Effects of food conditions on the development of the population of Temora stylifera: A modeling approach

Journal of Marine Systems 62 (2006) 71 – 84 www.elsevier.com/locate/jmarsys

Effects of food conditions on the development of the population of Temora stylifera: A modeling approach M.G. Mazzocchi a,⁎, G. Buffoni b , Y. Carotenuto c , S. Pasquali d , M. Ribera d'Alcalà a a

Laboratory of Biological Oceanography, Stazione Zoologica ‘A. Dohrn’, Villa Comunale, 80121 Napoli, Italy b ENEA, C.P. 224, 19100 La Spezia, Italy c Laboratory of Ecophysiology, Stazione Zoologica ‘A. Dohrn’, Villa Comunale, 80121 Napoli, Italy d CNR-IMATI, Via Bassini 15, 20133 Milano, Italy Received 13 December 2005; received in revised form 10 April 2006; accepted 12 April 2006 Available online 23 May 2006

Abstract We integrated field and laboratory data with modeling to determine the extent to which the temporal patterns in population abundance of a copepod species as observed at sea may be explained by differences in production and mortality rates due to diet. A Lagrangian individual-based model utilizing birth and mortality rates whose values and variance were derived from the effects of dietary composition was implemented to simulate the growth of the multi-staged population of Temora stylifera. The four diets considered were represented by unialgal cultures of the dinoflagellate Prorocentrum minimum or the diatom Thalassiosira rotula, a mixture of the two species, and natural particle assemblages < 50 μm. The aim of this work was to set up an exemplary study on a debated issue, i.e., whether the insidious effect of a diatom diet demonstrated in laboratory experiments plays a role in the time course of copepod populations in situ. Our numerical simulations showed that differences in life history parameters, as mainly dependent on diet, caused remarkably different population growth rates. However, our model reproduced the pattern of an average seasonal cycle of T. stylifera in Mediterranean coastal waters only when it utilized time-dependent field data, which evidently integrate all conditions the animals experience at sea. Proper tuning of the mortality term of developmental stages was crucial to reproduce the pattern of the time course of T. stylifera abundance in situ, which confirms that this term plays a major role in shaping the copepod population dynamics. The model also showed that, while dietary composition affects the population growth, it is far from being the only determinant of the cycle of abundance of T. stylifera at sea. © 2006 Elsevier B.V. All rights reserved. Keywords: Temora stylifera; Copepods; Population dynamics; Prorocentrum minimum; Thalassiosira rotula; Diatoms; Individual Based Model; Mediterranean; Tyrrhenian Sea; Gulf of Naples

1. Introduction The growth of zooplankton populations at sea is governed by the complex interplay of internal (biological) and external (environmental) factors, which ⁎ Corresponding author. Tel.: +39 081 5833212; fax: +39 081 7641355. E-mail address: [email protected] (M.G. Mazzocchi). 0924-7963/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmarsys.2006.04.005

interact on different temporal scales. Among exogenous factors, temperature is known to play a critical role, because it affects individual metabolism and, consequently, population dynamics and distribution. In copepods, which are the numerically dominant zooplankters in the oceans, the influence of temperature on species biology and production has been extensively discussed (Huntley and Lopez, 1992; Hirst and Bunker, 2003). However, other external factors such as food

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quantity and quality have also been shown to strongly affect growth and reproduction of these small pelagic crustaceans (Nejstgaard et al., 2001; Rey et al., 2001; Hassett, 2004). Food quality is often used in a broad sense, referring both to the biochemical composition of the food and to the biological diversity of the prey. Here we use the term dietary composition to distinguish the latter from the former, the latter being the main focus of our study. Diatoms are a significant food source for grazers in productive marine environments. However, their role as suitable food for copepods has been questioned (Ban et al., 1997), owing to the presence of noxious aldehydes (Miralto et al., 1999) that are produced when the cells are crushed during the grazing process (Pohnert, 2000). Several diatom species have been shown to negatively affect the reproductive performance of numerous calanoid species (reviewed by Ianora et al., 2003), although the biochemical reasons for that and the relevance of the phenomenon in nature are still being vigorously discussed (reviewed by Paffenhöfer et al., 2005). Experiments conducted in the laboratory indicated that a diet based on specific diatoms negatively impacts egg hatching success (Ianora and Poulet, 1993) and larval growth (Carotenuto et al., 2002) in Temora stylifera. This species belongs to a copepod genus that is very common and abundant in the northern hemisphere, particularly in coastal waters. T. stylifera is one of the dominant calanoids in the Western Mediterranean Sea, where its reproductive biology and development have been extensively investigated (e.g., Abou Debs and Nival, 1983; Halsband-Lenk et al., 2001). The feeding habits of this species have been less explored, and some data of feeding rates on natural diets have been acquired only recently (Broglio et al., 2004). Temora seems to be preferentially herbivorous on the basis of its smooth cruising motion associated with the creation of feeding currents (Paffenhöfer, 1998), which enable the copepod to efficiently capture phytoplankton cells. Abundant phytoplankton remains were indeed observed in T. stylifera fecal pellets (Turner, 1984) although ciliates can also represent a relevant component of its natural diet (Broglio et al., 2004). Therefore, as a putative herbivore potentially vulnerable to diatom toxins, T. stylifera is a suitable species to infer the extent to which a diatom diet may affect the time course of population dynamics in nature. The temporal distribution of T. stylifera is being monitored in a long-term study carried out at a coastal station (Stn MC) in the inner Gulf of Naples (Western Mediterranean) since 1984 (Ribera d'Alcalà et al.,

2004). This species is present in the area throughout the year, with a typical seasonal pattern characterized by the build-up of the population in late June–July, a peak in autumn, and a sharp decline in winter (Mazzocchi and Ribera d'Alcalà, 1995). Further, in the Gulf of Naples, diatoms represent a very important phytoplankton group in terms of both cell numbers and carbon content throughout the year (Ribera d'Alcalà et al., 2004). Therefore, any impact of a diatom-based diet in T. stylifera should be detected in the dynamics of the local population. The abundance and distribution of copepods in nature result from the interplay of several factors that affect recruitment rates, and multivariate analyses are not adequate for tracing the mechanisms shaping the patterns observed. We therefore chose to integrate experimental and observational data with the results of a numerical model specifically designed to address the issue. We simulated the population dynamics of T. stylifera with a Lagrangian stochastic model based on individual life histories that utilizes data produced in laboratory experiments where copepods were fed on different diets, and field data. We did not intend constructing a realistic and predictive model to simulate the time course of T. stylifera population at our sampling site. Rather, we wanted to set up an exemplary study on a debated issue, i.e., whether the insidious effect of a diatom diet demonstrated in laboratory experiments, also occurs in situ, and how such an effect compares with all the other factors that affect population growth in the natural environment, which in our analysis are not dealt with separately. Our study was based on an Individual Based Model (IBM), which represents a powerful tool for reconstructing the dynamics of a population by simulating the life histories of a very large number of individuals (reviewed by Carlotti et al., 2000). Only the notable improvement of computer power has made possible the application of IBMs and their widespread utilization (Judson, 1994). In zooplankton studies, this approach has been utilized for representing the development of copepod populations in relation to environmental features, such as the vertical distribution of temperature and food quantity (Batchelder and Miller, 1995) or the circulation of water masses (Miller et al., 1998). In our study, the model is a stage-structured IBM for two main reasons: 1) the specific purpose of analyzing the impact of the maternal effect of dietary composition on the survival of copepod early stages (Ianora et al., 2004); 2) a more general purpose of developing a tool to analyze, in the near future, the impact of other factors affecting population

M.G. Mazzocchi et al. / Journal of Marine Systems 62 (2006) 71–84

dynamics of the target species, as well as that of other copepods. 2. Materials and methods 2.1. The model The dynamics of the stage-structured population is obtained by a Lagrangian stochastic model that describes the time evolution of the life history of each individual (Judson, 1994; Buffoni and Pasquali, 2003; Buffoni et al., in press). It is assumed that the life of an individual is completely determined by the biological processes of development, reproduction and mortality. At any time, the status of an individual is defined by its stage and its physiological age in that stage; this is considered as a random variable and is defined as the percentage of development in a stage for a nonreproductive individual, and as the percentage of the potential reproductive effort realized by an adult female. Thus, the stochastic model describes the time evolution of the status of an individual from birth to death, following its development and, when the individual is an adult female, the production of eggs. The dynamics of the overall population abundance is obtained by performing numerical simulations of the life histories of the individuals of the initial population, and those of recruits over time. In general, the average values and standard deviations of rates of development, reproduction and mortality depend on environmental variables (e.g., temperature), which, in turn, are time-dependent; furthermore, some of these variables may depend on overall population size, which gives rise to a feedback on population growth (Berg and Getz, 1988). Here we consider three cases with constant rates when the numerical simulations are based on data produced in laboratory experiments, and a case with some rates dependent on time when the simulations are based on field data. Life history of an individual—The development process of an individual is viewed as an accumulation of small increments of development over time, and it is described in terms of a physiological age Xti = percentage of development of an individual in stage i at time t (see Curry and Feldman, 1987; Munholland and Dennis, 1992). We consider n stages; the first n − 1 stages include pre-reproductive individuals, and the stage n includes adult reproductive females and males. Let ti, i = 1,…,n, be the initial time of duration of an individual in the ith stage. When Xtii = 0, time ti+1 will be determined by Xtii+1 = 1. An average development rate (Curry and

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Feldman, 1987, p. 38) ri = 1 / Di, where Di = average duration in stage i, and a mortality rate μi, together with their standard deviations σi, are given for i = 1,2, …,n. Assuming one knows the status of an individual at a generic time t, i.e., its stage i and its physiological age Xti , we compute the status at age t + Δt by means of the stochastic equation i ¼ Xti þ maxf0; ri Dt þ gi DWti g; XtþDt

t > t i ; Xtii ¼ 0

ð1Þ p ffiffiffiffiffi where g i ¼ ri Dt is the level of noise (σi ispffiffiffiffiffi the standard deviation of development rate), DWti ¼ ait Dt , where αti , standard normal random numbers, are independent increments of a Wiener process. The computation of the time evolution of the development in stage i ends when either at a time ti+1 we register that Xtii+1 ≥ 1 or the individual is eliminated due to its death. When i < n and the individual is not dead, the computation of development in stage i + 1 begins. The choice process of the events survival or death of an individual in the time interval (t, t + Δt) is carried out by considering the mortality process as a Poisson process. This is a standard way to model a mortality process (Ross, 1983, p. 143) which grants that the time until the death of the individual is exponentially distributed. Let si = exp(− μiΔt) be the survival probability in the time interval (t, t + Δt) and βti a uniform random number in the interval [0,1]. We assume that: if βti ≤ si, the event is survival, if βti > si, the event is death. The sex of an adult entering the reproductive stage n is attributed as follows. Let ρ = number of females/ (females + males) be the sex ratio and let γt be a uniform random number in the interval [0,1]. We assume that: if γt ≤ ρ, the adult is a female, if γt > ρ, the adult is a male. The ageing of a female is assumed dependent on the reproductive process, so that it is possible to define female physiological age as the ratio between realized and potential fecundity (Roff, 1992; Buffoni et al., in press). Let τ = t − tn, t ≥ tn, be the reproductive age of a female. In general, the reproductive profile f(τ, t) (Curry and Feldman, 1987, p. 107) is defined as the average number of eggs produced per unit time by a female with reproductive age τ at time t. For the species considered in this paper, since the reproductive profile is not available, we assume it being independent of τ; moreover, we assume that, as a special case, its function of time f (t) is f (t) = f 0 = constant. This simplistic assumption is based on the results reported by Turner et al. (2001) who showed that egg production of T. stylifera females did not vary much during 20 days (about 70% of their life span) when feeding on a

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dinoflagellate-based or mixed diet. Though, interindividual variability is taken into account through the stochastic term. Let qt = number of eggs produced by a reproductive female from time tn up to time t. The evolution equation for qt is qtþDt ¼ qt þ maxf0; f ðtÞDt þ g 0 DWt0 g; t > t n ; qt n ¼ 0 ð2Þ p ffiffiffiffiffi where g 0 ¼ r0 Dt (σ0 p is ffiffiffiffiffi the standard deviation of egg production), DWt0 ¼ dt Dt , with δt standard normal random numbers. Then, the development of a reproductive female is described in terms of a physiological age Xtn defined by qt ð3Þ Xtn ¼ ; t > t n ; Xtnn ¼ 0 F R tn þL where F ¼ tn f ðsÞds, with L = female average life span. Dynamics of the overall population—Let an initial population be assigned at time t0. Then, according to the processes previously described, we perform numerical simulations of the life histories of the individuals of the initial population and of those from recruitment over time. The dynamics of the overall population is determined by the time evolution of the status of all its individuals. Thus, we can compute at any given time t > t0 the number of individuals in stage i with physiological age in (x, x + Δx). This number is clearly a random variable, and its average can be estimated by carrying out a large number of suitable realizations of life histories. Let ϕi(t, x)Δx be the average number of individuals in stage i at time t with physiological age in (x, x + Δx) and Z 1 N i ðtÞ ¼ /i ðt; xÞdx: ð4Þ 0

When the system is linear, the asymptotic solution shows an exponential trend N ðtÞ~ekt

ð5Þ

and a stable stage distribution is attained. When the system is either nonlinear, for example when the survival rate of the recruitment depends on the size of the population (Berg and Getz, 1988), or some rates are time dependent, the response of the model depends strongly on the type of feedback and on the time dependent driving forces. In the present study, T. stylifera individuals were grouped in six stages: stage 1 (eggs), stage 2 (NI), stage 3 (NII–NVI), stage 4 (CI), stage 5 (CII–CV), stage 6 (adult females and adult males). For simplicity, we did

not consider all the 13 stages that copepods go through during their life history from egg to adult, being aware that the aggregation of stages can affect the outputs in modeling copepod population dynamics (Souissi and Ban, 2001). We kept separated NI and CI because in T. stylifera the former is the only non-feeding larval stage and its physiology depends on the effect of the maternal diet, and the latter is a critical stage for moulting (Carotenuto et al., 2002). All parameters used in the model, their symbols and units are reported in Table 1. 2.2. The data The life history data of T. stylifera utilized for the model were taken from the literature (Ianora, 1998; Table 1 Symbols and units of the parameters utilized in the model Symbol n Xit

Parameter

Number of stage Physiological age defined as the percentage of development of an individual in stage i μi Average mortality rate (diet-related) mi Average mortality rate (additional term) si = exp(−μiΔt) Survival probability in the time interval [t, t + Δt] Di Average duration ri = 1/Di Average development rate σi Standard deviation of development rate p ffiffiffiffiffi gi ¼ ri p Dtffiffiffiffiffi Level of noise Dwit ¼ ait Dt Increment of a Wiener process αit, δt Standard normal random numbers βit, γt Uniform random numbers ρ Sex ratio L Female average life span τ = t − tn Reproductive age of a female f(τ, t), f(t), f0 Average number of eggs produced by a female with age τ at time t in the unit time qt Number of eggs produced by a female from time tn up to time t F Total fecundity ϕi(t, x)dx Average number of individuals in stage i at time t with physiological age in (x, x + dx) R1 Nti ¼ 0 /i ðt; xÞdx Average number of individuals in stage i at time t N(t) Average number of individuals at time t λ Parameter governing the exponential growth

Unit Adimensional Adimensional Day− 1 Day− 1 Adimensional Day Day− 1 Day− 1 day− 1/2 Day− 1/2 Adimensional Adimensional Adimensional Day Day Eggs female− 1 day− 1 Eggs Eggs Individuals

Individuals Individuals Day− 1

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Carotenuto, 2001; Turner et al., 2001; Carotenuto et al., 2002, in press). We considered four cases differing in the diets offered to the copepods in the laboratory: 1) a monospecific diet based on the dinoflagellate Prorocentrum minimum (PRO), 2) a monospecific diet based on the diatom Thalassiosira rotula (THA), 3) a binary diet represented by a mixture of the two above mentioned algae (MIX) (Table 2), 4) a field diet, obtained by sieving sea water through 50 μm mesh net and therefore represented by natural particle assemblages < 50 μm (FIELD) (Table 3). For the FIELD case, we utilized in situ egg production rates, egg viability, and NI mortality rates that were estimated in 10–15 T. stylifera females collected at sea in year 2000 (Table 3) as part of a study presented in Carotenuto et al. (in press). Those females were individually placed in crystallizing dishes containing 100 ml of 50 μm-sieved seawater (natural diet) and incubated at 20 °C and on a 12 h dark/12 h light cycle. After 24 hours, females were removed and egg production rates were determined with an inverted microscope. Experimental containers were then reincubated for additional 24 h under the same conditions as above to assess percentage of egg viability (the number of empty membranes with respect to the number of eggs produced). In order to avoid mortality due to handling artifacts, nauplii were left undisturbed in the crystallizing dishes for additional 24 h. Mortality of NI was therefore calculated from the number of dead nauplii NI settled on container bottoms, respect to the number of hatched NI. At that time, all freely swimming nauplii had successfully moulted to NII. The number of eggs released within 24 hours by T. stylifera is strongly dependent on the reproductive status of the female at the time of incubation (Ianora et al., 1989). Therefore, we utilized the weekly averaged values for the parameters monitored in females collected at sea (FIELD case), in order to smooth the observed individual variability that was likely related to their past histories. The individual variability was in any case

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Table 3 Weekly mean values for the egg production rates, egg viability and NI survival in the case of Temora stylifera wild females fed on natural diet and utilized in the model for the FIELD case (see Materials and methods for details) Date in year 2000

Progressive day for the model

Eggs f − 1 day− 1

% Egg viability

% NI survival

01 Jun 06 Jun 13 Jun 20 Jun 29 Jun 04 Jul 12 Jul 19 Jul 25 Jul 02 Aug 08 Aug 29 Aug 12 Sep 21 Sep 27 Sep 05 Oct 10 Oct 17 Oct 24 Oct 14 Nov 23 Nov 28 Nov 05 Dec 13 Dec 20 Dec

1 6 13 20 29 34 48 49 55 62 68 89 102 111 117 125 130 137 144 165 174 179 186 194 201

116.2 65.8 85.1 67.5 83.9 72.0 63.5 a 54.9 26.3 9.7 11.1 11.5 9.7 17.0 6.9 10.3 10.1 40.5 48.5 39.9 40.0 16.9 30.6 44.7 33.6

80.4 81.2 75.3 74.5 89.3 97.9 97.4 a 97.0 98.6 98.6 96.7 77.4 92.5 66.9 66.7 66.4 82.9 96.5 89.9 97.6 84.0 58.4 85.6 96.9 82.4

1.9 3.1 a 4.3 18.3 9.2 a 0.1 0.2 a 0.3 9.2 57.0 18.7 94.0 42.4 13.7 10.1 a 6.4 3.4 a 0.4 1.7 a 1.7 a 2.9 31.8 0.8 0.2 0.2

a Averaged values between the preceding and the successive ones, when the original data were unavailable or zero.

considered since the standard deviations were included in the model to reconstruct the life history of single females that contributed to the bulk of population abundance. To obtain values on a regular weekly basis for the model, when original data were not available or equal to zero the original data were interpolated using the values of the preceding and successive dates (Table 3). For the developmental times and mortality rates of stages 3–5 (parameters that were not directly measured for the natural diet), we considered three different cases, attributing to those parameters the values measured in

Table 2 Values of the Temora stylifera life history parameters utilized in the model: f0 (eggs f − 1 day− 1); D i (day); L (day); μi (day− 1)

PRO THA MIX

f0

D1

D2

D3

D4

D5

Lf

μ1

μ2

μ3

μ4

μ5

μ6

18.4 37.3 72.2

1 1 1

1 1 1

8.7 8 7

3 3 2

12 10 8.5

30 20 30

0.13 1.66 0.71

0.11 0.30 0

0.10 0.19 0.02

0.11 0.07 0.03

0.04 0.06 0.05

0 0 0

Data of f0, Lf, and μ1from Turner et al. (2001); data of D1–D5, and μ2–μ6 from Carotenuto (2001). PRO = copepods fed on a monospecific diet of the dinoflagellate Prorocentrum minimum; THA = copepods fed on a monospecific diet of the diatom Thalassiosira rotula; MIX = copepods fed on a mixture of the two phytoplankton species.

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the laboratory with the three diets mentioned before and reported in Table 2. A further mortality term mi due to external causes (e.g., predation, which is a very critical process on shaping the population patterns of copepods at sea) was here considered only as a tuning parameter, since our modeling was aimed at examining the impact of dietary composition on the development of T. stylifera population. In the absence of direct estimates of predation on T. stylifera, we made two strong assumptions: i) only the abundance of late copepodids and adults was affected by predation; ii) the predation impact was time-independent. We considered therefore an average and constant instantaneous mortality rate m5 = 0.1 day− 1 for stage 5 and m6 = 0.2 day− 1 for stage 6. The first assumption is based on the data of stage abundance distribution discussed in Di Capua and Mazzocchi (2004), while the mi values were chosen during the preliminary tuning of the model taking also into account the chaetognath feeding rates on Temora calculated in Mediterranean coastal areas (Durò and Saiz, 2000). Some indications of the effect of this additional mortality term on the dynamics of the population are derived from the sensitivity analysis reported below. For the present study, further assumptions were made, 1) the longevity of males is half that of females; 2) females start to release eggs at the beginning of their adult life; 3) reproduction is continuous during the life of an adult female. All these assumptions are based on multiannual observations conducted on T. stylifera from the Gulf of Naples in the Laboratory of Ecophysiology at Stazione Zoologica (Ianora, A., pers. comm.), although they reflect only the most commonly observed traits and not their variance. We simulated the population dynamics of T. stylifera for 210 days, corresponding to the period June– December. Over that time span, the multiannual average of the temperature in the upper 50 m of the water column ranges from 16.5 to 20.5 °C, while between the end of July and mid-November, when the population displays its annual burst, the average temperature over the same layer varies in the range 19.2–20.5 °C. Because of this, we did not apply any correction to the rates measured in the laboratory at 20 °C, while testing, in the sensitivity analysis, a possible impact of temperature variation through a change in the duration of the stages. As initial condition of the model, we considered the presence of a fertile female in a cubic meter (the reference volume), a case resembling what is observed in the Gulf of Naples at the beginning of June, the period when populations start to increase (Ribera d'Alcalà et al., 2004). To avoid the ultimate extinction of the

population, the initial female was allowed to live for at least 15 days. We also ran tests with 10 and 20 females to analyze whether and how the previous simplifying assumption would affect the final results. At least 20 realizations were run for each of the four cases considered (ensemble simulations), and the average outputs are presented here to illustrate the patterns produced by the model. Finally, the simulations for the FIELD case that show the seasonal cycles of stages 5 and 6 were compared with the abundance (ind. m− 3) of T. stylifera juveniles and adults collected at Stn MC in the Gulf of Naples in the period June–December 2000. The comparison with the in situ data has not been carried out as a model validation, but for two more limited scopes: 1) to better constrain the model parameters in order to have a plausible, not necessarily realistic, population time course, and 2) to determine, through the analysis of the residuals between the results based on the impact of dietary composition and a realistic time course, the relative weight of the former vs. all other factors. Populations were sampled at Stn MC weekly by vertical hauls performed from − 50 m to the surface with a Nansen net (113 cm mouth diameter, 200 μm mesh). Adults were identified according to sex, whereas copepodids were pooled together (CII–CV were retained by the net). The sex ratio in T. stylifera populations in the Gulf of Naples resulting from the field data is close to 1:1 on a mean annual basis, both in the year 2000 and on a much longer time interval (Mazzocchi, M.G. and Di Capua, I., unpubl. data). All biological parameters included in our model were considered density-independent. Indeed, density dependence of recruitment in the field attributed to egg cannibalism by females and CV was shown for Calanus finmarchicus (Ohman and Hirche, 2001). The abundance of T. stylifera in the Gulf of Naples in year 2000 was at least five times lower than that of C. finmarchicus as reported by Ohman and Hirche (2001) with a similar concentration of eggs suggesting that cannibalism can be reasonably excluded as drastically affecting population dynamics of T. stylifera in the area. 2.3. Sensitivity analysis A parametric analysis of the behavior of the system was performed by varying the key parameters in the runs relative to the three cases PRO, THA, MIX. The numerical simulations of either the exponential growth of the population or its extinction were carried out in the absence of any feedback. The following diagnostic

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variables of the model response to parameter perturbation were selected: the parameter λ governing the exponential growth, the number of specimens in stage 5, stage 6, and in the overall population at two times: ̂ N 6 ðt Þ; ̂ N ðt Þ; ̂ with t ̂ ¼ 120 days; 210 days: k; N 5 ðt Þ;

3. Results 3.1. Numerical simulations The numerical comparison of some life history parameters, from fecundity to NII recruitment in the first three cases considered in the present study, already indicates that differences in the diet will result in remarkably different fates of population development (Table 4). By simulating the time course of T. stylifera abundance in the case of copepods fed on a monospecific dinoflagellate diet (PRO), we can follow the population cycle for the entire period considered (210 days). The numerical increase of the population is quite slow during the first 120 days and more rapid afterwards, with oscillations that reflect the succession of different generations (Fig. 1a). Towards the end of the period, an exponential growth and, concomitantly, a stable stage structure are attained. The estimate λ = 0.02 day− 1 (see Eq. (5)) is obtained by fitting the computed population abundance N(t). At the 180th day, the expected abundance of stage 5 (Fig. 1b) is about 500 ind. m− 3, 10 times the abundance of stage 6 (Fig. 1c). In the case of copepods fed on a monospecific diatom diet (THA), the predicted abundance of the whole population (Fig. 2) attains a very low value (54 ind. m− 3) in 15 days, it declines rapidly afterwards with a very scarce presence of copepodids and adults and dies out before the 180th day. In the case of a diet constituted by a mixture of the two phytoplankton species (MIX), the predicted abundance increases very rapidly and oscillations are quickly

Fig. 1. Temporal dynamics of Temora stylifera (ind. m− 3) produced by ensemble simulation for (a) the whole population (eggs to adults) with the exponential fit (dotted line), (b) model stage 5 (CII–CV), (c) model stage 6 (adults), in the case of copepods fed on a monospecific dinoflagellate diet (case PRO).

absorbed in an exponential growth (λ = 0.22 day− 1), which is attained close to the 30th day (Fig. 3). The numerical simulations of population growth based on time-dependent values of egg production, egg and NI mortality rates from wild females fed on natural diet (FIELD) show that the temporal dynamics of T. stylifera changes dramatically according to differences in mortality rates of stages 3–5 resulting from different diets. Mortality rates taken from the two cases of monospecific diets lead to population extinction, more rapidly for THA (about 30 days) than for PRO (about 150 days) (not shown). Mortality rates of the MIX case allow the population to develop according to a cycle

Table 4 Comparison of fecundity ( f0), eggs produced by each female during 1 1 1 1 2 2 her life span (f0Lf), recruitment of NI (f0 e−μ D ) and NII (f0 e−μ D −μ D ), in the three cases of different diets from laboratory experiments considered during the present study

PRO THA MIX

f0

f0Lf

f0 e−μ D

18.4 37.3 72.2

552 746 2166

16.16 7.09 35.5

1

1

f0 e−μ D −μ D 1

14.47 5.25 35.5

1

2

2

Fig. 2. Temporal dynamics of the whole population of Temora stylifera (ind. m− 3, eggs to adults) produced by ensemble simulation in the case of copepods fed on a monospecific diatom diet (case THA).

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3.2. Comparison with field observations We compared the patterns of the model simulation for the FIELD case (integrated with mortality rates for stages 3–5 as in the MIX case) with the cycle of T. stylifera abundance recorded in year 2000 in the Gulf of Naples. The model captured, for stage 5 (Fig. 5a) and stage 6 (Fig. 5b), one important feature of the temporal pattern recorded at sea, i.e., the presence of only a major peak in the abundance cycle of T. stylifera, preceded by small fluctuations. But, in comparison with the field data, the model anticipates the peak by about 50 days, whereas the minimum in December (day 210) is slightly delayed. Fig. 3. Temporal dynamics of the whole population of Temora stylifera (ind. m− 3, eggs to adults) produced by ensemble simulation in the case of copepods fed on a mixed diet (Prorocentrum + Thalassiosira, case MIX).

3.3. Sensitivity analysis

with three periods of higher abundance (Fig. 4a). The highest values of abundance are concentrated from 105th to 155th day (corresponding to the period September–early November), whereas lower values occur at the beginning (July) and at the end (December) of the period. The temporal cycles of stage 5 (Fig. 4b) and stage 6 (Fig. 4c) are very similar in shape; the peaks of the latter, which represents the adults, occur almost nine days later, as a consequence of the total development time of stage 5, D5 = 9. The abundance of stage 6 is three times lower than the abundance of stage 5.

As mentioned before, the outcomes relative to the case PRO describe a slow growth of the population through successive generations for 210 days. In contrast, the numerical simulations relative to the cases THA and MIX produce, in relatively short time, extinction or outbreak of the population, respectively. Thus, the case PRO is expected to be more sensitive to parameter perturbation. Therefore, a set of numerical simulations were performed by varying the average values of some chosen parameters, leaving unchanged the values of the other parameters and the levels of the uncertainties (factors gi and g0) in Eqs. (1) and (2), respectively. For the case PRO, the perturbed parameters and the range of variability are listed below: f0 = 18.5 ± 10%, 20%; D1, D2,…,D6 ± 5%, 10%, 20% (original values in Table 2) μ 1 = 0.13, μ 2 = 0.11 ± 5%, 10%; m 5 = 0.1,

Fig. 4. Temporal dynamics of Temora stylifera (ind. m− 3) produced by ensemble simulation for (a) the whole population (eggs to adults), (b) model stage 5 (CII–CV), (c) model stage 6 (adults), in the case of copepods fed on natural diet (case FIELD with mortality rates for stages 3–5 as in the MIX case).

Fig. 5. Direct comparison between the patterns of temporal dynamics of Temora stylifera (ind. m− 3) recorded at Stn MC in year 2000 (dotted line) and the patterns simulated by our model (continuous line) for (a) model stage 5 (CII–CV) and (b) model stage 6 (adults) in the FIELD case (with mortality rates for stages 3–5 as in the MIX case).

M.G. Mazzocchi et al. / Journal of Marine Systems 62 (2006) 71–84

m6 = 0.2 ± 5%, 10%.The results are reported in Tables 5 and 6. The sensitivity of the results to the different parameters was reflected either by changes in λ and in the abundance of the last stages. In the following, we briefly focus on the variations in the abundance of the adults. The highest sensitivity was shown in respect to the external mortality of the late stages (m5, m6), with minor sensitivity to the duration of stages (Di). The sensitivity to changes in female fertility (f0) and to mortality of the early stages (μ1, μ2) was low. For simulations lasting the whole period (210 days), a decrease or increase in the external mortality by 10% may produce an increase or decrease in the number of adults by a factor of 3.6 or 4, respectively. For a simulation of 120 days the corresponding values were 1.9 and 2, respectively. Quite large variations resulted from ± 20% variations in the duration of all stages for the 210 days simulation (10 times more and 4 times less, respectively). The variations decrease by a factor of 5 and ∼2, respectively, after 120 days of simulation. As for the uncertainties, we kept fixed the average value f0 of thepreproductive process, and varied the ffiffiffiffiffi factor g0 ¼ r0 Dt in Eq. (2). Assuming that the standard deviation σ0 is proportional to the average f0, we obtained the results reported in Table 7. The results are comparable when σ0 is in the range 0–0.8 f0, as in the case under study. The increase of the uncertainty, Table 5 Results of the analysis of the model sensitivity to the key parameters of Eqs. (1) and (2) performed on the model run for tˆ = 210 days N5(tˆ)

N6(tˆ)

0.0206

811

83

5892

0.0150 0.0182 0.0239 0.0267 0.0276 0.0242 0.0170 0.0146 0.0215 0.0209 0.0201 0.0197 0.0325 0.0244 0.0214 0.0174 0.0127 0.0122

179 310 1388 2339 2701 1450 414 237 966 868 749 662 8295 1341 787 346 204 224

20 33 127 215 298 160 43 21 102 94 77 68 1405 213 115 41 25 14

1223 2383 10,412 17,384 20,987 11,184 3130 1638 7340 6567 5453 5026 77,060 13,834 7415 3289 1756 1392

Parameters

λ

Reference values in Table 2 for diet PRO 0.8f0 0.9f0 1.1f0 1.2f0 0.9m5, 0.9m6 0.95m5, 0.95m6 1.05m5, 1.05m6 1.1m5, 1.1m6 0.9μ1, 0.9μ2 0.95μ1, 0.95μ2 1.05μ1, 1.05μ2 1.1μ1, 1.1μ2 0.8Di 0.9Di 0.95Di 1.05Di 1.1Di 1.2Di

N(tˆ)

79

Table 6 Results of the analysis of the model sensitivity to the key parameters of Eqs. (1) and (2) performed on the model run for tˆ = 120 days Parameters

N5(tˆ)

N6(tˆ)

N(tˆ)

Reference values in Table 2 for diet PRO 0.8f0 0.9f0 1.1f0 1.2f0 0.9m5, 0.9m6 0.95m5, 0.95m6 1.05m5, 1.05m6 1.1m5, 1.1m6 0.9μ1, 0.9μ2 0.95μ1, 0.95μ2 1.05μ1, 1.05μ2 1.1μ1, 1.1μ2 0.8Di 0.9Di 0.95Di 1.05Di 1.1Di 1.2Di

150 59 80 204 256 280 208 99 75 174 158 142 134 519 144 134 99 68 29

13 5 6 16 20 26 18 10 7 15 14 13 13 66 30 18 6 6 8

924 306 433 1163 1526 1761 1235 634 405 1048 995 884 841 4062 1665 1068 619 586 694

above a critical level (when the standard deviation is of the order of the average) produced a very rapid growth of the population. In fact, the number of eggs produced at time t is a positive random variable and an increase in the variance produces an enlargement of the range of values (in particular in the right side of the interval). The tests that were performed with 10 and 20 females at the start resulted, at the end of the simulations, in a total population abundance that was, respectively, 2.6 and 4.6 higher than the value obtained with just one female. We also analyzed the MIX and THA cases to investigate for what values of fertility and mortality of the late stages the population would not explode or would not collapse, respectively. To keep the final abundance with the MIX diet at values similar to those obtained using the PRO diet, the fertility had to be decreased 16 times or the mortality of stages 5 and 6 to be increased 3.2 times. Whereas, to prevent the Table 7 Results of the analysis of the model sensitivity to changes in the uncertainty terms in Eqs. (1) and (2) performed on the model run for tˆ = 210 days σ0

λ

N5(tˆ)

N6(tˆ)

N(tˆ)

0.2f0 0.4f0 0.8f0 f0 1.2f0

0.0206 0.0206 0.0220 0.0235 0.0249

723 725 986 1315 1829

79 80 100 119 168

5534 5660 7513 9818 13,008

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extinction of the population with THA diet, fertility had to be increased by a factor of 3.5. 4. Discussion As thoroughly discussed in the literature (Grimm, 1999 among the others), the term IBM generally refers to a wide variety of models that have the common feature of tracking the differences in the life history among different individuals or stages of the same species. In our application, we exploited only partially the potential of IBMs, because of several of the simplifying assumptions we made, as described in the model presentation. The main rationale for using an IBM was to be able to track different critical life stages of a copepod species as well as to analyze the impact of the observed values of individual variance on the population development. For the problem addressed in this paper, the individuals can be characterized by only one parameter, their physiological age, and the population evolution can be simulated in a motionless medium. Under these assumptions both Eulerian and Lagrangian models can be successfully applied and produce results in good agreement (Buffoni and Pasquali, 2003). However, an individual-based Lagrangian model allows a further implementation in the perspective of taking into account the motion of water masses, which produces spatial heterogeneity at the individual scale (Bolker et al., 1997) even though more deterministic approaches are often equally informative (Plagányi et al., 1999). Our study shows that dietary composition, as parameterized in the model on the basis of laboratory and field data, can dramatically change the fate of population development. Feeding is one of the fundamental processes that shape the structure of communities and drive their functioning, in both aquatic and terrestrial ecosystems. It follows that trophic interactions in the pelagic food webs are intricate and flexible, and cannot be exhaustively predicted only on the basis of species, biomass or size distribution (Havens, 1998; Calbet, 2001). Feeding processes are generally prompted by nutritional needs, but are often mediated by behavioral or physiological responses that are species-specific. Even interactions with toxic food are different depending on the species involved (Turner and Tester, 1997), and the detrimental effects of diatom aldehydes have been shown to induce different responses in different copepod species (Ianora et al., 2003). Our modeling of the population dynamics of T. stylifera when the copepod diet was represented only by

T. rotula showed that, notwithstanding the high egg production rates, the steep decline of abundance would lead the population to extinction. The high mortality rates of the naupliar stages together with the very low hatching success of the eggs are the causes responsible for this negative fate of the copepod population. In other words, the very low recruitment to CI does not allow the population to develop even after the decrease in mortality and the shorter life cycles which occur after stage CI. In the Gulf of Naples, T. stylifera is always present throughout the year both in coastal and offshore waters although the abundance of copepodids and adults is very low from winter through spring (Ribera d'Alcalà et al., 2004; Di Capua and Mazzocchi, 2004). In the latewinter and spring, periods not analyzed in our study, T. rotula is present in the area and phytoplankton blooms are dominated by communities of large diatom species (Ribera d'Alcalà et al., 2004). Diatoms and small phytoflagellates were the dominant phytoplankton groups throughout the year 2000 considered in the present study (Carotenuto et al., in press); large colonial diatoms characterized the winter-early spring phytoplankton, whereas small diatoms were mainly responsible for blooms from spring to autumn. Assuming that the impairing effects of a T. rotula diet are similar to those of other diatoms, one could infer from the continuous presence of T. stylifera in the Gulf of Naples that either the natural diet of this calanoid in our area is not dominated by diatoms or the negative impact on recruitment may be much smaller at sea. As a matter of fact, the scenario is more complex. We derived from the data in Table 3 the mortality rates for the stages 1 and 2 in the case of a natural diet. For stage 1, the average mortality was 0.14 day− 1, while the minimum was as low as 0.02 day− 1. It is worth noting that during the first 55 days of our simulations, the mortality of stage 1 never exceeded 0.30 day− 1. For stage 2 instead, the values were dramatically high with maxima up to 6.9 day− 1, and an average value 4.0 day− 1. A comparison of the preceding values with the values in Table 2 shows that the physiological mortality for stage 1 in the worst case of a diatom diet (THA case) is at least 6 times (on the average 12 times) higher than the mortality of the eggs released by a female fed on a natural diet (FIELD case). This would suggest that the ‘diatom effect’ on the egg hatching of T. stylifera in the area is minimal in that period of the year, despite the relative contribution of diatoms to phytoplankton biomass is generally close to or above 50% both in terms of cell and carbon concentration (Ribera d'Alcalà et al., 2004; Carotenuto et al., in press). On the other hand, the mortality of stage 2 in the case of females fed on natural diet is on the

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average 13 times higher than the one observed when females were fed on a diatom diet. This would suggest that in nature the maternal effect is very strong on the survival of the first larval stage, but it can be interpreted to a minimum extent as due to a ‘diatom effect’ which may probably act as an aggravating term. It was recently found that the larval survivorship of T. stylifera and Centropages typicus can be related not only to maternal diet but also to the quality of the water in which the nauplii hatch (Carotenuto et al., in press). Our simulations show that even with such high values of NI mortality, the population does not go extinct, in contrast to what occurs in the THA case. This is due to the high survival rates of successive developmental stages (those of MIX) we used in the FIELD simulations. In synthesis, in the first 55 days of low abundance, the T. stylifera population seems to be affected by a ‘diatom diet’ effect to a minimum extent. Other physiological constraints may cause a very low recruitment to NII, such as those recently examined by Carotenuto et al. (in press). A similar analysis can be conducted for model days 68–102 (August–September), the period preceding the buildup of the population. During this phase, the average mortality rates of stages 1 and 2 in the FIELD case are 0.13 day− 1 and 0.88 day− 1, being respectively 13 times lower and 3 times higher than the corresponding mortality produced by the diatom diet. Also in this case, a possible ‘diatom effect’ does not seem to be a critical factor. To investigate the cumulative effect of mortality of stages 1 and 2, we computed the number of NII recruits per female per day derived from the model (same parameter as the value reported in Table 4, fifth column). During June–July (days 0–60), the NII recruited in the FIELD case were on the average lower than those observed for THA (2.75 vs. 5.25), but the population did not go extinct, as noted above. During August–September (days 68–102), the recruitment to NII was still slightly lower than THA (4.66 vs. 5.25) but the model with FIELD data predicted the outburst of the population. This suggests that the recruitment to NII is a critical step in shaping the fate of the population and that the survival rates of the following stages are the ones that make the difference with the fate of population in the THA case. It is worth noting that the two consecutive very low values of NI mortality on days 89 and 102 (Table 3) were likely the trigger of the population growth. To compensate for the low physiological survival rates after stage NII in the THA case, female fecundity should increase by a factor of 3.5, as shown by our sensitivity analysis, an unlikely or extreme event, which again confirms the reduced negative impact of

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diatom ingestion in situ. It has been shown that copepod egg viability is diatom density-dependent (Chaudron et al., 1996) and this can be supposed also for the effect on the other stages. Even being almost always dominant (Ribera d'Alcalà et al., 2004), diatoms are never the only phytoplankton group present (Carotenuto et al., in press) and never produce monospecific blooms in the Gulf of Naples (Sarno, D., pers. comm.). Moreover, it is possible that the copepod ingestion rates at sea are lower than in the food-replete calm conditions in a laboratory set up. Both aspects may account for the differences between in situ and laboratory conditions. Our numerical simulations with life history parameters consequent to a diet based exclusively on P. minimum showed that this dinoflagellate species supplies copepods with the appropriate energy input necessary to balance physiological mortality and predation rates as parameterized in the model, thus allowing the population to develop through successive generations. P. minimum is a small species (< 15 μm) with very low concentrations in the Gulf of Naples, high interannual variability but regular seasonal timing in mid summer (Sarno, D., pers. comm.), therefore cooccurring with T. stylifera. A natural diet based exclusively on P. minimum is unrealistic, but this species can be included in the category of small dinoflagellates actively grazed upon by T. stylifera in the field (Mazzocchi, M.G. and Trebini, F., unpubl.). A mixture of P. minimum and T. rotula was shown to be an optimal diet in the laboratory for T. stylifera in terms of recruitment rates (Turner et al., 2001), and, quite predictably, in our simulations it caused an exponential growth of the population, in the absence of a feedback, and without variability in the external forcing that was represented only by predation. The co-occurrence of optimal performances such as high egg production rates, and high egg and NI survival rates as observed in our MIX case are rarely observed in the field, as shown in our Table 3. On the other hand, individual energy consumption is likely much higher in situ for the other stages, due to the copepod continuous motion and escape reactions. Then, the rates of some life history parameters observed in the laboratory when copepods feed on a mixture of P. minimum and T. rotula are likely different from in situ values, due to differences in food density, and a concurrent decrease in the cost–benefit ratio for performing the feeding activities. The fact that laboratory mortality rates for stages 3–5 of the MIX diet seem to reproduce reasonably well those in nature prompts several hypotheses (e.g., more nutritious food,

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lower losses than assumed) which cannot be presently tested. The numerical simulations of our model reproduced patterns that, in comparison with the abundance of juveniles and adults collected at Stn MC in year 2000, were reasonably similar during the rising phase of the population development until the occurrence of the major annual peak. The major peak simulated between the 120th and 140th day (corresponding to September– October) did not occur in the field data in year 2000, when the highest abundance of T. stylifera was recorded in November (close to 170th day). However, it is worth noting that a late September–October peak of abundance is a common feature of the seasonal cycle of T. stylifera in the Gulf of Naples (Mazzocchi and Ribera d'Alcalà, 1995; Di Capua and Mazzocchi, 2004; Ribera d'Alcalà et al., 2004). Since the outburst of the population produced by the model derives from the FIELD recruitment data for stages 1 and 2, the discrepancy between the model and the in situ time course likely resides more in factors affecting the population growth in situ not well reproduced by our simulations, than in laboratory artifacts. The recruitment to NII observed in the laboratory is, in fact, independent of temperature and the decrease in the duration of stages 1 and 2 due to the difference between the laboratory and in situ temperature would be less than 13% according to the data by Halsband-Lenk et al. (2002). This should not produce the observed difference between the simulated and real patterns of abundance, according to our sensitivity analysis on Di . This difference might be due to processes that can take place in the field but cannot be introduced in numerical experiments without having the proper data, such as temperature anomalies due to meteorological events or massive and concentrated occurrence of potential predators. Temperature seems to influence the vertical distribution of T. stylifera (Di Capua and Mazzocchi, 2004), its reproduction and development (Halsband-Lenk et al., 2002). We may hypothesize a shift in the water column warming by 3–4 weeks and a slightly lower final temperature in the 0–50 m layer. Considering as an extreme case a decrease by 2 degrees respect to the climatological average over the typical period of population buildup (August–September), the increase in the duration of stages would have been of approximately 25% (Halsband-Lenk et al., 2002) thus depressing the abundance only slightly (see Table 6 for the order of magnitude with PRO after 120 days). In contrast, increased predation could have produced, on the time scale considered (3–4 weeks), the observed

depression of the abundance, model vs. in situ, but only with values significantly higher than the ones considered. For similar reasons, it is not easy, on the basis of the FIELD data used and the favorable diet assumed in the simulation, to interpret the reason for the delay of the highest peak observed in situ. With the very small number of NII recruits derived from the FIELD data (average 0.60 recruits per female over days 111–144) it is not possible to produce the peak. A putative factor for the inconsistency between the observed and the simulated population growth might be advection. However, the available data show that the annual peak in T. stylifera abundance is synchronous over the entire Gulf of Naples (Ianora et al., 1985; Di Capua and Mazzocchi, 2004), and therefore, the timing of the peak should not be much affected by advection. 5. Conclusions Our numerical simulations capture the pattern of an average time course of T. stylifera in coastal waters when the model utilizes time-dependent field data, which integrate all conditions the animals experience at sea. Our results clearly show that the mortality of developmental stages plays a major role in shaping population dynamics in T. stylifera. Differences in mortality dependent only on dietary composition contribute significantly to the temporal patterns of population growth. The very limited recruitment of T. stylifera consequent to feeding exclusively on a diatom species would have a dramatic effect on the fate of the population. This in turn would presumably affect zooplankton community structure and the dynamics of the pelagic food web, particularly in late summer– autumn. In the Gulf of Naples, the development of T. stylifera populations may be occasionally affected by the ingestion of diatoms, but this is not the factor that rules the seasonal cycle of this calanoid. While modeling the extent to which the dietary composition may affect the population growth, we infer that other more important factors must necessarily act (and interact) to determine the cycle of abundance of this species as it is observed at sea. Acknowledgments We acknowledge the generous collaboration of Adrianna Ianora for helpful discussions and Iole Di Capua for zooplankton counts at Stn MC in year 2000. This work was partially supported by the Italian

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