Adaptive responses of energy storage and ﬁsh life histories to climatic gradients

Adaptive responses of energy storage and fish life historiesto climatic gradients

Henrique C. Giacomini a,n, Brian J. Shuter a,b

a Department of Ecology and Evolutionary Biology, University of Toronto, 25 Harbord St., Toronto, ON, Canada M5S 3G5b Harkness Laboratory of Fisheries Research, Ontario Ministry of Natural Resources, 2140 East Bank Drive, Peterborough, ON, Canada K9J 7B8

a r t i c l e i n f o

Keywords:Fish bioenergeticsLife history optimizationSeasonal environmentsBiphasic growth modelEnergy budget

a b s t r a c t

Energy storage is a common adaptation of fish living in seasonal environments. For some species, theenergy accumulated during the growing season, and stored primarily as lipids, is crucial to preventingstarvation mortality over winter. Thus, in order to understand the adaptive responses of fish life historyto climate, it is important to determine how energy should be allocated to storage and how it trades offwith the other body components that contribute to fitness. In this paper, we extend previous life historytheory to include an explicit representation of how the seasonal allocation of energy to storage acts as aconstraint on fish growth. We show that a strategy that privileges allocation to structural mass in the firstpart of the growing season and switches to storage allocation later on, as observed empirically in severalfish species, is the strategy that maximizes growth efficiency and hence is expected to be favored bynatural selection. Stochastic simulations within this theoretical framework demonstrate that the relativeperformance of this switching strategy is robust to a wide range of fluctuations in growing season length,and to moderate short-term (i.e., daily) fluctuations in energy intake and/or expenditure within thegrowing season. We then integrate this switching strategy with a biphasic growth modeling frameworkto predict typical growth rates of walleye Sander vitreus, a cool water species, and lake trout Salvelinusnamaycush, a cold water specialist, across a climatic gradient in North America. As predicted, growthrates increased linearly with the duration of the growing season. Regression line intercepts werenegative, indicating that growth can only occur when growing season length exceeds a thresholdnecessary to produce storage for winter survival. The model also reveals important differences betweenspecies, showing that observed growth rates of lake trout are systematically higher than those of walleyein relatively colder lakes. This systematic difference is consistent with both (i) the expected superiorcapacity of lake trout to withstand harsh winter conditions, and (ii) some degree of counter gradientadaptation of lake trout growth capacity to the climatic gradient covered by our data.

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1. Introduction

Adaptive responses to shorter growing seasons and longerwinters have been reported for a wide variety of aquatic and terres-trial species. Examples include increased fat storage in northernpopulations of brown trout and Atlantic salmon (Berg et al., 2009,2011), increased metabolic capacity in fish and plants (e.g., Conoveret al., 2009) and a lowering of optimal performance temperatures inalgae, insects, reptiles and fish (Angilletta, 2009). One of the mostwidely documented examples of local adaptation to increased winterseverity involves a ‘counter-gradient’ adjustment upward of indivi-dual growth capacity. Many examples (Conover et al., 2009) of thistype of response have accumulated in the recent literature and thishas drawn attention to the question of why southern populations

would exhibit reduced growth capacity. This attention has focused onpossible costs associated with rapid growth, including both intrinsiceffects, such as physiological costs that might arise from maximizingfood processing rates, and extrinsic ecological effects, such as themortality costs associated with increased exposure to predationarising from extended feeding periods. Abrams has published anumber of studies related to these phenomena, beginning with earlystudies (Abrams, 1994, 1993, 1991, 1983; Abrams et al., 1996) on theimplications of growth costs for both life history characteristics andpopulation dynamics, and continuing with later studies (Lester et al.,2004; Quince et al., 2008a; Shuter et al., 2005) that extended andapplied the theoretical results of Kozlowski (Kozlowski andTeriokhin, 1999; Kozlowski, 1996) to factors shaping the optimal lifehistories of freshwater fish living in systems with strong seasonalityin growth. The Abrams' papers on growth seasonality and life historywere able to account for much of the observed inter- and intra-specific life history variation exhibited by freshwater fish living intemperate and northern limnetic ecosystems. However, none of the

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n Corresponding author. Tel. þ1 416 978 7338.E-mail address: [email protected] (H.C. Giacomini).

Please cite this article as: Giacomini, H.C., Shuter, B.J., Adaptive responses of energy storage and fish life histories to climatic gradients. J.Theor. Biol. (2013), http://dx.doi.org/10.1016/j.jtbi.2013.08.020i

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models in these papers explicitly included a detailed representation ofthe annual pattern of energy surplus and deficit that defines theseasonal growth pattern, and the constraints it imposes on growth andlife history. These constraints reflect the need to accumulate storedenergy during the summer season of energy surplus in order tosurvive the winter season of energy deficit. In this study, we extendthis approach to life history modeling by including an explicitrepresentation of the energy storage requirements imposed by winterstarvation. We evaluate the effects of this extension on predicted lifehistory patterns in general, and then go on to apply the model toevaluate evidence for growth limitation due to increasing winterseverity in two species of freshwater fish. We focused our applicationof this new model on comparing the inter-population shifts in growthrate evident for lake trout (Salvelinus namaycush), a species with lowoptimal performance temperatures (8 1C to 12 1C – Christie and Regier,1988), with the shifts evident for walleye (Sander vitreus), a specieswith much higher optimal performance temperatures (18 1C to 22 1C –

Christie and Regier, 1988), along similar climatic gradients. As a wintertoleration strategist, we expected walleye to be more sensitive toincreasing winter severity, showing a sharper decline of growth rateswith decreasing temperatures and duration of the growing season.In addition, by fitting this new model to population-level growth andclimate data for both species, we hoped to include the likely impact ongrowth of local adaptation of storage levels and thus isolate evidencefor local adaptation in growth capacity. Our expectation was thatevidence for local adaptation in growth capacity would be stronger forlake trout.

We begin our work with the development of the bioenergeticsframework used to model growth and storage allocation in fish. This

framework is related to the Dynamic Energy Budget approach ofKooijman (2000) and stems directly from the life history models ofLester et al. (2004) and Quince et al. (2008a). In order to use theframework to predict life history variation across a gradient inseasonality, we must first determine a particular form for thefunction defining how the proportion of net energy production thatis allocated to storage varies over a typical year. One logical choice isto assume that natural selection would favor an allocation strategythat maximizes individual fitness, so in the third section of the paperwe use an optimization approach to identify such a strategy, underdeterministic environmental conditions. We then go on to compareits performance to the performance of alternative allocation strate-gies under different regimens of environmental stochasticity. Finally,in the fourth section of the paper, we integrate the optimal storageallocation strategy with the biphasic growth model of Quince et al.(2008a) to predict how growth rate should vary with changes inseasonality. We then compare this pattern with observed associa-tions between growth rate and seasonality in walleye and lake troutpopulations. A list of variables and parameters used in this paper ispresented in Table 1.

2. Bioenergetics framework for storage allocation in seasonalenvironments

A simple and effective way to represent seasonality adopted byseveral life history and growth models (Kozlowski and Teriokhin,1999; Quince et al., 2008a) is to divide the year into two periods:(i) a growing season when temperature and prey availability are

Table 1Variables and parameters used in this paper, listed in alphabetic order. The values represent the default values or ranges used for the numerical examples.

Symbol Definition Values and functions

c Constant fraction of net production allocated to storage characterizing the Constant Allocation (CA) strategy See Appendix Dcq Rescaled fraction of net production allocated to storage characterizing the CA strategy 0–1D Growing season length (days) 180h Annual pre-maturation growth rate (cm3(1�β) year�1) h¼ ζGDΩβ�1ð1�βÞ if ζW¼0hn Effective annual pre-maturation growth rate (cm3(1�β) year�1) hn ¼ ζGD�ζW ð365�DÞ� �

Ωβ�1ð1�βÞL Body length (cm) m¼ΩL3

m Structural mass (g) VariableM Structural mass at the end of the growing season (g) M¼m(D)Mn Optimal M (g) Mn¼m(tn)m0 Initial structural mass (g) 0, 50Ms Structural mass (g) at the end of the growing season leading to Ys Ms ¼ β ζGð1�βÞDþm1�β

0

h in o 11�β

PG Net production rate during the growing season (g day�1) PGðmÞ ¼ ζGmβ

PW Net production rate during winter (g day�1) PW ðmÞ ¼ �ζWmβ

tn Time (days) at switching from structural to storage production that leads to optimal structure Mn and storage Yn

characterizing the Total Switching (TS) strategytn ¼D�ζW

ζGð365�DÞ

TG Average temperature (1C) during the growing season Variabletq Rescaled time at switching from structural to storage production characterizing the TS strategy 0–1ts Time (days) at switching from structural to storage production that leads to maximal storage Ys ts ¼D�M1�β

sζGβ

TW Average temperature (1C) during winter Variableu Fraction of net production allocated to storage Variabley Storage mass (g) VariableY Storage mass at the end of the growing season (g) Y¼y(D)Yn Optimal Y (g) Yn ¼ θζWMβ ð365�DÞYs Maximal storage (g) at the end of the growing season Ys ¼ θζGM

βs D�tsð Þ

αG Temperature-independent coefficient of growth during the growing season (g1�β day-1 e5.02/C) ζG ¼ αGe�5:02=TG

αW Temperature-independent coefficient of energy loss during winter (�g1�β.day�1 e5.02/C) ζW ¼ αWe�5:02=TW

β Allometric exponent of production–mass relationship 2/3ζG Coefficient of growth during the growing season (g1�β day�1) 0.05ζW Coefficient of growth (energy loss) during winter (�g1�β day�1) 0.01θ Ratio of energy content between structural and storage mass 0.5μD Mean growing season length (days) characterizing stochastic simulations with inter-annual variability 180μζ Mean value of ζG (g1�β day�1) characterizing stochastic simulations with short-term variability 0.05sD Standard deviation of growing season length (days) characterizing stochastic simulations with inter-annual variability 0–180sζ Standard deviation of ζG (g1�β day�1) characterizing stochastic simulations with short-term variability 0–0.05Ω Coefficient of weight–length relationship (g cm�3) 0.01

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favorable and the organism is able to assimilate energy in excess ofmetabolic losses (i.e., the organism has a positive net production),and (ii) a winter, here used to refer to the period when lowtemperatures lead to zero or negative net production due to lowprey productivity, low organism activity, or a combination of both(Shuter et al., 2012). We assume here that the annual cycle startswith the growing season, whose duration is D days, followed bywinter in the remaining [365�D] days. Although the cumulativeenergetic deficit over winter requires the existence of a corre-sponding surplus of energy stored during the previous growingseason, such storage is considered only implicitly in the abovecited life history models. Here we include storage explicitly,employing a model structure that is essentially equivalent to theDynamic Energy Budget approach pioneered by Kooijman (2000)(Nisbet et al., 2000; 2012). Our focus is on the somatic componentof body mass, treating reproductive mass as a separate compart-ment, as in other optimal resource allocation models (e.g.,Kozlowski, 1996; Quince et al., 2008a, b). We divide total somaticmass into two compartments: (i) storage mass (y, grams), whichcan be mobilized to cover metabolic losses under starvationconditions and which is composed primarily of lipids in fish(Shul’man and Love, 1999; Shul’man, 1974); (ii) structural mass(m, grams), which consists of tissue that either cannot be remo-bilized (e.g., bones, circulatory and nervous tissue, membranelipids) or, if remobilized, imposes a significant mortality cost onthe individual (e.g., muscle protein). Lipid storage is a relativelyinert tissue in fish (i.e., its presence does not contribute substan-tially to the processes responsible for energy acquisition and it haslow maintenance costs, Kooijman and Troost, 2007; Kooijman,2000); therefore, we assume that net production is determined bystructural mass only (Kooijman, 2000; Nisbet et al., 2000). Therelationship between net production and structural mass can beapproximated by a power function (Ernest et al., 2003; Quinceet al., 2008a):

PGðmÞ ¼ ζGmβ for growing season ð1aÞ

PW ðmÞ ¼ �ζWmβ for winter ð1bÞ

where PG and PW are the net production (g day�1) during thegrowing season and winter, respectively; β is the allometricexponent (0oβo1); ζG and ζW are the positive normalizationconstants whose values are genotype and environment-specific.

At any point in time (t) during the growing season, a givenfraction u¼u(t) of PG is allocated to storage, and the remainingproportion (1�u(t)) is allocated to structure. The dynamics ofstorage (y(t)) and structure (m(t)) within a growing season thenfollow the system of differential equations:

dydt

¼ θPGðmðtÞÞuðtÞ ð2aÞ

dmdt

¼ PGðmðtÞÞ 1�uðtÞ½ � ð2bÞ

where θ is the ratio of energy content between structural andstorage mass. The allocation function u(t) takes on a value some-where in the interval [0,1]. Larger values for u(t) lead to greaterimmediate growth of y(t), but at the expense of future netproduction as PG depends on m(t). As structural mass is stronglycorrelated with fitness via higher fecundity, dominance againstconspecifics and/or defense against predators (Abrams, 2003;Dmitriew, 2011; Nelissen, 1992; Persson et al., 1996; Quinceet al., 2008a; Werner and Gilliam, 1984), we expect the optimalallocation function to be the one that produces just enoughstorage to cover winter energetic demands while maximizingstructural growth.

Let M and Y denote the structural and storage mass at the endof the growing season (i.e., M¼m(D) and Y¼y(D)), and let Yn bethe total amount of storage required to exactly match the cumu-lative winter energy loss. The rate of energy loss during winter willbe determined by structural size at the end of the precedinggrowing season, i.e., M. Then Yn will be given by

Yn ¼ θζWMβð365�DÞ ð3Þnoting that structural mass will remain the same throughout thewinter, i.e., m(t)¼M for Drtr365. Eq. (3) assumes no nutrientlimitation and that the costs of maintaining lipid or of convertingit into products needed for maintenance are negligible, assump-tions that we feel are acceptable given our objective of comparingthe relative performance of different allocation strategies. If themajor function of storage is to cover winter energy deficit, thenany storage produced in excess of Yn would be of little use, withthe adverse effect of compromising structural growth. Conversely,if the storage available at the beginning of the winter (Y) is lowerthan Yn, then the fish is expected to die by starvation. So we shallassume here that Yn represents the optimal amount of storage tobe produced through the growing season. This assumption isconsistent with empirical observations that show that:(i) lipidlevels at the onset of winter vary widely across populations andare positively related to body size and winter length, closelymatching the projected winter energy deficit (Biro et al., 2004;Bull et al., 1996; Hurst and Conover, 2003; Schultz and Conover,1997); (ii) lipid levels at the end of winter converge toward valuessimilar to the minimum required for survival (Biro et al., 2005,2004; Finstad et al., 2010), which we assume to be the lipidportion of the structural mass. The optimal (¼the maximal)structural mass, denoted by Mn, will depend on the choice for u(t).

3. Optimal storage allocation strategy

The problem now is to determine the allocation function u(t)that maximizes structural growth (i.e., maximizes M) with theconstraint that Y¼Yn. From Eq. (2a) and (b):

Y ¼Z D

0θPGðmðtÞÞ uðtÞdt ð4Þ

By replacing Y in Eq. (4) with Yn from Eq. (3) and rearranging forM,the function to be optimized then becomes

M¼R D0 PGðmðtÞÞuðtÞdtζW ð365�DÞ

" #ð1=βÞ

ð5Þ

As ζW, D, and β are positive constants, and Do365, themaximization of Eq. (5) is satisfied through the maximization ofthe definite integral in the numerator (¼Y/θ), which is thefunction containing u(t). In other words, the problem of maximiz-ing the final structural mass (M), subject to the constraint thatstorage mass Y equals Yn, can be solved by finding the strategy thatmaximizes the storage mass for each level of structural mass (i.e.,maximization of Eq. 4). This problem can be solved using thePontryagin Maximum Principle from optimal control theory,following the approach that Kozlowski and Teriokhin (1999) usedto find the optimal lifetime reproductive allocation. In our case,the focal time scale is the growing season (i.e., 0otoD) andsurvivorship is assumed to have no influence on the outcome (butsee Discussion on potential effects of size-dependent mortality).

In Appendix A, we demonstrate that the allocation strategy thatmaximizes Y for each level of M is a ‘bang–bang’ strategy where allnet production is devoted to structural growth during the first partof the growing season and then, at a given point in time, all netproduction is switched entirely to storage growth. We will refer to

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this strategy as the Total Switching (TS) strategy. The exact swit-ching time depends on the particular optimization criterion,whether it is to maximize the final amount of storage (i.e., tomaximize Eq. (4)) or to maximize the final amount of structuresubject to the constraint that Y¼Yn (i.e., to maximize Eq. (5)).In the first case, the optimal switching time ts is defined by aswitching curve that separates the plane (t,m) into two regions: ifthe system is in any state below the switching curve (assumingstructural mass as the ordinate and time as the abscissa), it isoptimal to allocate all production to structure (i.e., u(t)¼0); abovethe switching curve, it is optimal to allocate all production tostorage (i.e., u(t)¼1, Fig. 1a). So for any growth trajectory startingbelow the switching curve, the structural mass (and structuralmass only) will grow according to Eq. (2b); when the massintersects the switching curve at a time ts and size Ms, structuralgrowth will cease and give way to storage growth, resulting in afinal (maximal) storage mass Ys (Fig. 1a). The switching curverelating Ms to ts, derived in Appendix A, is given by

ts ¼D�M1�βs

ζGβð6Þ

There is a unique switching curve for any given combination ofβ, ζG, and D. If any two growth trajectories differ only in initialmass (m0), they will be associated with the same switching curvebut will intersect it at a different time ts and a different structuralmass Ms, leading to a different final storage Ys.

Given a particular growth trajectory (as defined by m0, β, andζG), our objective is to find the switching time (tn) that willmaximize M (Mn) subject to the constraint that Y¼Yn (i.e., tomaximize Eq. 5). Now, tn will likely be larger than ts because themaximum amount of storage that can possibly be produced duringthe growing season will generally be higher than the amount justnecessary to cover the winter metabolic losses of Mn (i.e., YsZYn).The optimal switching time tn (see Appendix A) is given by

tn ¼D�ζWζG

ð365�DÞ ð7Þ

Unlike ts, the switching time tn does not depend on body mass,being represented by a vertical line in the (t,m) plane (Fig. 1b).

The correspondence between the two optimization criteria canbe better understood if we consider a continuum of switching times(for the same bioenergetics parameters β, ζG, D, and m0) and assessthe relationship between the resulting structural and storagemasses. If the organism decides to switch at a time shorter than ts,the final structural size will be correspondingly smaller than Ms. Asthe rate of storage production depends on structural mass only (Eq.

(1a)), the final amount of storage will also be smaller than Ys despitethe relatively longer time in the growing season devoted to storageproduction. Switching later than ts will lead to a structural masslarger than Ms. However, in this case the shortening of the perioddevoted to storage production would overcome the advantage of ahigher net production rate associated with a larger structural mass,leading to a final storage that is also smaller than Ys. The result is ahump-shaped relationship between M and Y (Fig. 2, Appendix B),whose equation is

YTS ¼θ ζGð1�βÞDþm1�β

0

h iMβ

TS�θMTS

ð1�βÞ ð8Þ

The subscript ‘TS’ refers to the fact that this relationship results fromthe Total Switching strategy. In Appendix C, we demonstrate that thestructural mass at the peak of this relationship coincides with Ms

(the structural mass associated with the switching curve of Eq. (6)and which maximizes Eq. (4)). The final structural mass resultingfrom maximization of Eq. (5) (i.e., Mn) is determined by the non-trivial interception between YTS and Yn (Fig. 2), found by settingequation Eq. (8) equal to Eq. (3). Mn will be a real and positive

Fig. 1. Growth trajectories of structural mass along a growing season (continuous black lines). The switching curves (dashed lines) divide the state space into two regions:the gray area where it is optimal to allocate all production to structure, i.e., u(t)¼0; and the white area where it is optimal to allocate all production to storage, i.e., u(t)¼1.(a) The optimization criterion is to maximize the final amount of storage. The switching curve is defined by Eq. (6), and the final structural mass is given bym(D)¼Ms. (b) Theoptimization criterion is to maximize the final structural mass with the constraint that the final amount of storage is given by Yn. The switching curve is defined by Eq. (7),and the final structural mass is given by m(D)¼Mn.In all cases, D¼180, ζG¼0.05, ζW¼0.01, β¼2/3, m0¼50, θ¼0.5.

Fig. 2. Relationship between the final structural mass and storage (black line)resulting from the TS strategy for a continuum of switching times from 0 to D. Thegray line represents the optimal amount of storage (Yn, Eq. 3). Parameter values arethe same as in Fig. 1. Ms is the final structural mass leading to maximum storage(Ys), and has the same value as in Fig. 1a. Mn is the maximum final structural massleading to the optimal amount of storage, and has the same value as in Fig. 1b.






number if ζGD4[ζW(365�D)], and it will be larger thanMs (as showin Fig. 2) if ζGD4[ζW(365�D)�m0

1�β]/(1�β) (see Appendix C).The fitness advantage of adopting the TS strategy is illustrated

below by comparing it to an alternative strategy characterized by aconstant fraction allocated to storage production throughout thegrowing season (i.e. u(t)¼c, here called the Constant Allocation orCA strategy). The analysis is greatly simplified if we assume m0¼0,which is a reasonable representation of the critical first year of life.The equation relating the final storage Y to the final structure Mcan be derived for the CA strategy in a similar manner as that forthe TS strategy (Appendix B):

YCA ¼ θζGð1�βÞDMβCA�θMCA ð9Þ

It can be seen from Eqs. (8) and (9) that if m0¼0, YTS ¼YCA/(1�β), so the difference between the two strategies is entirelydependent on the allometric exponent β. As β is generallybetween 0.5 and 1 (Quince et al., 2008a), the storage producedby the TS strategy will be at least twice as large as that producedby the CA strategy. Therefore, the Y(M) curve from the TS strategywill always be higher than the curve from the CA strategy for anyfeasible value of M that leads to Y40. As Yn is a monotonicallyincreasing function of M (see Eq. 3), the optimal structural mass atthe end of the growing season will also be larger (i.e., Mn

TS4MnCA,

Fig. 3a). Fig. 3b–c shows numerical examples of the divergence ingrowth trajectories between the TS and CA strategies within a year(Fig. 3b) and illustrates the consequences for growth across years(Fig. 3c). As the metabolic processes that generate egg productionare dependent on structural mass (e.g., Roff, 2002; Shuter et al.,

2005), the difference between allocation strategies can have largeconsequences for fitness, as illustrated by cumulative fecunditiesin Fig. 3d (see Appendix D for details on numerical methods).

The above analysis represents a deterministic scenario, one inwhich perfect predictability facilitates the evolution of physiolo-gical timing traits that enable the fish to exactly match energyallocation to future energetic needs. However, in natural circum-stances stochastic fluctuations prevent perfect predictability andcan have important influences on the performance of alternativeallocation strategies. Below we present a restricted set of simula-tions to illustrate the influence of environmental stochasticity.A complete analytical treatment or a comprehensive simulationstudy of optimal allocation strategies in stochastic environments,although recommended for future work, is beyond the scope ofthis paper. For the present simulations, we used the same para-meter values as in the deterministic example of Fig. 3, but wevaried trait values characterizing the TS and CA strategies as wellas the degree of stochastic fluctuations in environmental condi-tions. Here we distinguish two temporal scales of stochasticity: (i)inter-annual fluctuations in the length of the growing season D,which can arise mainly from climatic variation; (ii) short-term (e.g., daily) fluctuations in the growth coefficient ζG, which can arisealso from climatic fluctuations as well as changes in food avail-ability or predation risk (which influences foraging activity, e.g.,Abrams, 2003).

To simulate inter-annual fluctuations, we assumed that thelength of the growing season in a given year ‘i’ (Di) follows anormal distribution Di�N(μD, sD), and that, despite annual varia-tion, the fish has a fixed trait value determining when to switch

Fig. 3. Comparison between the Total Switching (TS, continuous lines, white dots) and the Constant Allocation (CA, dashed lines, black dots) strategies. Parameter values arethe same for all graphs: D¼180, ζG¼0.05, ζW¼0.01,β¼2/3, m0¼0, θ¼0.5. (a) The optimal final structural mass Mn is defined where the final storage (hump-shaped) curveintersects the optimal storage curve (gray line). As the gray line is monotonically increasing and the final storage is always higher for the TS strategy, the optimal structuralmass will also be larger for the TS than for the CA strategy (i.e., Mn

TS4MnCA). (b) Optimal growth trajectories along a year. Gray lines represent the storage mass, the dotted

vertical line marks the end of the growing season.(c) Numerical examples of divergence in growth trajectories across years, with reproduction starting in third year. The dotsmark the end of each growing season. The allocation to reproduction was successively adjusted so that the adult has a constant gonad-somatic index of 0.4at the end of eachyear. (d) Cumulative amount of offspring resulting from the growth trajectories shown in (c).






from structure to storage (tn, in the case of the TS strategy) or afixed trait determining the yearly fraction of allocation to storage(ci, in the case of the CA strategy; see Appendix D for details).For each strategy, we simulated 30 trait values covering theirpossible range and 30 values of the standard deviation sDrepresenting degrees of stochastic variability. We determined sDusing coefficients of variation (CV¼sD/μD) varying from 0 to 1. Themean value μD corresponds to the value of D used in thedeterministic case (Fig. 3, D¼180 days). For each one of the30�30 combinations of trait and CV, we simulated 1000 repli-cates of fish growth and reproduction assuming a lifespan of 10years, age of maturity of 2 years, and a gonad somatic index of 0.4.During a simulation, the fish dies whenever stored energy over agiven growing season is not enough to cover losses of thefollowing winter. The lifetime offspring production (kg, averagedacross 1000 simulations) was used as a measure of performancefor each trait-variability combination. In order to deal with anystorage remaining at the end of winter, we assumed that the fish isa spring spawner, so that the remaining storage is incorporated bythe gonad (we assumed no cost in this process) contributingimmediately to fecundity. Conversely, energy that would other-wise be devoted to gonads during the growing season can be usedto cover metabolic losses during winter if storage is insufficient (e.g., Henderson et al., 1996). Fig. 4a and b shows the performance ofthe two allocation strategies. The trait values are presented in a

standardized form as tq or cq, for the TS or CA strategy respectively,so that they vary between 0 and 1, corresponding to the minimumand maximum possible values, and 0.5 corresponding to the traitvalue predicted to be optimal in a deterministic scenario (seeAppendix D for details). When inter-annual variation is null ornegligible, performance peaks at a value of tq or cq close to thedeterministic optimum (0.5). As variability increases, performanceat these trait values declines sharply, becoming more uniformlydistributed across the trait range, especially for the TS strategy.

To make a more direct comparison, we took only the maximumperformance value at each sD and for each allocation strategy (TSor CA, representing selection for the best trait values at a givenlevel of inter-annual variability), and plotted the performance in alogarithmic scale against sD ( Fig. 4c). It can be seen that themaximum performance of both strategies declines with increasingenvironmental variability (and unpredictability), but also that theTS outperforms the CA strategy by producing about twice as muchoffspring throughout the investigated range of sD.

To simulate short-term fluctuations in productivity within thegrowing season, we maintained fixed growing season and winterlengths but introduced daily random fluctuations in the growthcoefficient ζG. Within a growing season (0rtrD), the daily valueof ζG followed a normal distribution with mean μζ and standarddeviation sζ. If the daily value selected for ζG reaches a negativevalue low enough to exhaust the pooled levels of gonad and

Fig. 4. Results of stochastic simulations of inter-annual variation in the length of growing season (a–c) and short-term variation in the growth coefficients (d–f).The three-dimensional graphs show the performance (measured as offspring production) of Total Switching (TS) strategy (a,d) and Constant Allocation (CA) strategy (b,e) for everycombination of stochastic variability and the respective trait value. The two dimensional graphs (c,f) show the maximum offspring production (in a log scale) at each value ofstochastic variability for the TS strategy (open dots) and the CA strategy (closed dots).






storage available to the fish on that day, then the fish dies. At theend of each winter (t¼365), all residual content of storage plusgonads is used to produce offspring. The cumulative offspringproduction (kg) across a maximum life time of 10 years was usedas a measure of performance just as in the simulations of inter-annual variability. We also used 30�30 combinations of traitvalues and short-term variability (CV¼sζ/μζ), and 1000 simulationreplicates. The results are presented in Fig. 4d–f. The TS strategyoutperforms the CA strategy for coefficients of variation lowerthan 30% (sζ/μζo0.3), but afterwards it becomes much moresensitive to increasing variability and the advantage shifts to theCA strategy.

4. Adding storage to the biphasic growth model

The biphasic growth model has been successfully applied topredict life history variation in fish (Lester et al., 2004; Quinceet al., 2008b; Shuter et al., 2005). It has the same bioenergeticsframework as the one adopted here, except that winter andstorage are not considered explicitly. Within a growing season ofa given year ‘i’, the adult devotes the first fraction pi of time togrow somatically, and the remaining fraction 1�pi is entirelydevoted to gonad production. This temporal switching betweenallocation to soma and allocation to reproduction is similar to theTS strategy used here for structure–storage switching and it isalso predicted as optimal in terms of maximization of lifetimeoffspring production (Kozlowski and Teriokhin, 1999; Kozlowski,1996). The adult decreases the fraction pi from year to year as itgets older (i.e., pi 4piþ1), resulting in the asymptotic growthpattern usually observed in organisms with indeterminate growthand of which the von Bertalanffy model is a special case (e.g.,Quince et al., 2008a). In the general biphasic model of Quince et al.(2008a), body size is represented by a transformed variable

v¼ ðm=ΩÞ1�β ;where Ω is the coefficient determining the weight–length

relationship m¼ΩL3. This transformation allows the ‘size’ variablev to grow linearly from year to year before maturation:

vðiÞ ¼ v0þh ∑i

j ¼ 1pj ð10Þ

where v0 is the initial size and h is the annual pre-maturationgrowth rate (cm3(1�β)/year), defined by

h¼ ζGDΩβ�1ð1�βÞ ð11Þ

If β¼2/3, the size variable v becomes equivalent to body length L(cm), the annual growth rate h becomes a linear growth ratemeasured in cm/year, and the growth pattern predicted by thebiphasic model during the adult period becomes identical to thevon Bertalanffy model. This scenario represents a reasonableapproximation, given that empirical estimates of β are usuallynot far from 2/3 and that the von Bertalanffy model has beenwidely and successfully fitted to fish growth data (e.g., Lester et al.,2004; Pauly, 1980). It is also a useful approximation because itimplies that the growth rate h – a parameter of paramountimportance for life history – can be estimated directly from pre-maturation length at age data.

The above equation for h assumes that growth in length ispossible throughout the part of the growing season devoted tosoma. However, if storage is to be produced in order to coverfuture winter metabolic losses, only a fraction of this period will beavailable for the growth in structural mass associated with growthin length. The actual period of time devoted to structural growth,hereafter called the effective growing season, results from the TSstrategy for energy allocation developed in the previous section.

The effective growing season is given by tn, whose equation (Eq.(7)) shows that the extra cost imposed by winter (i.e., the fractionof the growing season that has to be sacrificed to build energystorage) is proportional to winter length (365�D) and to the ratiobetween the rate of energy loss during winter and the rate ofenergy production during the growing season (ζW/ζG). Moreover,the fraction of time used to build structure is the same every year,independent of body size (which results from our assumption ofa common allometric exponent β). This means that the onlyinfluence of storage on growth is to make the effective growingseason shorter, which in turn leads to a slower effective growthrate, hn:

hn ¼ ½ζGD�ζW ð365�DÞ�Ωβ�1ð1�βÞ ð12Þ

5. Empirical analysis

The model developed in this paper can be used to predict howindividual growth and life history should be reshaped by thechanges in growth performance that accompany the longerwinters found along the south to north climatic gradient in thenorthern hemisphere. We tested our model using populationgrowth data from two species of freshwater fish: specifically, weused data from 104 lake trout (S. namaycush) and 52 walleye (S.vitreus) populations found across a latitudinal gradient in Canada(Bozek et al., 2011; McDermid et al., 2010). Intra-specific variationin life histories for both species is well described by a bi-phasicgrowth model (Shuter et al., 2005). Lake trout is a cold waterspecialist species with the following characteristics: (i) its optimaltemperature range for growth is from 8 to 12 1C (Christie andRegier, 1988); (ii) its primary habitat is the pelagic zone of deepstratified lakes; (iii) it avoids the epilimnetic zone when tempera-tures there exceed its optimal temperature range; thus thetemperatures it experiences during a typical growing season arenot expected to exceed its optimal temperature range or to belower than �5 1C below the lower bound of its optimal tempera-ture range. Walleye is a cool water specialist species with thefollowing characteristics: (i) its optimal temperature range forgrowth is from 18 to 22 1C (Christie and Regier, 1988); (ii) itsprimary habitat is the littoral zone of low transparency lakes(Lester et al., 2004); (iii) given its epilimnetic habitat, the max-imum growing season temperatures it experiences will declinewith increasing winter severity, reaching values well below thelower bound of its optimal temperature range, and the wintertemperatures it experiences will be typically �15 1C below thelower bound of its optimal temperature range.

We will use the simpler model of Eq. (11) as a null model to testwhether storage acts as a constraint to structural growth in thesetwo species: this model ignores the detrimental effect of winter ongrowth during the growing season, being a special case of themore general model of Eq. (12). Both models predict a linearrelationship between annual growth rate h and growing seasonlength D; however the simpler model predicts a strictly propor-tional relationship while the more general model predicts that, ifwinter energy loss is important (i.e., ζW40), growth will cease at avalue of D larger than zero. Thus, if a linear regression of h on Dyields a significant negative intercept, then we can conclude thatthe null model should be rejected and that the data support thehypothesis that winter energy demands limit annual structuralgrowth. Before carrying out the regressions, we must control forthe effects of population-specific differences in environmentaltemperature. The major component expected to be affected bytemperature is the growth coefficient ζG (Brown et al., 2004;Clarke and Johnston, 1999; Ernest et al., 2003). It is assumed todepend on temperature according to the Arrhenius equation with






a temperature coefficient (5.02) derived empirically from Clarkeand Johnston (1999):

ζG ¼ αGe�5:02=TG ð13Þwhere TG is the average temperature experienced during the growingseason, and αG is a temperature-independent coefficient, which canbe interpreted as an intrinsic growth capacity. Substituting ζG by Eq.(13) and rearranging Eq. (11) gives a temperature-corrected equationfor annual growth rate in the null model:

he5:02=TG ¼ αGDΩβ�1ð1�βÞ ð14Þ

To estimate D and TG, we modeled the daily variation of tempera-ture in each lake through the model of Shuter et al. (1983, equations4 and 8), using as input parameters the annual average airtemperature (1C) for the period 1960–1990 (IPCC, 2005) and thearea (ha) of each lake (which was converted to fetch size, in km,assuming a circular lake shape). Fig. 5 illustrates how we deter-mined the growing season and average temperatures from theannual temperature profile. We estimated h by dividing length atmaturity (cm) by age at maturity (years) of females in eachpopulation. This procedure assumes linear growth in length before

maturity, which means that we are assuming β¼2/3. A commonvalue of Ω¼0.01 was used, which is within the range of valuesobserved for both species (Froese and Pauly, 2012) and is a usualvalue in fisheries literature (Pope et al., 2006). To carry out theregressions, we chose the Standard Major Axis regression model,which is appropriate in our case as it accounts for random variationin both variables (Legendre and Legendre, 1998).

Fig. 6a shows the temperature-corrected estimates of growth rateand the growing season lengths for both species, accompanied by theregression lines. The correlation is significant for both species (r¼0.600 and 0.637 for lake trout and walleye respectively, po0.001). Theintercepts are negative and their confidence intervals do not overlapzero ([�10.91,�3.54] for walleye, [�3.90,�0.33] for lake trout), giv-ing support to the more general model that accounts for storage. Totest for robustness of this result, we changed the temperaturecoefficient used to correct growth rate estimates (5.02 in the analysisabove), varying it over a broad range from 0 to 10. Fig. 6b shows thatthe estimated intercept is maintained below zero for both species overmost of this range. In addition, the walleye intercept is lower than thatfor lake trout, which is consistent with known differences in thermaltolerance and life history strategies of these two species.

Fig. 5. Seasonal variation of surface water temperature from the model of Shuter et al. (1983), for a lake with surface area 100 ha and an average annual air temperature of5 1C. The shaded area marks the range of experienced temperatures that lead to positive growth for (a) lake trout and (b) walleye. The horizontal dotted lines mark the rangeof preferred temperatures. The temperature experienced by the fish follows the surface water temperature (continuous line) while it is below the upper limit of the shadedarea, which marks the optimal temperature for each species, given by the midpoint of the preferred range (i.e., 10 1C for lake trout and 20 1C for walleye, Christie and Regier1988). When the surface temperature exceeds this optimal value, the fish is assumed to stay at this optimal value, i.e., we assume that the fish is able to choose deeper(cooler) parts of the lake to avoid exceeding the optimal value. The winter is defined as the period when the experienced temperature is equal or lower than the lower limitof the shaded area, which marks the temperature below which growth is not expected to occur, either due to physiological constraints (walleye) or due to scarcity of prey(lake trout).

Fig. 6. (a) Relationship between the temperature-corrected growth rate he5.02/T and the growing season length D for walleye (closed circles) and lake trout (open circles).The continuous and the dashed lines are Standard Major Axis (SMA) regression lines for walleye and lake trout, respectively. (b) Intercepts estimated from SMA and theircorresponding 95% confidence bands across a range of temperature coefficients used to correct growth rate estimates. The continuous line and the dashed line representwalleye and lake trout, respectively.






A direct assessment of the more general model (Eq. 12) bymeans of regression is not feasible because: (i) the two growthcoefficients ζG and ζW are associated with different averagetemperatures and thus the effect of temperature cannot beisolated to the right-hand side of the equation; (ii) there is a highdegree of colinearity between growing season length and tem-perature. Our approach was to compare observed growth rateswith model predictions by attributing reference values to ζW. Weassumed that the rate of energy loss during winter is equal to therate of standard metabolism (i.e., the fish is considered inactive),which is temperature dependent (Clarke and Johnston, 1999):

ζW ¼ αWe�5:02=TW ð15Þ

where Tw is the average temperature experienced during winter,and αW is a temperature-independent coefficient of winter energyloss. To determine the values of αW, we used empirical estimationsfrom Clarke and Johnston (1999) for the fish orders Salmoniformes(lake trout) and Perciformes (walleye). After adjustments for mass(g) and daily units, using calorific constants from Stewart et al.(1983), the values were 0.023 and 0.020 respectively. We did nothave empirical estimates for the growing season coefficient αG, soto determine it we chose the value that minimized the sum ofsquared distances between hn (the predicted growth rate) and the‘observed’ growth rate estimated from life history data, resultingin values of 0.0438 for lake trout and 0.0395 for walleye.

The relationship between observed and predicted growth rates ispresented in Fig. 7a. The correlation is strong in both species(r¼0.628 and 0.683 for lake trout and walleye respectively,po0.001). The regression slopes, estimated from standard majoraxis regression, are significantly different between these two species:the slope for lake trout is shallower (b¼0.737, 95%CI¼0.625–0.850)than the slope for walleye (b¼1.155, 95%CI¼0.915–1.395). The laketrout regression is also shallower than the 1:1 line, primarily becausethe observed growth rates for relatively colder lakes systematicallyexceed predicted growth rates, and vice-versa. On the other hand,there is no indication of biased predictions for walleye. Our use ofstandard metabolic rates as a proxy for energy loss during winter isconsistent with a tolerance strategy adopted by several freshwaterfish species inhabiting seasonal environments (Shuter et al., 2012).The results support walleye fitting in this category, but the same isnot true for lake trout, which is better characterized as a winterspecialist, capable of active foraging under the harsh conditions ofwinter. Indeed, if we assume no energetic cost during winter for laketrout (αW¼0), the trend in the model fit is reversed, and theregression line between observed and predicted growth ratesbecomes steeper than the 1:1 line (b¼1.216, 95% CI¼1.031–1.401),indicating that winter net production during winter should besomewhere between standard metabolic losses and zero.

A complementary possibility is the development of increasedintrinsic growth capacity among lake trout populations located inthe northern segment of the species range in North America (e.g.,the development of counter-gradient variation in αG). Many fresh-water fish species are thermal specialists whose growth andreproductive performances peak over relatively narrow tempera-ture ranges that have a strong genetic basis, shaped in part by thephylogenetic history of the species (Hasnain et al., 2013). Shuteret al. (2012) suggested that the costs of developing physiologicalstrategies to maintain energy acquisition under winter conditionswill be lowest for cold water specialists, such as lake trout, becausethe difference between winter temperatures and the optimalperformance temperatures for this group will be relatively low,leading to relatively low costs in terms of the time and energyneeded for the re-tooling of enzyme systems that would be requiredto improve growth performance under winter conditions (e.g.,Pörtner, 2006). Conover et al.(2009) presented extensive evidencethat counter-gradient intra-specific adaptation of growth capacity is

a common response to the shorter growing seasons that areassociated with higher latitudes in the northern hemisphere. Allthese lines of thought are consistent with the hypothesis that local

Fig. 7. (a) Predicted versus observed annual pre-maturation growth rates (h, cm/year) of 104 populations of lake trout (open circles) and 52 populations of walleye(closed circles). The continuous and the dashed black lines are from a StandardMajor Axis regression for walleye and lake trout respectively. The gray dotted line isthe 1:1 line where h(observed)¼h(predicted). (b) Relationship between thetemperature-corrected growth coefficient αG (Eq. (13)) and the length of thegrowing season (D). The growth coefficients were calculated so that the predictedannual growth rates hn matched observed growth rates in Lake trout (open circles)and Walleye (closed circles), assuming winter losses are equivalent to standardmetabolic rates. The dashed line is the regression line for lake trout; the walleyeregression was not significant so it is not shown. (c) Pearson correlation (r)between the population-specific growth coefficient αG and growing season lengthD and their corresponding 95% confidence bands across a range of values for thetemperature-independent coefficient of winter energy loss αW. The continuous lineand the dashed line represent walleye and lake trout, respectively.






adaptation of growth performance to deal with the increasingseverity of winter should be most evident in cold water specialiststhat experience shorter, but thermally similar (i.e. the range ofexperienced temperatures remains relatively constant) growingseasons with increases in winter severity. This hypothesis can bebetter illustrated using our model if we adjust the growth normal-ization constant αG on a population by population basis, so thatpredicted growth rates match the observed growth rates(i.e., hn¼h), and plot the resulting values against the length of thegrowing season (Fig. 7b). There is a clear negative trend for laketrout (r¼�0.752, po0.001), but none for walleye (r¼�0.246,p¼0.079). This pattern is maintained even if we use the samerange of D and/or the same number of populations for both species(through random resampling, results not shown). The pattern isnonetheless dependent on the choice for the winter coefficient ofenergy loss (αW). By varying this coefficient and evaluating thecorrelation structure between D and population-specific αG we havea better idea of how likely is the possibility of counter-gradientadaptation given our expectation that αW should lie somewherebetween 0 and 0.023. Fig. 7c shows that there is evidence forcounter-gradient variation in lake trout (i.e., negative correlationbetween D and population-specific αG) for the entire range ofpositive values of αW.

6. Discussion

Our model provides a mechanistic justification for the assump-tion of Kozlowski and Teriokhin (1999) that the period devoted tothe production of storage could be considered as part of winter,if winter is defined as a non-growing season. It also demonstratesthat the temporal partitioning between production of structuralmass and production of storage is consistent with the optimalityframework adopted by resource allocation models in general. Inaddition, it provides a more mechanistic way of linking climatevariation (i.e., through changes in D and the ratio ζW/ζG,Eqs. (12-13) and (15)) to life history responses of fish populations.

Empirical support for the model is extensive. Looking first atobserved and predicted patterns of storage accumulation over thegrowing season, we find examples of accumulation patterns thatare consistent with a bang–bang allocation strategy in both therecent freshwater (Biro et al., 2005; Hurst and Conover, 2003;Mogensen and Post, 2012; Post and Parkinson, 2001) and oldermarine (see citations in Shul’man, 1974) literature. More complexallocation patterns have been observed (Shul’man, 1974), but thesecan be accounted for, within the general framework of ourmodeling approach, by noting that these observations are typicallyassociated with environments where the seasonal patterns ofenergy accumulation and deficit are much more complex thanthe simple alternating, fixed length phases of growth and deficitassumed in our model. In these cases, our stochastic simulationssuggest that a more uniform pattern of energy allocation – such asin the CA strategy – will be favoured by selection. Looking next atobserved and predicted patterns of storage accumulation acrosspopulations spread along a climatic gradient, Eq. (7) predicts thatfall storage levels should increase systematically with increasingwinter length. This pattern is confirmed in a variety of studieslooking at various species of freshwater fish (e.g., Atlantic salmon –

Berg et al., 2009, Atlantic silverside – Schultz and Conover, 1997).Finally, our use of the model to identify differences in growthpatterns between species along a climatic gradient proved quitefruitful – adding to the overall credibility of the approach. For laketrout, common garden experiments to measure differences ingrowth potential between northern and southern populationsare recommended to test whether the observed systematic

deviations in growth rate reflect some degree of local adaptationin growth capacity (and/or winter tolerance), or whether they aresolely a reflection of specialization to winter conditions in waysthat offset metabolic losses or even allow for positive productionduring winter.

The explanation for the aforementioned temporal switchbetween structure and storage in empirical studies usually hingeson size-dependent predation risk (Biro et al., 2005, 2004; Post andParkinson, 2001). Predation mortality seems to be especiallyrelevant during the first year of life, when young fish are mostexposed to gape-limited predators and should grow as fast aspossible in order to achieve less vulnerable sizes. Such selectionpressures would favor an allocation strategy that privileges struc-tural growth in the first part of the growing season (Post andParkinson, 2001). However, our model predicts the same patternof allocation without invoking predation mortality (or any othersource of variation in survivorship). In our case, the temporalswitching emerges as an optimal allocation strategy simplybecause it allows for more efficient growth (i.e., when comparedto alternative strategies, it produces larger structural mass for thesame bioenergetics parameters, environmental conditions andstorage mass). In addition, as this enhanced growth in structureis not caused by changes in bioenergetics parameters which couldbe related to foraging activity (i.e., ζG and ζW),it is free from theenergy acquisition trade-offs usually associated with fast growthrates, such as increased risk of detection by predators (Abrams,2003; Enberg et al., 2012; Lima and Dill, 1990). So enhancedgrowth efficiency and reduced predation mortality are expected toreinforce each other as selective agents favouring the total switch-ing strategy in seasonal environments. Disentangling the relativecontribution of these two factors will be a fruitful subject forfuture empirical and theoretical research, including extensions ofthe model that explicitly account for predation mortality.

There are at least two other areas where extensions of thismodeling approach might prove fruitful. These areas focus on twocritical assumptions that simplify some relatively complex aspectsof fish biology. The first involves links between body size andsurvival: by assuming that the optimal allocation strategy willmaximize structural mass, we are implicitly assuming a strong andconsistently positive association between body size and fitness.By making this relationship explicit and including the possibility ofmore complex relationships (e.g., a unimodal relationship), themodel could be used to explore life history responses to specificchanges in predator behavior and the consequences of such lifehistory variation for population dynamics – the kinds of behaviorthat Abrams examined (e.g., Abrams, 1983; Day et al., 2002) usingmore general approaches. Survival may depend also on growthrate, and not only on structural size per se, through allocationtrade-offs (Enberg et al., 2012). For any given net production rate,building structural tissues relatively faster can increase mortalitydue to cellular damage, body deformities or asymmetries, nutrientlimitation and increased sensitivity to starvation (Enberg et al.,2012; Lee et al., 2012). Structural growth also requires metabolicpower, thus compromising the scope for activity and reducing theaerobic capacity for important functions such as escape frompredators (Dmitriew, 2011). So it is important to realize thatprocesses leading to resource acquisition (embodied in our modelby net production coefficients ζG and ζW) and processes determin-ing resource allocation (through the function u(t)) are not inde-pendent as assumed by our model.

The second simplifying assumption is that the objective for thestorage allocation strategy is to store exactly enough energy tomeet the winter maintenance costs of structural mass. Thisassumption masks the complex reality of a stochastic environmentin which winter length varies extensively from year to year, drivingyear to year variation in winter energy demands (as in Hurst and






Conover, 2003) or in which unpredictable short term fluctuationsin food availability could demand a more constant production ofstorage during the growing season. Our restricted set of stochasticsimulations shows that inter-annual variation in the length ofwinter does not affect the relative advantage of the total switchingstrategy, but that short-term variation within a growing season canbe influential if net production rates drop to levels low enough topromote starvation mortality. In seasonal environments with mod-erate short-term fluctuations in energy intake and/or expenditure,the best allocation strategy is probably something intermediatebetween the TS and the CA strategies, which in turn must beenvisioned as extremes of a continuum of possibilities. Indeed,empirical examples show a non-negligible allocation to storage evenearlier in the growing season when investment in structural massshould be maximal (e.g., Biro et al., 2005; Post and Parkinson, 2001).In general, our results highlight that the temporal heterogeneity inallocation to storage within a year should reflect the dominanttemporal scale of variation in net production. Non-seasonal orweakly seasonal environments with unpredictable fluctuations –

characteristic of low latitudes – should favor a more constantallocation over the year, while a clearer separation between a periodof structural growth and a period of storage should be favored instrongly seasonal and predictable environments characteristic of highlatitudes. Therefore, it is not only the overall level of investment instorage that should change with latitude, but also the degree ofuniformity in allocation over the year.

Another important aspect identified by the stochastic simulationsis the interchangeability of storage and reproductive mass. In thedeterministic model version, the environment is perfectly predictableso storage and gonads can be treated as separate compartments, butin a stochastic environment there will always be some degree ofmismatch between optimal and realized levels of energy allocation toeach compartment. In our case, we assumed that energy thatwould otherwise be devoted to gonadal tissue can be used to fuelmetabolism if somatic reserves are not enough, and, conversely, thatstorage remaining at the end of winter is converted into gonads.It highlights the fact that fish are typical examples of capital breeders,i.e., their reproduction is fueled by energy gained earlier and stored,as opposed to income breeders that rely on current energy acquisi-tion (Bonnet et al., 1998). There are several advantages associatedwith capital breeding in ectotherms (reviewed by Bonnet et al., 1998),one of which is to allow parents to match the timing of offspringproduction with the peak of offspring’s reproductive value, whichgenerally occurs before the peak of food productivity (Varpe et al.,2009). When exactly it is best to spawn is a decision that will dependon the relative risks of winter mortality and the relative advantagesof early reproduction (Shuter et al., 2012). For species adopting awinter tolerance strategy, such as walleye, reproduction typicallyoccurs in spring, which is advantageous as it gives priority to the useby parents of energy reserves to cover metabolic losses and preventsyoung offspring from experiencing deadly winter conditions. Forwinter specialists, such as lake trout, relatively higher survivorshipunder winter conditions promotes spawning during the fall season,thus allowing offspring to hatch and begin feeding at the start of thefollowing growing season. This dichotomy between spring versus fallspawning is just one of the factors related to the interchangeabilitybetween storage and other body components. For instance, storageremaining at the end of winter can in principle be used to fuel furtherstructural growth or to exempt the fish from foraging, thus eliminat-ing the predation risks associated with energy acquisition (e.g.,predation risk trade-offs, Abrams 2003). These considerationsemphasize the complexity of the relationships linking different bodycomponents and highlight the importance of carefully defining thecosts of converting energy from one compartment to another, since itis these costs that will strongly influence how different stochasticenvironments will lead to different optimal allocation strategies.

One useful feature of our deterministic model is that, throughEqs. (7) and (12), it provides a clear link between climaticcharacteristics and fish life history and performance. This link willalso be useful in identifying how climate change may affect lifehistory. In this context, it is interesting to note the parallelismbetween the allocation model for storage developed here, and theallocation models for reproductive effort developed by Kozlowski(1996) and others (e.g., Lester et al., 2004; Quince et al., 2008a;b).A critical aspect of both these strategic analyses is the implicitassumption that the organism has a timing mechanism that willidentify when, within the growing season, the allocation switch(from soma to storage or from soma to reproductive tissue) shouldbe made. There is an extensive literature on the mechanisms thatunderlie reproductive allocation switches and, in fish (and manyother organisms), these switches are almost always associatedwith a photoperiod cue (Bradshaw and Holzapfel, 2010, 2007).It seems at least plausible that storage switches may also bedependent on a photoperiod cue. If this is so, then it is interestingto speculate on the consequences for organism performance underclimate change. Under climate change, winters will shorten butphotoperiod will remain unchanged. Therefore allocation switch-ing will occur at a time that is progressively less optimal for theorganism, generating less soma and more storage than is optimal,given the changing climate. While these changes may not beseriously deleterious for the organism if its supporting communityremains unchanged, they will almost certainly reduce its ability tocompete effectively with invading, warmer water species that arepre-adapted to deal with shorter winters (Emerson et al., 2008).

Acknowledgments

This work was supported by the Natural Sciences and Engi-neering Research Council of Canada, the Ontario Ministry ofNatural Resources and the University of Toronto. H.C.G. is sup-ported by a postdoctoral fellowship funded by NSERC and theUniversity of Toronto. We thank Peter A. Abrams and Nigel Lesterfor advice and suggestions on the manuscript. Nigel Lester wasextensively involved in compiling and validating the lake trout andwalleye life history data bases.

Appendix. Supporting information

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.jtbi.2013.08.020.

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Adaptive responses of energy storage and ﬁsh life histories to climatic gradients

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