A high-resolution modeling study on diel and seasonal vertical migrations of high-latitude copepods

Despite diel and seasonal vertical migrations (DVM and SVM) of high-latitude zooplankton have been studied since the late-19th century, questions still remain about the inﬂuence of environmental seasonality on vertical migration


Introduction
Vertical migration is a common behavior of many zooplankton taxa.Based on the periodicity, vertical migrations of high-latitude zooplankton are classified into diel and seasonal components, which have been studied since the late-19th century (reviewed in Russell, 1927;Cushing, 1951;Banse, 1964).The short-term diel vertical migration (DVM) has a periodicity of up to 24 h, and is understood as a strategy that trades off growth potential to reduce the mortality risk imposed by visual predators (Lampert, 1989; Table 1 Some endogenous and exogenous cues that are believed to proximately or ultimately regulate diel and seasonal vertical migrations of marine and freshwater zooplankton.Literature do not come from an exhaustive review and only serve as examples.

Cue
DVM SVM Temperature McLaren (1963), Enright (1977) Hirche (1991), Heath and Jónasdóttir (1999), Astthorsson and Gislason (2003) Light (absolute or relative irradiance from sun, moon, stars, or aurora borealis, photoperiod, spectral quality, polarization etc.) (Zink, 2002), and may complicate the understanding of the relationships between vertical strategies and environmental variables (see Table 1 for examples).Moreover, since diel and seasonal vertical migrations occur on different spatial and temporal scales, studying these migrations together in the field in adequate resolution remains a major challenge.Although novel optical and acoustic methods of in-situ observation offer a solution to some of these problems (e.g.Basedow et al., 2010;Sainmont et al., 2014b;Bozman et al., 2017;Darnis et al., 2017), long-term deployment and accurately resolving the identity of the migrants remain as key challenges.
Mechanistic models offer an alternative means of studying zooplankton vertical strategies in higher resolution.Models related to DVM usually encompass the highest spatial (≤1 m), temporal (≤1 h) and biological (=individual) resolution (e.g.Fiksen and Giske, 1995;Eiane and Parisi, 2001;Liu et al., 2003;Burrows and Tarling, 2004;Hansen and Visser, 2016).Models related to SVM and diapause (i.e.hibrnation in deeper waters, e.g.Hirche, 1996) encompass the same biological resolution, but are usually coarse in spatiotemporal resolution.Here, the time intervals range from 1 h to 1d and vertical spatial elements are usually resolved to either absolute depth units (e.g. 1 m bins) or segregated habitats (e.g.Fiksen and Carlotti, 1998;Miller et al., 1998;Hind et al., 2000;Ji, 2011;Ji et al., 2012;Sainmont et al., 2015;Banas et al., 2016).The choice of a coarser spatio-temporal resolution of these models reflects the broader space and time scales at which the SVM and diapause occurs.This contrasting spatio-temporal scale makes it difficult to harbor lifetime dynamics of DVM to be simulated in SVM models without significantly increasing computer time.Consequently, most models that simulate SVM tend to either fully (e.g.Hind et al., 2000) or partly (i.e. of younger developmental stages, e.g.Fiksen and Carlotti, 1998) disregard DVM.However, the validity of such simplifications are questionable, given the geographically and taxonomically widespread nature of zooplankton DVM behavior and its ontogenetic patterns (Huntley and Brooks, 1982;Huang et al., 1993;Osgood and Frost, 1994;Hays, 1995).It is thus interesting to investigate whether the extra biological information resulting from modeling DVM and SVM in concert is a worthy trade-off for the elevated computer time.If so, such models may lead to improvements of the current understanding about how environmental seasonal- a The upper limit of ␣ changes with the maximum surface irradiance of the model environment, i.e.Imax = 1500 mol m −2 s −1 for Environment-L, 1300 mol m −2 s −1 for Environment-M and 1100 mol m −2 s −1 for Environment-H (cf.Fig. 1).
b Time of being spawned.
ity shapes up vertical strategies, and the means of which the latter influences life histories of high latitude zooplankton.
In this study, we present a model of zooplankton vertical strategies.The model operates in a high-latitude setting and simulates both DVM and SVM of a herbivorous copepod with an annual life cycle in high spatial (vertical) and temporal resolution.Using this model, we aim to investigate the influence of environmental variables on vertical strategies, and how vertical strategies affect fitness and phenology in seasonal environments.We further discuss how short-term behavior (DVM) influences and interacts in the longerterm and shape-up different life history components of copepod strategies.

Materials and methods
Although the model is not strictly individual-based, it is described following the Overview, Design concepts and Details (ODD) protocol (Grimm et al., 2006(Grimm et al., , 2010) ) to improve reproducibility.

Purpose
The purpose of the model is to investigate the bottom-up and top-down influences of environmental variability (i.e.irradiance, temperature, food-availability and predation risk) on vertical strategies of a high-latitude herbivorous copepod, and to understand the influences of vertical strategies on its fitness and phenology.

Entities, state variables and scales
The model consists of three entities: vertical strategies, model organism and the model environment.Vertical strategies define the timing, amplitude and the ontogenetic trajectories of DVM and SVM, and are described using six evolvable (soft) parameters (Table 2).These are hardwired to the model organism, i.e. copepods spawned in different times of the year.
The model organism is a hypothetical herbivorous semelparous female copepod (hereafter, the copepod) with an annual life cycle that resembles Calanus finmarchicus and C. glacialis in terms of body size, behavior and life history strategies (Conover, 1988).These two species often dominate the copepod biomass in the North Atlantic and most Eurasian sub-Arctic and Arctic seas and shelves (Falk-Petersen et al., 2009).Their life cycle consists of an embryonic stage (egg), six naupliar stages (NI-NVI), five copepodite stages (CI-CV) and an adult.Eggs that are released in near-surface waters in the spring usually develop into CIV or CV stages toward the end of the productive season.As further development is typically constrained by the duration of the productive season and seasonal peaks of visual predation risk, CIVs and CVs descend into deeper waters and remain in a state of diapause/dormancy with minimal phys-iological activity (Hirche, 1996).Overwintering stages ascend to near-surface waters as the primary production commences in the following year, molt into adults and start to reproduce (Conover, 1988;Varpe, 2012).The life cycle of the two species is usually completed within one year in most sub-Arctic and Arctic locations (Falk-Petersen et al., 2009;Daase et al., 2013), within which reside the model environments of this study.
The model runs in three 500-m deep artificial seasonal environments that represent three high-latitude locations along the southern and southeastern coast of Norway (60-70 • N).These environments do not point to specific geographic locations, but the modelled environmental dynamics were adopted from field measurements from the above region (Appendix A1 in Supplementary material).The baseline model simulation (hereafter, the basic run) runs in Environment-L, representing the lower end (ca.60 • N) of the selected geographical range.Here, the modelled irradiance, temperature and food availability are highly seasonal and vertically structured (Fig. 1a-c), but are assumed constant between years.The irradiance incident on the sea surface follows the global clear-sky horizontal irradiance model of Robledo and Soler (2000), and peaks at ca. 1500 mol m −2 s −1 (Fig. 1a, Appendix A1 in Supplementary material).The sea surface temperature reaches a maximum of 18 • C in the summer (e.g.Bagøien et al., 2000), and distributes evenly in the surface mixed layer (Fig. 1b).Below this, the temperature decreases with depth and converges to a minimum of 4 • C at ca. 100 m (e.g.Ingvaldsen and Loeng, 2009).The pelagic productive season extends ca.180 days, with a chlorophyll-a peak at 8 mg m −3 in mid-April (Fig. 1c: Sakshaug et al., 2009;Daase et al., 2013).We manipulated the environmental parameters of Environment-L to formulate two additional artificial environments: Environment-M (ca.65 • N, Fig. 1d-f) and Environment-H (ca.70 • N, Fig. 1g-i), Fig. 2. The model overview.Vertical strategies that define the timing and amplitude of DVM and SVM are hardwired to copepods born in different times of the year.Growth, survival and reproduction of these copepods are simulated in a seasonal environment to derive a fitness estimate that is heuristically maximized by the GA to derive the optimal vertical strategy, time of birth and several associated life history traits emerging from the model.Dashed line represents the indirect dependency of the fitness estimate on growth (Section 2.6.4).
representing the mid-point and the higher end of the selected geographical range (Appendix A1 in Supplementary material).
Copepods are characterized by six states: vertical location (depth), structural body mass, energetic reserve, reproductive output (fecundity), survivorship and developmental stage.The model has a temporal coverage of an annual cycle and a unidimensional (vertical) spatial coverage of 500 m.The time and space consist of 1 h and 1 m discreet intervals.

Process overview and scheduling
At each timestep, the model follows vertical strategies hardwired to copepods born in different times of the year and simulates their growth, survival and reproduction.State variables are updated simultaneously.Vertical strategies are evaluated using a fitness function based on the expected survival and reproductive per-formances.The fitness is heuristically maximized using a Genetic Algorithm (GA, Holland, 1975) to estimate the optimal vertical strategy and optimal time of birth for a given set of environmental conditions (Fig. 2).

Basic principles
The high spatial and temporal resolution implemented in the model allow both DVM and SVM to be simulated over the entire annual life cycle of the copepod.Carlotti and Wolf (1998) have implemented a similar construct, but the SVM of their model was constrained by fixing the timing of ascent and descent to match the field observations of the region of interest.In contrast, the timing and the amplitude of DVM and SVM of our model are flexible and allowed to evolve according to the environmental conditions.To achieve this level of flexibility, we used multiple evolvable proxies to represent vertical migration (Table 2).This resulted in a complex seven-dimensional optimization problem that can be efficiently solved using heuristic techniques (Zanakis and Evans, 1981).
As evolutionary algorithms provide an efficient means of solving multi-dimensional optimization problems (Deb, 2001;Eiben and Smith, 2003), we used a GA as the optimization platform of this model.Further, to increase the precision of the evolvable parameters and that of the behavioral strategies and life history traits ensued (Fig. 2), we used a GA variant with floating point representation (i.e. a Real-Coded Genetic Algorithm, Davis, 1989;Lucasius and Kateman, 1989;Herrera et al., 1998).
The strategy-oriented construct of this model contrasts classic individual-based models of zooplankton life history and behavior in two main ways: first, trading off of biological resolution (strategies vs. individuals) to accommodate higher spatio-temporal resolution, and second, the lack of population-level responses such as density dependence.As a result, modelled vertical strategies do not interact with each other and show no quantitative feedbacks with the model environment (e.g.impact of grazing on food concentration and duration of the productive season).

Emergence
The behavioral strategies and life history traits emerging from the model are presented in Fig. 2 and described in Table 3.

Adaptation and sensing
Copepods are sensitive to their internal states (i.e.structural body mass, mass of the energetic reserve and developmental stage) and external stimuli (i.e.irradiance, temperature, food concentration and depth).Altogether, these determine the size-or stage-specific patterns of growth, metabolism, reproduction and vertical behavior (Section 2.6).

Objectives
The model uses a fitness estimate that evaluates the expected reproduction and survival performances rendered by different vertical strategies (Section 2.6.4).

Prediction and stochasticity
The vertical search pattern of copepod behavior is based on a semi-stochastic predictive algorithm (Section 2.6.2.2 and Appendix A2 in Supplementary material).Stochasticity plays a central role in the model initialization (Section 2.5) and selection, recombination and mutation operators of the GA (Section 2.6.4).

Observations
For a given model environment, the model produces heuristic estimates of the optimal vertical strategy and optimal time of birth, along with a range of associated life history traits (Fig. 2, Table 3).

Initialization
The model initializes with seeding of N (=10 6 ) eggs at random times of the year to random depths (<50 m) of the water column.Each seed represents an embryonic stage of a copepod with a specific vertical strategy, which is determined by randomly assigning values to the evolvable proxies.The ranges (bounds) and resolutions of these proxies are listed in Table 2.

Growth and development
We modelled somatic growth in Carbon units (g C) according to the growth model of Huntley and Boyd (1984) (Eqs.(1)-(8) below), using a Chlorophyll-a/C ratio of 0.030 (Båmstedt et al., 1991;Sakshaug et al., 2009).This growth sub-model was used due to its simplicity and general applicability, which are shown by its utility to model several different copepod taxa with varying body sizes representing a wide range of geographical locations (e.g.Robinson, 1994;Fiksen and Giske, 1995;Roman et al., 2000).Definitions and units of all the terms described henceforth are listed in Table 4.
For ambient food concentrations (F: g C ml −1 ) above a specific saturation concentration (f), growth is food-independent, and occurs at a maximum rate (G T : g C ind −1 h −1 ) dependent only on the ambient temperature (T) as; Here, i represents individual, t time and z is depth, where G' max (g C mg dry mass h −1 ) is the maximum temperature-dependent mass-specific growth rate, assuming a Carbon: dry body mass (W, mg) ratio of 0.40 (Huntley and Boyd, 1984), defined as; If the ambient food concentration drops below the saturation concentration, the growth occurs at a rate limited by food availability (G F ) as; Non food-limited growth rate Eq. ( 1) Scalar for visual predation risk Respiratory coefficient Eq. ( 5) a g C mg dry mass h −1 (Mn)t,z Non-visual predation risk Section 2.6.2.1 - Starvation risk Eq. ( 12) mt,z Exponent (respiration) Eq. ( 6) a -(Mv) i,t,z Visual predation risk Eq. ( 10) -N No. of initial seeds 1,000,000 nt,z Exponent (clearance) Eq. ( 7) a -R i Fecundity Eq. ( 13) no. of eggs Cruising velocity Eq. ( 11) Dry body mass (assuming 40% C) -mg (Wq) i,t Catabolized structural mass (proportion to the maximum lifetime structural mass) Parameter for weighing fitness 0 or 1 -˝i Fitness Eq. ( 14) a Huntley and Boyd (1984).b Fiksen and Giske (1995).c Robledo and Soler (2000).d Calculated from Salzen (1956).
where two terms of the right-hand side of the equation refer to the assimilation and respiratory rates respectively.The assimilation coefficient (a) is assumed to be constant (Table 4), but Huntley and Boyd (1984) found that the coefficients of clearance (b) and respiration (k), and the exponents (n and m) vary with ambient temperature as; At the point where F reaches f, Eqs. ( 1) and (3) balance out, and the f becomes; This growth sub-model is not applicable to the first two nauplii stages, which do not feed (Fig. 3a, Marshall and Orr, 1972;Mauchline, 1998).For simplicity, we assumed the growth of NI and NII stages to occur at a temperature-dependent rate (Eqs.( 1) and (2)).The growth of early developmental stages (NI-CIII) is solely allocated to the building up of structural mass (W c , g C, Fig. 3a, b and Table 5).
The embryonic development follows a Bělehrádek temperature function (Campbell et al., 2001;Ji et al., 2012).The post-embryonic development (from stage j to j + 1) occurs only if W c exceeds a stage-specific critical molting mass (W x , g C, Table 5).However, for simplicity, we did not model the dependence of molting process on the physiological state (Nival et al., 1988) and the limitation of growth by the exoskeleton (Mauchline, 1998).
2.6.2.Survival 2.6.2.1.Predation risk.Visual (v) and non-visual (n) predators induce mortality, which is estimated as a probability following Eiane and Parisi (2001) as; where I z and I 0 are irradiance at depth z and surface at a given time, and (=0.06 m −1 ) is the attenuation coefficient for downwards directed irradiance in the water column.We remapped irradiance (I) between 0.1-0.9(I ) so that visual predation risk is not nullified even at the lowest levels of irradiance, and the copepod has some chance of survival even at highest levels of irradiance.2).A comparative summary is given in Table 5.
The detection efficiency of visually orientating planktivores increases with the size of their prey (Brooks and Dodson, 1965;Batty et al., 1990).For simplicity, we modelled the size-dependent visual predation risk using a linear model, assuming that the largest developmental stage is ca. 10 times more vulnerable to visual predators compared to the smallest developmental stage (Fig. 4a, Table 5, De Robertis, 2002).This was implemented using the scalar The initial value of K (i.e.K value at the embryonic stage, range = 1 × 10 −4 -1.5 × 10 −2 ) was decided so that it produces hourly estimates of visual predator-induced mortality.
We assumed the mortality risk caused by non-visual predators (non-visual predation risk, M n ) to be 1% of the maximum visual predation risk and constant over time and depth (Eiane and Parisi, 2001).
2.6.2.2.Diel vertical migration.The copepod may perform DVM to trade off growth potential to minimize the visual predation risk.We used the photoreactive behavior as a proxy to estimate the timing and amplitude of DVM (e.g.Kerfoot, 1970;Carlotti and Wolf, 1998).Here, ␣, an evolvable light sensitivity parameter (Table 2) was used to define an irradiance threshold above which induces a negative phototatic response in the vertical swimming behavior (Båtnes et al., 2015;Cohen et al., 2015).At any given time, the copepod occupies a depth with an irradiance level (I t,z ) below ␣.From a series of possible depth bins that satisfy the I t,z < ␣ condition, we assumed that the copepod searches and occupies the depth that maximizes its growth potential.For simplicity, we further assumed that internal state-dependent factors, such as hunger and satiation have a negligible influence on the modelled DVM.The vertical search pattern was predicted using a biased random walk algorithm (Codling, 2003, Appendix A2 in Supplementary material), assuming that the copepod is neutrally buoyant and vertically moves in the water column at a maximum velocity (hereafter cruising veloc-   (1985) and Heywood (1996) (points in panel b).The different linear models for ˇ, that scale the light sensitivity parameter (␣) are optimized in the model (Table 2).The lower and upper border of the shaded polygon (panel d) represent the total body mass for growth allocation parameter ( ) = 0 and 1 respectively.ity, U).We used several stage-specific cruising velocity estimates of Calanus spp.available in the literature (Fig. 4b), and related those to body mass as; We considered the size-or stage-specific variability of DVM as a response to size-dependent visual predation risk (Zaret and Kerfoot, 1975;Uye et al., 1990;Hays et al., 1994;Eiane and Ohman, 2004) and modelled it by scaling the light sensitivity parameter (␣) with the body mass (W c ).As data on the light sensitivity of younger developmental stages (NI-CIII) of Calanus spp. is rare, we could not derive a general relationship between W c and ␣.To address this, we defined an evolvable parameter ˇ that describes the size specificity of ␣, which, at its maximum (ˇ = 10) downscales ␣ of the adult female to 10% of that of the egg/NI (Fig. 4c).Higher trajectories than ˇ = 10 were not used, as it was shown in the trial runs that the model always converges on ˇ < 10 even at highest levels of visual predation risk.
2.6.2.3.Energy storage.CIV and CV stages can allocate a specific fraction from surplus growth (evolvable growth allocation parameter: , Table 2) to build up an energy reserve (Fig. 3c) that possesses a maximum size of 70% of the total body mass (Fig. 4d, Fiksen and Carlotti, 1998).
2.6.2.4.Seasonal vertical migration.Similar to most high-latitude marine zooplankton, which descend to depths during the unproductive part of the year (reviewed in Conover, 1988;Hagen and Auel, 2001;Falk-Petersen et al., 2009), the copepod may perform SVM.We used the state of the energetic reserve as a proxy of timing of the SVM (cf.Visser and Jónasdóttir, 1999).Here, the copepod descends to a specific depth (evolvable overwintering depth , Table 2) when the stores account for a specific fraction of the total body mass (evolvable seasonal descent parameter: ı, Table 2).Upon reaching the overwintering depth, the copepod remains stagnant at a diapause state (Hirche, 1996) with its metabolic rate reduced by 90% from that under normal conditions (Fig. 3d, Table 5, Pasternak et al., 1994;Varpe et al., 2007).The overwintering period terminates when a specific fraction (evolvable seasonal ascent parameter: ε, Table 2) of the energetic reserve is exhausted.After the overwintering period, surplus gains are not allocated to develop further energetic reserves, but may be used for structural growth and reproduction (Fig. 3e and f, Table 5).2.6.2.5.Metabolism.The basal metabolic cost relates with the body mass and ambient temperature, expressed as k•W m in Eq. (3) (terms as defined above and in Table 4).The metabolic cost of zooplankton vertical movements can account for 0-300% of the basal metabolic demand (Vlymen, 1970;Foulds and Roff, 1976;Morris et al., 1985;Dawidowicz and Loose, 1992).For simplicity, we assumed the cost of vertical movement to be 150% of the basal metabolic cost (midpoint of the above range).This additional cost is subtracted from the growth Eqs.(1) or (3).The energy reserve is used to balance the metabolic demands that cannot be sustained under low ambient food concentrations (Fig. 3c-f).
2.6.2.6.Starvation risk.When energy reserves are depleted, the metabolic demands that cannot be balanced by food intake are met by catabolizing structural body mass (Fig. 3b-f).This elevates the mortality risk due to starvation (starvation risk, M s ), which is defined as a probability that increases as a linear function of catabolized structural mass as; Here, W q is the catabolized structural mass expressed as a proportion of the maximum structural mass prior to structural catabolization.W q can reach a maximum of 0.5, during which M s peaks following Eq.( 12), and the copepod dies according the Chos-sat's rule (Chossat, 1843), which posits that starving animals may catabolize about half of their body weight before death.Irrespective of the age of this generalized rule, it has been used as a constraint in starvation studies of many vertebrate and invertebrate taxa (e.g.Threlkeld, 1976;Spencer, 1997;Costello, 1998;Loos et al., 2010).

Reproduction
We assumed that somatic growth ceases after the final molt, and all adults become sexually mature at a constant structural body mass (Fig. 3f, Table 5).Energetic input to egg production may be sourced from food intake (income breeding) or allocating a specific amount of matter (C) equivalent to the maximum growth rate (G T : Eqs.(1) and ( 2)) from the remaining energetic reserve (capital breeding, cf.Varpe et al., 2009).The fecundity (R) from the time of sexual maturity (t R = time of final molt) to a given time horizon (t X ) is estimated using the matter allocated to egg production (W R ) and the unit egg mass (W E = 0.55 g C) as;

Fitness function and optimization
To evaluate the performance of a vertical strategy, we derived a fitness estimate (˝) as a function of survivorship and fecundity as; Here, ω is a weight that adjusts fitness (see below) and H is the survivorship, i.e. the probability of survival from birth (t B ) to a given time horizon (t X ) estimated as a function of visual, non-visual and starvation risks (M v , M n and M s ) as; The term ˝ technically resembles the net reproductive rate (e.g.Stearns, 1992), and is used in some optimization models (e.g.Kiørboe and Hirst, 2008) but may not bare the same interpretation given the strategy-oriented construct of this model.When the model predicts an optimal vertical strategy and time of birth for a particular environment, we can assume that those predicted optima should persist from one generation to the next if the environment remains constant.If a copepod's spawning period lasts from time t R to t D (time of death) we assumed that it produces a series of offspring with the same vertical strategy, but born at different times of the year (ranging from t R to t D ).However, only the offspring with a time of birth matching that of the mother can represent the entire evolvable (soft) parameter set of the mother, and guarantee its persistence from one generation to another (Fig. 5a-c).Therefore, we adjusted the fitness using a binary weight (ω) by setting ω = 0 if the copepod's spawning season does not overlap its time of birth (Fig. 5a and b) and vice versa (Fig. 5c).
We used a Real-Coded Genetic Algorithm (RCGA) to derive heuristic estimates of optimal vertical strategy and time of birth that maximizes fitness in a given model environment (Fig. 5d).In the RCGA, six proxies of vertical strategies and the time of birth of the copepod that those are hardwired to (Table 2) are considered as genes on a single chromosome.The RCGA begins by selecting a mating pool of N chromosomes (=parents, i.e.N vertical strategies seeded in different times of the year) from the initial seeds using a binary (two-way) deterministic tournament selection (Goldberg and Deb, 1991;Miller and Goldberg, 1995).Genes of two randomly selected parents from the mating pool are recombined through blend crossover following the BLX-␣ method (Eshelman and Schaffer, 1993), which produces two offspring (recombinants).Genes of the recombinants are mutated at a probability of 0.02 by random replacement (uniform mutation: Eiben and Smith, 2003;Haupt and Haupt, 2004).The population of strategies resulting from these operations comprises of N parents, whose fitness is known and N offspring, whose fitness is not yet known.Parents with unique gene combinations are selected to construct a library (hereafter, the reference library), which is updated at each iteration.Each offspring is compared with those in the reference library to assess their fitness.Fitness of the offspring with similar gene combination to those in the library are assigned in-situ, while the rest goes through the life cycle simulation to determine fitness (LS-2 in Fig. 5d).Once the fitness of all 2N individuals are known, N survivors are selected following a round-robin (all-play-all) tournament of size 10 (Harik et al., 1997;Eiben and Smith, 2003).This process is repeated for a minimum of 100 iterations, and terminated when the mean fitness of the population shows no improvement for 25 consecutive iterations ( in Fig. 5d, Eiben and Smith, 2003).

Programming, execution and analysis of the model
We used R version 3.3.1 (R Core Team, 2016) and R Studio integrated development environment (IDE) version 1.0.136(RStudio Team, 2016) along with the high-performance computing packages Rcpp (Eddelbuettel et al., 2011) and bigmemory (Kane et al., 2013) to construct, simulate and analyze the model.
A basic run was performed in the Environment-L using default values for model parameters (Table 4).In order to test the influence of model parameters and environmental variables on modelpredicted vertical strategies and fitness, we performed a sensitivity analysis following (Jørgensen and Bendoricchio, 2001).Here, we calculated a sensitivity score (S x ) as; where X is the predicted model output of the basic run (X BR ) and the modified run (X M ) for a given change (±25%) of input parameter value between the basic run (P BR ) and the modified run (P M ).We tested the sensitivity of vertical strategies and fitness for 13 different input parameters (Appendix A3 in Supplementary material).
For the convenience of interpretation of these results, we presented the sensitivity scores under three categories: no-sensitivity (S x = 0), low sensitivity (0 < S x ≤ 3) and high sensitivity (S x > 3).Finally, we

Table 6
Predicted variability of emergent behavioral strategies and life history traits (Fig. 2, Table 3) induced by model parameters and environmental variables analyzed for sensitivity (Fig. 7, Appendix A3 in Supplementary material).
Only the input parameters with highest influence on fitness (sensitivity index >3) are tabulated.studied the changes of heuristically optimized vertical strategies by performing model simulations in the three model environments at different levels of visual predation risk, while maintaining the rest of the parameter values at its default levels.
As GAs produce heuristic estimates of the maximum fitness, there is no guarantee that it would converge on the global maximum given a potentially diverse fitness landscape (Record et al., 2010).Therefore, we replicated each model run 10 times with different starting values assigned to the soft parameters (Table 2) to check if the algorithm converges on the same set of solutions.As the optimized parameter values showed little variability between replicate runs (<5%), we used the mean of the replicates for each parameter for analyses.

The basic run
In the basic run, the life cycle emerging from the model began as an egg spawned at 20 m depth in late-April.The first two nauplii stages did not perform DVM, but DVM and the associated metabolic cost (swimming cost) increased ontogenetically from NIII onwards (Fig. 6a, b, e and f).The somatic growth of all developmental stages beyond NV occurred under food limitation (Fig. 6c), and because of reduced growth rates, their predicted development times were higher than those estimated from Bělehrádek temperature functions (Fig. 6d).As the energetic reserve reached 65% of the total body mass (W s ≈ 196 g C, Fig. 6g), the developmental stage CV descended to an overwintering depth of 150 m in mid-June, ca. 2 months before the pelagic primary production had terminated (Fig. 6e).It remained there for ca.290 days, and ascended into nearsurface waters again in early-April of the following year, ca. 10 days after the pelagic primary production had commenced (Fig. 1c), with fully depleted energetic reserves.Although the energetic cost of seasonal migration was quite high, the cost of ascent was ca.¼ of that of the descent due to the loss of body mass during overwintering (Fig. 6f and g).The copepod developed to an adult female in mid-April, and thenceforth produced eggs (ca.3000) via income breeding until mid-June and then died (Fig. 6h).

Sensitivity analysis
The model-predicted fitness was highly sensitive to visual predation risk, food concentration and temperature (Fig. 7).A 25% change in the visual predation risk (K = 7.5 × 10 −3 and 1.25 × 10 −2 ) influenced the DVM, which intensified at the higher-end of K and vice versa (Table 6).Although the overwintering depth deepened by ca.13% under higher visual predation risk, it did not change under lower visual predation risk.Furthermore, higher visual predation risk lowered the fecundity and longevity, and vice versa (Table 6).
A 25% change in food concentration (F = 10 and 6 mg m −3 Chl.-a) notably influenced the DVM, timing of SVM and time of birth, but not the overwintering depth (Fig. 7).Under low food concentration, the DVM was less pronounced and the seasonal descent was delayed ca. 15 d compared to the basic run, possibly because of foraging later into the feeding season due to lower growth potential sustained under increased food limitation (Table 6).However, the copepod overwintered as a significantly large CV with elevated energetic reserves, and made ca.7-d earlier spring ascent (late March), followed by spawning that preceded the pelagic bloom by ca. 2 days (cf.Fig. 1c).Here, ca.2% of the total egg production was sourced from capital breeding (Table 6).Early seasonal ascent, capital breeding and early spawning thus appear as strategies employed to avoid seasonal peak in visual predation risk (cf.Fig. 1a, Eqs. ( 9) and ( 10)) when foraging efforts are elevated to cope with lower  growth potential.However, this came with a cost of decreased fecundity (80%) and longevity (7%) (Fig. 7, Table 6).Increased food concentration had the opposing effects on the predicted behavioral strategies and life history traits described above (Fig. 7, Table 6).
The influence of 4.5 • C change in temperature (T = 22.5 and 13.5 • C) on copepod's behavior and life history followed the same general trends described for food concentration (Fig. 7, Table 6), and highlight the equally important roles played by food availability and temperature in growth and development.

Latitudinal environmental variability and visual predation risk
Model-predicted optimal time of birth, body mass (W c and W s ) at seasonal descent, overwintering depth and longevity changed with visual predation risk (K), but showed less variability along the modelled latitudinal environmental gradient (Fig. 8b-d and  g).The predicted optimal time of birth changed from late-April to mid-May with increasing visual predation risk, and was con-stant across the three model environments, with the exception that it occurred the earliest in mid-April at Environment-H under the lowest visual predation risk (K = 10 −4 , Fig. 8d).At lower levels of visual predation risk, the copepod overwintered as relatively large CVs with elevated energetic reserves at relatively shallow depths (Fig. 8b and c).However, as the visual predation risk increased, the copepod overwintered as smaller CVs or CIVs with relatively less energetic reserves at greater depths.Although the predicted longevity decreased by ca.80 d along the modelled visual predation risk gradient (Fig. 8g), longevity at Environment-H under K = 10 −4 was lower (365 d) compared to those predicted under higher visual predation risk levels (384-430 d).
The predicted timing of SVM showed significant variability across the three model environments, but was less affected by visual predation risk (Fig. 8a).Both the descent and ascent occurred earliest at the lowest latitude environment, but happened later in the season at higher-latitude environments, with a shift of about a month.Although this reflects the delayed occurrence of the pelagic bloom along the modelled latitudinal gradient (Fig. 1c, f and i, Appendix A1 in Supplementary material), the seasonal ascent at Environment-H under lowest visual predation risk (K = 10 −4 ) occurred ca. 25 days before the pelagic primary production had commenced (Figs.1i and 8a).
The predicted onset of spawning, fecundity and breeding mode index (Fig. 8d-f), along with the predicted timing and amplitude of DVM, food limitation index and development time (Fig. 9) varied with both the visual predation risk and latitudinal environmental gradient.In all model environments, the spawning started earliest under the lowest visual predation risk (K = 10 −4 , Fig. 8d).Here, spawning commenced ca.5-7 days earlier than the onset of spring primary production in lower latitude environments (Fig. 1c and  f), and ca.2.5-5% of the total egg production were sourced from capital breeding (Fig. 8f).Spawning at Environment-H commenced ca. 25 d prior to the pelagic bloom, but lasted only for ca. 10 days (Figs.1i, 8d and g).Consequently, the expected fecundity was the lowest (ca.145 eggs, Fig. 8e) and all eggs were sourced from capital breeding (Fig. 8f).The onset of spawning shifted later into the season at higher latitude model environments at higher levels of visual predation risk, and occurred after the commencement of the pelagic primary production (Figs.1c, f, i and 8d).Here, all eggs were produced via income breeding (Fig. 8f).At lower levels of visual predation risk (10 −4 ≤ K ≤ 5 × 10 −3 ), the predicted DVM pattern was similar across the three model environments, where developmental stages until early copepodites did not perform DVM (Fig. 9a and b).Although the model predicted the younger developmental stages (NIII onwards) to perform DVM under elevated visual predation risk at Environment-L, this effect gradually waned in higher-latitude model environments.The food limitation index strongly followed the DVM pattern, where developmental stages that performed DVM suffered from increased food limitation (Fig. 9c).Food limitation significantly reduced the growth rates (cf.Eqs. ( 1)-( 3), see also Appendix A4 in Supplementary material), and consequently, the development times increased along the modelled environmental gradient (Fig. 9d).Further, in each model environment, lowest development times were predicted under the lowest level of visual predation risk.

Diel vertical migration
In this model, visual predation risk had the highest influence on the DVM, which diminished under low visual predation risk (Figs. 7 and 9, Table 6) and completely ceased when visual predation was removed from the model (K = 0, data not presented).Conversely, under high visual predation risk, also younger developmental stages reduced the time spent in food-rich surface waters by performing low-amplitude (shallow) DVM (Fig. 9a and b).Food concentration and temperature also influenced the DVM (Fig. 7, Table 6).Lower food concentrations or temperatures produced lowamplitude DVM, possibly due the low growth potential attained in cold, food-limited conditions (Fig. 9, Eqs.( 1)-( 8), Appendix A4 in Supplementary material).Under these conditions, it appears that modelled copepods do not possess sufficient growth potential to trade off for survival and perform high-amplitude (deep) DVM, a conclusion also drawn in empirical work (e.g.Huntley and Brooks, 1982;Loose and Dawidowicz, 1994).Reduced or absence of DVM under low food concentrations and temperatures are reported from several other modeling studies on copepods and euphausiids (e.g.Andersen and Nival, 1991;Fiksen and Giske, 1995;Fiksen and Carlotti, 1998;Tarling et al., 2000) and from empirical work on marine copepods and freshwater cladocerans (e.g.Hardy and Gunther, 1935;Huntley and Brooks, 1982;Johnsen and Jakobsen, 1987).However, the largely exogenous-regulated DVM behavior emerging from this model does not render a complete view on the subject matter, as DVM can also be sensitive to internal (physiological) states of zooplankton (e.g.hunger and satiation, Hays et al., 2001;Pearre, 2003).
The effect of temperature on growth potential further explains the diminished influence of visual predation risk on the timing and amplitude of DVM predicted at higher latitude model environments (Fig. 9).Albeit similar food concentrations, the modelled temperatures decreased from lower-to higher-latitude model environments, reflecting a decreasing gradient of growth potential (Fig. 1, Appendix A4 in Supplementary material).Consequently, the model-predicted optimal DVM strategy for higher-latitude environments was to elevate the growth potential by spending more time foraging in near-surface waters (Fig. 9a and b).This effect was most pronounced among younger developmental stages (NIII-CI), whose DVM reduced from environment-L to -M, and completely ceased at environment-H.DVM of younger developmental stages (NIII onwards) are most commonly reported from lower latitudes for Calanus spp.(e.g.Huntley and Brooks, 1982;Uye et al., 1990;Huang et al., 1993;Osgood and Frost, 1994;Zakardjian et al., 1999) and Metridia spp.(e.g.Hays, 1995).While some field studies failed to detect notable DVM in high-latitudes (e.g.Blachowiak-Samolyk et al., 2006;Basedow et al., 2010), others reported ontogenetic increase of DVM (CI onwards, e.g.Dale and Kaartvedt, 2000;Daase et al., 2008) in Calanus spp.However, empirical data with high spatial, temporal and biological (i.e.developmental stage) resolution is needed to test the ontogenetic and latitudinal patterns of DVM predicted by our model.
The predicted DVM amplitudes spanned across the productive part of the water column (i.e.upper 30 m, cf.Figs. 1, 6 and 9), and showed a positive relationship with the vertical extent of food availability (Fig. 7).Moreover, strategies that involve higheramplitude DVM lead to increased food-limitation, where younger developmental stages with no energetic reserves tend to suffer from starvation risk due to low temperatures and food concentrations that prevail in deeper parts of the model environments (Fig. 1).Therefore, low-amplitude DVM appears to be a strategy that efficiently trades off growth potential for survival, by balancing both the visual predation and starvation risks (Kerfoot, 1970;Fiksen and Giske, 1995;De Robertis, 2002).Although higher-amplitude DVM can be predicted either by not modeling starvation risk or imposing starvation tolerance (e.g.Andersen and Nival, 1991;Carlotti and Wolf, 1998;Zakardjian et al., 1999;Tarling et al., 2000), we did not follow these approaches because our model sufficiently represents the relative importance of DVM across the modelled environmental gradients.

Seasonal vertical migration
Food availability and temperature had the most notable influence on the model-predicted timing of SVM (Fig. 7, Table 6).The predicted shift in timing of seasonal descent and ascent coincided with those of the pelagic algal bloom and thermal stratification along the modelled latitudinal gradient (Figs. 1 and 8a).This agrees with the argument that food availability is the ultimate factor influencing the timing of seasonal vertical migration of Calanus spp.(Herman, 1983;Head and Harris, 1985;Hind et al., 2000).However, field estimates of timing of SVM of Calanus spp.from low to high latitudes do not point to a simple south-north gradient as predicted in our model (Table 7, see also Melle et al., 2014).This discrepancy of model predictions and field estimates underlies the differences between location-specific variability in hydrography, algal bloom dynamics and species composition (e.g.Hirche, 1991;Daase et al., 2013), diversity of generation lengths and breeding strategies (e.g.Conover, 1988;Falk-Petersen et al., 2009) and climate-driven and other stochastic oscillations of environmental conditions (e.g.Reid et al., 1998;Eiane and Parisi, 2001;Ji, 2011).However, direct comparisons between vertical migratory patterns predicted by a strategy-oriented model and field estimates should be done with caution, as an environment-specific optimal vertical strategy predicted by the model contrasts the diversity of vertical behavior exhibited by individuals of a zooplankton population.
Visual predation risk and depth of thermal stratification (summer-autumn) were the only environmental variables that influenced the model-predicted overwintering depth (Figs. 7 and 8b, Table 6).The overwintering depth deepened at higher levels of visual predation risk and deeper thermal stratification depths, and agrees with Hirche (1991), Kaartvedt (1996), Dale et al. (1999), Bagøien et al. (2000) and Astthorsson and Gislason (2003) that Calanus spp.prefer colder water masses with low predator abundance for overwintering.However, the overwintering depths predicted by or model underestimate those of field observations, which can extend well below 1000 m (e.g.Østvedt, 1955).Apart from the shallow bottom depths modelled, this discrepancy largely reflects how overwintering habitat selection of Calanus spp. is influenced by the buoyancy-effect of stored lipid reserves (Visser and Jónasdóttir, 1999), convective mixing of surface waters (Irigoien, 2004) and vertical distribution of water masses and predator populations, such as mesopelagic fish, predatory ctenophores and krill (Hirche, 1991;Kaartvedt 1996;Bagøien et al., 2000;Bandara et al., 2016).

Diel vertical migration
In the model, high-amplitude DVM caused increased food limitation that led to slow growth and development and reduced fecundity (Figs. 7 and 9, Table 6).This ultimately resulted in lower fitness relative to that predicted for low-amplitude DVM.It is therefore apparent that decisions to fully or partly disregard DVM in models focusing SVM and other seasonal strategies should be made with caution, as our findings indicate that DVM can have a notable negative influence on growth and development of younger developmental stages, especially at lower latitudes.
At higher levels of visual predation risk, the model predicted up to a one month delay in the onset of spawning (Fig. 8d), and highlights the influence of predation risk on the reproductive phenology (Magnhagen, 1991;Stibor, 1992;Varpe et al., 2007).These latespawned copepods appeared to possess higher fitness compared to those spawned earlier (Fig. 8h).This seems counterintuitive as zooplankton are more vulnerable to visual predation risk later in the season due to the higher irradiance levels that persist in latespring and summer.In this model, the early feeding season (i.e. until the time of peak pelagic bloom) is characterized by higher food concentrations and lower temperatures (Fig. 1).Although the food concentration decreases by ca.20% by late spring or early-summer, the ambient temperature increases by ca.2-4 times.Further, even at the onset of the productive season, the visual predation risk had reached ca.70% of its maximum in all model environments (Fig. 1a,  d and g).Therefore, it is likely that copepods born relatively later in the season use the higher temperatures to attain a higher growth (Eqs.( 1)-( 8), Appendix A4 in Supplementary material), which is then efficiently traded off for survival through DVM to counter the risk of increasing visual predation risk (Fig. 9).Conversely, due to lower temperatures, copepods born earlier in the season must elevate the time spent foraging in near-surface waters to attain higher growth rates, and become more vulnerable to visual predation risk.However, it should be noted that our model does not consider the ability of Calanus spp. to use the darker and seasonally ice-covered period of the year to attain growth with minimal influence from visual predators by feeding on alternative food sources, such as ice algae and microzooplankton (Conover and Siferd, 1993;Søreide et al., 2010).
Compared to the phenology of reproduction, the elevated visual predation risk had little influence on the timing of seasonal migration (Fig. 8a).The SVM strategy predicted by the model was to descend to overwintering depth approximately at the same period of the year (mid-late summer), but with ca. 1 ⁄3 lesser the body mass (both structural and energetic reserve mass) compared to that under the lowest visual predation risk (Fig. 8a and c).As higher visual predation risk tends to intensify DVM in this model (Fig. 9a and b), it appears that trading off growth potential for survival makes an earlier seasonal descent unfavorable, as foodlimitation and slower growth rates (Fig. 9c and d) demands more time to acquire sufficient energy reserves to overwinter, despite the smaller body mass of the overwintering stage.Further, as the model-predicted body mass of the overwintering stage reaches a lower threshold at K > 10 −4 (Fig. 8c), it is likely that modelled copepods overwintered with minimum reserves to last the overwintering duration, and therefore makes an earlier descent (with lesser energy reserves) nearly impossible.In the contrary, occupying near-surface waters later into the season and descend to overwintering depths with elevated energetic reserves is also unfavorable as the visual predation risk in this model is not nullified even at the deepest parts of the water column (Eq.( 10)).The lesser influence of visual predation risk on the timing of SVM does not align with Kaartvedt (2000) and Varpe and Fiksen (2010) who view predation by planktivorous fish as a key driver of generation lengths and timing of seasonal descent in C. finmarchicus in the Norwegian Sea.However, the consequences of DVM on the timing of seasonal descent presented here may diminish if there is an energetic benefit of DVM (e.g.McLaren, 1963;Enright, 1977), if copepods are capable of utilizing alternative food sources (e.g.Runge and Ingram, 1991;Hirche and Kwasniewski, 1997) or if there is a strong size selection against larger developmental stages by visual predators than the linear relationship applied in our model (cf.Fig. 4a with Brooks and Dodson, 1965;Batty et al., 1990;Langbehn and Varpe, 2017).

Seasonal vertical migration
SVM was essential for the wintertime survival of the modelled copepods, given its food source is only available during the primary production season (spring-autumn, Fig. 1).Different combinations of proxies (Table 2) yielded non-seasonally migrating strategies, in which the copepods developed to adults and reproduced within the same productive season.Although this strategy had the potential to produce more than one generation per year (especially in the relatively lower-latitude environment-L, Fig. 1a-c), we did not peruse this further, as our focus was on an annual life cycle (see the fitness weighing process, Eq. ( 14), Fig. 5a-c).
The body mass and the size of energetic reserve at seasonal descent together with the timing of seasonal ascent had a profound influence on the predicted timing of reproduction, breeding strategy and fecundity (Fig. 8).Overwintering as large CVs with elevated energetic reserves at lower visual predation risk enabled the copepod to allocate the post-overwintering surplus energetic reserves to capital breeding in the following year (Fig. 8c and f, and see also Sainmont et al., 2014a;Ejsmond et al., 2015;Halvorsen, 2015).As capital breeding emerged in environments with lower temperatures and food concentrations (Fig. 7, Table 6), it appears as a strategy that allows the new generation to feed from the very start of the feeding season, while avoiding the seasonal peak in visual predation risk later in the year (Fig. 1, see also Varpe et al., 2009).The proportional increase of capital breeding eggs from relatively lower-latitude environment-L to higher-latitude environment-H reflects the decreasing temperature gradient that occur at overwintering depths of these environments (Figs. 1, 8b and f).Overwintering in colder water masses reduces the metabolic costs and conserves the energetic reserve, which ultimately boosts the fecundity through capital breeding (Hirche, 1991;Hirche, 1996;Astthorsson and Gislason, 2003).The pure capital breeding strategy predicted at environment-H under the lowest visual predation risk more resembles the spawning strategy of C. hyperboreus than C. finmarchicus and C. glacialis (Conover, 1988;Falk-Petersen et al., 2009).The sensitivity of the model-predicted breeding strategy to visual predation risk indicates an extensive pre-breeding cost of capital breeding imposed by the size-dependent visual predation risk and acquisition and carriage of energy reserves (Jönsson, 1997;Varpe et al., 2009).Moreover, excess energy storage (i.e. more than to overwinter) and capital breeding do not emerge as dominant strategies in this model as the environmental parameters are modelled in a perfectly predictable manner, without any yearto-year variability.However, capital breeding and energy storage may possess a much larger adaptive significance in nature, where spatio-temporal environmental heterogeneity and unpredictability are more pronounced compared to our model (e.g.Jönsson, 1997;Fischer et al., 2009).

Concluding remarks
Findings of this study highlight the influence of environmental variables on vertical strategies, and suggest that in seasonal environments, DVM and SVM should be studied in concert, as these behavioral strategies can have profound and largely different effects on fitness and phenology of herbivorous zooplankton.Therefore, given the significance of biological information ensued, sacrificing computer time to adopt higher spatio-temporal resolution in behavioral and life-history models seems to be an appealing practice.However, strong recommendations should only be made after testing our model predictions further, especially, through improvements to cope with environmental stochasticity (e.g.Eiane and Parisi, 2001;Ji, 2011), and to incorporate the plasticity of feeding strategies, generation times and body sizes of Calanus spp.(e.g.Broekhuizen et al., 1995;Fuchs and Franks, 2010;Ji et al., 2012;Banas et al., 2016).

Fig. 1 .
Fig. 1.The modelled dynamics of irradiance incident on the sea surface (hourly estimates; a, d, g), temperature (b, e, h) and food availability (c, f, i, expressed as Chlorophyll-a biomass) in the three model environments.See Appendix A1 in Supplementary material for a detailed comparison.

Fig. 3 .
Fig. 3. Simplified physiological pathways modelled in this study.Some life stages are grouped together due to their similarities in energy allocation patterns (a-f).Starvation (highlighted in red) triggers catabolic pathways marked in red.T and F are Boolean values true and false. is the growth allocation parameter (Table2).A comparative summary is given in Table5.

Fig. 4 .
Fig. 4. Relationships of (a) visual predation risk scalar, (b) cruising velocity, (c) light sensitivity parameter and (d) the total body mass of the copepod with its structural mass (Wc ).The cruising velocity (U) model was fitted using laboratory and field estimates of Calanus spp.fromHardy and Bainbridge (1954),Greene and Landry (1985) andHeywood (1996) (points in panel b).The different linear models for ˇ, that scale the light sensitivity parameter (␣) are optimized in the model (Table2).The lower and upper border of the shaded polygon (panel d) represent the total body mass for growth allocation parameter ( ) = 0 and 1 respectively.

Fig. 5 .
Fig. 5. (a-c) Mechanism of weighing fitness.Fitness of a copepod is multiplied by a binary weight ω = 0 if its egg production season (tD − tR) does not overlap the time of birth (tB, May 1 in this example, denoted by a black dot) and vice versa.(d) Simplified workflow of initialization and optimization steps of the model.The initial set of strategies enter the optimization loop after going through the first life cycle simulation (LS1).The GA optimizes seven evolvable (soft) parameters (Table 2) by repeatedly applying selection, recombination and mutation operators until a termination condition (ϕ) is satisfied.T and F are Boolean true and false conditions.No. of strategies (i.e.size of the GA-population, N or 2N) at each operation is indicated to the right.

Fig. 6 .
Fig.6.Predicted optimal vertical strategy and associated growth and reproductive performances of the copepod in the basic run at Environment-L (cf.Fig.1a-c).The surface time (a) is the stage-specific mean no. of hours per day that the copepod occupies food-rich surface waters, and amplitude (b) is its vertical range.Panel d compares predicted development times (excluding overwintering duration) to those estimated for C. finmarchicus and C. glacialis following Bělehrádek functions parameterized byCampbell et al. (2001) andJi et al. (2012).Wc and Ws refer to structural body mass and size of the energetic reserve respectively.

Fig. 7 .
Fig. 7. Graphical summary of the sensitivity analysis.Model parameters and environmental variables tested for sensitivity are presented on the vertical dimension, and the model-predicted optima of time of birth and vertical strategy, and the associated fitness on the horizontal dimension.+/−: 25% increase/decrease in the parameter value, E/D: 15-d earlier/delayed and S/L: 15-d shorter/longer scenarios regarding timing and duration of the productive season (see Appendix A3 in Supplementary material).
Wc = structural mass, Ws = mass of energetic reserve.a Mean of all stages.b From egg to adult excluding the overwintering period.

Fig. 8 .
Fig. 8. Predicted optima of time of birth (tB), vertical strategy and associated life history traits of the copepod in the three model environments under variable levels of visual predation risk.Visual predation risk is scaled by varying the parameter K in a range of 1-150 × 10 −4 .The fitness is cube-root transformed for the convenience of visualization.Time is presented as day of the year, where day 1 = 1 January.Wc and Ws are structural and energy reserve masses, and tR is time of first reproduction.

Fig. 9 .
Fig. 9. Predicted stage-specific surface time (a), DVM amplitude (b), food limitation index (c) and the development times (egg to a given stage excluding the overwintering period, d) of the copepod in the three model environments under variable levels of visual predation risk.

Table 2
Evolvable (soft)parameters optimized in the model.The first six are proxies that define the vertical strategy.Vertical strategies of copepods spawned in different times of the year (tB) are optimized using the GA.

Table 3
Emergent properties of the model.The timing and amplitude and of DVM and SVM altogether forms the vertical strategy of a copepod.

Table 4
Definitions, values and units of the terms used in the model.
a Feeding ceases during diapause.b Does not allocate surplus growth to develop the energetic reserve, but inherit the reserves from its developmental progression.c Reduces during diapause.d Not relevant during diapause.

Table 7
Melle et al. (2014)ascent and descent of Calanus spp.estimated by several high-latitude field investigations.These estimates are based on observation of zooplankton populations oftentimes containing various combinations of C. helgolandicus, C. finmarchicus, C. glacialis and C. hyperboreus.Geographical location is approximate.Data for North-Atlantic are available inMelle et al. (2014).