Climate warming is predicted to enhance the negative effects of harvesting on high‐latitude lake fish

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2019 The Authors. Journal of Applied Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society 1Faculty of Biosciences, Fisheries and Economics, UiT – The Arctic University of Norway, Tromsø, Norway 2Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria 3Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies (Sokendai), Hayama, Japan


| INTRODUC TI ON
The effects of climate change on aquatic ecosystems have been studied extensively, and projections of future changes are presently under intense scrutiny (Bryndum-Buchholz et al., 2018;Parmesan, 2006). However, most studies do not incorporate additional anthropogenic stressors that are likely to interact with climatic effects, hindering understanding and predictions of the impact of multiple environmental stressors (Woodward, Perkins, & Brown, 2010). In ectotherms, temperature-dependent growth mediates some of the most notable effects of climate warming on individuals and populations (Deutsch et al., 2008;Ohlberger, 2013), and growth-mediated population-level effects are influenced by size-selective environmental pressures such as harvesting (Fenberg & Roy, 2008). Under climate warming in sub-Arctic regions, fish will experience increased temperatures, possibly favouring improved growth conditions at the northern limits of their distributional range (Deutsch et al., 2008;Ohlberger, 2013;Pörtner et al., 2001;Reist et al., 2006). Accordingly, the impacts of climate change and harvesting need to be addressed jointly (Brander, 2007).
The effects of increasing water temperature on the vital rates and demography of fish are primarily mediated by growth and reproduction (Ficke, Myrick, & Hansen, 2007;Wootton, 1998). In many fish species, growth may influence reproduction, because maturation schedules are phenotypically plastic, with the corresponding maturation reaction norms determining the age and size at maturation conditional on somatic growth (Heino, Dieckmann, & Godø, 2002). The changes in vital rates mediated by temperature-dependent growth have implications for fish demography, influencing population size, age structure and stock biomass.
Harvesting of fish populations is often size-selective, targeting large individuals (Fenberg & Roy, 2008;Hansen, Madenjian, Selgeby, & Helser, 1997). A common outcome of size-selective harvesting is a truncation of size and age distributions as a consequence of the removal of large individuals (Conover & Munch, 2002;, which may change the character of size structured interactions, leading to altered growth rates and changed ages and sizes at maturation of the fish that remain in the population (Law, 2000;Olsen et al., 2005). In many populations, large fish contribute the most to recruitment and may provide a buffer against environmental perturbations (Anderson et al., 2008;Berkeley, Hixon, Larson, & Love, 2004;Hsieh, Yamauchi, Nakazawa, & Wang, 2010). The use of efficient gears and the absence of sufficient regulation further increase the risk of overexploitation in freshwater fish populations (Allan et al., 2005;Post, Persson, Parkinson, & Kooten, 2008).
High latitudes are experiencing more rapid warming than temperate or tropical regions (Parmesan, 2006), and cold-water fish species, such as salmonids, are among the taxa most sensitive to climate change (Blanchet, Primicerio, Smalås, Arias-Hansen, & Aschan, 2019). Salmonids are also among the numerically dominant and ecologically most important freshwater fish in these regions (Klemetsen et al., 2003). Due to their large size and active behaviour, salmonids are vulnerable to size-selective gillnet fisheries (Finstad, Jansen, & Langeland, 2001). Among salmonids, Arctic charr Salvelinus alpinus (L.) has the northernmost distribution of all freshwater fish species (Klemetsen, 2010;Klemetsen et al., 2003).
Arctic charr has been predicted to experience a large-scale extinction towards the southern end of its distribution; however, at higher latitudes and altitudes this pattern so far is not empirically evident (Hein, Öhlund, & Englund, 2012). On the contrary, it has been suggested that, in the latter locations, the somatic growth of Arctic charr might even increase under climate change, due to warmer water temperatures and a prolonged ice-free season (Pörtner et al., 2001;Reist et al., 2006), thereby opening new opportunities for their exploitation.
Here, we examine the combined effects of climate change and size-selective fishing on Arctic charr populations using an ecogenetic individual-based model ). Arctic charr population dynamics are modelled over the period 1950-2100 for climate scenarios characterized by the representative concentration pathways (RCPs) RCP-4.5 and RCP-8.5, and for five different levels of size-selective harvesting. The model is parametrized and evaluated based on long-term data from a sub-Arctic lake Amundsen et al., 2019;Persson et al., 2007). We investigate whether climate change will increase individual growth rates of Arctic charr in high-latitude lakes, as water temperatures approach the optimum for summer growth, resulting in larger size at age and higher stock biomass and production. We further address the truncation of size 4. Synthesis and applications. Our model-based analyses highlight the combined effects of climate change and size-selective fishing, emphasizing the emerging vulnerability of fish populations to multiple stressors. We recommend carefully climate-adapted management strategies permitting only a narrow range of gillnet mesh sizes for inland fisheries at high latitudes.

K E Y W O R D S
age and size truncation, Arctic charr, climate change, ecological modelling, management of freshwater fish, population dynamics, salmonids, size-selective fishing and age distributions by size-selective fishing and the effects on stock biomass and yield contingent on fishing effort and climate scenario. In light of our findings, we discuss climate-adaptation strategies for inland fisheries at high latitudes that can promote sustainable exploitation.

| Data sources and model parametrization
Our eco-genetic individual-based model for Arctic charr is forced by climate, using two different RCP scenarios, RCP-4.5 and RCP-8.5. These scenarios describe the projected increases, of either 4.5 or 8.5 W/m 2 , in radiative forcing in the year 2100 resulting from rising greenhousegas concentrations in the atmosphere and their corresponding greenhouse effects on climate warming (IPCC, 2007). Climate variables are obtained at the finest grid resolution available (0.11°) from a regionally downscaled climate model (MPI-M-MPI-ESM-LR), forced by the global circulation model CLMcom-CCLM4-8-17. The climate model outcomes, made available through the EURO-CORDEX project, cover the period 1950-2100. To obtain daily lake water temperatures from the climate model outcomes, we adopt the one-dimensional air-to-water temperature model called 'General Lake Modelling,' using the r package GLM r (Hipsey, Bruce, & Hamilton, 2014). More detailed descriptions of the climate models and of the modelling of physical limnology are available in Appendix S2.
The eco-genetic model is parameterized and evaluated based on long-term data for the Arctic charr population of Lake Takvatn (69°07′N, 19°05′E). Lake Takvatn is located about 300 km north of the Arctic Circle in northern Norway, has an area of 15 km 2 and is situated 215 m above sea level. Data on Arctic charr have been collected yearly since the early 1980s  and include individual age, length, weight, maturation status, sex and fecundity data Henriksen et al., 2019). Parameters used for our model are listed in Table S1 in Appendix S1, and data from Lake Takvatn charr are visualized in Figure S1 in Appendix S1. Analyses of robustness and sensitivity to changes in somatic growth and natural mortality are also available in Appendix S2.

| Eco-genetic model overview
We use an individual-based model designed according to the ecogenetic modelling framework introduced by Dunlop et al. (2009). Our model describes demographic processes without evolutionary effects on life-history traits. The model runs by accounting for successive life-history events during each annual cycle, including mortality, maturation, growth and reproduction . Growth is described by temperature-dependent daily length increments to capture climate-related growth effects. In each model run, the Arctic charr population is initialized with 3,000 individuals and traced for 150 years. Results are averaged over 50 replicate model runs.

| Mortality
Annual mortality is calculated as where Z is the total mortality, M the natural mortality, and F the fishing mortality (all expressed as instantaneous mortality rates). The natural mortality for many fishes, including salmonids, is assumed to be negatively correlated with their body size (Elliott, 1993;Gislason, Daan, Rice, & Pope, 2010), following an allometric relation, where L is the length of fish, M r the natural mortality at the reference length L r , and c the allometric exponent. The observed size distribution of Arctic charr in Lake Takvatn is used to calibrate L r and c. To estimate M r , we use the equation given by Pauly (1980), where z-values are constants provided by Pauly (1980), all logarithms are natural logarithms, L ∞ (= 50 cm) and K (= 0.14 year −1 ) are the asymptotic length and the growth rate of Lake Takvatn Arctic charr, respectively, both of which are estimated from empirical data using the von Bertalanffy growth model (Chen, Jackson, & Harvey, 1992), and T (= 4.4°C) is the observed mean water temperature of Lake Takvatn over the period 2017-2018.
We investigate five fishing-mortality scenarios, representing different levels of harvesting pressures by gillnets. Gillnet fishing is regulated by mesh size, which is recommended to be between 26 and 35 mm by the regional management institutions (Statskog, 2017). Size-selectivity of the minimum mesh size is modelled based on catch data for Lake Takvatn Arctic charr and used to parametrize the length-dependent fishing mortality, where L is the length of fish, F 0 the size-independent component, F 1 scales the size-dependent component, F 2 the steepness of the size-dependent component, and F 3 the inflection point of the size-dependent component.

| Maturation
Age at maturation is assumed to be phenotypically plastic and determined by a probabilistic maturation reaction norm (PMRN) describing the length-and age-specific probabilities of maturation (Dieckmann & Heino, 2007;. We estimate the PMRN from long-term data on Arctic charr in Lake Takvatn (Table S1 in Appendix S1) using the so-called demographic method assuming a linear reaction norm (Barot, Heino, O'Brien, & Dieckmann, 2004). Following , we implement a PMRN that involves both age and size, and assume that these two variables have independent and linear effects, where L is the length of fish, a the age of fish, i the PMRN intercept, s the PMRN slope, and d the PMRN width.

| Temperature-dependent growth
We assume a temperature-dependent von Bertalanffy growth model, where L t is the length of fish at age t, Δt the time interval over which growth is considered, L ∞ is the asymptotic length at which growth is zero, and K t is the temperature-dependent growth rate at age t 1965; see also Haddon, 2001, pp. 241-242). For our model, we account for daily variations in the growth rate K t and accordingly consider daily growth increments, that is ∆t = 1 day = 365.25 −1 year = 0.0027379 year, with a year's growth beginning on 1 January and ending on 31 December. Growth starts at age 0 from an initial length randomly drawn from a normal distribution with mean m (L 0 ) and SD σ (L 0 ).
The temperature dependence of K t follows a dome-shaped curve with a maximum of 0.35 (K max ) at the temperature optimum (T opt ) of 14.1°C (Larsson & Berglund, 1998Siikavuopio, Foss, Saether, Gunnarsson, & Imsland, 2013). The maximum growth rate, K max , is calibrated to the growth of Arctic charr in Lake Takvatn, and individual variability in growth rate is implemented by random sampling from a normal distribution centred on K max . The the temperature is smaller than 1˚C (T min ) or larger than 20˚C (T max ) (Larsson & Berglund, 1998Siikavuopio, Knudsen, & Amundsen, 2010;Siikavuopio, Skybakmoen, & Saether, 2009). Otherwise, K t is calculated as follows, where K max is the maximum growth rate parameterized for the Takvatn charr population using the average von Bertalanffy growth rate (K) and the average annual water temperature (from the GLMr) for the last 10 years of the long-term data series, T t is the average water temperature for the upper ten metres on day t, and T min , T max and T opt are the minimum, maximum and optimum water temperatures for Arctic charr, respectively (Table S1 in Appendix S1). Arctic charr at high latitudes predominantly utilize the shallow-water habitat, especially during the ice-free season (Hawley, Rosten, Haugen, Christensen, & Lucas, 2017), and therefore, we use the average water temperature for the upper 10 m.

| Reproduction and recruitment
The fecundity f of individual adult females is described by an allometric function estimated for the fecundity-length relationship, where L is the length of fish, f r is the fecundity-length relationship coefficient, and b is the allometric exponent.
Annual recruitment is dependent on the size of the spawning stock, as well as on the fecundity of adult fish and the density-dependent mortality of eggs and hatchlings (Haddon, 2001). The latter density dependence is assumed to follow a Beverton-Holt stock- where R t is the total number of recruits, that is surviving offspring, to the population in year t, f tot,t the stock's total fecundity in year t (given by the sum of the fecundities f according to Equation 4a of all adult females reproducing in that year), R max the maximal number of recruits, and f tot,1/2 the total fecundity at which density-dependent recruitment mortality kills 50% of the offspring. This Beverton-Holt stock-recruitment model predicts a saturating relationship between the total population fecundity f t and the total number R t of recruits. affecting the annual recruitment. Ignoring density-dependent growth will affect model outcomes for individual-level growth rates and population-level biomass and yield, particularly in low-fishing-mortality scenarios when abundance is relatively high. However, the maximum temperature-dependent growth coefficient K max is calibrated to Arctic charr growth from Lake Takvatn (von Bertalanffy growth curve, Figure S1 in Appendix S1), thereby implicitly taking into account resource availability. Interspecific interactions are omitted, as Arctic

| Climate warming increases somatic growth and stock biomass
Our model predicts that an increase in water temperature (Figure 1) substantially increases the length at age of Arctic charr ( Figure 2).
For example, the mean length of 4-year-old Arctic charr in the RCP-

| Increased harvesting masks the temperature effects on stock biomass and yield
Increased harvesting masks the positive effects of temperature on stock biomass: for the year 2100, a fishing mortality of

| Climate warming increases the vulnerability of harvested populations
The Year 2050 for RCP−4.5 Year 2050 for RCP−8.5 Year 2100 for RCP−4.5 Year 2100 for RCP−8.5 The size distribution of the Arctic charr population does not change with climate warming ( Figure S4 in Appendix S4). The age distributions of all individuals and harvested individuals are truncated as fishing mortality is increased (Figure 5b,d); the same truncation effect is also empirically observed in the size distribution of Artic charr in Lake Takvatn ( Figure S4 in Appendix S4).

| D ISCUSS I ON
Our model predicts that higher water temperatures will accelerate the somatic growth of Arctic charr at high latitudes, leading to larger body size at age and increased stock biomass. Interestingly, the potential increase in biomass with future climate warming is masked by harvesting, which has a strong negative effect on biomass due to the increase in the fishing mortality of larger individuals. According to our model, yield will increase substantially under climate warming only when fishing mortality is low, and the sensitivity of yield to fishing mortality will increase as water temperature rises. In addition, under climate warming, harvesting will target younger individuals, resulting in a more pronounced age truncation and a larger proportion of immature individuals in the catches, which might elevate the vulnerability of the population to environmental perturbations.
Despite a significant increase in mean annual water temperature (by 1.5°C in the RCP-8.5 climate scenario for 2000-2100), the projected water temperatures are unlikely to exceed Arctic charr's optimum for somatic growth for the majority of the growing season in sub-Arctic areas: only 10.2 days above optimum are predicted for the year 2100. Temperature-dependent somatic growth in high-latitude Arctic charr populations has been studied extensively and has revealed positive somatic growth between about 1°C and about 20°C, with an optimum temperature of about 14°C (Larsson & Berglund, 1998Siikavuopio et al., 2010Siikavuopio et al., , 2009).
According to our study, the projected rise in water temperature will result in a significant increase in mean size at age and stock biomass. Higher growth rates and production have been suggested to be a consequence of climate warming for freshwater fish populations living in high-latitude lakes (Brander, 2007;Reist et al., 2006). There are few studies testing the impact of climate warming on somatic growth in salmonids; however, a study on rainbow trout revealed that a 2°C increase in water temperature enhanced growth throughout most of the growing season (Morgan, McDonald, & Wood, 2001). This is further supported by a recent study showing that freshwater salmonid populations experiencing climate warming within their temperature tolerance range will exhibit increased growth rates (Symons, Schulhof, Cavalheri, & Shurin, 2019). It is therefore likely that Arctic charr inhabiting areas where current water temperatures are substantially lower than the optimum for somatic growth will experience increased somatic growth and production from climate warming (Karlsson, Jonsson, & Jansson, 2005). This expectation assumes that the out-

(c)
Year 2000 Year 2050 for RCP−4.5 Year 2050 for RCP−8.5 Year 2100 for RCP−4.5 Year 2100 for RCP−8.5 Age ( whereas with future climate warming, these yields will diverge, resulting in substantially higher yield for F = 0.1 year −1 than for F = 0.2 year −1 . Brander (2007) suggested that yield may increase in high-latitude fisheries as a consequence of increasing water temperatures, but emphasized the need to reduce fishing mortality in fully exploited stocks as a mitigation strategy against climate change. Our results suggest that climate-warming effects in highly exploited stocks might be hard to detect, because they will be masked by harvesting.
Long-term empirical studies (with study periods longer than 10 years; Lindenmayer & Likens, 2010) are especially important for assessing population impacts of climate warming. However, such studies are rare and often examine systems simultaneously impacted by other anthropogenic stressors such as harvesting . A review of long-term empirical time series of freshwater fish in Europe indicates that declines in Arctic charr populations can be attributed to climate warming, even though somatic growth rates have often increased over time (Jeppesen et al., 2012). Indeed, in addition to experiencing climate warming, most of the studied populations were also influenced by other anthropogenic stressors including harvesting (Jeppesen et al., 2012). Climate-change effects might therefore be hard to disentangle from the impacts of other factors. Our model-based analyses help identify possible negative effects of the combined exposure to warming and harvesting.
We have found severe demographic effects of size-selective harvesting on Arctic charr, a phenomenon documented for many harvested fish populations (Anderson et al., 2008;Jørgensen et al., 2007;Longhurst, 2006). Our model predictions show a sharper truncation of the age and size distribution as harvesting is increased. A population experiencing size and age truncation typically becomes more vulnerable and less resilient to environmental perturbations and stochastic events (Anderson et al., 2008;. Larger and older (and thus more experienced) individuals tend to tolerate fluctuating environmental pressures and survive hard times better through bet-hedging strategies than smaller and younger individuals (Bobko & Berkeley, 2004;Marteinsdottir & Steinarsson, 1998). Higher vulnerability due to size and age truncation by fisheries might be particularly detrimental under the widely predicted increase in the frequency of extreme climate events (Beniston et al., 2007). Arctic charr individuals are extremely vulnerable to gillnet fisheries, and only a few gillnets with large mesh sizes can remove the production of large piscivorous individuals (Finstad et al., 2001).
In addition to ecological effects of size and age truncation, evolutionary effects that might not be easily reversed are found in populations of fish under size-selective harvesting (Enberg, Jørgensen, Dunlop, Heino, & Dieckmann, 2009;Jørgensen et al., 2007;Olden et al., 2010). Climate warming will increase with climate warming: this effect is particularly pronounced for fishing mortalities F > 0.  (Anderson et al., 2008;Berkeley et al., 2004;Hsieh et al., 2010). In Arctic charr, older individuals produce larger eggs (Lasne, Leblanc, & Gillet, 2018), and thus larger larvae, which have faster initial growth and higher survival than their smaller counterparts (Leblanc, Benhaïm, Hansen, Kristjánsson, & Skúlason, 2011). Also, the stronger age truncation of adults induced by climate warming results in a very narrow adult age range, which implies that weak cohorts will have a greater negative impact on recruitment. In addition to the ecological effects, removing a high proportion of immature, fast-growing fish might lead to fisheries-induced selection towards smaller size at maturation (Enberg et al., 2009). The decline in the number of mature individuals and recruits eventually leads to a reduction in population abundance for high fishing mortality, further increasing vulnerability (see Figure 6 for a conceptual summary of the possible combined effects of climate warming and size-dependent harvesting).
For the management of exploited stocks under climate change, our results suggest that monitoring should address not only stock abundances and biomasses, but also size and age distributions, as well as maturation status, to detect demographic changes triggered by increased water temperatures. In many freshwater systems, monitoring of populations is based on catch statistics, which often do not include information about the age of fish, and climate-change effects may therefore be difficult to detect. In light of our findings, we recommend a moderation of fishing effort (i.e. limiting the number of gillnets/night or licensed fishermen, or establishing a temporal window for harvesting) and a narrow range of gillnet mesh sizes (excluding large mesh sizes, thus protecting larger individuals), as climate adaptations of the management of inland fisheries at high latitudes. Such mitigation strategies will help maintain the old and large individuals in the population and limit the harvesting of juvenile individuals. Current regulations in northern Scandinavia are highly variable; however, decision-makers are increasingly realizing that climate-adaptation plans are necessary for sustainable harvest.
Our model ignores temperature-driven changes in other candidate parameters that may mitigate or exacerbate the combined effects of climate warming and size-selective fisheries. One candidate parameter related to growth is the asymptotic length L ∞ , which might increase with climate warming (Quince, Abrams, Shuter, & Lester, 2008). This would mitigate some of the negative demographic effects for high levels of harvesting if older, larger individuals could survive harvesting. To the extent that the maximum recruitment R max may be limited by basal production available to the larvae, R max might increase with climate warming due to higher production (Karlsson et al., 2005). Such an increase in R max would mitigate the increased vulnerability associated with high levels of fishing mortality and climate warming.
The effects of multiple anthropogenic stressors on freshwater fish populations are presently poorly understood and hard to predict (Olden, Hogan, & Zanden, 2007). Scenario-based modelling helps to understand how combined pressures might interact (Folt, Chen, Moore, & Burnaford, 1999), which aids the future management and preservation of harvested freshwater fish stocks. The present study demonstrates that the combined effects of climate warming and size-selective fishing can be large, influencing both stock biomass and yield, as well as the size-and age structure of exploited Arctic charr populations. Harvested fish populations may thereby become less resilient and more vulnerable to climate warming.

ACK N OWLED G EM ENTS
Thanks are due to the Freshwater Ecology Group at UiT-The Arctic University of Norway, for collecting and sharing their long-term time series from Lake Takvatn. Thanks are also due to Prof. Malcolm

AUTH O R S ' CO NTR I B UTI O N S
A.S. and R.P. conceived the ideas and planned the paper. A.S., R.P., J.F.S. and U.D. contributed significantly to model development.
P.-A.A., A.S. and R.P. collected data. A.S. and R.P. analysed model results with substantial input from P.-A.A. and U.D. A.S. led the writing. All authors contributed significantly to the drafts and approved the final manuscript.