Ectotherm species, constituting 99% of species globally (Atkinson and Sibly, 1997; Wilson, 1992), are commonly predicted to shrink in a warming world (Gardner et al., 2011; Sheridan and Bickford, 2011). However, as the size distribution of many species spans several orders of magnitude, and temperature effects on size may depend on size or age, it is important to be specific about which sizes- or life stages are predicted to shrink (usually mean or adult is meant). For instance, warming can shift size distributions without altering mean size if increases in juvenile size-at-age outweigh the decline in size-at-age in adults, which is consistent with the temperature size rule, TSR (Atkinson, 1994). Resolving how warming induces changes in population’s size distribution may thus be more instructive (Fritschie and Olden, 2016), especially for inferring warming effects on species’ ecological role, biomass production, or energy fluxes (Gårdmark and Huss, 2020; Yvon-durocher et al., 2011). This is because key processes such as metabolism, feeding, growth, and mortality scale with body size (Andersen and Link, 2020; Blanchard et al., 2017; Brown et al., 2004; Pauly, 1980; Thorson et al., 2017; Ursin, 1967). Hence, as the value of these traits at mean body size is not the same as the mean population trait value (Bernhardt et al., 2018), the size distribution within a population matters for its dynamics and for how it changes under warming.

The population size distribution can be represented as a size-spectrum, which generally is the frequency distribution of individual body sizes (Edwards et al., 2017). It is often described in terms of the size-spectrum slope (slope of individuals or biomass of a size class over the mean size of that class on a log-log scale [Edwards et al., 2017; Sheldon et al., 1973; White et al., 2007]) or simply the exponent of the power law individual size distribution (Edwards et al., 2017). The size-spectrum thus results from temperature-dependent ecological processes such as body growth, mortality, and recruitment (Blanchard et al., 2017; Heneghan et al., 2019). Despite its rich theoretical foundation (Andersen, 2019) and usefulness as an ecological indicator (Blanchard et al., 2005), few studies have evaluated warming effects on the species size-spectrum in larger-bodied species (but see Blanchard et al., 2005), and none in large scale experimental set-ups. There are numerous paths by which a species’ size-spectrum could change with warming (Heneghan et al., 2019). For instance, in line with TSR predictions, warming may lead to a smaller size-spectrum exponents (steeper slope) if the maximum size declines. However, changes in size-at-age and the relative abundances of juveniles and adults may alter this decline in the size-spectrum slope. Warming can also lead to elevated mortality (Barnett et al., 2020; Berggren et al., 2022; Biro et al., 2007; Pauly, 1980), partly because a faster pace of life with higher metabolic rates is associated with a shorter lifespan (Brown et al., 2004; Munch and Salinas, 2009) or due to direct lethal effects of extreme temperature events. This truncates the age distribution towards younger individuals (Barnett et al., 2017), which may reduce density dependence and potentially increase growth rates, thus countering the effects of mortality on the size-spectrum exponent. However, not all sizes may benefit from warming, as e.g. the optimum temperature for growth declines with size (Lindmark et al., 2022). Hence, the effect of warming on the size-spectrum depends on several interlinked processes affecting abundance-at-size and size-at-age.

Size-at-age is generally predicted to increase with warming for small individuals, but decrease for large individuals according to the mentioned TSR (Atkinson, 1994; Ohlberger, 2013). Several factors likely contribute to this pattern, such as increased allocation to reproduction (Wootton et al., 2022) and larger individuals in fish populations having optimum growth rates at lower temperatures (Lindmark et al., 2022). Empirical support in fishes for this pattern seems to be more consistent for increases in size-at-age of juveniles (Huss et al., 2019; Rindorf et al., 2008; Thresher et al., 2007) than declines in adult size-at-age (but see Baudron et al., 2014; Oke et al., 2022; Smoliński et al., 2020), for which a larger diversity in responses is observed among species (Barneche et al., 2019; e.g., Huss et al., 2019). However, most studies have been done on commercially exploited species, since long-time series are more common in such species. This may confound or interact with the effects of temperature because fishing mortality can affect density-dependent growth (van Gemert et al., 2018), but also select for slow-growing individuals and changes in maturation processes, which also influences growth trajectories (Audzijonyte et al., 2016).

The effect of temperature on mortality rates of wild populations is often studied using among-species analyses (Pauly, 1980; Thorson et al., 2017). These relationships based on thermal gradients in space may not necessarily be the same as the effects of warming on mortality in single populations. Hence, the effects of warming on growth and size-at-age, and mortality within natural populations constitute a key knowledge gap for predicting the consequences of climate change on population size spectra.

Here, we used data from a unique, large-scale 23-year-long heating experiment of a coastal ecosystem to quantify how warming changed fish body growth, mortality, and the size structure in an unexploited population of Eurasian perch (Perca fluviatilis, ‘perch’). We compare fish from this enclosed bay exposed to temperatures approximately 5–10 °C above normal (‘heated area’) with fish from a reference area in the adjacent archipelago (Figure 1). Using hierarchical Bayesian models, we quantify differences in key individual- and population-level parameters, such as body growth, asymptotic size, mortality rates, and size spectra, between the heated and reference coastal areas.

Figure 1

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Analysis of perch size-at-age using the von Bertalanffy growth equation (VBGE) revealed that fish cohorts (year classes) in the heated area both grew faster initially (larger size-at-age) and reached larger predicted asymptotic sizes than those in the unheated reference area (Figure 2). The model with area-specific VBGE parameters ($L_{\infty }$ , $K$, and $t_0$) had the best out-of-sample predictive accuracy (the largest expected log pointwise predictive density for a new observation; Supplementary file 1a). Models where both $L_{\infty }$ and $K$ were shared did not converge (Supplementary file 1a). Both the estimated values for fish asymptotic length ($L_{\infty }$) and growth coefficient ($K$) were larger in the heated compared to the reference area (Figure 2—figure supplement 8). We estimated that the asymptotic length of fish in the heated area was 16% larger than in the reference area (calculated as $\frac{L_{\infty \mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}-L_{\infty \mathrm{r}\mathrm{e}\mathrm{f}}}{L_{\infty \mathrm{r}\mathrm{e}\mathrm{f}}}$) ($L_{\infty \mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}=45.7[36.8,56.3]$, $L_{\infty \mathrm{r}\mathrm{e}\mathrm{f}}=39.4\left[35.4,43.9\right]$ , where the point estimate is the posterior median and values in brackets correspond to the 95% credible interval). The growth coefficient was 27% larger in the heated area (${\displaystyle K_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}=0.19[0.15,0.23]}$, ${\displaystyle K_{\mathrm{r}\mathrm{e}\mathrm{f}}=0.15[0.12,0.17]}$). These differences in growth parameters lead to fish being approximately 7%–11% larger in the heated area at any age relative to the reference area (Figure 2—figure supplement 4). Due to the last three cohorts (1995–1997) having large estimates of $L_{\infty \mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}$ and low $K$ (potentially due to their negative correlation and because of the young age with data far from the asymptote, Figure 2—figure supplements 3 and 5–6), we fit the same model with these cohorts omitted to evaluate the importance of those for the predicted difference between the areas. Without these, the predicted difference in size-at-age was still clear, but smaller (between 4%–7%, Figure 2—figure supplements 9–10).

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In addition, we found that growth rates in the reference area were both slower and declined faster with size compared to the heated area (Figure 3). The best model for growth ($G=\alpha L^{\theta }$) had area-specific $\alpha$ and $\theta$ parameters (Supplementary file 1b). Initial growth ($\alpha$) was estimated to be 18% faster in the heated than in the reference area (${\alpha }_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}=512\left[\mathrm{462,565}\right]$, ${\alpha }_{\mathrm{r}\mathrm{e}\mathrm{f}}=433\left[\mathrm{413,454}\right]$), and the growth of fish in the heated area declines more slowly with length than in the reference area (${\theta }_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}=-1.13[-1.16,-1.11]$, ${\theta }_{\mathrm{r}\mathrm{e}\mathrm{f}}=-1.18[-1.19,-1.16]$). The distribution of differences of the posterior samples for α and only had 0.3% and 0.2% of the density below 0, respectively (Figure 3C and E), indicating a high probability that length-based growth rates are faster in the heated area.

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By analyzing the decline in catch-per-unit-effort over age, we found that the instantaneous mortality rate $Z$ (the rate at which log abundance declines with age) is higher in the heated area (Figure 4). $Z$ was estimated as a fixed effect, as the model where only intercepts varied among years had the best out-of-sample predictive ability. The overlap with zero is 0.07% for the distribution of differences between posterior samples of $Z_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}$ and $Z_{\mathrm{r}\mathrm{e}\mathrm{f}}$ (Figure 4C). We estimated $Z_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}$ to be 0.73 [0.66,0.79] and $Z_{\mathrm{r}\mathrm{e}\mathrm{f}}$ to be 0.62 [0.58,0.67], which corresponds to annual mortality rates (calculated as $1-e^{-Z}$) of 52% in the heated area and 46% in the reference area.

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Lastly, analysis of the size- and age-structure in the two areas revealed that, despite the faster growth rates, higher mortality, and larger maximum sizes in the heated area Figure 5A, the size-spectrum exponents were largely similar Figure 5B, C. In fact, the size-spectrum exponent was only slightly larger in the heated area (Figure 5B), and their 95% confidence intervals largely overlap. However, results from the lognormal model fitted to the size- and age-distributions revealed that the average size was two centimeters longer and the average age 0.4 years younger in the heated compared to the reference area (Figure 6).

Figure 5

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Our study provides strong evidence for warming-induced differentiation in growth and mortality in a natural population of an unexploited, temperate fish species exposed to an ecosystem-scale experiment with 5–10°C above normal temperatures for more than two decades. Interestingly, these effects largely, but not completely, counteract each other when it comes to population size-structure—while the fish are younger, they are also larger on average. However, differences in the rate of decline in abundance with size are less pronounced between the areas. It is difficult to generalize these findings since it is a study of only a single species. It is, however, a unique climate change experiment, as experimental studies on fish to date are much shorter and often on scales much smaller than whole ecosystems, and long-time series of biological samples exist mainly for commercially exploited fish species (Baudron et al., 2014; Smoliński et al., 2020; Thresher et al., 2007) (in which fisheries exploitation affects size-structure both directly and indirectly by selecting for fast-growing individuals). While factors other than temperature could have contributed to the observed elevated growth and mortality, the temperature contrast is unusually large for natural systems (i.e. 5–10°C, which can be compared to the 1.35°C change in the Baltic Sea between 1982 and 2006 [Belkin, 2009]). Moreover, heating occurred at the scale of a whole ecosystem, which makes the findings highly relevant in the context of global warming.

Interestingly, our findings contrast with both broader predictions about declining mean or adult body sizes based on the GOLT hypothesis (Cheung et al., 2013; Pauly, 2021), and with intraspecific patterns such as the TSR (temperature-size rule, Atkinson, 1994). The contrasts lie in that both asymptotic size and size-at-age of mature individuals, as well as the proportion of larger individuals, were slightly larger and higher in the heated area—despite the elevated mortality rates. This result was unexpected for two reasons: optimum growth temperatures generally decline with body size within species under food satiation in experimental studies (Lindmark et al., 2022), and fish tend to mature at smaller body sizes and allocate more energy into reproduction as it gets warmer (Niu et al., 2023; Wootton et al., 2022). Both patterns have been used to explain how growth can increase for small and young fish, while large and old fish typically do not benefit from warming. Our study species is no exception to these rules (Huss et al., 2019; Karås and Thoresson, 1992; Niu et al., 2023; Sandstrom et al., 1995). This suggests that growth dynamics under food satiation may not be directly proportional to those under natural feeding conditions (Railsback, 2022). It could also mean that while temperatures is near optimum for growth in the warmest months of the year for a 15 cm individual (and above optimum for larger fish as the optimum declines with size) (Huss et al., 2019; Lindmark et al., 2022), the exposure to such high temperatures is not enough to cause strong reductions in growth and eventually size-at-age. Our results highlight that we need to focus on understanding to what extent the commonly observed increase in size-at-age for juveniles in warm environments can be maintained as they grow older.

Our finding that mortality rates were higher in the heated area was expected—warming leads to faster metabolic rates (faster ‘pace of life’), which in turn is associated with a shorter life span (Brown et al., 2004; McCoy and Gillooly, 2008; Munch and Salinas, 2009). Extreme temperatures, which may be more common in warmed systems under natural variability, can also be lethal if e.g., acute oxygen demands cannot be met (Sandblom et al., 2016). Warming may further increase predation mortality, as predators’ feeding rates increase in order to meet the higher demand for food (Biro et al., 2007; Pauly, 1980; Ursin, 1967). However, most evidence to date of the temperature dependence of mortality rates in natural populations stems from across-species studies (Gislason et al., 2010; Pauly, 1980; Thorson et al., 2017, but see Berggren et al., 2022; Biro et al., 2007). Across-species relationships are not necessarily determined by the same processes as within-species relationships; thus, our finding of warming-induced mortality in a heated vs control environment in two nearby con-specific populations is important.

Since a key question for understanding the implications of warming on ectotherm populations is if larger individuals in a population become rarer or smaller (Ohlberger, 2013; Ohlberger et al., 2018), within-species mortality and growth responses to warming need to be further studied. Importantly, this requires accounting also for the effects of warming on growth, and how responses in growth and mortality depend on each other. For instance, higher mortality (predation or natural, physiological mortality) can release intra-specific competition and thus increase growth. While e.g., benthic invertebrate density was not affected by the initial warming of the heated area (Sandstrom et al., 1995), warming-induced mortality may have led to higher benthic prey availability per capita for the studied perch. Conversely, altered growth and body sizes can lead to changes in size-specific mortality, such as predation or starvation, both of which are expected to change with warming (Thunell, 2023). In conclusion, individual-level patterns such as the TSR can only be used to predict changes in the population-level size structure in limited cases, as it does not concern changes in abundance-at-size via mortality. Mortality may, however, be an important driver of the observed shrinking of ectotherms (Peralta-Maraver and Rezende, 2021). Understanding the mechanisms by which the size- and age-distribution change with warming is critical for predicting how warming changes species functions and ecological roles (Audzijonyte et al., 2020; Fritschie and Olden, 2016; Gårdmark and Huss, 2020). Our findings demonstrate that a key to do this is to acknowledge temperature effects on both growth and mortality and how they interact.

All raw data and R code to clean and reproduce the results reported in this paper are available on GitHub (copy archived at Lindmark, 2023) and have been deposited on Zenodo.

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Decision letter after peer review:

Thank you for submitting your article "Faster growth rates and higher mortality but similar size-spectrum in heated, large-scale natural experiment" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Meredith Schuman as the Senior Editor. The following individual involved in the review of your submission has agreed to reveal their identity: Christine Stawitz (Reviewer #1).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

Both reviewers raised questions about the validity/meaning of CPUE values for different treatments. Please revise in response to these comments and amend the text when possible.

Reviewer #1 (Recommendations for the authors):

Congratulations on an excellent paper – I really enjoyed reading it.

58: Is this a common way of measuring changes in size? Looking strictly at mean body size (w/o age structure) seems simplistic – but a citation would convince me this is a common practice

240 – 244: There was a bit more information in your Github repository – it looks like you started with the default priors then had to tighten them to achieve convergence in some of the VBGF models? I agree this is too much detail to include in the main body of the paper but for future scientists' use, I would recommend adding a supplementary section describing how you did this and a table with the priors you used so readers can find them without going to Github.

376: please add the full citation.

Figure 4A: Does it mean anything that CPUE has a lower rate at the beginning of the time series in the heated area than the unheated area? Or is the slope the only thing that matters?

Equations 1- 12: I find it confusing to reuse mu, eta, and σ throughout the three different modeling approaches and would prefer to see a unique letter applied for each of the three models to improve clarity.

Reviewer #2 (Recommendations for the authors):

I'd like to see more consideration of faster life history vs higher mortality in this paper. Have these fish adapted a faster life history in response to warmed conditions that happen to result in higher mortality because of the demands of the faster pace of life? Or, given that adults did not shrink, is the increased mortality due to some other factor, like increased predation or stress from the heat? Perhaps this cannot be answered in this system, but it seems like a worthwhile consideration, especially given the unexpected results.

I did have some more substantial questions on the CPUE section, which I'll try to put together here. It seems that CPUE is always lower for the heated population. Could the unexpected increased size observed in heated adults be due to a tradeoff between slower growth due to temperature but higher growth due to a release from density dependence? I think the authors suggest this might be the case, but it would be helpful to state it more explicitly.

Can the authors explain how the initial population size is known and whether it differs between the heated and reference population? It seems there are many reasons why reproductive potential could differ between the heated and reference populations, especially if warming shifts reproductive investment (as would be expected). Why does the CPUE figure start at age 3? It seems younger fish were caught and the fishbase entry on perch says they can mature earlier than 3. Is the mortality rate they measure only applied to fish that have been 'recruited' to the survey? And if fish can mature younger than 3, are some being missed by looking at CPUE for 3+ only?

Finally, the grammar could use some editing, although the errors do not impact readability. I've made a few suggestions below but did not point out all places where grammar could be improved.

Reviewer #1 (Recommendations for the authors):

Congratulations on an excellent paper – I really enjoyed reading it.

58: Is this a common way of measuring changes in size? Looking strictly at mean body size (w/o age structure) seems simplistic – but a citation would convince me this is a common practice

Thank you. We think statements/predictions about shrinking (without specific mentioning of the age and/or size-structure) often is made when talking about “large scale” or general shrinking of organisms as a universal rule. The temperature-size rule (TSR) on the other hand, which we describe in more detail further down (line 68) describes changes in size over ontogeny, and hence does not make predictions about the size-distribution of organisms or populations, which is also affected by other processes such as mortality. The reason we open the introduction with the universal prediction about shrinking (and the papers we cite here do focus on average shrinking of species or taxa, to address your specific question) is to make it clear that the predictions about organism shrinking with warming is based on various, sometimes related, biogeographical pattens across space and time, and on the other hand, individual-level experimental rules. Therefore, we think there is a need to distinguish these patterns and rules because there are situations where they do not conform. The example we give is that the TSR predicts larger size-at-age for young specimens, meaning that mortality (and/or shrinking of adults) must increase to offset that size-increase for population-level shrinking to occur.

We have edited the second sentence (lines 64–66) to make it clearer.

240 – 244: There was a bit more information in your Github repository – it looks like you started with the default priors then had to tighten them to achieve convergence in some of the VBGF models? I agree this is too much detail to include in the main body of the paper but for future scientists' use, I would recommend adding a supplementary section describing how you did this and a table with the priors you used so readers can find them without going to Github.

Thank you for pointing out that need. Perhaps a detail, but for the record, brms forces the user to specify priors in non-linear models, so we never started with the standard default priors that are used for general regression parameters. Instead, we first defined broad priors centered on what we believed were reasonable values for this fish species, and then progressively tightened them until convergence was achieved. We have added text in the model fitting paragraph (lines 330–338) describing the iterative approach to finding priors for the non-linear model and removed the single sentence describing this approach under each model description and a reference. All priors are given in the main text under each model with in-line equations, so perhaps it is not needed to put them also in a table.

376: please add the full citation.

Done

Figure 4A: Does it mean anything that CPUE has a lower rate at the beginning of the time series in the heated area than the unheated area? Or is the slope the only thing that matters?

We are not sure what is meant by “a lower rate of CPUE (catch per unit effort) in the beginning of the time series”, but we suspect the reviewer means that the catch rate is lower in the heated area on average (since Figure 4 depicted data and the global prediction without the random cohort effect). For mortality estimates, the slope is what matters, because it relates to the instantaneous mortality parameter in a population with exponential decay when log transformed, whereas the intercept does not matter directly for the mortality estimate. Note also that we have added a model for the average age, which is complementary to the analysis of mortality but is conceptually a different approach to showing the same thing: that the heated population consists of younger fish. As also Reviewer#2 pointed out, we do observe a difference in CPUE between the areas (i.e., the intercept), but we can only speculate why this is (possibly linked to size of the habitat).

Equations 1- 12: I find it confusing to reuse mu, eta, and σ throughout the three different modeling approaches and would prefer to see a unique letter applied for each of the three models to improve clarity.

We thought about this but decided that it would probably be clearer to have a unique letter for the response variable, and a general definition for the parameters of the distribution, e.g., L_i for length and G_i for growth and mu for the mean of the distribution in question. The alternative would be to add more subscripts, but we have already 3 levels of subscripts in some models, and adding another level make it difficult to read. Instead, we hope the structure of the methods (one paragraph per model) the variable spelled out or abbreviated makes it clear that these are separate models.

Reviewer #2 (Recommendations for the authors):

I'd like to see more consideration of faster life history vs higher mortality in this paper. Have these fish adapted a faster life history in response to warmed conditions that happen to result in higher mortality because of the demands of the faster pace of life? Or, given that adults did not shrink, is the increased mortality due to some other factor, like increased predation or stress from the heat? Perhaps this cannot be answered in this system, but it seems like a worthwhile consideration, especially given the unexpected results.

It is difficult to say with the data we have available, and it becomes speculative. Since there are other fish predators (mainly pike and larger perch), which also need to feed at higher rates in the warmer water, it seems inevitable that higher predation mortality to some degree contributes to the higher mortality in perch. However, we do not know nor have any way of testing with the data we have available how important this is compared to e.g., physiological stress, ageing and pace-of-life responses in the heated area experience. We do agree however, that it is an important point, and now bring forth this in the introduction, on lines 112–113, and in the discussion, line 497.

I did have some more substantial questions on the CPUE section, which I'll try to put together here. It seems that CPUE is always lower for the heated population. Could the unexpected increased size observed in heated adults be due to a tradeoff between slower growth due to temperature but higher growth due to a release from density dependence? I think the authors suggest this might be the case, but it would be helpful to state it more explicitly.

Yes, we agree that could be part of the explanation. As we replied to Reviewer#1, the issue is that the effect of living in a smaller area (essentially a small lake compared to the open coast, which could affect density), is largely confounded with the temperature effect. That said, there exists data from a few years prior to the warm water pollution in the heated basin (but after its construction), that indicate the CPUE was always lower in the basin (Huss et al., 2019) (doi: 10.1111/gcb.14637). The lower CPUE could therefore be an artefact of the enclosing of the basin, possibly related to its size. However, in those first years of the enclosing, but before the warm water pollution started, growth rates had not yet differentiated (Huss et al. 2019). However, the effect of density also depends on food availability. While prey data are scarce, Sandström et al. (1995) (doi: 10.1111/j.1095-8649.1995.tb01932.x) show that the density of benthic prey was relatively constant over time (including 4 years prior to warming), suggesting that it is the warming itself that drives the difference in size. We have expanded on this in the discussion (lines 516–518).

Can the authors explain how the initial population size is known and whether it differs between the heated and reference population? It seems there are many reasons why reproductive potential could differ between the heated and reference populations, especially if warming shifts reproductive investment (as would be expected). Why does the CPUE figure start at age 3? It seems younger fish were caught and the fishbase entry on perch says they can mature earlier than 3. Is the mortality rate they measure only applied to fish that have been 'recruited' to the survey? And if fish can mature younger than 3, are some being missed by looking at CPUE for 3+ only?

First, we just want to clarify that the initial size here refers to N₀, the recruitment or abundance at age 0, not the first population size in time. This is not directly observed but is the intercept in the catch curve regression. It likely differs between the areas for many reasons: e.g., the size of the system (potentially affecting the overall abundance and density of the heated population), and differences in reproductive investment due to life history optimization in warmer waters. However, with the latter it is less known if this also translates to a difference in actual “recruitment” to the fishable population, i.e., the abundance at age 3, due to unknown mortality rates early in life.

It is true that fish younger than age 3 were caught. But age 3 is the age when the catches start to descend, and it is thus assumed that only fish above this age are caught representatively (i.e., that catches of age 2 fish are lower is not because these individuals are rarer in the population, but because they are not caught as effectively in the size-selective gill nets). Therefore, using fish older than 2 years is done to ensure that the catchability of certain ages does not affect the slope estimate, it should only be the true catch rate that does that. Ideally, we would want to avoid filtering the catch data like this, but this is the only way to handle the age/size-based catchability of the fishing gear, and it is standard practice in catch curve regression (Dunn et al., 2002) (doi: https://doi.org/10.1016/S0165-7836(01)00407-6).

We have added a figure illustrating the dome-shaped relationship between CPUE and age that is due to both catchability and declines in abundance by age (Figure 4—figure supplement 1), and we describe this procedure in the main text now (lines 280–283 and see also lines 310–312).

Finally, the grammar could use some editing, although the errors do not impact readability. I've made a few suggestions below but did not point out all places where grammar could be improved.

Thank you for pointing that out. We have now checked and corrected errors throughout the manuscript.

Author details

1. Max Lindmark

   Swedish University of Agricultural Sciences, Department of Aquatic Resources, Institute of Coastal Research, Öregrund, Sweden

   Present address

   Max Lindmark, Swedish University of Agricultural Sciences, Department of Aquatic Resources, Institute of Marine Research, Lysekil, Sweden

   Contribution

   Conceptualization, Formal analysis, Supervision, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   max.lindmark@slu.se

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-3841-4044

2. Malin Karlsson

   Swedish University of Agricultural Sciences, Department of Aquatic Resources, Institute of Coastal Research, Öregrund, Sweden

   Contribution

   Formal analysis, Investigation, Writing – original draft

   Competing interests

   No competing interests declared

3. Anna Gårdmark

   Swedish University of Agricultural Sciences, Department of Aquatic Resources, Uppsala, Sweden

   Contribution

   Data curation, Supervision, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1803-0622

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