Modelling the effect of constant and fluctuating food supply on egg production rates of Acartia grani

Ecological Modelling 221 (2010) 495–502

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Modelling the effect of constant and fluctuating food supply on egg production rates of Acartia grani F. Carlotti a,∗ , L. Eisenhauer a , A. Calbet b a Aix-Marseille Université; CNRS; LOPB-UMR 6535, Laboratoire d’Océanographie Physique et Biogéochimique, OSU/Centre d’Océanologie de Marseille Rue de la Batterie des Lions, F-13007 Marseille, France b Institut de Ciències del Mar CMIMA (CSIC), Passeig Marítim de la Barceloneta 37–49, 08003 Barcelona, Spain

a r t i c l e

i n f o

Article history: Received 22 July 2008 Received in revised form 19 October 2009 Accepted 22 October 2009 Available online 5 December 2009 Keywords: Individual energetic budget Copepod Food fluctuation Egg production rate

a b s t r a c t A mathematical model of the individual budget of a spawning female of the copepod Acartia grani (Sars) has been used to simulate the time-scale of egg production over various external forcings (or inputs) of food fluctuation conditions. The budget matter in the body of the copepod females is distributed through four compartments: the whole digestive tract (globally named as gut), the hemolymph (which include the body fluid with available nutriments for the organs), the structural body weight, and the gonad. This small calanoid species does not carry lipid reserves but cumulate some labile reserves in its body, according to food availability. The model results show how the continuous spawning varies with food fluctuations, and suggest the mechanisms inducing the delay of response to starvation by using the metabolic reserves. Three different patterns in egg production response are observed: food fluctuations with frequencies below 12 h have no effect on egg production; food fluctuations of 12 h to 5 days induce synchronous egg production fluctuations; beyond 5 days the strong physiological changes induced by long starvation durations create delays in the responses to food replenishment. The available data of cultivated cohorts under laboratory conditions are used to validate the model. The properties underlined by the model, in particular its weak capacity to respond to starvation, allow explaining A. grani distribution in specific habitats. Different experimental protocols for complementary experiments are proposed to complete the model validation in other forcing conditions. © 2009 Published by Elsevier B.V.

1. Introduction Copepod females egg production rate (EPR) has become one of the most common index of secondary production, because it is a relatively simple measurement in comparison to somatic growth rate of all stages, particularly during field studies (Sekigushi et al., 1980; Bergreen et al., 1988; Poulet et al., 1995; Runge and Roff, 2000; Rey-Rassat et al., 2002). EPR represents most of the production of the female stage, as adult copepods do not molt and grow, and drives the recruitment of the population. However, numerous internal and external factors to the female organisms as well as the used protocols influence the observed EPR. Copepod fecundity variations are related to factors such as temperature and food supply in laboratory and field studies (Harris et al., 2000), but their relative importance remains controversial. Differences are probably caused by geographical variability of environmental conditions, changes in

∗ Corresponding author. Present address: Centre d’Océanologie de Marseille (COM), Station Marine d’Endoume, Rue de la Batterie des Lions, F-13007 Marseille, France. Tel.: +33 0 4 91 04 16 44. E-mail address: [email protected] (F. Carlotti). 0304-3800/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.ecolmodel.2009.10.035

planktonic food community structure, but also on individual characteristics such as the state of maturity, the feeding history and the reserve content, the size of the females, the age of the females, etc. (Carlotti et al., 1997). To get a most robust use of the easy to be done EPR method, it is essential to build egg production model to synthesize our understanding of the involved processes, to help in the preparation of future protocols, and to interpret results of new experiments. A few egg production models of copepods have been built to understand the mechanisms of processes involved in the egg production, both to analyze either laboratory experiments in controlled conditions or field studies. These models range from simple empirical function of chlorophyll a and temperature (Uye, 1981; Prestidge et al., 1995) used to interpret field studies, to more elaborate individual budget model including several internal body pools (Sciandra et al., 1990; Caparroy and Carlotti, 1996; Carlotti and Hirche, 1997; Kuijper et al., 2004) used to analyze experimental results. All these budget models consider at least two internal state variables, the structural body weight and reserves. Gonads are either implicitly represented as the reserve pool (DEB model, Kuijper et al., 2004) or explicitly represented as supplementary variable (Sciandra et al., 1990; Caparroy and Carlotti, 1996; Carlotti

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Table 1 Differential equations for the state and outputs variables. See symbols of processes in Table 2. State variables

Differential equations

• GUT: gut content

• GON: mass of gonads

d(GUT) =I−A−E dt d(NUT) =A−G−M dt d(SM) = G − R2 dt d(GON) = M−L dt

Output variables

Differential equations

• EGGS: cumulated egg mass

d(EGGS) =L dt d(CO2 ) = R1 dt d(FP) = E dt

• NUT: nutrients in hemolymph • SM: structural mass

• CO2 : cumulated produced CO2 • FP: cumulated faecal pellets

− R1

+ R2

Derived entities

Equations

• Individual body weight

W = GUT + NUT + SM + GON

• Number of spawned eggs

NEGGS =

EGGS EGGMASS

and Hirche, 1997). Whereas the DEB model does not explicitly represent the dynamics of the gut content (Kuijper et al., 2004; van der Meer, 2006), other copepod models explicitly take into account a gut variable (Caparroy and Carlotti, 1996; Carlotti and Hirche, 1997). Many planktonic organisms, and particularly copepods, present intermittent feeding with a filtration behaviour not only dependant on food concentrations but also to other external factors such as turbulence, and to internal factor, such as the fullness of the foregut and the midgut (Dagg, 1983). In their model, Caparroy and Carlotti (1996) showed how the satiety effect explains the shape of the functional response of Acartia tonsa. The genus Acartia has been extensively studied both for its physiological properties (Kiørboe et al., 1985; Gifford and Dagg, 1988; Kleppel et al., 1988; Saiz and Alcaraz, 1991; Jónasdóttir, 1994; Calbet and Alcaraz, 1996; Besiktepe and Dam, 2002; Thor,

2003) and its population dynamics in several habitats (Landry, 1978; Irigoien and Castel, 1995). The calanoid copepod Acartia grani (Sars) is a pelagic coastal species in the Mediterranean Sea and in the North Atlantic common in enclosed or semi-confined coastal areas with high POM concentrations (Rodriguez and Jimenez, 1990). It is easily reared under laboratory conditions (Calbet and Alcaraz, 1996). It is a broadcast spawning copepod that continuously releases its eggs. Some Acartia sp., such as Acartia longiremis or Acartia clausi, are known to be batch-spawner (Norrbin, 2001; Niehoff, 2007), but this is still not documented for A. grani. A. grani does not show diel spawning rhythm when food is sufficient (Rodríguez et al., 1995). Resting rates for this species have been observed (Guerrero and Rodriguez, 1997). A. grani does not carry lipid reserves which means that the assimilated matter transferred through the gut wall is distributed in the hemolymph and represent a stock of nutritive matter in the hemolymph quickly available for metabolic and production processes. Several individual budget models have been applied to A. tonsa (Caparroy and Carlotti, 1996; Kuijper et al., 2004), but not yet to A. grani. The aim of this work is to propose a simple mathematical representation of the individual budget and egg production of A. grani which satisfyingly reproduces its limited buffer capacity to food fluctuations, and help to understand its distribution in regards to environmental parameters. 2. Model concept and equations The conceptual model of the individual energetic budget of A. grani female is presented in Fig. 1. The individual body weight is structured in four pools, as state variables: the gut content, the nutrient pool (metabolites) in the internal body fluid or hemolymph, the structural mass and the gonad mass. Food and temperature, which are considered as the most important external parameters for the survival of Acartia are used as forcing variables. The model takes into account carbon currency to treat

Table 2 Mathematical functions of the different processes. Rates of processes in condition not explicitly stated are equal to zero. Process

Functions

Ingestion

I = P1

Assimilation Egestion

A = P5 × GUT E = P6 × GUT



FOOD FOOD+P2



P3(TEMP−18) W P4

Case 1: Non-reproductive copepod female (SM < P16) Growth Respiration - Good physiological conditions (NUT ≥ P15) - Bad physiological conditions (NUT < P15)

Growth = P7 × NUT R1 = P11 × SM × P12(TEMP−18) + P13 × I R2 = 0 R2 = P11 × SM × P12(TEMP−18) R1 = 0

Case 2: Reproductive copepod female (SM ≥ P16) Oocyte maturation - Oocyte maturation in good feeding conditions (GUT ≥ P17) - Control of oocyte maturation process through digestive activity (GUT < P17)

M = P8 × NUT M=0

Egg laying - Egg laying in good gonad conditions (GON ≥ P10) - No egg laying if immature gonads (GON < P10)

L = P9(GON − P10) L=0

Respiration - Respiration in good physiological conditions (NUT ≥ P15) - Respiration in physiological conditions (NUT < P15)

R1 = P11 × SM × P12(TEMP−18) + P13 × I + P14 × GON R2 = 0 R2 = P11 × P11 × SM × P12(TEMP−18) R1 = 0

PREY: food concentration. TEMP: temperature. P1 to P17: biological parameters (see Table 3). Other symbols are presented in Table 1.

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Table 3 Values of the parameters used in the model. Parameter

Value

P1 P2

1.02 279

mass fluxes through different compartments. Each internal pool (state variable) is connected with either external variables, or other state variables, or the output variables, by physiological processes (arrows). Output variables are represented by the non-assimilated food (faecal pellets), the metabolic losses (respiration) and the egg production. The differential equations and the functions representing these processes are, respectively, listed in Tables 1 and 2. The gut is filled by the ingestion of matter. The gut content is either assimilated through the gut wall or egested in the form of faecal pellets. Food quantity, temperature and total body weight are the key variables influencing the ingestion rate (Vidal, 1980). The ingestion rate depends on food density following the Michaelis–Menten relation limited to a maximum ingestion rate (P1) and characterized by the half-saturation grazing coefficient (P2). The maximum ingestion rate P1 is defined at 18 ◦ C and varies with temperature following an exponential curve with a coefficient P3. The ingestion rate also depends on the individual body weight following an allometric relationship with coefficient P4. The assimilation and the egestion rates are supposed to be proportional (respectively parameters P5 and P6) to the gut content at any time. The assimilated matter is then collected in the circulating hemolymph in body the copepod and represents a “nutrient pool” of immediately available energy (Fig. 1). This nutrient pool is used for metabolic requirements and for building tissue, either for the structural mass (growth) or for the gonad mass (reproduction). The metabolic requirements are quantified by the respiration rates. Metabolism is subdivided in basal metabolism, the minimum calorific requirement, and active metabolism, which represents the metabolic rate in the maximum level of activity. In the model, these processes are simply represented as in Carlotti and Sciandra (1989): the rate of basal metabolism is proportional to structural body mass and is temperature-dependent (parameters P11 and P12), and the additional rate of active metabolism is proportional to ingestion rate (parameter P13). Thus these metabolic rates are realised by using metabolites from the nutrient pool and produced CO2 . When nutrient pool is sufficiently high to cover the metabolic requirements (above P15), the copepod allocates matter for its structural growth until a critical mass characterizing its maturity at the adult stage. If the nutrient pool is nearly empty (below P15), after a long starvation time, the metabolism is reduced to the basal metabolism

Description

−1

day

␮g C l

−1

P3

1.071

wd

P4

0.8

wd

P5 P6 P7

19.2 12.8 0.5

day−1 day−1 day−1

P8

0.5

day−1

P9

Fig. 1. Conceptual diagram of the individual energetic budget model of Acartia grani female. The individual body weight is structured in different pools i.e. the state variables (in square) which are connected by physiological processes (arrows) with the external variables (forcing variables prey density; output variables fecal pellets, eggs and CO2 ) and between themselves. Temperature influences ingestion and respiration rates.

Unit

10

␮g C l−1

P10

0.4

␮g C

P11 P12

0.06 1.082

day−1 wd

P13

0.1

day−1

P14

0.1

day−1

P15

0.05

␮g C

P16 P17

3.85 0.01

␮g C ␮g C

P18

0.012

␮g C

Maximal specific ingestion rate at 18 ◦ C Half-saturation constant of ingestion function Tenth root of Q10 ingestion coefficient Allometric relationship of ingestion to individual body weight Rate of assimilated gut content Rate of egested gut content Rate of nutrient flux from body fluid to the structural body Rate of nutrient flux from body fluid to the gonad Proportionality between egg production and gonad mass Threshold value of gonad mass allowing egg laying Respiration rate at 18 ◦ C Tenth root of Q10 respiration coefficient Proportionality between metabolic and ingestion rates Proportionality between metabolic and oocyte maturation rates Hemolymph threshold concentration to undergo oocyte maturation Critical weight for egg building Threshold value of gut content allowing gonad maturation Mean weight of an egg

wd: dimensionless.

and the matter is directly taken from the structural body weight (shrinkage), see Carlotti and Hirche (1997) for details. At the adult stage, when female weight exceeds the critical maturity mass (P16), then the exceeding matter of the nutrient pool is used for gonad maturation and egg production. Gonads initiate then oogenesis, starting to produce oocytes which undergo themselves a maturation process using nutrient input (Carlotti and Hirche, 1997). Mature eggs are spawned only if gonads reach a minimal threshold mass (P10). The egg production is then proportional (P9) to the exceeding gonad weight beyond the threshold value (P10). Any egg spawning phase reduces the weight of the gonad down to P10. When the oogenesis occurs, an additional metabolic cost is considered proportional to the gonad weight (parameter 14). The oocyte maturation is also considered to respond quickly to food shortage by a control related to the gut content (parameter 17). 3. Calibration The time step of the model simulation is fixed to 0.01 day and the numerical integration is the Euler method. The coefficient values (named P1 to P18) are presented in Table 3. The maximum ingestion rate defined at 18 ◦ C (P1) and the halfsaturation grazing coefficient (P2) have been derived from Calbet and Alcaraz (1997) and Henriksen et al. (2007). The temperature coefficient P3 is equal to 1.071 (i.e. the 10th root of Q10 equal to 2) and the exponent of the allometric relationship is fixed to 0.8 (P4), which are common values for small calanoid copepods in the Mediterranean sea (Carlotti et al., 2000). We derived the coefficients of proportionality between the assimilation and egestion rates and the gut content from two papers: Hansen et al. (1990) established that, in good food conditions, the daily ingested mass is equal to 32 times the gut content per day. Mayzaud et al. (1998) find an assimilation rate of A.

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Fig. 2. Standard simulation: Acartia grani spawning female in saturated food conditions (800 ␮g C l−1 ) at 18 ◦ C. Variables and processes time-scale. Left: details of the first 24 h. (A) Fluxes of ingestion, assimilation and egestion; (B) gut, hemolymph and gonad dynamics; (C) structural body weight and total weight; (D) metabolic fluxes; and (E) cumulated ingestion, cumulated production of fecal pellets, cumulated respiration and cumulated spawned egg mass.

clausi fed with Thalassiosira weissflogii around 75% of the daily ingested mass, but dropping down to 40% when they added detritus. Besiktepe and Dam (2002) found the daily egestion rate of A. tonsa fed with T. weissflofgii around 60% of the ingestion rate, which means an assimilation rate equal to 40%. As a mean, we keep a classical mean value of assimilation efficiency for small calanoid copepods equal to 60% (Carlotti et al., 2000). Then, we derive the rate of assimilation from the matter in gut content (P5), to be 60% of 32 times the equivalent of daily ingested gut contents per day, which is 19.2 (P5).Then, the rest of 32 times the equivalent of daily ingested gut contents per day are egested (P6 = 12.8). Allocation rate of matter from the nutrient pool to the structural body (P7) or to gonads (P8) has been fixed at 0.5 day−1 for both processes, similarly to Carlotti and Hirche (1997). The minimal threshold mass of gonads for spawning (P10) is fixed 0.4 ␮g C. The flux of egg production (P9) beyond this value is set to 10; which means that a clutch of eggs is spawned and the gonad mass dropped below P10. The critical weight of mature female (P16) and the egg weight (P18) have been derived for observed weights (Calbet and Alcaraz, 1997; Rodríguez et al., 1995), and the minimal gonad weight for egg production (P10) has been extrapolated from comparison with near calanoid species (Niehoff, 2007). Other parameter values related to the metabolic rates (P11, P12, P13, P14) and feedback controls (P15) are taken from Carlotti and Hirche (1997). P17 has been fixed equal to 10% of the gut content in saturation condition.

4. Experimental data of egg production experiment Calbet and Alcaraz (1996) made egg production experiments of cultivated A. grani under various food fluctuations of 12, 24 and 48 h, and starvation of 3, 4 and 5 days. Experiments were conducted in temperature controlled rooms (18 ◦ C) and copepod were fed with T. weissflogii either high (1.6 ppm) or low (0.2 ppm) concentrations (see Calbet and Alcaraz, 1996 for details).

5. Model results 5.1. Simulation of a freshly moulted female under constant food conditions A standard simulation of the growth and egg production and associated physiological processes of A. grani adult female over 30 days in constant temperature (18 ◦ C) and constant optimal food conditions (800 ␮g C l−1 ) are presented in Fig. 2. The female starts with initial structural body mass fixed to 3.85 ␮g C just equal to the critical weight for egg building (P17) and the gonads are not developed, i.e. their mass is equal to 0 ␮g C. At the beginning of the simulation, the gut is empty and the nutrient pool has an initial amount of 0.15 ␮g C. The high level of food induces immediately a high ingestion rate around 2.3 ␮g C ind−1 day−1 (Fig. 2A), The gut is filled within 30 min (Fig. 2B), and the gut content is either assimilated or egested. After the first 30 min, a stable state of the gut content occurs due to the balance between the ingestion rate on one side and the assimilation and egestion rates on the other side. Both assimilation and egestion processes increase from zero to values corresponding to the rates with the full gut content (Fig. 2A). This gut content is stabilized at 0.1 ␮g C ind−1 in 2 h. At this time, the egestion and the assimilation rates reach 1.4 ␮g C and 0.9 ␮g C ind−1 day−1 , respectively. The nutrient content in the hemolymph (Fig. 2B) increases almost linearly during the first day which induces the growth of the gonads during the two first days. The nutrient content in hemolymph increases until a steady state reached after 12 days. The exponential growth of the gonads (Fig. 2B) during the 2 first days of simulation uses a large part of matter from the nutrient pool. The gonad reaches a nearly maximum size at the end of the second day. Then, the nutrient pool reaches slowly a steady state at a value of 1.27 ␮g C after 14 days. Gonads and nutrient pool induce the increase and then stabilization of the total body weight (Fig. 2C). The slight increase of ingestion within the first 12 days is due to

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Fig. 3. Simulations of egg production rates and cumulated egg production for different fluctuation periods of presence (800 ␮g C l−1 ) and absence (0 ␮g C l−1 ) of food. Data (mean values and associated standard deviations) from Calbet and Alcaraz (1996). 12–12 h alternating food condition (A). Time-scale of the gut content, nutrient content in hemolymph, weight of gonads (B) structural weight and total weight (C) and cumulated egg production (D); 24–24 h alternating food condition (E) and cumulated egg production (F); 48–48 h alternating food condition (G) and cumulated egg production (H).

the allometric relationship to weight which increases from 4 ␮g C to reach a final stable mass of 5.8 ␮g C. The increase of gonad mass (Fig. 2C) presents a change in slope during the third day which corresponds to the beginning of spawning process (Fig. 2D). The gonad mass is stabilized at 0.55 ␮g C on day 10 which represented around 10% of total final body mass. The time-scale of the various physiological fluxes (Fig. 2D) shows that the gonad development and the egg maturation process start as soon as the beginning of the simulation whereas the spawning response occurs after a time-lag of 3.9 days. At the end of the simulation, at day 15, the weight is stabilized at 5.8 ␮g C (Fig. 2C), the cumulated ingested matter is 43.18 ␮g C which have used for 27.27 ␮g C of faecal pellets, 8.49 ␮g C for respiration and 7.42 ␮g C for egg production, which correspond to 600 eggs. 5.2. Simulations under short-term food fluctuations Several simulations have been run with regular switch between high food and starvation conditions with periods of 12, 24 and 48 h (Fig. 3). Food concentration oscillated from zero to favourable saturating concentration of 800 ␮g C l−1 . Food fluctuations started when female’s physiological state was considered near to steady state condition, i.e. on day 12 of the standard simulation (see Fig. 2), and occurred during 7 days (Fig. 3A, E and G). Simulated egg production rates of A. grani were compared to experimental datasets from Calbet and Alcaraz (1996). Results of simulated experiments of 12–12 h food fluctuation cycles (Fig. 3A) show that all internal compartments respond to these fluctuations (Fig. 3B), but with various time-lag. The gut content responds within the first half-hour following the beginning of starvation or food replenishment, whereas the hemolymph

nutrient content increases and decreases following the state of gut content. During the starvation, although the nutrient content in hemolymph is sufficiently high, the empty gut content induces a stop of gonad maturation (threshold value P18) but the egg production continues as long as the gonad mass is large enough. When food is available, the gut fullness allow to resume the gonad maturation and the egg production, if the gonad mass is large enough. The mass of gonads fluctuations is due to the nutrient content: because the nutrient pool is never completely restored to its initial level after a cycle “12 h food–12 h starvation”, the mean available quantity of nutrients for egg production decreases progressively and reaches a minimum of 30% of its initial value at the end of day 19. Consequently, the replenishment of gonads is lower and lower, but because the gonad mass fluctuates above the critical mass of 0.4 ␮g C it did not induce any interruption of the spawning activity, only a decrease of the rate (Fig. 3B). Similarly, the total body weight decreases but it stays above the structural body weight (Fig. 3C). Finally, the reproductive response is characterized by a constant increase of cumulated egg production with an oscillating pattern (Fig. 3D). The spawning rhythm is synchronous to food fluctuation over the entire time span of simulated experiment from days 12 to 19. The mean slope of the cumulated egg production rate decreases with time as a result of the slow reduction of nutrient content in hemolymph. Reproductive response for simulated experiments of alternating 24–24 h and 48–48 h food–starvation cycles showed oscillating patterns (Fig. 3F and H). The comparison of the simulated egg productions for the 12–12 h, 24–24 h and 48–48 h food fluctuations cycles with experimental datasets showed that cumulated egg production rate was slightly overestimated excepted at the end of the

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Fig. 4. Effect of starvation periods on egg production followed by respective recovery phases in saturated food conditions (800 ␮g C l−1 ). Time-scale of structural weight (dotted line) and total body weight bold line for starvation regimes starting between days 12 and 15 (A), between days 12 and 16 (B) and between days 12 and 17 (C). (D) Cumulated egg production since day 12 and up to day 23 for four different regimes: constant food supply, starvation between days 12 and 15, starvation between days 12 and 16, starvation between days 12 and 17.

simulation of the 12–12 h simulation. In all three experiments with food fluctuations, the cumulated reproductive response shows a very low dispersion level of measured values (Fig. 3 D, F and H). The modelled mean reproductive response remains higher than the estimated range of variability in measured cumulated EPR. That is due to its higher production rates during saturating food conditions and an interruption of egg production shortly after entering in starvation phase. For each food fluctuation regime, the amplitude of the fluctuations in egg productions in the model was more pronounced than in the data, whereas the oscillations duration was constant. Under the 24–24 h and 48–48 h food–starvation cycles obvious spawning breaks occur after starvation phases. These long phases induce a decrease of the gonad mass below the critical spawning mass (P10) stopping the egg production. 5.3. Simulations of longer starvation and recovery egg production durations Longer starvation durations of 3, 4, 5 days have been simulated (Fig. 4A) to study the egg production response and the associated physiological mechanisms. The egg production was stopped for durations equal to the starvation durations for the first two cases, but in the latter case, 5 days starvation were followed by 6 days to recover egg production. The maturation is quickly stopped (halfhour) when the gut content is below P18, and the gonad becomes quickly atrophied during the first day of food deprivation. The egg production stops when the gonad is below its critical mass (P10). At the same time, the organism ensures its basal metabolism using the remaining nutrients in hemolymph which decreases linearly. 3 and

4 days of starvation do not fully exhaust the nutrient pool. At the end of starvation period, over 90% of mass losses is due to decrease of hemolymph nutrient. The structural weight did not change (Fig. 4 B and C). After 3 and 4 starvation days, food replenishment directly restores the nutrient content, increase the gonad mass and the total body mass (Fig. 4 B and C) which allow to resume egg maturation and spawning activity at days 15 and 16, respectively (Fig. 4A). In both cases a constant maximal egg production rate is reached 3 days later (days 18 and 19, respectively). With 5 days starvation, the nutrient pool becomes empty at the fourth day and induces a switch in metabolism using substrate provided by the hemolymph nutrient to substrate produced by degradation of structural body mass. Thus energy for respiration is taken on the structural body mass as long as the nutrient content is below its threshold (P16). Consequently the structural body weight starts to decrease (Fig. 4D). When food is offered again, the organism firstly use the hemolymph nutrient pool to recover its structural mass until reaching the critical maturity mass (P17), and only afterwards the hemolymph nutrient pool is used to resume the gonad growth, egg maturation and egg spawning. Consequently, the egg production is resumed 2 days after the food replenishment (day 18), and a constant maximal egg production rate is not reached before the end of the simulation (day 23). Compared results of simulated cumulated EPR with the data show strong correlation coefficients (R > 0.99) in all cases (Fig. 4A). Particularly, the modelled reproductive response to longer starvation periods (in all three starvation experiments) was similar to observations, with a right timing of the re-initiation of egg production following recovering from starvation. In constant food

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conditions EPR slightly underestimates experimental data from days 14 to 17 but stays still in the range of the measured variability.

and total body weight. Such dataset will allow a full test of the model mechanisms suggested in this paper.

6. Discussion and conclusion

References

The control exerted by food availability conditions on lifehistory parameters of copepods has to be better understood for its ecological implications on zooplankton dynamics at scales of physical and biological variability in natural systems (Varpe et al., 2007). For the different starvation treatments presented by Calbet and Alcaraz (1996), the simulated cumulated EPR with our model is in good agreement with experimental results both in term of EPR values and in term of time-lag to recover the previous production level. When copepod female are submitted to 12–12 h fluctuation frequencies, egg production rate decreases during the starvation periods but it is partially buffered by the nutrient reserves in the hemolymph which inflows matter in the gonad. 24–24 h and 48–48 h food fluctuations cycles and long starvation periods below 4 days pointed out a synchronous oscillation of egg production with forcing food fluctuations. Beyond 5 days of starvation, nutrient reserves in the hemolymph content are exhausted and the female switch to another metabolism by degradation of structural body mass. Thus, the presented model offers a scenario of mechanistic functioning of a spawning A. grani female. Because copepods switch from body growth to egg production at the adult stage, the egg production and growth processes are tightly coupled, particularly for copepod species with restricted reserves. Egg production in fluctuating conditions depends on a combination of the states of different internal component of the organism, and our simulations clearly suggest that the instantaneous egg production response of A. grani to food fluctuations depends on the feeding history at different time scales: long-term due to the body and the gonad weights, mediumterm due to nutrient reserves in hemolymph, and short-term due to gut content. In the present fluctuations, the gut content quickly switches from emptiness to fullness because the mimic patterns of food fluctuations were very crude. In nature, copepods encounter variable food and turbulence patchiness, and Saiz (1994) has experimentally shown turbulence-enhanced flux of prey through the gut under the effect of turbulence at low food concentrations in A. tonsa. Thus, response of gut fullness to such conditions should be further explored. A. grani mature females quickly respond to available food availability in spring (Rodríguez et al., 1995), labelling them as income breeders (Stearn, 1992; Varpe et al., 2007), spawning shortly after energy for egg production becomes available. Its low capacity for buffering food fluctuations is firstly compensated by its relative high egg production and secondly minimized by its coastal habitat with high POM concentrations. The copepod egg production rate is a rather easily measurable during field studies and is used to deliver estimates of the secondary production of copepod populations. The simulations show that it cannot directly be correlated with measurements of instantaneous food concentrations. Food-patchiness at different scales is probably a key issue to be considered in further studies using phytoplankton distributions at high resolution. The behaviour of the copepod should be considered as well. In the present paper, we initiated a step by step approach combining both observations (Calbet and Alcaraz, 1997) and modelling to understand the underlying physiological mechanisms between body components which induce the egg production response to food fluctuations. The present mechanistic model is itself appealing for complementary laboratory experiments guiding parameters to be observed. The respiration rate and ingestion rate measurements could be measured in parallel to the egg production rate, and individuals should be regularly sacrificed to measure both gut content

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