grid cells with overlap > 0.001) between immature cod and capelin showed a positive trend across the study period, while the extent was more variable for the mature cod-capelin overlap (Fig 9, lower left panel).

Cod-capelin overlap in winter.

Cod had a wider distribution than capelin also in winter (Fig 7). Immature cod overlapped with acoustic capelin mainly near the northern limit of the area covered by the winter survey, except in the first years when they also overlapped farther south (Fig 8B, upper panels, S3 Appendix). There was also a region of overlap between immature cod and trawl capelin in the central-eastern part of the surveyed area and along the coast of Norway and Russia (Fig 8B, second row panels). Mature cod had a more southerly distribution than immature cod and this was reflected in the overlap with capelin. The highest overlap was along the Russian and Norwegian coasts; this was particularly pronounced for overlap with trawl capelin (Fig 8B, lower panels). There was also some overlap with acoustic capelin in the south and north (Fig 8B, third row panels). The highest mean overlap in winter was between mature cod and trawl capelin, and this overlap increased over time (Fig 9, upper right panel). The overlap extent was highly variable in winter for all component pairs, but increased over time for both the immature and mature cod-trawl capelin components (Fig 9, lower right panel).