Larger but younger fish when growth outpaces mortality in heated ecosystem
Figures
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig1-v1.tif/full/617,/0/default.jpg)
Map of the area with the unique whole-ecosystem warming experiment from which perch in this study was sampled.
Inset shows the 1 km2 enclosed coastal bay that has been artificially heated for 23 years, the adjacent reference area with natural temperatures, and locations of the cooling water intake, and where the heated water outlet from nuclear power plants enters the heated coastal basin. The arrows indicate the direction of water flow.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-v1.tif/full/617,/0/default.jpg)
Fish grow faster and reach larger sizes in the heated enclosed bay (red) compared to the reference area (blue).
Points depict individual-level length-at-age and lines show the median of the posterior draws of the global posterior predictive distribution (without group-level effects), both exponentiated, from the von Bertalanffy growth model with area-specific coefficients. The shaded areas correspond to 50% and 90% credible intervals.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp1-v1.tif/full/617,/0/default.jpg)
Prior predictive distribution for the von Bertalanffy growth equation (posterior draws from the prior only, ignoring the likelihood).
The solid line is the median and the shaded area is the 95% credible interval.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp2-v1.tif/full/617,/0/default.jpg)
The best model of the von Bertalanffy growth equation: (A) trace plot to illustrate chain convergence for key (population-level) parameters, (B) residuals, (C) QQ-plot, and (D) posterior predictive check.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp3-v1.tif/full/617,/0/default.jpg)
Cohort-specific predictions from the best von Bertalanffy model (i.e. with cohort-specific and ).
Points correspond to data; solid lines correspond to the median of the posterior prediction from the model and the shaded area corresponds to the 95% credible interval.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp4-v1.tif/full/617,/0/default.jpg)
The average length-at-age is larger for fish of all ages in the heated enclosed bay compared to the reference area, and the relative difference declines very slightly with age.
Violin plots depict size-at-age in the heated relative to the reference area, based on draws from an expectation of the posterior predictive distribution (without random effects). The points and vertical lines depict the median and the interquartile range.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp5-v1.tif/full/617,/0/default.jpg)
Posterior distributions of the cohort-varying parameter in the best von Bertalanffy growth model.
Points correspond to the median and the horizontal lines correspond to the 95% credible interval. Note that the distributions of in the warm areas extend beyond the x-axis for cohorts 1995–1997 (also evident in Figure 3). The range of the x-axis was set to be wide enough to include the posterior medians of the larger estimates but narrow enough to allow for comparison between the other cohorts and areas.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp6-v1.tif/full/617,/0/default.jpg)
Posterior distributions of the cohort-varying parameter in the von Bertalanffy model.
Points correspond to the median and the horizontal lines correspond to the 95% credible interval.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp7-v1.tif/full/617,/0/default.jpg)
Prior vs posterior distributions for parameters (A), (B) and (C) in the best model of the von Bertalanffy growth equation.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp8-v1.tif/full/617,/0/default.jpg)
Posterior distributions of (A) and (B) for both areas and the distribution of their difference (C, D).
Panel (A) depicts the posterior distributions for the Brody growth coefficient (parameters (red) and (blue)) and (B) the distribution of their difference. Panel (C) depicts the posterior distributions for asymptotic length (parameters and ), and (D) the distribution of their difference (3%). The fill color depicts the area below 0 (3% and 11% for and , respectively).
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp9-v1.tif/full/617,/0/default.jpg)
Analysis of sensitivity of including the most recent cohorts, with a smaller age range and, therefore, less certain estimates of .
Panel (A) depicts the predicted size-at-age from the full model (green) and the same model fitted without cohorts 1995–1997. The violin plots depict size-at-age in the heated relative to the reference area, based on draws from an expectation of the posterior predictive distribution (without random effects). The points and vertical lines depict the median and the interquartile range. Panels (B) and (C) depict the posterior distribution of differences in and , respectively, where color again indicates full or subset models.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig2-figsupp10-v1.tif/full/617,/0/default.jpg)
Analysis of sensitivity of including the most recent cohorts, with a smaller age range and, therefore, less certain estimates of .
The distributions depict the differences between the full and the subset models' posterior distributions for , with colors corresponding to the estimate for the heated and reference area.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig3-v1.tif/full/617,/0/default.jpg)
The faster growth rates in the heated area (red) compared to the reference (blue) are maintained as fish grow in size.
The points illustrate specific growth rate estimated from back-calculated length-at-age (within individuals) as a function of length, expressed as the geometric mean of the length at the start and end of the time interval. Lines show the median of the posterior draws of the global posterior predictive distribution (without group-level effects) from the allometric growth model with area-specific coefficients. The shaded areas correspond to the 90% credible interval. The equation uses mean parameter estimates. Panel (B) shows the posterior distributions for initial growth ( (red) and (blue)), and (C) the distribution of their difference. Panel (D) shows the posterior distributions for the allometric exponent ( and ), and (E) the distribution of their difference. The fill color depicts the area below 0 (0.3% and 0.2% for and , respectively).
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig3-figsupp1-v1.tif/full/617,/0/default.jpg)
Prior predictive distribution for the allometric growth model (posterior draws from the prior only, ignoring the likelihood).
The solid line is the median and the shaded area is the 95% credible interval.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig3-figsupp2-v1.tif/full/617,/0/default.jpg)
The best allometric growth model: (A) trace plot to illustrate chain convergence for key (population-level) parameters, (B) residuals, (C) QQ-plot, and (D) posterior predictive check.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig3-figsupp3-v1.tif/full/617,/0/default.jpg)
Prior vs posterior distributions for parameters (A) and (B) in the best allometric growth model (inset in panel (B) is a zoomed-in version to better visualize the priors in the range of the posteriors).
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig4-v1.tif/full/617,/0/default.jpg)
The instantaneous mortality rate () is higher in the heated area (red) than in the reference (blue).
Panel (A) shows as a function of , where the slope corresponds to . Lines show the median of the posterior draws of the global posterior predictive distribution (without group-level effects) and the shaded areas correspond to the 50% and 90% credible intervals. The equation shows mean parameter estimates. Panel (B) shows the posterior distributions for mortality rate ( and ), and (C) the distribution of their difference, where the fill color depicts the area below 0 (0.07%).
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig4-figsupp1-v1.tif/full/617,/0/default.jpg)
Catch per unit effort (CPUE) as a function of age, by area and year, for determining which ages are representatively caught by the fishing gear.
Since the CPUE starts to decline for fish older than 2 years, we selected only fish aged three or older for the catch curve regression analysis. Colors indicate catch year.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig4-figsupp2-v1.tif/full/617,/0/default.jpg)
The best catch curve model: (A) trace plot to illustrate chain convergence for key (population-level) parameters, (B) residuals, (C) QQ-plot, and (D) posterior predictive check.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig5-v1.tif/full/617,/0/default.jpg)
The heated area (red) has a larger proportion of large fish than the reference area (blue), illustrated both in terms of histograms of proportions at size (A) and the biomass size-spectrum (B, C), but the difference in the slope of the size spectra between the areas is not statistically clear (C).
Panel (A) illustrates histograms of length groups in the heated and reference area as proportions (for all years pooled). Panel (B) shows the estimate of the size-spectrum exponent, , where vertical lines depict the 95% confidence interval. Panel (C) shows the size distribution and MLEbins fit (red and blue solid curves for the heated and reference area, respectively) with 95% confidence intervals indicated by dotted lines. The vertical span of rectangles illustrates the possible range of the number of individuals with body mass ≥ the body mass of individuals in that bin.
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig6-v1.tif/full/617,/0/default.jpg)
The average size is larger (A, B), but the average age (C, D) is younger in the heated area compared to the reference area.
The violin plots (A, C) are based on draws from the global posterior predictive distribution (without group-level effects) for mean size and age from the lognormal model, respectively, with the random year effect omitted, while the density plots (B, D) depict the difference between areas based on draws from the expected value of the posterior predictive distribution. Hence, the latter has a smaller variation and the difference in means is more pronounced. The average size is 2 cm larger in the heated area, and the average age is 0.4 years younger (B, D).
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig6-figsupp1-v1.tif/full/617,/0/default.jpg)
Size (top) and age (bottom) distribution of catches, all years pooled, as used in the lognormal model estimate the mean size and catch.
Heated area is shown in the left column (in red) and the reference area in the right (blue).
![](https://iiif.elifesciences.org/lax:82996%2Felife-82996-fig6-figsupp2-v1.tif/full/617,/0/default.jpg)
Lognormal length and age models model diagnostics and fit.
(A–B) trace plot to illustrate chain convergence for key (population-level) parameters in the lognormal length and age models (respectively), (C–D) posterior predictive checks for the length and the age model, respectively.
Additional files
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Supplementary file 1
Expected log pointwise density (elpd) for different growth models.
(a) Comparison of von Bertalanffy growth models with different combinations of shared and area-specific parameters (ordered by the difference in expected log pointwise density (elpd) from the best model). Note that in all models, and vary among cohorts. (b) Comparison of allometric growth models with common or unique -parameter (exponent in the allometric growth model), ordered by the difference in expected log pointwise density (elpd) from the best model.
- https://cdn.elifesciences.org/articles/82996/elife-82996-supp1-v1.docx
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MDAR checklist
- https://cdn.elifesciences.org/articles/82996/elife-82996-mdarchecklist1-v1.docx