Advertisement
Browse Subject Areas
?

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here.

  • Loading metrics

A Day in the Life of Fish Larvae: Modeling Foraging and Growth Using Quirks

A Day in the Life of Fish Larvae: Modeling Foraging and Growth Using Quirks

  • Klaus B. Huebert, 
  • Myron A. Peck
PLOS
x

Abstract

This article introduces “Quirks,” a generic, individual-based model synthesizing over 40 years of empirical and theoretical insights into the foraging behavior and growth physiology of marine fish larvae. In Quirks, different types of larvae are defined by a short list of their biological traits, and all foraging and growth processes (including the effects of key environmental factors) are modeled following one unified set of mechanistic rules. This approach facilitates ecologically meaningful comparisons between different species and environments. We applied Quirks to model young exogenously feeding larvae of four species: 5.5-mm European anchovy (Engraulis encrasicolus), 7-mm Atlantic cod (Gadus morhua), 13-mm Atlantic herring (Clupea harengus), and 7-mm European sprat (Sprattus sprattus). Modeled growth estimates explained the majority of variability among 53 published empirical growth estimates, and displayed very little bias: 0.65%±1.2% d−1 (mean ± standard error). Prey organisms of ∼67% the maximum ingestible prey length were optimal for all larval types, in terms of the expected ingestion per encounter. Nevertheless, the foraging rate integrated over all favorable prey sizes was highest when smaller organisms made up >95% of the prey biomass under the assumption of constant normalized size spectrum slopes. The overall effect of turbulence was consistently negative, because its detrimental influence on prey pursuit success exceeded its beneficial influence on prey encounter rate. Model sensitivity to endogenous traits and exogenous environmental factors was measured and is discussed in depth. Quirks is free software and open source code is provided.

Introduction

It is of considerable ecological interest to estimate the environmental conditions that are necessary to support feeding and growth of marine fish larvae, and to predict how well theoretical or observed conditions match larval requirements. “Matches” can facilitate growth, enhance survival, and increase fish recruitment potential, while “mismatches” can prevent larvae from thriving, and limit both the short-term productivity and the long-term biogeographic distribution of fish stocks [1], [2]. While many studies have related larval growth to one or more environmental factors, our understanding of the interplay between variables such as temperature, turbulence, and prey concentration is still quite limited. Individual-based models (IBMs) synthesizing empirical and theoretical insights can be used to apply and test our cause-and-effect understanding of the essential physical, behavioral, and physiological processes governing growth [3]. Recently, there has been a dramatic increase in studies employing larval fish IBMs to these ends [4], [5]. Most of these studies have focused on one fish stock or species and have not provided the model source code. Our new model “Quirks” is free and open source software written in the R programming language [6] (Source Code S1, https://sourceforge.net/projects/larvalfishquirks/), easy to parameterize for different types of larvae, and, as we show here, performs well across multiple species and environments.

Design Goals

Our main technical objective was to provide the scientific community with a free and useful comparative modeling tool for the study of larval fish foraging and growth. To this end, we tried to make Quirks as transparent (understandable without prior modeling experience), mechanistic (based on cause-effect understanding of biophysical principles), and generic (appropriate for different types of larvae and environments) as possible. Further, we aimed to synthesize published data and did not “tune” Quirks to perform well in the presented applications. Quirks was written in R, a free programming language and software environment commonly used for statistical data analysis, which is familiar to many scientists besides modelers [6]. The underlying equations were kept simple, while still mechanistically representing physiological processes and interactions between larvae and their biophysical environment. A trait-based modeling approach was chosen for simple parameterization and comparison of different larval types. Trait-based modeling has become a popular tool to investigate how marine phytoplankton [7] or zooplankton [8] are adapted to prevailing environmental conditions, and trait-based IBMs have previously been used to compare exogenous and endogenous factors influencing larval fish survival [9]. The standard dynamic energy budget (DEB) model [10] is another bioenergetic model that can be considered trait-based, and has been applied to study, for example, larval fish stage duration [11]. However, DEB traits are not particularly transparent (some cannot or have not been measured in fish larvae, and are parameterized by fitting model output to empirical growth curves). Further, standard DEB theory does not mechanistically represent foraging behavior. In summary, Quirks uniquely represents larval fish foraging and growth in a transparent, mechanistic, and generic model, and thus facilitates ecologically meaningful comparisons between different early life history strategies and different environments.

Application

The present study quantifies how well Quirks depicts the foraging and growth of marine fish larvae. Traits were chosen to characterize larvae 2 to 4 mm beyond the length of yolk depletion, which we refer to as “young larvae”. This size range was chosen for various reasons. First, the growth dynamics of larvae with yolk reserves are dominated by the quantity of yolk and the effect of temperature on the conversion of yolk to somatic tissue, as opposed to the success of foraging on prey organisms [12], [13]. Second, larvae are most susceptible to starvation and have the most specific prey requirements (high concentrations of small prey) immediately after yolk depletion, due to the combination of small size and obligate exogenous feeding [14][16]. Third, data on first-feeding larvae are sparse and difficult to interpret, because rapid behavioral and physiological changes occur during this stage of development. Our compromise was not to model first-feeding larvae, but young larvae that are still small, yet already accomplished predators, for which more and better empirical data were available.

We parameterized Quirks based on the characteristics of young larvae of four marine fish species inhabiting the North Sea: “anchovy” (European anchovy, Engraulis encrasicolus), “cod” (Atlantic cod, Gadus morhua), “herring” (Atlantic herring, Clupea harengus), and “sprat” (European sprat, Sprattus sprattus). These species provide several contrasts that are important to the development of a generic model. First, they differ in developmental morphology. For example, the standard length by which 95% of larvae deplete their yolk reserves varies three-fold, and the dry mass of young larvae of the same length varies 15-fold (Figure 1) [17][19]. Second, the four species differ in their biogeographic distribution. The North Sea is near the lower latitudinal limit for cod and herring in the northeast Atlantic (sub-Arctic to temperate species favoring relatively cool waters), whereas it is the higher latitudinal limit for sprat and anchovy (temperate to sub-tropical species favoring relatively warm waters). Quirks is not specific to the North Sea or any other ecosystem, and the chosen species allowed us to use field data from many other locations (e.g., the northwest Atlantic, northeast Arctic, Baltic Sea, and Mediterranean Sea) to validate the model. Third, each species has a different spawning period in the North Sea: cod (winter to spring), sprat (spring to summer), anchovy (summer), and herring (autumn to spring) [20][23]. Consequently, young larvae experience environmental conditions that vary in temperature from <5 to >15°C and in photoperiod from <12 to >16 h of daylight in the North Sea (and to even greater extremes in other locations) [24], [25]. Finally, the four species span three different families (Clupeidae, Engraulidae, and Gadidae), which display different behavioral and physiological characteristics shortly after first-feeding.

thumbnail
Figure 1. Morphological and behavioral traits of modeled fish larvae.

This comic illustrates the four types of modeled fish larvae (cones), their effective visual fields (open cylinders), and their maximum ingestible prey (orange). Standard length, maximum prey length (additionally represented by mouth length), visual field radius, and encounter distance are rendered to scale (1 mm3 gray cubes). Visual field length and volume represent 1 s of swimming (mm s−1) and foraging (mm3), respectively. Fish and prey volume are scaled such that 1 mm3 = 100 µg dry mass (tissue of 91% water content and 1 g ml−1 density). Blue: 7-mm sprat (Sprattus sprattus), red: 5-mm anchovy (Engraulis encrasicolus), green: 13-mm herring (Clupea harengus), purple: 7-mm cod (Gadus morhua).

https://doi.org/10.1371/journal.pone.0098205.g001

Methods

Quirks was developed from larval fish IBMs for herring [23] as well as cod and sprat [26] that, in turn, were based on other previous models such as the generalized IBM by Letcher and colleagues [9] and the seminal model of cruise predation by Gerritsen and Strickler [27]. Therefore, many processes were represented by equations familiar to (larval fish) ecologists and modelers. However, model development also involved a thorough review of empirical studies and measurements of larval fish behavior and physiology. In synthesis of this literature, we developed several new, simplified, or generalized equations. To facilitate comparative modeling, different types of larvae were fully defined by a list of traits (constants, Table 1), while all biophysical processes were modeled using one unified set of rules (equations, Table 2). Finding appropriate values for many traits required the re-interpretation of published laboratory and field data [9]. An unusual aspect of Quirks was that, under highly favorable conditions (warm temperature, long photoperiod, high prey concentration), larvae quickly grew beyond the intended 2-mm length range of the model parameterization. Slightly smaller or larger larvae must have quite similar traits, but we did not attempt to quantify this in the present study. Instead, we ensured that larvae did not outgrow their size-specific traits, by limiting each simulation to a period of 24 h. These short simulations provided snapshots of modeled ecology much like field sampling produces snapshots of ecology in situ, and were thus well suited for model validation.

thumbnail
Table 1. Biological traits of modeled anchovy (Engraulis encrasicolus), cod (Gadus morhua), herring (Clupea harengus), and sprat (Sprattus sprattus) larvae.

https://doi.org/10.1371/journal.pone.0098205.t001

Model Structure

Nomenclature.

To ease the understanding of mathematical notation, we applied the following rules of nomenclature. Larval traits were denoted by x if treated as species-specific and by y if treated as generic, with subscripts abbreviating the role of the trait. Variables with the subscript t were re-calculated every time-step. Variables with the subscript i were calculated separately for each size bin of potential prey items.

Growth physiology (equations 1–9).

To calculate growth, the two state variables standard length L and dry mass M were initialized, then a series of equations was iteratively solved for 24 hourly time steps, one night followed by one day (Tables 23). Initial L was set to xlen. Initial M and positive L-growth were determined according to the body shape trait xbody, which functioned as an upper limit to M/L3 and a reference point for larval condition (M/L3 is often termed Fulton’s condition factor). A loss of M never resulted in a loss of L. All L-changes were thus modeled as isometric growth, an approximation simplifying direct comparisons of xbody among different larval types. Changes in M were calculated from the balance of metabolic gains from ingested prey (with metabolic efficiency yeff) and losses to active respiration. Respiration was modeled as a percentage of M lost per hour at 10°C (routine respiration xres), corrected for ambient temperature by a Q10 factor (xrQ10). We converted respiration from units of oxygen uptake to units of dry mass using a conversion factor of 0.85 µg µl−1, which is typical for young marine fish larvae [28][33]. Respiration was increased between sunrise and sunset to account for the cost of foraging activity (yact). The ingestion of prey was limited by the lesser of either digestive capacity or foraging capacity during the daylight fraction of the time step. Digestive capacity was represented as a percentage of M evacuated per hour at 10°C (ydig) corrected for ambient temperature by a Q10 factor (ydQ10). Larvae encountering temperatures in excess of their upper thermal tolerance (xtol) were excluded.

Prey fields (equations 10–12).

Potential prey were binned into groups of characteristic length li, individual dry mass mi, biomass concentration bi, and numeric concentration ci. The relationship among these variables was idealized as a normalized size spectrum sensu Platt and Denman [34], by assuming a linear slope s between the logarithm of normalized bi (i.e., bi divided by the width of the mi bin) and the logarithm of mi. This simplification was consistent with empirical data from diverse aquatic systems [35][37] and a growing body of literature on size spectrum theory [34], [36], [38]. Prey fields were specified in terms of li bins, btotal, and s. For each bin, ci was equal to bi divided by mi. The distribution of btotal among prey size bins (according to s) was solved analytically. The present study used prey from 0.04 to 2 mm length in 196 discrete 0.01-mm bins. A power function fit to this size range of copepods [39][41] and protist plankton [42] was used to calculate mi (n = 109, r2 = 0.95, two outliers removed, 45% carbon content assumed when necessary).

Foraging behavior (equations 13–21).

Quirks modeled foraging capacity based on a predation sequence of proximity, encounter, pursuit, attack, and ingestion, and assumed optimal diet selection (accounting for handling time yhand) [9], [43]. Proximity: The number of prey passing in proximity of larvae was calculated from prey concentration multiplied by the volume of a visually scanned cylinder. The radius of the cylinder represented larval visual ability (yvis). The length of the cylinder represented the combined velocities of larval swimming (yswim), prey swimming, and turbulence. Relative turbulent velocity between predator and prey (separated by encounter distance ydist) was calculated according to “Kolmogorov 1941 theory” [44], [45], assuming a universal Kolmogorov constant of 0.53 [46], [47]. While this approach is theoretically only valid for larger separation distances, it has been empirically validated at the scale of larval fish predation events [48], [49]. Encounter: In addition to proximity, encounters required prey detection (observation success), which was varied as a type 2 functional response with half-detected prey length ydet, based on herring larvae reacting to prey of different sizes [15]. Pursuit: As observed in data of cod larvae feeding under turbulent conditions [49], relative pursuit success was linearly reduced from 100% at zero turbulence to 0% at a maximum corrigible turbulent velocity yturb. Capture: Based on herring larvae attacking prey of various sizes [15], relative capture success was linearly reduced from 100% for infinitesimally small prey length to 0% for the maximum ingestible prey length (xing).

Model Parameterization

Larval traits.

Estimates for all traits were open to interpretation, due to the uncertainty, variability, and availability of empirical data. Some of the variability among published measurements reflected different environmental conditions. To realistically model maximum growth potential, measurements representing favorable conditions were used for traits related to morphology, such as larval shape (relating growth and condition) or ingestible prey size. To realistically model prey-limited growth and starvation, measurements characterizing low prey concentrations were used for foraging-related traits, such as swimming speed or metabolic efficiency (high efficiency for low rates of ingestion). In some cases, contradictory results were found in the literature, and averaged parameter estimates were used. Only six traits were deemed adequately studied and sufficiently variable among species to merit species-specific parameterization. Of these six, the traits xres and xrQ10 were estimated for E. encrasicolus based on measurements in two closely related species: Northern anchovy (Engraulis mordax) and Bay anchovy (Anchoa mitchilli). For young sprat larvae xres and xrQ10 were estimated by the herring parameters.

Generic digestion.

Quirks represented the complex process of digestion in a greatly simplified, mechanistic form. Conceptually, M-gain from digestion depended on how much prey fit inside the larval gut at one time, how quickly the gut contents were digested and evacuated (temperature dependent), and an efficiency term accounting for losses to excretion as well as the costs of digestion and growth. A literature review of these factors (Table 1) yielded too little information for species-specific parameterization, so generic traits were used for digestion. The trait yeff = 67.5% combined an assimilation efficiency of 75% and specific dynamic action of 10% (75% · 90% = 67.5%). The trait ydig = 2.5% incorporated a gut capacity of 5% M divided by an evacuation time of 2 h. For every 10°C increase in temperature, the gut evacuation rate was multiplied by a Q10 factor of ydQ10 = 2.5.

Volumetric foraging rate.

Parameterizing the rate at which larvae effectively scanned their environment for prey was of particular importance. Two main types of estimates were available from the literature: the multiplication of visual fields by swimming speeds and the division of predator reaction rates by prey concentrations. In studies using the multiplication approach, video recordings of larval reactions to prey were used to measure the size and shape of larval visual fields. Then, the continuous (cruise predator) or saltatory (pause-travel predator) movements between successive visual fields were used to calculate volumetric foraging rate. This method generally involves the unrealistic assumption that larvae actually detect 100% of the potential prey organisms passing through their visual fields [50], and is likely to overestimate foraging rate. In studies using the division approach, the rate at which larvae pursued, attacked, or ingested prey at very low concentrations was recorded. Then, volumetric foraging rate was estimated by dividing the mean reaction rate (e.g., the number of strike postures per minute) by the prey concentration. This approach is likely to underestimate foraging rate, if any prey are detected but not pursued, pursued but not attacked, or attacked but not ingested. Various other sources of bias likely affect both approaches (prey type, size, and concentration; experimental water volume, turbidity, and turbulence; larval size, concentration, condition, and satiation). In synthesis of available experimental data for species of anchovy (A. mitchilli and E. mordax), cod, and herring, we chose a generic effectively scanned cylinder radius of yvis = 0.6 L s−1 and a generic effective swimming speed of yswim = 0.75 L s−1. This resulted in foraging rates of 0.5 l h−1 for 5.5-mm anchovy, 1.0 l h−1 for both 7-mm cod and sprat, and 6.7 l h−1 for 13-mm herring larvae (not accounting for prey swimming, turbulence, or imperfect prey detection). For an illustration of the four larval types and their foraging rates, see Figure 1.

Model Runs

Validation.

We compiled a list of empirical studies estimating growth rates of young anchovy, cod, herring, and sprat larvae (Table 4), and used it to validate Quirks results. Data used for validation were independent from data used for parameterization except for one study yielding anchovy body shape [51] and one of five studies yielding generic metabolic efficiency [52]. Studies comparing different environmental conditions (including starvation experiments), reporting particularly high growth rates, or applying alternative methodologies were preferentially selected, and all those allowing for temperature, photoperiod, and prey concentration estimates were used. One sprat study by Dulčić [53] was included under the explicit assumption that growth had not been prey limited. The assumption was warranted, since Dulčić [53] replicated essentially identical and high growth measurements in two different years, despite a relatively cold temperature and a short photoperiod. The validation list included field and laboratory growth estimates based on larval length, mass, or protein content, otolith microstructure, and biochemical condition (RNA-DNA ratio). Quirks was set up to mimic the environmental conditions of each study and estimate growth. The slope s of the normalized size spectrum could not be calculated for most studies and was otherwise set to a default value of −1.2. This number has frequently been used as a reference point [36] ever since it was predicted from theoretical considerations of oligotrophic aquatic systems in equilibrium [34], [36]. For field studies, turbulent kinetic energy dissipation rate ε was set to 10−7 W kg−1, approximating wind-driven turbulence at 30 m depth in storm conditions or near the surface in calm conditions [54], and sufficient to significantly influence larval fish foraging success [49], [55]. The default for laboratory studies was zero turbulence. Temperature was set to match experimental treatments (lab) or the surface layer (field). For several studies, photoperiod was estimated from date and latitude using the NOAA solar calculator, as implemented in the R package “maptools” [25]. For field studies, prey concentrations were matched to larval growth rates on a station-by-station basis when possible; otherwise, median prey concentrations were used.

thumbnail
Table 4. List of studies used to validate Quirks growth rate estimates.

https://doi.org/10.1371/journal.pone.0098205.t004

Sensitivity analysis.

We measured the influence of endogenous larval traits and exogenous environmental factors on Quirks output in two series of individual parameter perturbations [5]. The first series quantified the sensitivity of modeled growth potential assuming ad libitum feeding. The second series examined parameter influence on the prey concentration required for M-growth of exactly 5% d−1. For each parameter and larval type, we determined the parameter range for which the output changed by less than ±10%. For example, model sensitivity to a hypothetical trait xhyp could be such that any value between 80% and 200% of xhyp results in similar growth potential (G±10%). Perturbations were performed with respect to species-specific reference points, representing the environmental conditions that young exogenously feeding larvae would typically experience in the central North Sea. Temperature and photoperiod were set to average conditions two weeks after the approximate midpoint of the adult spawning season (Table 5). Turbulence and prey fields were approximated by ε = 10−7 W kg−1 and s = −1.2, as in the validation runs. Since prey concentration was fixed in the first sensitivity analysis (to ensure ad libitum feeding), and functioned as the output variable of the second analysis, the importance of prey concentration was separately quantified. This was done by determining the minimum level required for positive growth (starvation point), 5% growth, and maximum growth (satiation point).

thumbnail
Table 5. Comparison of anchovy (Engraulis encrasicolus), cod (Gadus morhua), autumn-spawned herring (Clupea harengus), and sprat (Sprattus sprattus) larvae in the North Sea.

https://doi.org/10.1371/journal.pone.0098205.t005

Optimal foraging conditions.

Here, we quantified the suitability of different prey sizes, prey-size distributions, and turbulence levels (increasing turbulence enhances encounters with prey, but decreases pursuit success) for young larvae. First, we examined encounters with each of the 196 modeled prey bins, in terms of the average ingested dry mass per encounter, standardized by handling time. This metric is used in foraging theory (and in Quirks) to determine the ranking of different prey types for inclusion in an optimal diet [9], [43]; from a predator’s perspective, it determines the optimal prey length. Second, we calculated a numerical solution for the value of s (normalized size spectrum slope) resulting in the lowest possible starvation (and satiation) point for each larval type. In the idealized model framework, s fully defines the size distribution of available plankton biomass, and thus also the optimal prey field. To further examine the effects of turbulence, we also calculated starvation and satiation points for ε-values of 10−12 to 10−4 W kg−1.

Results

Validation

A total of 53 growth estimates from 17 studies was used to validate Quirks output (Table 4). Prey concentration ranged from zero (cod, herring) to levels well above larval requirements (all species), temperature ranged from <3°C (cod) to >24°C (anchovy), and photoperiod ranged from <10 h daylight (cod, sprat) to continuous light (cod). We initially divided the data into two subsets: the “satiated” data with prey concentration in excess of the (modeled) satiation point and the “prey-limited” data with prey below the satiation point (Table 6, Figure 2). In the satiated subset (Figure 2A), there was a strong positive association between predicted and observed growth (Kendall rank correlation tau = 0.53, p<<0.001). Variability in the model estimate explained r2 = 58% of variability in the empirical estimate (linear regression method), and data scatter matched the 1∶1 identity line with R2 = 47% (sum of squares method). These statistics quantify model validity and skill in predicting growth across the four parameterizations (but not necessarily for any given one) under conditions of (modeled) ad libitum feeding. The prey-limited subset (Figure 2B), which did not include any sprat data, yielded equivalent statistics (R2 = 51%). Model performance was therefore not noticeably reduced under conditions of (modeled) prey limitation. Model performance was also equivalent for the complete dataset (R2 = 52%, Figure 2C). Prediction error (predicted minus observed growth) was independent of temperature (tau = 0.04, p = 0.66) but significantly associated with photoperiod (tau = 0.37, p<<0.001). For each hour of daylight above 13.4 h, Quirks tended to overestimate specific growth rate by 1.9% ±6.7% d−1 (median ± inter quartile range), and vice versa. We calculated model performance one more time, after excluding extreme photoperiods (n = 3 at ∼9 h daylight, n = 1 at 24 h daylight, circled in Figure 1C). The resulting “12 to 18 h daylight” subset matched the identity line to R2 = 65%, a marked increase over the other subsets (Table 6).

thumbnail
Figure 2. Validation of growth rates predicted by Quirks.

For validation, 53 larval fish growth estimates from 17 publications were compared to model predictions for matching environmental conditions. Panel A shows the subset of data with prey concentrations that did not limit modeled growth. Panel B shows the subset in which modeled growth was prey limited. Panel C combines all data, and highlights four cases (circled) with extreme photoperiods (see text). Accurate predictions should fall near the dashed 1∶1 identity line (see table 6 for statistics). Empty symbols: laboratory studies, full symbols: field studies. Red squares: 5-mm anchovy (Engraulis encrasicolus), purple circles: 7-mm cod (Gadus morhua), green point-up triangles: 13-mm herring (Clupea harengus), blue point-down triangles: 7-mm sprat (Sprattus sprattus). aTotal dry mass of plankton in the length range from 0.04 to 2 mm.

https://doi.org/10.1371/journal.pone.0098205.g002

thumbnail
Table 6. Summary statistics quantifying model skill in matching published larval fish growth rates.

https://doi.org/10.1371/journal.pone.0098205.t006

Sensitivity Analysis

Quirks output was highly sensitive to both endogenous traits and exogenous environmental factors (Tables 78). For growth potential to remain within ±10% of the reference values, the traits ydig (digestion at 10°C) and yeff (metabolic efficiency) could not be perturbed outside ∼95% to 105% of the original value for cod, herring, and sprat or outside ∼97%–103% for anchovy. The permissible range was up to ∼90%–110% for xres (routine respiration at 10°C) and ∼80%–120% for yact (cost of foraging activity). Growth potential changed by ±10% following photoperiod perturbations around ±6% in all species, but the sensitivity to temperature was quite species-specific. At one extreme, temperature influenced growth potential of young anchovy larvae more than any other parameter. At the other extreme, temperature was less influential than the five previously mentioned parameters for young cod larvae. Ranges for ydQ10 and xrQ10 (temperature dependency of digestion and respiration) were provided for the sake of completeness (Table 7), but primarily reflect whether water temperature was close to 10°C during the different spawning seasons. No other parameters influenced growth potential, unless larvae were rendered entirely unable to forage (e.g., due to zero vision or unmanageable turbulence). On the other hand, all 20 parameters influenced the prey requirement for 5% growth (Table 8). Here, the most critical parameters were effective visual cylinder radius yvis (all species) and normalized size spectrum slope s (sprat). Perturbing these parameters outside a range of ∼95–105% resulted in a >10% change in prey requirement. The next most important parameters, in approximate order of influence, were s (anchovy), yeff (all), xbody (all), yswim (all), xres (all), xlen (all), and photoperiod (all), with permissible ranges between ∼93%–110% and 83%–127% depending on the parameter and larval type (Table 8).

thumbnail
Table 7. Ranges (%) of individual parameter perturbations resulting in <10% change in modeled growth potential of North Sea anchovy (Engraulis encrasicolus), cod (Gadus morhua), autumn-spawned herring (Clupea harengus), and sprat (Sprattus sprattus) larvae.

https://doi.org/10.1371/journal.pone.0098205.t007

thumbnail
Table 8. Ranges (%) of individual parameter perturbations resulting in <10% change in modeled prey requirement for 5% d−1 growth of North Sea anchovy (Engraulis encrasicolus), cod (Gadus morhua), autumn-spawned herring (Clupea harengus), and sprat (Sprattus sprattus) larvae.

https://doi.org/10.1371/journal.pone.0098205.t008

At the species-specific reference conditions, the starvation point prey requirement ranged from 1.4 (sprat) to 2.7 (herring) to 7.1 (cod) to 7.4 (anchovy) mg m−3 (Table 5). The satiation point was between 1.6 (anchovy) and 2.3 (herring) times as high as the starvation point, while intermediate prey concentrations resulted in positive, prey-limited growth.

Optimal Foraging Conditions

Optimal prey length primarily depended on maximum ingestible prey length, and was therefore smallest in sprat (0.18 mm), intermediate in anchovy (0.30 mm), and larger in herring (0.69 mm) and cod (0.74 mm) (Table 9, Figure 3). These values corresponded to 67%±0.4% (mean ± standard deviation) of the maximum ingestible prey length. The optimal normalized size spectrum slope s was –2.5 for sprat, –1.9 for anchovy, and –1.4 for herring and cod. While larvae could reach their full growth potential at any value of s, optimal size spectra resulted in reduced starvation and satiation points (Figure 4). Although turbulence had a positive influence on prey encounters and a negative influence on prey pursuit success, the overall effect was consistently negative. In all four larval types, starvation and satiation points increased monotonically with turbulent kinetic energy dissipation rate (Figure 5). Over 90% of the change occurred between 10−8 and 10−4 W kg−1.

thumbnail
Figure 3. Suitability of different prey sizes for young anchovy, cod, herring, and sprat larvae.

Encounters between young fish larvae and 196 size classes of plankton from 0.04 to 2(thick line) depended on pursuit success, capture success, prey dry mass, and handling time. The expected benefit per nearby prey organism (thin line) additionally “corrected” for imperfect observation success and the combined velocity of predator swimming, prey swimming, and turbulent velocity. Panel A shows ingestion and prey length in absolute units, highlighting dramatic differences among the four larval types. Panel B shows normalized values, revealing that the optimal prey length was ∼67% of the maximum ingestible length in all cases. Shading in A indicates the probability of successful pursuit and capture, as labeled. Medium-dashed red: 5-mm anchovy (Engraulis encrasicolus), solid purple: 7-mm cod (Gadus morhua), long-dashed green: 13-mm herring (Clupea harengus), short-dashed blue: 7-mm sprat (Sprattus sprattus). Turbulent kinetic energy dissipation rate was set to 10−7 W kg−1.

https://doi.org/10.1371/journal.pone.0098205.g003

thumbnail
Figure 4. Starvation and satiation points of young fish larvae foraging in different prey fields.

The minimum prey biomassa that fish larvae required for positive growth and maximum growth was modeled for prey fields of varying normalized size spectrum slope s. At prey concentrations below the starvation point (lower line) larvae lost mass. Above the satiation point (upper line), larvae achieved their maximum growth potential. Intermediate growth rates occurred in the colored area between the starvation and the satiation points. The thin vertical line indicates the reference point of s = −1.2. Medium-dashed red: 5-mm anchovy (Engraulis encrasicolus), solid purple: 7-mm cod (Gadus morhua), long-dashed green: 13-mm herring (Clupea harengus), short-dashed blue: 7-mm sprat (Sprattus sprattus). aTotal dry mass of plankton in the length range from 0.04 to 2 mm.

https://doi.org/10.1371/journal.pone.0098205.g004

thumbnail
Figure 5. Starvation and satiation points of young fish larvae foraging at different levels of turbulence.

The prey biomassa that fish larvae experiencing various levels of turbulence required for growth was modeled. Maximum, negative, and intermediate positive growth rates occurred at prey concentrations above the satiation point (upper line), below the starvation point (lower line), and between the starvation and satiation points (colored area), respectively. The thin vertical line indicates the turbulence reference point used throughout much of the study. Medium-dashed red: 5-mm anchovy (Engraulis encrasicolus), solid purple: 7-mm cod (Gadus morhua), long-dashed green: 13-mm herring (Clupea harengus), short-dashed blue: 7-mm sprat (Sprattus sprattus). aTotal dry mass of plankton in the length range from 0.04 to 2 mm.

https://doi.org/10.1371/journal.pone.0098205.g005

thumbnail
Table 9. Optimal foraging conditions for the indicated sizes of anchovy (Engraulis encrasicolus), cod (Gadus morhua), herring (Clupea harengus), and sprat (Sprattus sprattus) larvae.

https://doi.org/10.1371/journal.pone.0098205.t009

Discussion

A solid understanding of the processes governing larval fish growth is of great scientific value. Even subtle differences in growth during fish early life history can result in dramatically different cumulative mortality and, ultimately, recruitment to adult populations [2], [3]. Evidence for prey-limited growth in nature is scarce, since it requires sampling at the appropriate spatial and temporal scales and across wide ranges in prey conditions. This is an additional reason why mechanistic models of larval fish foraging are in high demand [5]. Some field studies have successfully linked sub-optimal larval growth to low prey concentrations. For example, Buckley and Durbin [16] showed that the growth rates of <12-mm Atlantic cod and <7-mm haddock (Melanogrammus aegelfinus) on Georges Bank (northwest Atlantic) were strongly reduced in areas of low in situ prey concentration. Larger individuals captured at the same stations were not significantly affected. This is consistent with Quirks results: in all species, smaller larvae required higher prey concentrations than larger individuals, primarily because they scanned less water, and secondarily, because their capture success was lower. Buckley and Durbin’s [16] study illustrates that obtaining a large body size quickly, by rapid growth through the early larval stage, confers a clear survival advantage. Further, the authors concluded that rapid larval growth may be necessary (although not sufficient) for a strong year class [16]. In combination with the appropriate fisheries data, Quirks could be applied to study not only foraging and growth, but also the likelihood of strong year classes. While not addressed here, larval transport is another factor greatly influencing year-class strength, and there is a trend towards using coupled bioenergetic-transport models of fish larvae [4], [5]. Quirks can certainly be adapted for that approach, by defining traits that vary with growth and development.

Validation

Model skill.

In the validation runs, there was a good match between growth predicted by Quirks and growth observed empirically (R2 = 52%, Table 6, Figure 2). Further, the distribution of slopes between any two data points was centered near one (median = 0.72, interquartile range = 0.98), and the corresponding distribution of intercepts was centered at approximately zero (median = 0.04, interquartile range = 0.19). In other words, Quirks had surprisingly low bias (a slope of one and intercept of zero would indicate no systematic bias whatsoever). We did observe a statistically significant photoperiod effect, thus predicting growth at extreme photoperiods may require extra care. For example, Quirks predicted much too low growth potential (∼6% vs. ∼29% d−1) for sprat larvae in the northern Adriatic Sea in January (∼11°C, ∼9 h daylight) [53]. At the other extreme, Quirks predicted a growth rate of 24% vs. the observed 7% d−1 for cod larvae reared in continuous daylight at 8°C [56]. Here, modeled growth potential may not have been grossly inaccurate, because another study of cod larvae at the same 8°C temperature (and ∼15 h daylight) measured a growth rate of 22% d−1 [57]. In any case, model skill was noticeably higher among the “12 to 18 h daylight” subset of data (R2 = 65%, Table 6), which excluded the above outliers and one other (unproblematic) data point. Note that we did not “tune” the model equations or larval traits to optimally fit the validation dataset, and that we used almost entirely independent data for parameterization and validation (there was overlap with respect to one trait in two studies).

Growth.

The list of validation studies encompassed a wide range of different approaches (Table 4), each subject to potential bias and random sampling error. For example, many lab studies are biased towards low growth, because larvae rarely thrive as well in artificial environments as they might under ideal natural conditions. Field studies, on the other hand, are likely to overestimate growth. For example, among simultaneously occurring and equally sized larvae, faster-growing individuals have, so far, suffered a shorter period of exposure to predation [2], [58], and may additionally have experienced lower instantaneous predation rates [59], [60]. Random sampling of the survivors is thus not sufficient for an unbiased characterization of the original population. Attempting to correct for these and other sources of uncertainty was beyond the scope of the present study, as was the distinction among individual growth rates (e.g., RNA-DNA ratios), “vertical” or “horizontal” population growth rates (i.e., based on patterns among simultaneously collected larvae or time-series of samples, respectively). Conceptually, it should be clear that the presented parameterizations represent average individuals, and that Quirks was used to model individual growth rates.

Prey concentration.

Matching (i.e., simulating) empirical prey concentrations for the purpose of validation was also problematic. Given the complexity of plankton dynamics in the field, and the difficulty of maintaining nominal food levels in small-scale experiments, constant “matched” prey concentrations can only have roughly approximated the actual conditions experienced by larvae. For this reason we were surprised that Quirks performed equally well (in terms of R2) for the satiated and prey-limited subsets of validation data. The fact that 10 of 12 data points fell very near the 1∶1 line (Figure 1B) is encouraging, but should not be over-interpreted. Quirks underestimated growth in 9 of 12 cases (including 5 of 5 with empirically observed negative growth), which may indicate that our parameterization slightly overestimated larval respiration or slightly underestimated foraging capacity. In summary of model validation, a long list of uncertainties would have prevented even a perfect model from reproducing 100% of variability in the validation dataset. The observed R2 of up to 65% (Table 6) is therefore a conservative (low) estimate of Quirks’ model skill.

Sensitivity Analysis

The sensitivity of model predictions to individual parameter perturbations is useful for several purposes. First, regarding Quirks in isolation, model sensitivity simply quantifies the influence of each trait and environmental factor on model output. This information helps potential users evaluate whether Quirks is a suitable tool for their questions and objectives. Second, with respect to larval traits estimated from the literature, model sensitivity quantifies the propagation of parameter uncertainty to model output. Any uncertain yet influential traits point to knowledge gaps particularly deserving of future research [5]. Third, sensitivity analysis is itself a form of model application that is well suited for the theoretical study of larval fish ecology [9]. Individual parameter perturbations essentially transform dissimilar processes into comparable units and provide a basis for conceptually difficult comparisons (e.g., between photoperiod and body shape). Finally, to the extent that Quirks is an accurate synthesis of larval fish ecology, model sensitivity also quantifies natural selection acting on potential larval fish phenotypes in situ. This information may shed light on the evolutionary ecology of fish early life history and help predict climate change effects. Note that systematically perturbing multiple parameters and interpreting the complex patterns of interaction effects can yield additional information about model sensitivity, including a more robust ranking of the most important factors.

Maximum growth.

As expected, growth potential and prey requirement for 5% growth were sensitive to different parameters, and model sensitivity/parameter influence varied by larval type. Of the factors influencing growth potential, only respiration (traits xres and xrQ10) and the environment (temperature and photoperiod shortly after peak spawning, Table 5) differed among species. All other traits were either generic or rendered inconsequential by the arbitrarily high food concentration. In all larvae, growth potential was more sensitive to ydig and yeff (given ad libitum feeding, both are simply coefficients of digestion), than to xres and yact (coefficients of total and active respiration, respectively). Young anchovy larvae were most sensitive to all of the above traits, due to their high mass-specific respiration. For example, anchovy required a mere 3.4% increase in ydig to boost growth potential by 10% while the other species required 4.5% to 4.9%. Young cod and herring larvae were similar in their sensitivities, even though herring had ∼18% higher xres and were exposed to ∼10°C warmer water. On the other hand, young sprat larvae were 5%–31% more sensitive than herring, despite effectively identical traits, because they experienced much longer photoperiods (>16 versus <12 h daylight). Relative temperature changes were most important for anchovy (at 15.0°C), followed by herring (at 14.7°C), sprat (at 8.9°C) and cod (at 5.1°C). In contrast, the parameter influence of photoperiod was independent of the absolute photoperiod reference values. These initially counterintuitive results highlight the importance of species-specific reference points (i.e., realistic environmental conditions).

Prey requirement.

Unlike growth potential, prey requirement (for 5% growth) was sensitive to all endogenous traits and exogenous environmental factors. The influence of several important traits was similar among species. Prey requirement was approximately proportional to xbody, yeff, and yswim, and approximately inversely proportional to yvis2, making yvis the most influential trait in all cases. Perturbations of several other parameters affected prey requirement very differently. Notably, young sprat and anchovy were much more sensitive to s than cod and herring larvae. The same pattern was also apparent for the less influential traits xing and ydet. To generalize this relationship, parameters differentially affecting access to small prey sizes are expected to be particularly influential in species with a developmental morphology similar to sprat and anchovy, i.e. small size at yolk depletion and small mouth gape. The influence of xres and yact was greatest in young anchovy and least in young cod larvae, primarily due to their vastly different ecophysiology. To generalize, larvae with low temperature-specific respiration rates in combination with cold environments (e.g., cod) are expected to be less sensitive to perturbations in xres and yact than larvae displaying the opposite pattern (e.g., anchovy). The influence of xlen perturbations was related to body shape, such that the thinnest larvae (sprat) were most sensitive, the somewhat less thin herring and anchovy were only slightly less sensitive, but the dramatically thicker cod were only half as sensitive. Neither yhand, nor the parameters related to turbulence (ε, ydist and yturb) had a strong influence on prey requirement (see detailed discussion below). Since larvae only used from 64.8% (herring) to 88.4% (cod) of their full digestive capacity to achieve 5% growth, and inhabited waters well below their upper thermal tolerance, small changes in ydig or xtol were entirely without consequence.

Uncertainty.

Uncertainty in many traits clearly exceeded the range affecting 10% changes in growth potential or prey requirement. However, our literature review uncovered too little data for a meaningful trait-by-trait assessment of uncertainty. Instead, we will highlight just a few traits and processes of particular interest. First, uncertainty in gut evacuation rate (used to parameterize ydig) and assimilation efficiency (the main component of yeff) primarily limited the reliability of growth potential estimates, thus better measurements of digestion would be invaluable. The importance of these factors for mechanistic larval fish IBMs is well known and has recently been reviewed in detail [5], [61]. Second, uncertainty in volumetric foraging rate (used to parameterize yvis) overshadowed all other factors influencing prey requirements, indicating a need for further experimental research in this area. For example, Rosenthal and Hempel [62] determined that 11- to 13-mm herring could search 3.1 to 5.2 l h−1 based on estimated swimming speeds and visual fields. For the same 11 to 13 mm length range, Munk and Kiørboe calculated 3.2 l h−1 from feeding strike rates and 9.2 l h−1 from attack posture rates [63], while additional feeding strike data by the same authors for ∼13 mm herring yielded rates from 1.6 to 3.1 l h−1 [15], [64]. Reanalysis of four studies of 6- to 8-mm cod resulted in estimates of 0.4 to 5.2 l h−1 [55], [65][67], while three estimates for 5.5-mm anchovy (based on A. mitchilli and E. mordax) ranged from 0.17 to 0.55 l h−1 [68][70]. Prey used in the above studies varied from 0.04-mm protozoans to 0.8-mm copepods, but 0.12- to 0.23-mm copepod nauplii were most common. Our results for 13-mm herring, 7-mm cod (and sprat), and 5.5-mm anchovy feeding on 0.2-mm prey were 5.0, 0.78, and 0.38 l h−1, respectively, and took into account prey swimming and detection of prey. Treating prey detection as a type 2 functional response to prey size (equation 19) was consistent with the above studies, in that it helped explain some of the variability among literature estimates. However, our estimate of ydet = 0.07 mm was based on a single study of 13- to 18-mm herring reacting to 0.1- to 0.8-mm copepods [15], thus the value is quite uncertain. Third, handling time estimates for anchovy and sprat provided a nice example of a highly uncertain parameter that was, nevertheless, fairly inconsequential for Quirks output. Mean handling time in seven studies of cod, herring, and closely-related species of anchovy (E. mordax, and A. mitchilli) varied from ∼0.5 to 3.5 s. It seems likely that the generic value of 1.5 s was perfectly adequate for anchovy and sprat, since any value below 8.9 s (anchovy) or 17.7 s (sprat) would have yielded very similar model output.

Natural selection.

Our results led to several hypotheses regarding the evolutionary ecology of marine fish larvae. Due to the strong links between larval growth and survival [2], [3], [14], [58][60], phenotypes resulting in better growth are almost certainly favored by natural selection, yet the traits most likely to affect growth (assuming phenotypic variation among individuals) differ, depending on food limitation. When food is abundant, selection is likely to favor phenotypes with a fast metabolism, since the benefits of increased digestive capacity exceed the costs of increased respiration. There should also be selection for gains in digestive capacity or efficiency even at the expense of losses in foraging capacity or efficiency. In contrast, phenotypes with high foraging capacity and high gross growth efficiency (growth per ingestion) should be favored under food limitation. This reversal would result in selection towards slow metabolism and improved foraging (e.g., increased vision in all species, mouth gape in young anchovy and sprat) at the expense of digestive capacity or even metabolic efficiency.

Taking this line of reasoning a step further, we hypothesize that body plans prioritizing jaw and eye development over gut development may indicate species adapted to environments characterized by relatively low prey concentrations. In a previous study we estimated by principal component analysis that 16% of variability in the body shape of marine fish larvae involves a morphological gradient from a small head, eye, and jaw with a thick trunk to a large head, eye, and jaw with a thin trunk [3]. We may be able to use those data to test the above hypothesis. Given the strong influence of initial L on prey requirement, early life history strategies adapted to low-prey environments may also involve larger first-feeding larvae. This mechanism is independent from and synergistic with the finding that larger (longer) larvae can generally survive greater periods of starvation [14]. Note that the influence of xbody (body shape) perturbations is difficult to interpret in an evolutionary context, because changes in L affected both vision and mouth gape, while changes in M did not. Modeled larvae of enormous L and miniscule M would have a lower prey requirement than any realistic parameterization, following the computer science principle of “garbage in, garbage out.”

Absolute prey concentration.

While it was easy to find species-specific temperature and photoperiod reference points for sensitivity analyses (Table 5), prey concentration would have been a more elusive variable. This is why we originally chose maximum growth potential as the first and prey requirement for fixed growth as the second sensitivity analysis output variable. Both metrics and analyses are, by design, independent of estimates of prey concentration. This does not change the fact that absolute prey concentrations below the satiation point had a strong negative influence on modeled growth (Table 5). In the range between starvation and satiation, the influence of prey concentration was roughly linear with 1 mg m−3 of plankton resulting in growth of 0.8% (cod), 3.5% (anchovy), 9.3% (sprat), and 4.7% (herring) d−1. Model sensitivity aside, it is interesting to compare absolute prey requirements of the four species. One might expect the requirements to be highest for larvae spawned in summer, when zooplankton biomass is highest in the North Sea [71]. Our model estimates do not agree with this expectation, since young cod larvae required a higher prey concentration in winter than sprat in spring, anchovy in summer or herring in autumn. This may simply reflect that our parameterizations were imperfect. Alternatively, the thermal tolerance of adults, eggs, or larvae may be more important in determining spawning seasonality than larval prey limitation.

Optimal Foraging Conditions

Optimal prey size.

Plankton at 67% of the maximum ingestible prey size constituted highly favorable prey for all four larval types. This pattern arose primarily from the trade-off between the decreasing probability of capture success and the increasing benefit of successful capture (Figure 3). Note that the chosen metric is independent of encounter rate, and therefore somewhat different from the expected benefit per nearby prey organism (e.g., in an aquarium). The latter can be slightly increased by prey movement or substantially reduced by low observation success (Figure 3). More variable optima have been reported in previous modeling studies, e.g.: 54% for 7-mm cod [26], 44% for 13-mm herring [23], and 85% for 7-mm sprat larvae [26]. Since those models applied different assumptions (equations) for each species, it is unclear whether this variability reflected differences among species or among models.

Empirical studies have rarely provided sufficient information to calculate the favorability of different prey sizes for young fish larvae. One exception was a series of laboratory experiments by Munk, where 13.5-mm herring larvae were fed low concentrations of copepods of various sizes [15]. In that study, the largest prey treatment (0.6 mm, ∼57% of maximum ingestible length) yielded the highest estimated ingestion per encounter (prey dry mass • capture success) as well as the highest ingestion rate (prey dry mass • capture success • attack rate). However, a much smaller prey treatment (0.2 mm, ∼19%) was considered optimal by the author, whose definition was based on the number of ingested copepods, as opposed to their mass. This logic permeates the literature, and is often quantified in terms of Chesson’s α, also known as Chesson’s (or Manley’s) measure of prey preference [72]. When applied to fish larvae, α should perhaps be called a measure of prey “sampling,” as the terms “preference” and “selection” are quite misleading. In fact, α neither reflects theoretical benefits (since prey mass is not considered), nor empirical behavior (since prey detection and capture success are assumed to be constant). Instead, it indicates sampling bias for different prey types, i.e. the relative probability of ingestion corrected by ambient numeric concentration (which is different from encounter rate). For comparison with Munk’s data, we calculated Chesson’s α for 13.5-mm herring larvae as simulated by Quirks: the prey length with maximal α was equivalent (0.21 mm, ∼21%). Note that the nutritional quality (e.g., fatty acid composition) of prey organisms also influences their benefit to larval fish predators [73]. This further level of detail was not considered in the present study, but could be modeled by “correcting” prey mass by a food quality coefficient in the determination of foraging capacity (equation 13).

Diet composition.

Quirks assumes optimal foraging behavior, meaning that larvae only pursue and attack prey organisms when this is more profitable than spending the same time searching for better prey instead [9], [43]. Interestingly, optimal foraging was neither necessary for the model runs performed in this study, nor did it influence the results. In all cases, larvae achieved ad libitum feeding at prey concentrations far below the level at which they began actively excluding any ingestible prey from their diet. In other words, hungry larvae pursued everything from the smallest modeled prey class to the largest one they might possibly capture, while satiated larvae sometimes engaged in more complex selective feeding, but gained no benefit from doing so (because ingestion was limited by digestion). At later stages of development this would not hold true, and the explicit assumption of optimal foraging could become quite important.

Prey fields.

Quirks’ representation of plankton size structure as normalized size spectra with independent biomass and slope s, presented an opportunity to determine optimal prey fields for each larval type (Figure 4). In all four cases, optimal prey fields were so “steep” that they consisted to >95% biomass of plankton smaller than the optimal prey size. This demonstrates that the integrated benefit of all prey sizes can be quite independent from the concentration of optimal prey. The optimal values of s for anchovy (−1.9), cod (−1.4), and herring (−1.4) fell within the range from 0 to −2, which is regularly observed in the nearby Bay of Biscay [37], while the optimum for sprat (−2.5) may be unrealistically steep [36]. In any case, there was relatively little change in prey requirements among such steep prey size spectra, while “flat” prey fields became increasingly unfavorable for young larvae (Figure 4).

Turbulence.

Since the recognition that turbulence increases the rate of encounters between fish larvae and their prey [55], [74] but decreases subsequent pursuit success [49], [75], it has become common to include turbulence effects in individual-based models of larval fish foraging [5], [76], [77]. The relationship between foraging and turbulence is often assumed to be dome-shaped, with an optimal intermediate turbulence level that enhances encounter rates more than it reduces pursuit success. We can reproduce this shape in Quirks, but only for larvae swimming much more slowly than those discussed here. At the parameterized effective speeds of >4 mm s−1 the net influence of turbulence was always negative (Figure 5). In the laboratory, optimal intermediate turbulence has also been demonstrated only for small (poorly developed, slow) larvae [78][80]. In one study, small (<5 mm L, 7–9 d post hatch) Japanese flounder (Paralichthys olivaceus) larvae benefited significantly from turbulent kinetic energy dissipation rates between 10−7 and 10−5 W kg−1, while slightly larger individuals (<7 mm, 12–14 d) did not [80]. A pattern of diminishing benefits of turbulence with increasing size (development, speed) also emerges from most models, with the pattern of decline depending on assumptions regarding visual field geometry, foraging behavior, pursuit success, and relative turbulent velocity w between predator and prey [67], [81][83]. As discussed, Quirks assumes a continuously but imperfectly scanned visual cylinder, and empirically validated Kolmogorov 1941 theory determines w, which effectively increases the visual cylinder (equation 15) and reduces pursuit success (equation 20). Our linear reduction in pursuit success to zero at w>yturb (1 L s−1) was more simplistic than previous approaches, but gave very similar results (e.g., there was a correlation of R2 = 95% between equation 20 and Fiksen and MacKenzie’s preferred “Mod4” [83] in the w range from 0.1 to 10 mm s−1). Note that in situ turbulence varies with depth, allowing larvae to influence their exposure by vertical swimming behavior. Since Quirks does not account for such behavior, it makes little sense to address turbulence in even greater detail. For the same reason, light intensity was simplified as either insufficient (nighttime) or sufficient (daytime) for visual feeding, even though it varies continuously with time and depth in the field.

Known Limitations

Mathematical models of complex biophysical processes always have limitations, and Quirks is no exception. First, several environmental factors that may particularly influence larval fish foraging and growth in estuarine nursery areas (e.g., salinity, oxygen, turbidity), were not included in the model. With respect to our validation dataset, any one of these variables presumably contributed only a small portion of the ∼35% unexplained (and photoperiod-unrelated) variability in published growth rates. Nevertheless, Quirks is free software, and users may extend the model to include additional variables and processes.

Stochasticity.

Another limitation of Quirks (and many other IBMs) is that highly stochastic processes such as prey encounters are represented by simple averages. On the one hand, this allows for a fully deterministic model, in keeping with the design goal of transparency. On the other hand, this precludes Quirks (in its current form) from modeling stochastic variability in growth or foraging success. Further, the lack of a state variable tracking larval gut contents means that various behavioral and physiological mechanisms related to stochastic foraging success are not represented. For example, modeled larvae cannot fill their guts towards the beginning and then save energy towards the end of a modeled time step. They also cannot benefit from increased metabolic efficiency during times of reduced gut turnover [30], [61], [84], e.g. after dusk.

Thermal tolerance.

Larval tolerance of high temperatures does not emerge mechanistically from the model and must therefore be defined a priori via the xtol trait. This causes modeled growth potential to increase with temperature until just below the specified upper limit, which is unrealistic [3], [85]. Instead, unfavorable enzyme kinetics or insufficient aerobic scope for metabolism should cause growth potential to diminish as temperature approaches an ecological limit somewhat below the physiologically lethal temperature. We are not aware of any larval fish model that successfully incorporates such proximate mechanisms. There is a pressing need for additional research into the mechanisms limiting larval fish thermal tolerance, so that models such as Quirks can become more useful for climate research. Until this is accomplished, extra care should be taken in the interpretation of model growth predictions for temperatures that have not been empirically validated.

Summary and Conclusions

North sea fish larvae.

The most distinguishing features of young exogenously feeding anchovy, cod, herring (autumn-spawned), and sprat larvae at environmental conditions they typically experience in the North Sea were as follows. Young anchovy larvae were shortest, had the fastest metabolism, required a high prey concentration, and had the potential to grow fast. Young cod larvae were heavy and had the slowest metabolism, benefited from large prey, required a high prey concentration, and achieved the lowest growth potential. Young herring larvae were both long and heavy, benefited from large prey, had a low prey requirement, and could grow fast. Young sprat larvae were lightest and required the lowest prey concentration despite being limited to feeding on the smallest prey.

Quirks.

We found that Quirks could mechanistically explain the majority of variability among growth measured by numerous approaches for larvae of four species, from <30 to >300 µg in dry mass, at temperatures from <3 to >24°C and at photoperiods from <10 h to continuous daylight. To the best of our knowledge, this level of model skill is unprecedented for a diverse set of fish larvae and environments. By releasing Quirks as free software (Source Code S1, https://sourceforge.net/projects/larvalfishquirks/), we hope to encourage others to build on our efforts.

Supporting Information

Acknowledgments

Many hours of discussion with Marc Hufnagl were invaluable for model development. Marta Moyano and two reviewers offered helpful comments on the manuscript. The ORCID identifier for K.B. Huebert is http://orcid.org/0000-0002-2432-7337.

Author Contributions

Conceived and designed the experiments: KBH MAP. Performed the experiments: KBH. Analyzed the data: KBH. Contributed reagents/materials/analysis tools: KBH MAP. Wrote the paper: KBH MAP. Developed the Quirks model: KBH.

References

  1. 1. Durant JM, Hjermann DØ, Ottersen G, Stenseth NC (2007) Climate and the match or mismatch between predator requirements and resource availability. Clim Res 33: 271
  2. 2. Houde ED (2008) Emerging from Hjort’s Shadow. Journal of Northwest Atlantic Fishery Science 41: 53–70
  3. 3. Peck MA, Huebert KB, Llopiz JK (2012) Intrinsic and extrinsic factors driving match-mismatch dynamics during the early life history of marine fishes. Adv Ecol Res 47: 177–302
  4. 4. Miller TJ (2007) Contribution of individual-based coupled physical-biological models to understanding recruitment in marine fish populations. Mar Ecol Prog Ser 347: 127–138
  5. 5. Peck MA, Hufnagl M (2012) Can IBMs tell us why most larvae die in the sea? Model sensitivities and scenarios reveal research needs. J Mar Syst 93: 77–93
  6. 6. R Development Core Team (2013) R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Available: http://www.R-project.org/.
  7. 7. Follows MJ, Dutkiewicz S (2011) Modeling Diverse Communities of Marine Microbes. Ann Rev Mar Sci 3: 427–451
  8. 8. Record NR, Pershing AJ, Maps F (2013) Emergent copepod communities in an adaptive trait-structured model. Ecol Modell 260: 11–24
  9. 9. Letcher BH, Rice JA, Crowder LB, Rose KA (1996) Variability in survival of larval fish: disentangling components with a generalized individual-based model. Can J Fish Aquat Sci 53: 787–801
  10. 10. Kooijman SALM (2009) Dynamic energy budget theory for metabolic organisation. Cambridge: Cambridge University Press. 532 p.
  11. 11. van der Veer HW, Kooijman SALM, van der Meer J (2003) Body size scaling relationships in flatfish as predicted by Dynamic Energy Budgets (DEB theory): implications for recruitment. J Sea Res 50: 257–272
  12. 12. Laurel BJ, Hurst TP, Copeman LA, Davis MW (2008) The role of temperature on the growth and survival of early and late hatching Pacific cod larvae (Gadus macrocephalus). J Plankton Res 30: 1051–1060
  13. 13. Peck MA, Kühn W, Hinrichsen HH, Pohlmann T (2009) Inter-annual and inter-specific differences in the drift of fish eggs and yolksac larvae in the North Sea: A biophysical modeling approach. Sci Mar 73: 23–36
  14. 14. Miller TJ, Crowder LB, Rice JA, Marschall EA (1988) Larval size and recruitment mechanisms in fishes: toward a conceptual framework. Can J Fish Aquat Sci 45: 1657–1670
  15. 15. Munk P (1992) Foraging behavior and prey size spectra of larval herring Clupea harengus. Mar Ecol Prog Ser 80: 149–158.
  16. 16. Buckley LJ, Durbin EG (2006) Seasonal and inter-annual trends in the zooplankton prey and growth rate of Atlantic cod (Gadus morhua) and haddock (Melanogrammus aeglefinus) larvae on Georges Bank. Deep Sea Res Part II Top Stud Oceanogr 53: 2758–2770
  17. 17. Geffen AJ (2002) Length of herring larvae in relation to age and time of hatching. J Fish Biol 60: 479–485
  18. 18. Palomera I, Morales-Nin B, Lleonart J (1988) Larval growth of anchovy, Engraulis encrasicolus, in the Western Mediterranean Sea. Mar Biol 99: 283–291
  19. 19. Peck MA, Clemmesen C, Herrmann JP (2005) Ontogenic changes in the allometric scaling of the mass and length relationship in Sprattus sprattus. J Fish Biol 66: 882–887
  20. 20. Brander KM (1994) The Location and Timing of Cod Spawning Around the British Isles. ICES J Mar Sci 51: 71–89
  21. 21. Munk P, Nielsen JG, editors (2005) Eggs and Larvae of North Sea Fishes. Frederiksberg, Denmark: Biofolia. 215 p.
  22. 22. Baumann H, Malzahn AM, Voss R, Temming A (2009) The German Bight (North Sea) is a nursery area for both locally and externally produced sprat juveniles. J Sea Res 61: 234–243
  23. 23. Hufnagl M, Peck MA (2011) Physiological individual-based modelling of larval Atlantic herring (Clupea harengus) foraging and growth: insights on climate-driven life-history scheduling. ICES J Mar Sci 68: 1170–1188
  24. 24. Locarnini RA, Mishonov AV, Antonov JI, Boyer TP, Garcia HE, et al.. (2010) World Ocean Atlas 2009, Volume 1: Temperature. NOAA Atlas NESDIS 68. Washington, D.C.: U.S. Government Printing Office. p. 184.
  25. 25. Bivand R, Lewin-Koh N (2013) maptools: Tools for reading and handling spatial objects. Available: http://CRAN.R-project.org/package=maptools.
  26. 26. Daewel U, Peck MA, Schrum C (2011) Life history strategy and impacts of environmental variability on early life stages of two marine fishes in the North Sea: an individual-based modelling approach. Can J Fish Aquat Sci 68: 426–443
  27. 27. Gerritsen J, Strickler JR (1977) Encounter probabilities and community structure in zooplankton: a mathematical model. J Fish Res Board Can 34: 73–82
  28. 28. Eldridge MB, Echeverria T, Whipple JA (1977) Energetics of Pacific herring (Clupea harengus pallasi) embryos and larvae exposed to low concentrations of benzene, a monoaromatic component of crude oil. Trans Am Fish Soc 106: 452–461
  29. 29. Brett JR, Groves TDD (1979) Physiological Energetics. Fish Physiology 8: 279–352.
  30. 30. Boehlert GW, Yoklavich MM (1984) Carbon assimilation as a function of ingestion rate in larval pacific herring, Clupea harengus pallasi Valenciennes. J Exp Mar Biol Ecol 79: 251–262
  31. 31. Laurence GC, Lough RG (1985) Growth and survival of larval fishes in relation to the trophodynamics of Georges Bank cod and haddock. NOAA Technical Memorandum NMFS-F/NEC-36: 1–150.
  32. 32. Theilacker GH (1987) Feeding ecology and growth energetics of larval northern anchovy, Engraulis mordax. Fish Bull (Wash D C) 85: 213–228.
  33. 33. Arrhenius F, Hansson S (1996) Growth and seasonal changes in energy content of young Baltic Sea herring (Clupea harengus L.). ICES J Mar Sci 53: 792–801
  34. 34. Platt T, Denman K (1977) Organisation in the pelagic ecosystem. Helgol Mar Res 30: 575–581
  35. 35. Sheldon RW, Prakash A, Sutcliffe WH Jr (1972) The size distribution of particles in the ocean. Limnol Oceanogr: 327–340. doi:10.4319/lo.1972.17.3.0327.
  36. 36. Kerr SR, Dickie LM (2001) The Biomass Spectrum: A Predator-Prey Theory of Aquatic Production. New York: Columbia University Press. 352 p.
  37. 37. Irigoien X, Fernandes JA, Grosjean P, Denis K, Albaina A, et al. (2009) Spring zooplankton distribution in the Bay of Biscay from 1998 to 2006 in relation with anchovy recruitment. J Plankton Res 31: 1–17
  38. 38. Brown JH, Gillooly JF, Allen AP, Savage VM, West GB (2004) Toward a metabolic theory of ecology. Ecology 85: 1771–1789
  39. 39. Uye S, Sano K (1995) Seasonal reproductive biology of the small cyclopoid copepod Oithona davisae in a temperate eutrophic inlet. Mar Ecol Prog Ser 118: 121–128.
  40. 40. Hay SJ, Evans GT, Gamble JC (1988) Birth, growth and death rates for enclosed populations of calanoid copepods. J Plankton Res 10: 431–454
  41. 41. Ruzicka JJ, Gallager SM (2006) The importance of the cost of swimming to the foraging behavior and ecology of larval cod (Gadus morhua) on Georges Bank. Deep Sea Res Part II Top Stud Oceanogr 53: 2708–2734
  42. 42. Menden-Deuer S, Lessard EJ (2000) Carbon to volume relationships for dinoflagellates, diatoms, and other protist plankton. Limnol Oceanogr 45: 569–579.
  43. 43. Stephens DW, Krebs JR (1986) Foraging Theory. Princeton: Princeton University Press. 262 p.
  44. 44. Kolmogorov AN (1991) The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 434: 9–13
  45. 45. Pope SB (2000) Turbulent Flows. Cambridge: Cambridge University Press. 802 p.
  46. 46. Sreenivasan KR (1995) On the universality of the Kolmogorov constant. Phys Fluids (1994) 7: 2778
  47. 47. Yeung PK, Zhou Y (1997) Universality of the Kolmogorov constant in numerical simulations of turbulence. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 56: 1746
  48. 48. Hill PS, Nowell ARM, Jumars PA (1992) Encounter rate by turbulent shear of particles similar in diameter to the Kolmogorov scale. J Mar Res 50: 643–668
  49. 49. MacKenzie BR, Kiørboe T (2000) Larval fish feeding and turbulence: A case for the downside. Limnol Oceanogr 45: 1–10
  50. 50. Rosenthal H (1969) Untersuchungen über das Beutefangverhalten bei Larven des Herings Clupea harengus. Mar Biol 3: 208–221
  51. 51. Catalán IA, Folkvord A, Palomera I, Quílez-Badía G, Kallianoti F, et al. (2010) Growth and feeding patterns of European anchovy (Engraulis encrasicolus) early life stages in the Aegean Sea (NE Mediterranean). Estuar Coast Shelf Sci 86: 299–312
  52. 52. Kiørboe T, Munk P, Richardson K (1987) Respiration and growth of larval herring Clupea harengus: relation between specific dynamic action and growth efficiency. Mar Ecol Prog Ser 40: 1–10.
  53. 53. Dulčić J (1998) Larval growth of sprat, Sprattus sprattus phalericus, larvae in the Northern Adriatic. Fish Res 36: 117–126
  54. 54. Burchard H, Bolding K, Rippeth TP, Stips A, Simpson JH, et al. (2002) Microstructure of turbulence in the Northern North Sea: A comparative study of observations and model simulations. J Sea Res 47: 223–238
  55. 55. MacKenzie BR, Kiørboe T (1995) Encounter rates and swimming behavior of pause-travel and cruise larval fish predators in calm and turbulent laboratory environments. Limnol Oceanogr 40: 1278–1289.
  56. 56. Puvanendran V, Brown JA (2002) Foraging, growth and survival of Atlantic cod larvae reared in different light intensities and photoperiods. Aquaculture 214: 131–151
  57. 57. Otterlei E, Nyhammer G, Folkvord A, Stefansson SO (1999) Temperature-and size-dependent growth of larval and early juvenile Atlantic cod (Gadus morhua): a comparative study of Norwegian coastal cod and northeast Arctic cod. Can J Fish Aquat Sci 56: 2099–2111
  58. 58. Houde ED (1987) Fish early life dynamics and recruitment variability. Am Fish S S 2: 17–29.
  59. 59. Takasuka A, Aoki I, Mitani I (2003) Evidence of growth-selective predation on larval Japanese anchovy Engraulis japonicus in Sagami Bay. Mar Ecol Prog Ser 252: 223–238
  60. 60. Takasuka A, Aoki I, Oozeki Y (2007) Predator-specific growth-selective predation on larval Japanese anchovy Engraulis japonicus. Mar Ecol Prog Ser 350: 99–107
  61. 61. Peck MA, Daewel U (2007) Physiologically based limits to food consumption, and individual-based modeling of foraging and growth of larval fishes. Mar Ecol Prog Ser. doi:10.3354/meps06976.
  62. 62. Rosenthal H, Hempel G (1970) Experimental studies in feeding and food requirements of herring larvae (Clupea harengus L.). In: Steele JH, editor. Marine Food Chains. Berkeley: University of California Press. 344–364.
  63. 63. Munk P, Kiørboe T (1985) Feeding behaviour and swimming activity of larval herring (Clupea harengus) in relation to density of copepod nauplii. Mar Ecol Prog Ser 24: 15–21.
  64. 64. Kiørboe T, Munk P (1986) Feeding and growth of larval herring, Clupea harengus, in relation to density of copepod nauplii. Environ Biol Fishes 17: 133–139
  65. 65. Munk P (1995) Foraging behaviour of larval cod (Gadus morhua) influenced by prey density and hunger. Mar Biol 122: 205–212
  66. 66. Hunt von Herbing I, Gallager SM (2000) Foraging behavior in early Atlantic cod larvae (Gadus morhua) feeding on a protozoan (Balanion sp.) and a copepod nauplius (Pseudodiaptomus sp.). Mar Biol 136: 591–602
  67. 67. Galbraith PS, Browman HI, Racca RG, Skiftesvik AB, Saint-Pierre JF (2004) Effect of turbulence on the energetics of foraging in Atlantic cod Gadus morhua larvae. Mar Ecol Prog Ser 281: 241–257
  68. 68. Hunter JR (1972) Swimming and feeding behavior of larval anchovy Engraulis mordax. Fish Bull (Wash D C) 70: 821–838.
  69. 69. Houde ED, Schekter RC (1980) Feeding by marine fish larvae: developmental and functional responses. Environ Biol Fishes 5: 315–334
  70. 70. Chesney EJ (2008) Foraging behavior of bay anchovy larvae, Anchoa mitchilli. J Exp Mar Biol Ecol 362: 117–124
  71. 71. Fransz HG, Colebrook JM, Gamble JC, Krause M (1991) The zooplankton of the north sea. Neth J Sea Res 28: 1–52
  72. 72. Chesson J (1978) Measuring preference in selective predation. Ecology: 211–215. doi:10.2307/1936364.
  73. 73. Paulsen M, Hammer C, Malzahn AM, Polte P, von Dorrien C, et al.. (2013) Nutritional situation for larval Atlantic herring (Clupea harengus L.) in two nursery areas in the western Baltic Sea. ICES J Mar Sci. doi:10.1093/icesjms/fst168.
  74. 74. Rothschild BJ, Osborn TR (1988) Small-scale turbulence and plankton contact rates. J Plankton Res 10: 465–474
  75. 75. MacKenzie BR, Miller TJ, Cyr S, Leggett WC (1994) Evidence for a Dome-Shaped Relationship Between Turbulence and Larval Fish Ingestion Rates. Limnol Oceanogr 39: 1790–1799
  76. 76. Werner FE, Perry RI, Lough GR, Naimie CE (1996) Trophodynamic and advective influences on Georges Bank larval cod and haddock. Deep Sea Res Part II Top Stud Oceanogr 43: 1793–1822
  77. 77. Fiksen Ø, Utne ACW, Aksnes DI, Eiane K, Helvik JV, et al. (1998) Modelling the influence of light, turbulence and ontogeny on ingestion rates in larval cod and herring. Fish Oceanogr 7: 355–363
  78. 78. Kato Y, Takebe T, Masuma S, Kitagawa T, Kimura S (2008) Turbulence effect on survival and feeding of Pacific bluefin tuna Thunnus orientalis larvae, on the basis of a rearing experiment. Fish Sci 74: 48–53
  79. 79. Kimura S, Nakata H, Margulies D, Suter JM, Hunt SL (2004) Effect of oceanic turbulence on the survival of yellowfin tuna larvae. Nippon Suisan Gakk 70: 175–178
  80. 80. Oshima M, Kato Y, Masuda R, Kimura S, Yamashita Y (2009) Effect of turbulence on feeding intensity and survival of Japanese flounder Paralichthys olivaceus pelagic larvae. J Fish Biol 75: 1639–1647
  81. 81. Pécseli HL, Trulsen J, Fiksen Ø (2012) Predator–prey encounter and capture rates for plankton in turbulent environments. Prog Oceanogr 101: 14–32
  82. 82. Kiørboe T, MacKenzie B (1995) Turbulence-enhanced prey encounter rates in larval fish: effects of spatial scale, larval behaviour and size. J Plankton Res 17: 2319–2331
  83. 83. Fiksen Ø, MacKenzie B (2002) Process-based models of feeding and prey selection in larval fish. Mar Ecol Prog Ser 243: 151–164
  84. 84. Govoni JJ, Boehlert GW, Watanabe Y (1986) The physiology of digestion in fish larvae. Environ Biol Fishes 16: 59–77
  85. 85. Pörtner HO, Peck MA (2010) Climate change effects on fishes and fisheries: towards a cause-and-effect understanding. J Fish Biol 77: 1745–1779
  86. 86. Tudela S, Palomera I, Quílez G (2002) Feeding of anchovy Engraulis encrasicolus larvae in the north-west Mediterranean. J Mar Biolog Assoc UK 82: 349–350
  87. 87. Broughton EA, Lough RG (2010) General trends and interannual variability in prey selection by larval cod and haddock from the southern flank of Georges Bank, May 1993–1997. NOAA Technical Memorandum NMFS-NE-217 1: 32.
  88. 88. Voss R, Köster FW, Dickmann M (2003) Comparing the feeding habits of co-occurring sprat (Sprattus sprattus) and cod (Gadus morhua) larvae in the Bornholm Basin, Baltic Sea. Fish Res 63: 97–111
  89. 89. Kühn W, Peck MA, Hinrichsen HH, Daewel U, Moll A, et al. (2008) Defining habitats suitable for larval fish in the German Bight (southern North Sea): An IBM approach using spatially-and temporally-resolved, size-structured prey fields. J Mar Syst 74: 329–342
  90. 90. Finn RN, Fyhn HJ, Evjen MS (1995) Physiological energetics of developing embryos and yolk-sac larvae of Atlantic cod (Gadus morhua). I. Respiration and nitrogen metabolism. Mar Biol 124: 355–369
  91. 91. Houde ED, Schekter RC (1983) Oxygen uptake and comparative energetics among eggs and larvae of three subtropical marine fishes. Mar Biol 72: 283–293
  92. 92. Lough RG, Buckley LJ, Werner FE, Quinlan JA, Pehrson Edwards K (2005) A general biophysical model of larval cod (Gadus morhua) growth applied to populations on Georges Bank. Fish Oceanogr 14: 241–262
  93. 93. Regner S (1985) Ecology of planktonic stages of the anchovy, Engraulis encrasicolus (Linnaeus, 1758), in the central Adriatic. Acta Adriat.
  94. 94. Yin MC, Blaxter JHS (1987) Temperature, salinity tolerance, and buoyancy during early development and starvation of Clyde and North Sea herring, cod, and flounder larvae. J Exp Mar Biol Ecol 107: 279–290
  95. 95. Peck MA, Baumann H, Bernreuther M, Clemmesen C, Herrmann JP, et al. (2012) The ecophysiology of Sprattus sprattus in the Baltic and North Seas. Prog Oceanogr 103: 42–57
  96. 96. Pedersen BH (1984) The intestinal evacuation rates of larval herring (Clupea harengus L.) predating on wild plankton. Dana 3: 21–30.
  97. 97. Pepin P, Penney R (2000) Feeding by a larval fish community: impact on zooplankton. Mar Ecol Prog Ser 204: 199–212
  98. 98. Tilseth S, Ellertsen B (1984) Food consumption rate and gut evacuation processes of first feeding cod larvae (Gadus morhua L.). Flodevigen Rapportserie 1: 167–182.
  99. 99. Ré P (1987) Ecology of the planktonic phase of the anchovy, Engraulis encrasicolus (Linnaeus, 1758), within Mira Estuary (Portugal). Invest Pesq 51.
  100. 100. Blaxter JHS (1965) The feeding of herring larvae and their ecology in relation to feeding. CalCOFI Reports 10: 79–88.
  101. 101. Houde ED, Zastrow CE (1993) Ecosystem-and taxon-specific dynamic and energetics properties of larval fish assemblages. Bull Mar Sci 53: 290–335.
  102. 102. Checkley DM Jr (1984) Relation of growth to ingestion for larvae of Atlantic herring Clupea harengus and other fish. Mar Ecol Prog Ser 18: 215–224.
  103. 103. Ruzicka JJ, Gallager SM (2006) The saltatory search behavior of larval cod (Gadus morhua). Deep Sea Res Part II Top Stud Oceanogr 53: 2735–2757
  104. 104. Buskey EJ, Coulter C, Strom S (1993) Locomotory Patterns of Microzooplankton: Potential Effects on Food Selectivity of Larval Fish. Bull Mar Sci 53: 29–43.
  105. 105. Titelman J, Kiørboe T (2003) Motility of copepod nauplii and implications for food encounter. Mar Ecol Prog Ser 247: 123–135
  106. 106. Regner S (1996) Effects of environmental changes on early stages and reproduction of anchovy in the Adriatic Sea. Sci Mar 60: 167–177.
  107. 107. García A, Cortés D, Ramírez T (1998) Daily larval growth and RNA and DNA content of the NW Mediterranean anchovy Engraulis encrasicolus and their relations to the environment. Mar Ecol Prog Ser 166: 237–245
  108. 108. Sabatés A, Salat J, Palomera I, Emelianov M, Fernández de Puelles ML, et al. (2007) Advection of anchovy (Engraulis encrasicolus) larvae along the Catalan continental slope (NW Mediterranean). Fish Oceanogr 16: 130–141
  109. 109. Laurence GC (1978) Comparative growth, respiration and delayed feeding abilities of larval cod (Gadus morhua) and Haddock (Melanogrammus aeglefinus) as influenced by temperature during laboratory studies. Mar Biol 50: 1–7
  110. 110. Caldarone EM, St Onge-Burns JM, Buckley LJ (2003) Relationship of RNA/DNA ratio and temperature to growth in larvae of Atlantic cod Gadus morhua. Mar Ecol Prog Ser 262: 229–240
  111. 111. Johannessen A, Blom G, Folkvord A (2000) Differences in growth pattern between spring and autumn spawned herring (Clupea harengus L.) larvae. Sarsia 85: 461–466.
  112. 112. Folkvord A, Johannessen A, Moksness E (2004) Temperature-dependent otolith growth in Norwegian spring-spawning herring (Clupea harengus L.) larvae. Sarsia 89: 297–310
  113. 113. Alshuth S (1988) Daily growth increments on otoliths of laboratory-reared sprat, Sprattus sprattus L., larvae. Meeresforschung 32: 23–29.
  114. 114. Munk P (1993) Differential growth of larval Sprat Sprattus sprattus across a tidal front in the eastern North Sea. Mar Ecol Prog Ser 99: 17–27.
  115. 115. ICES (2013) Report of the Herring Assessment Working Group for the Area South of 62 N (HAWG).