Oxyrrhis Marina-Based Models As a Tool to Interpret Protozoan Population Dynamics

JOURNAL OF PLANKTON RESEARCH j VOLUME 33 j NUMBER 4 j PAGES 651–663 j 2011

Oxyrrhis marina-based models as a tool to interpret protozoan population dynamics

KEITH DAVIDSON 1*, FOTOON SAYEGH 2 AND DAVID J. S. MONTAGNES 3 1 2 SCOTTISH ASSOCIATION FOR MARINE SCIENCE, SCOTTISH MARINE INSTITUTE, OBAN, ARGYLL PA37 1QA, UK, PO BOX 100569, JEDDAH 21311, KINGDOM 3 OF SAUDI ARABIA AND SCHOOL OF BIOLOGICAL SCIENCES, UNIVERSITY OF LIVERPOOL, BIOSCIENCES BUILDING, CROWN STREET, LIVERPOOL L69 7ZB, UK Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 *CORRESPONDING AUTHOR: [email protected]

Received May 18, 2010; accepted in principle June 22, 2010; accepted for publication July 29, 2010

Corresponding editor: John Dolan

Oxyrrhis marina-based experiments have frequently been used to underpin the construction and, or, parameterization of protozoan mathematical models. Initially, we examine the suitability and limitations of O. marina for this task. Subsequently, we summarize the range of aut- and synecological modelling studies based on O. marina, examining the questions asked and conclusions drawn from these, along with the range of processes and functions employed within the models. Finally, we discuss future modelling directions based on studies of O. marina.

KEYWORDS: dinoﬂagellate; experimental design; Oxyrrhis marina; models

INTRODUCTION Oxyrrhis marina, that can act as a model for others and With improved understanding of the pivotal role that the insights that have been obtained from mathematical protozoa play within microbial food webs (Azam et al., models based on its study. 1983; Pomeroy et al., 2007), an increasing body of exper- The heterotrophic flagellate O. marina is an ideal can- imental work has investigated their response to a range didate organism for the experimental study and model- of environmental conditions. Knowledge of the func- ling of the natural and theoretical population dynamics tional relationships that underpin protozoan growth and of protozoan predators. It is easy to find, isolate, main- grazing, in turn, allows us to derive mathematical tain in culture and manipulate in the laboratory and models that represent their behaviour. Such protozoa- has been maintained in culture for over 50 years in a specific modelling studies provide a means of under- number of culture collections (see Montagnes et al., standing predator–prey interactions than could not be 2011a). Oxyrrhis marina is, therefore, often a natural achieved from observation alone. Furthermore, the specific inclusion of protozoa within more general choice as a model organism and is extensively used for population and ecosystem models allows us to assess experimental studies, some of which have been employed their role in the natural environment. Finally, as proto- to develop or parameterize mathematical models. Within zoa exhibit rapid generation times and are easily this paper, we review the literature to: (i) examine the manipulated, they are an excellent tool for population limitation of using O. marina as a model organism; (ii) dynamic studies and model parameter generation in indicate the breadth of responses and functions that are general. Protozoa have, therefore, for a considerable available for its use, and thus facilitates mathematical time, been used as the basis for mathematical models of population growth (e.g. Gause et al., 1936; Painting model development; (iii) summarize modelling studies et al., 1993; Fenton et al., 2010). Inevitably, such models that have been conducted with O. marina, and briefly are derived for the species that we can grow in the review the questions asked and conclusions drawn from laboratory, and for planktonic protozoa these have these and finally (iv) discuss continued directions of proven to be few. This paper is about one such species, research for modelling studies using O. marina.

doi:10.1093/plankt/fbq105, available online at www.plankt.oxfordjournals.org. Advance Access publication August 26, 2010 # The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please email: [email protected] JOURNAL OF PLANKTON RESEARCH j VOLUME 33 j NUMBER 4 j PAGES 651–663 j 2011

TO WHAT EXTENT IS OXYRRHIS Capriulo, 1990). Examples of such an approach include MARINA AREPRESENTATIVE the semi-benthic rock pool dwelling Stombidium sulcatum MODEL ORGANISM? (S. inclinatum;seeModeo et al., 2003) that has been extensively used to represent planktonic ciliates and the fre- Meta analysis studies (e.g. Hansen et al., 1997) suggest quently studied mixotrophic chrysophyte Ochromonas danica, that O. marina is representative of the dinoflagellates. which was originally isolated from an acidic moor However, phagotrophic protozoa are diverse and abun- (Pringsheim, 1955). There is, thus, considerable pre- dant organisms in aquatic environments, including taxa cedence for using taxa like O. marina as model pelagic typically with a size range of 2–200 mm(Montagnes organisms, mainly because they are easy to grow, maintain et al., 2008a). Hence, no single species or even genus and collect, as indicated above. We, therefore again, will be representative of the functional group, and support the past and continued use of the O. marina,with Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 championing O. marina as a representative of the hetero- the codicil that it is not necessarily typical of open water trophic dinoflagellates or even heterotrophic protists en taxa and should, ultimately, be compared to them. mass raises some reservations. Therefore, we first consider factors that may limit the general applicability of O. marina-based results to phagotrophic protozoa. Taxonomy Oxyrrhis marina is unlikely to be a single species, and there are strain-differences in eco-physiological Mode of nutrition responses (Lowe et al., 2005a, 2010). There are serious Oxyrrhis marina is a raptorial feeder that directly engulfs implications regarding this point, related to population its prey. Although protozoa exhibit a range of nutri- studies. For instance, the growth response of O. marina tional modes (Montagnes et al., 2008a), many, and poss- strains differs based on responses to: salinity (Lowe et al., ibly most, of the protozoa in aquatic pelagic ecosystems 2005a), prey concentration and type, and temperature (e.g. ciliates, flagellates) also engulf their prey, and thus (Montagnes, unpublished results). However, such strain- O. marina might be considered directly comparable to specific responses are far from unique to O. marina; e.g. these. Furthermore, anecdotal data suggest that O. marina similar strain-specific differences occur in a model fresh- ingests prey between 1 and 12 mm, indicating that its water ciliate, Urotrichia (Weisse and Montagnes, 1998). predator:prey size ratio includes, but also exceeds, the Thus, modellers must simply be aware of these differ- approximate 10:1 ratio predicted by others (e.g. Azam ences and consider them when interpreting results. In et al., 1983). Thus, as a first approximation, we support fact, as strain differences are becoming topical in eco- the use of O. marina as a model organism in this sense. logical research (see Weisse and Montagnes, 1998), this “problem” can become an asset, and modellers will undoubtedly begin to use the responses of the various Habitat strains to examine potential strain–succession, as we are Oxyrrhis marina is rarely seen in pelagic samples, at present doing (Yang et al., 2011). Finally, modelling although “red-tide” blooms occur in large bays, reach- studies based on O. marina typically use defined strains, ing up to 105 cells mL21, and it can regularly be found and we are exceptionally fortunate with O. marina that in some estuaries at abundances of 10–100 mL21 several commercial and personal culture collections (Johnson et al., 2003; Begun et al., 2004; Jeong et al., have maintained these (Lowe et al., 2011). Hence, not- 2004). In contrast, O. marina is typically found in shallow withstanding the caveats highlighted above, and the rec- waters associated with the shoreline, such as splash ognition that further comparative studies of the pools and tide pools (Johnson, 2000; Kimmance et al., behaviour of O. marina and other planktonic protozoa 2006). Still, O. marina is planktonic, not benthic, and in are required, O. marina seems fit for purpose as a repre- mixed cultures remains well distributed (Davidson, sentative protozoan, from which mathematical models Montagnes, unpublished results), although it may can be derived. accumulate at mid-water column interfaces (Menden- Deuer and Gru¨nbaum, 2006).Thus,again,inthissense,it seems an appropriate model organism for planktonic pro- OXYRRHIS MARINA-BASED cesses. Furthermore, using protists associated with very MATHEMATICAL MODELS shallow waters to model planktonic systems is not uncom- mon; much of the earlier work on protozoa, used to obtain We, therefore, now turn to those studies that have rate processes and conversion factors for pelagic ecosystem derived or parameterized mathematical models based models, has been obtained from semi-benthic species (e.g. on O. marina. Broadly, these fall into two categories:

652 K. DAVIDSON ET AL. j OXYRRHIS MARINA-BASED MODELS

Table I: Studies that determine or apply O. marina-based equations and their functional forms

Selected works that employ the Equation type and number Equation (see caption for symbols) function

1. Functional response I p Kimmance et al. (2006); I ¼ max kI þ p Strom (1993) r p 2. Numerical response r ¼ max Jeong et al. (2008) kr þ p r ðp p0Þ 3. Numerical response with threshold prey level (p0) r ¼ max Kimmance et al. (2006); k þðp p0Þ included. r Strom (1993) I p 4. Functional response modiﬁed by ambient I ¼ max aðT bÞc Kimmance et al. (2006) kI þ p temperature 0 rmax ðp p Þ

5. Numerical response modified by ambient r ¼ aT Kimmance et al. (2006) Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 k þðp p0Þ temperature r v p 6. O. marina volume as a function of prey v ¼ max þ v 0 Kimmance et al. (2006) k þ p abundance v v p 7. O. marina volume response modulated by v ¼ max þ v 0 aðT bÞc Kimmance et al. (2006) k þ p temperature v r Nt 8. Difference equation for O. marina increase in Nt 1 ¼ Johnson (2000) þ 1 þ a N abundance t D 9. Ingestion of detrital particles modulated by Re ¼ I SF Strom (1993) D þ p a selection factor (SF) 1 10. distance a predator has to travel to encounter @ ¼ Neq a Sp p Flynn et al. (1996) a volume of prey equal to its own volume I ðaÞp 11. Functional response modified (decreased) by I ¼ max Davidson et al. (1995a); Mitra k þ p the influence of inhibitor (a) obtained from I et al. (2003); Mitra and Flynn ingestion of non optimal prey (2005) I e p2 12. Ratio-based selectivity function for multiple prey I ¼ max i i Fasham et al. (1990); Mitra and k ðe p þ e p þ ...Þþe p2 þ e p2 þ ... I 1 1 2 2 1 1 2 2 Flynn (2006) 13. Rate of prey capture related to a selectivity Ci ¼ fi pi Mitra and Flynn (2006) function fi that defines the relationship with a specific prey (p ) concentration i n u 1 14. Nitrogen regeneration as a function of predator E ¼ a pred b Davidson et al. (1995b) N u N content and protozoan C:N ratio pred R 1 S 15. Nitrogen regeneration as a function of E ¼ Caron and Goldman (1988); 1 S u u respiration, gross growth efficiency and prey and prey pred Davidson et al. (1995b); predator C:N ratios Davidson et al. (2005) 16. Nitrogen regeneration as a stepwise function of if u . aE¼ b, else E ¼ c Davidson et al. (2005) protozoan C:N ratio a, b, c are constants; I the ingestion rate; Imax the maximum ingestion rate; p the prey abundance; kI the half saturation constant of the ingestion 0 0 curve; r the specific growth rate; rmax the maximum specific growth rate; p the threshold prey abundance (at which r ¼ 0); kr a constant (kr –p ¼ half saturation constant of the growth curve); T the temperature; v the volume; vmax the maximum volume; kv the half saturation constant of the volume curve; v0 the volume at zero food abundance; N the O. marina concentration; Re the re-ingestion of faecal particles; D the concentration of faecal particles; SF the selection factor; Neq the number of prey cells equivalent to one predator in terms of biovolume; a the variable related to the swimming speed of prey and predator; Sp the cross-section of encounter party of predator and a given prey species; ei the preference for different prey types; Ci the capture rate of specific prey species; fi the capture rate parameter; E the nitrogen excretion rate; n the O. marina nitrogen content; ui the C:N ratio of prey or predator; R the respiration rate, S the gross growth efficiency.

(i) autecological studies that specifically simulate the typically characterized by a rectangular hyperbolae or a response of O. marina to a set of physical, biological or “type II Holling” response. Such rectangular hyperbolic chemical conditions and (ii) synecological studies that responses are used extensively to characterize the embed O. marina-based responses within food web simu- behaviour of protozoa (e.g. Taylor, 1978; Montagnes, lations, to study the wider role of ecosystem processes. 1996; Jeong et al., 2004; Fenton et al., 2010). Their suit- These models are reviewed (grouped in relation to the ability to simulate ingestion and growth of O. marina has hypotheses tested) below with the mathematical been supported by a number of studies [Table I, responses that underpin them summarized (Table I). equations (1–2)] on a range of prey species (for further details beyond the scope of this modelling-based review, see Lowe et al., 2011; Montagnes et al., 2011b; Roberts Autecological models et al., 2011). Modifications of these two responses (Table I) are also fundamental to a number of the math- Functional and numerical responses ematical models that we review; e.g. equation (3) Functional and numerical response relationships are (Table I) is a modified version of equation (2) (Table I), often central to population models (Turchin, 2003), where the numerical response is recognized to be

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negative below a threshold (p0) abundance of prey aerosols. Models that assess such factors in governing (Fenton et al., 2010). It is also important to note that, to distributions are potentially useful not only for protozoa our knowledge, for O. marina there are no data that but also for small metazoa, such as invertebrate larvae. suggest inhibition of growth or grazing rates at elevated An example of abiotic influence is that of tidal action prey concentrations, as has been indicated for other on coastal O. marina populations. Johnson (Johnson, protozoa (e.g. Montagnes and Lessard, 1999), although 2000) developed a simple mathematical model to study see Prey inhibition of grazing, below. this phenomenon and specifically to test the hypothesis that O. marina has a competitive advantage that makes it The influence of abiotic factors prevalent in rock pool shoreline environments. The Various abiotic factors will modify protist (and specifi- model simulated cell abundance in rock pools using a cally O. marina) population dynamics; e.g. salinity simple difference equation [Table I, equation (8)] to Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 (Droop, 1959; Samuelsson et al., 2006), turbulence determine population size, based on the intrinsic popu- (Peters and Marrase´, 2000), temperature (Montagnes lation growth rate and the carrying capacity of the et al., 2003; Kimmance et al., 2006) and pH (Droop, environment. The influence of flushing and the effects 1959; Pedersen and Hansen, 2003). Two O. marina of extreme conditions on the upper shore were included modelling-based studies have specifically sought to in the model by making growth rate a function of pool investigate the role of such abiotic factors. location in relation to tidal height. The model predicted that O. marina distribution was influenced by both rock Temperature pool height on the shore and tidal cycle and that it Trends of increasing water temperature have the differs from other protozoa in the pools, in that it is potential to influence the productivity and biodiversity more stress tolerant. The stress tolerance of O. marina is of marine phytoplankton (Bresnan et al., 2009). consistent with its success in the rock pool habitat and Understanding the temperature response of protozoa is its success in the (presumed somewhat stressful) con- equally important, as any temperature-induced mis- ditions of laboratory culture. However, it also indicates match between predators and prey in pelagic commu- that mathematical models based on O. marina are most nities could have significant implications for trophic appropriate for other stress tolerant protozoa, and transfer (Montagnes et al., 2008a; Koeller et al., 2009). observations of this species should be viewed in this Using O. marina, Kimmance et al.(Kimmance et al., light. 2006) demonstrated the need for an adequate representation of temperature response by making a range of rate parameters within an O. marina model a (exper- Other abiotic factors imentally determined) function of temperature and prey Clearly, there is scope to extend modelling work on density [Table I, equations (4) and (5)]. Furthermore, O. marina to examine other physical factors. There are recognizing that both prey abundance and temperature data in the literature that would potentially allow a will alter cell volume, Kimmance et al.(Kimmance relationship between growth rate and salinity to be et al., 2006) established a relationship between these established (Droop, 1959; Lowe et al., 2005a); possibly and O. marina volume [Table I, equation (6)], allowing assuming growth rate is a quadratic function of salinity models to determine the production in terms of (Lowe et al., 2005b). Similarly, the data of Droop carbon (assuming a relation between volume and (Droop, 1959) and Pedersen and Hansen (Pedersen and carbon content; Menden-Deuer and Lessard, 2000). Hansen, 2003) could be used to establish a growth Application of these functions within a mathematical response to pH, which superficially appears to be either model demonstrated different dynamics when the full sigmoidal or rectangular hyperbolic in shape. We have temperature-prey response was incorporated, in com- also conducted preliminary experiments to parameterize parison to the more commonly used Q10 based function the influence of turbulence on growth of O. marina (see Montagnes et al., 2003). The potential of these (Montagnes, unpublished results), following similar functions to improve model predictions suggests that work on the autotrophic flagellate Isochrysis galbana they should now be incorporated into larger ecosystem (Downes-Tettmar and Montagnes, 2008), and it appears models. that only the level of turbulence generated by heavy wave action in rock pools will reduce O. marina growth Physical influences on the distribution of protozoan rate. We, therefore, recommend that (i) further exper- population imental data are collected on these physical parameters Protozoa may be locally and globally distributed by and (ii) existing data are used to parameterize new func- abiotic factors such as currents and wind driven tions for incorporation into models.

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Swimming behaviour and aggregation was associated). Protozoan growth was made a function Study of O. marina to characterize the swimming behav- of phytoplankton prey [Table I, equation (1)], with a iour of protists is dealt with in a separate study (Boakes selection factor for phytoplankton cells or faecal par- et al., 2011), and representation of O. marina searching ticles that allowed the determination of an ingestion rate trajectories using Le´vy walk or other similar encounter for faecal particles [Table I, equation (9)] and hence, by statistics is discussed by Bartumeus et al.(Bartumeus subtraction from the functional response, an ingestion et al., 2003) and Reynolds (Reynolds, 2008).Inamore rate for phytoplankton cells. Although the model did not general sense, modelling-based interpretation of O. lend support to the notion that re-ingestion governed marina foraging in response to prey aggregations was phaeopigment distributions, it demonstrated that the conducted by Menden-Deuer and Grunbaum re-ingestion of faecal material by protozoa was a plaus-

¨ Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 ible trophic pathway that may have significant impli- (Menden-Deuer and Gru¨nbaum, 2006) who characterized the availability of patchy prey by means of the cations for energy flow within the microbial loop. Frost number, a composite parameter based on forager speed, turning interval, distance between prey patches Multi prey selectivity and patch longevity. In addition, O. marina has also been Following Strom’s (Strom, 1993) model-based demon- used in models that assess mesozooplankton swimming stration of discrimination between live and dead food and feeding (e.g. Mariani et al., 2008). Thus, we see the by protozoa, the selection of alternative live prey by potential for this species to be incorporated into multi- O. marina was addressed by Flynn et al.(Flynn et al., level behavioural models in the future. 1996) who presented a theoretical relationship for the distance travelled by a raptorial predator to encounter a volume of prey equal its own volume [d, Table I, Feeding behaviour equation (10)]. To illustrate how such simulations are Protozoa can discriminate between prey types, with developed, below we use this model as an example. selective grazing, on the basis of prey quantity or The model was developed by first determining that quality, now being recognized as a key issue in the func- the cross-sectional area (Sp) of the encounter path for tioning of microbial food webs (Montagnes et al., the predator and a given prey (p) species is 2 2008a). A range of factors such as morphology, chemi- Sp ¼ p rpred þ rp , where rpred and rp are the radius of cal defence and nutritional quality may govern the the predator and prey cells, respectively. The rate of selectivity of prey items by protozoa (Montagnes et al., prey encountersqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi per predator (E) was then given by 2008a). The O. marina-based studies that have exper- E S N C2 C2 imentally addressed these factors are not germane to ¼ p p p þ pred, where speeds of predator our work, but the interested reader is directed to and prey are Cpred and Cp, respectively, and Np is the (Roberts et al., 2011); here we specifically review how number of prey. The number of prey cells equivalent, in models have addressed feeding behaviour. terms of biovolume, to one predator (Neq) was then 1 determined from Neq ¼ Vpred Vp , where Vpred and Vp Modelling re-ingestion of faecal material are mean predator and prey cell volumes, Coprophagy is a well-recognized process in planktonic respectively. This allows the calculation of the systems that may have considerable impact on food web encounter distance d ¼ N a S N 1, where qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi eq p p dynamics. For instance, low chlorophyll:phaeopigment 1 2 2 ratios have been proposed to indicate high levels of a ¼ Cpred Cp þ Cpred . mesozooplankton coprophagy, but given the importance If predation of a particular prey type continues when of microzooplankton in food webs (e.g. Azam et al., d is greater than that of alternative prey, then the preda- 1983; Davidson, 1996), it may be that they too are tor is deemed to select the former item. This concept important in this process. To this end, Strom (Strom, was applied to a set of laboratory experiments in which 1993) developed a mathematical model to test the O. marina ingested three differently sized prey species. hypothesis that re-ingestion of faecal material by proto- The analysis demonstrated the occurrence of selection zoa could account for the observed variation in the con- of live cells and suggested that selective grazing in version of chlorophyll to phaeopigment. In this model, microbial communities may be complex and dependent which was applied to her experiments on Strombidium on both prey size and prey quality, both of which may and Gymnodinium and to the O. marina-based data of change with time, rather than simple random encoun- Klein et al.(Klein et al., 1986), protozoa preyed on phyto- ter. Clearly, in this case, O. marina acted as a model plankton and faecal particles (with which phaeopigment organism to test general issues associated with selection.

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Prey inhibition of grazing this response has yet to be documented for O. marina, The role of selective grazing in governing the temporal and again we suggest that experiments in this direction changes of both prey and predator was further studied are needed. by Davidson et al.(Davidson et al., 1995a) through simulation of two independent data sets: the I. galbana– Prey quantity governing predator assimilation response O. marina study of Flynn and Davidson (Flynn and While Mitra et al.(Mitra et al., 2003) focused on the Davidson, 1993b) and the multi prey–O. marina exper- effect of prey quality on assimilation rate, Fenton et al. iments of Flynn et al.(Flynn et al., 1996). (Fenton et al., 2010) have explored the relationship Flynn and Davidson (Flynn and Davidson, 1993b) between prey abundance and protozoan assimilation suggested that O. marina initially ingested but then efficiency; they indicate that many protozoa, including rejected the flagellate prey, but Davidson et al. O. marina, exhibit a decreasing assimilation efficiency Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 (Davidson et al., 1995a) found that no parameterization with increasing prey concentration. Then, by comparing of a standard type II functional response [Table I, simple Rosenzweig–MacArthur-based predator–prey equation (1)] generated adequate simulations of their models (using O. marina and I. galbana parameters, data. Instead, qualitatively better simulations were derived from Kimmance et al., 2006) with either a con- achieved if the maximum ingestion rate was made to stant or variable assimilation efficiency, Fenton et al. decrease with continued prey ingestion [Table I, (Fenton et al., 2010) indicate that prey carbon pro- equation (11)], a factor that was attributed to the build duction may be increased by .65% when a variable up of an inhibitor within O. marina through the ingestion assimilation efficiency is applied. Thus, using O. marina of the prey. The same model structure was also able to as a model, they conclude that, from an applied per- simulate the O. marina–multiple prey data of Flynn et al. spective, such as examining biomass productivity for (Flynn et al., 1996). Thus, this O. marina-based model food web dynamics or examining the recycling of nutri- quantitatively demonstrated that the quality of a prey ents within an ecosystem, including prey abundance- item as well as its abundance or size may govern its dependent assimilation efficiency, leads to very different suitability as a prey item for protozoa. Given the tract- quantitative predictions from those given following com- ability of using O. marina for grazing experiments (e.g. monly applied models. Kimmance et al., 2006), it would now seem appropriate to test these model predictions with empirical data. Stoichiometry and selectivity Mitra and Flynn (Mitra and Flynn, 2005) continued to study the influence of stoichiometrically driven ingestion Prey quality governing predator functional response and assimilation, using a model that was optimized by The role of prey quality was further explored by Mitra fitting to the I. galbana–O. marina-based data of Flynn et al.(Mitra et al., 2003) who hypothesized that it could and Davidson (Flynn and Davidson, 1993b). The influence predation through modulation of either (i) the authors reached similar conclusions to Davidson et al. rate of ingestion [Table I, equation (11)], with “a”in (Davidson et al., 1995a), with best simulations being equation (11) being a variable rather than a constant or obtained with “negative modulation” of ingestion; i.e. a (ii) the efficiency of assimilation of this ingested material. decrease in ingestion rate on the flagellate in response The study examined the relative importance of these to non-optimal quality of this prey [Table I, equation processes through a model that related both maximum (11)]. However, when this analysis was extended to rate of predation and assimilation efficiency to prey mesozooplankton-based data sets (Jones et al., 2002), quality (defined as its C:N ratio) in a range of different simulation required assimilation of non-optimal prey to functional forms. By making the maximum predation also be linked to the prey quality. This difference was rate a function of prey quality, the model simulated related to O. marina’s (and other protists’) lack of a gut experimentally observed phenomena exhibited by and hence the greater likelihood of modulation at the O. marina of “surge feeding” (O¨ pik and Flynn, 1989) point of capture and ingestion rather than digestion in and prey rejection (Flynn et al., 1996). In particular, this protozoa. study indicated that while different functional formu- Mitra (Mitra, 2006) extended the above work through lations for ingestion and assimilation of prey caused the the derivation of a generic multi-nutrient zooplankton model to predicted similar trophic transfer of carbon, model that included specific representation of both this occurred on very different timescales, demonstrating ingestion and assimilation, both of which were functions that such physiological responses of protozoa could of prey nutrient stoichiometry, which she termed “stoi- influence the temporal availability of organic matter for chiometric modulation of predation”. This model was trophic transfer. However, it is important to note that again fitted to the experimental data of Flynn and

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Davidson (Flynn and Davidson, 1993b), with similar and the rate of change of O. marina N was simulated by conclusions to those reached above, i.e. it is necessary to decrease ingestion rate for poor quality prey to obtain a dOxN IsN ¼ I Ox EOx Ox; fit of the model to the data. dt Is In the most recent of their suite of O. marina-related publications, Mitra and Flynn (Mitra and Flynn, 2006) where Ox, Is, OxN and IsN represent the number and studied the influence of two alternative modelling for- N-content of O. marina and I. galbana, respectively; I is mulations to represent predator selectivity. They incor- the ingestion rate of O. marina; and EIs and EOx are the porated either a ratio-based function [Fasham et al., N-regeneration rates of I. galbana and O. marina, respect- 1990, Table I, equation (12)] governed by the relative ively. Within the equations, N-regeneration by O. marina abundance of different prey types or made prey capture was simulated either as a constant or on the basis of an Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 a function of prey availability and a capture rate par- “optimal” O. marina C:N ratio, using a range of N ameter [Table I, equation (13)], that could take a range regeneration models. of functional forms based on prey quality (or other The study demonstrated a need to include factors). Again, the model response was compared to N-regeneration in protozoan-based models to ade- the data of Flynn et al.(Flynn et al., 1996) and Flynn quately simulate experimental data. This model obser- and Davidson (Flynn and Davidson, 1993b). The new vation is consistent with many mathematical models of prey capture function [equation (13)] was found to be microbial communities. However, such models often most appropriate, albeit with the caveat that further simulate this process in an unsophisticated manner, modulation of ingestion based on prey quantity and making regeneration a constant amount of nutrient, quality was necessary to optimize the fit, a finding that independent of prey or predator physiology or compo- is consistent with the models above. sition (Davidson, 1996). Using O. marina, Davidson et al.’s (Davidson et al., 1995b) model lent support to arguments about protozoa made by Goldman et al. (Goldman et al., 1985) by indicating that a dynamic The quantitative importance of nutrient regeneration [Table I, equation (14) and (15)], rather than constant, and cycling regeneration rate must be applied to protozoan nutrient While mathematical models are often used in predictive cycling, indicating the utility of an O. marina-based mode, an equally important application is the analysis model to provide more general insights. It may now be of processes that cannot be easily understood by simple possible to use developing methods, such as stable observation. One of the most important of these for isotope labelling, to assess nutrient cycling and assess microbial community population dynamics is the regen- empirically if O. marina behaves according to model eration of inorganic nutrients by protozoa, and their predictions. subsequent use by phytoplankton (Goldman et al., 1987). This process maintains the stoichiometric Summary of autecological work balance of nutrients within the predator and fuels Four main insights are clear from the above review of further growth of the prey (Caron, 1991). autecological models: (i) O. marina is useful as a “model To this end, Davidson et al.(Davidson et al., 1995b) organism”; (ii) there are O. marina experimental data in studied nutrient regeneration using a predator–prey the literature that could be used to more fully parame- model that included O. marina and I. galbana, to assess terize its numerical and functional response; (iii) not- the response of different nitrogen (N) regeneration withstanding the previous point, we need to collect equations. The model incorporated the phytoplankton more data to extend and improve upon the responses growth model of Davidson et al.(Davidson et al., 1993) that need parameterization (e.g. given concerns of that simulates both carbon (C) and N dynamics of ocean acidification, to pH); and (iv) we need to extend I. galbana during unbalanced growth, allowing simu- our empirical testing of predictions that have been lation of experiments in which prey exhibit active obtained from O. marina-based models. growth. Again, as an example of how such models are developed, we provide the relevant equations. The equation for the rate of change of I. galbana Nis Synecological Oxyrrhis marina-based give by models Above, our review has revealed an extensive range of dIsN IsN ¼EIs Is I Ox; autecological models associated with O. marina; these dt Is provide an understanding of its behaviour and how it

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can be used to assess key ecological processes. regeneration equation; Caron and Goldman, 1988; Therefore, it may be surprising that application of such Table I, equation (15)]. O. marina-based models to study the influence of proto- Simulations demonstrated quantitative differences zoa in food webs is, to date, relatively limited. To indi- between the output generated by the different models, cate how O. marina might be incorporated into larger particularly between the switching and dynamic models models, we examine case studies, below. and the constant NRE model in terms of the density of phytoplankton blooms. Differences in C:N ratio of Parameterizing microplankton models model components were also evident with only the Lee et al.(Lee et al., 2003) developed a carbon– dynamic model predicting a stoichiometrically balanced nitrogen-based model of the phytoplankton, bacterial zooplankton C:N ratio close to 6.6, the Redfield value, Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 and protozoan components of a planktonic food web, similar to the values that experimental estimates suggest which was embedded in a three layer physical frame- that protozoa, including O. marina, maintain (Goldman work. The protozoan model was developed as a single and Dennett, 1992; Nakano, 1994; Davidson et al., compartment with constant C:N ratio consistent with 1995a). Such O. marina-derived results have important experimental and modelling results discussed above. implications for the formulation of the multiple O. marina parameters, from Fuller (Fuller, 1990), were functional type models that are now being formulated used to parameterize the protozoan component of the to better understand the global C cycle (e.g. le Que´re´ model. Given the substantial increase in parameter et al., 2005). estimates for O. marina over the past 15 years (Table I) since Fuller (Fuller, 1990), it may be appropriate to Summary of synecological work revisit such models. Considering the importance of protozoa within marine ecosystems and the relative wealth of data, response Control of toxic dinoflagellate blooms by microzooplankton relationships and models based on O. marina (Table I), it and parasites is unclear why so few synecological modelling studied Montagnes et al.(Montagnes et al., 2008b) incorporated have drawn on this resource, to date. Clearly, consider- O. marina parameters into a model that examined the able scope exists to develop and improve existing relative role of microzooplankton grazing (by large models, and to produce alternative formulation for ciliates) and protozoan parasites in the control of comparison, as illustrated above (The influence of N regener- dinoflagellate blooms. O. marina was included as a repre- ation on a food web). Moreover, the now recognized diver- sentative grazer of nanoflagellates and zoospores, the sity of O. marina (e.g. Lowe et al., 2005a, 2010) offers the dispersal stage of the parasite. The conclusion of this potential to produce data sets that will allow an “organ- model was that parasites, not microzooplankton, could ism sensitivity analysis” to better quantify biologically control dinoflagellate blooms, even when the dispersal reasonable ranges of model parameter values. It may stages can be reduced by top-down control from also be possible to examine spatial distributions using O. marina-like predators. the framework established by Johnson (Johnson, 2000) and the physical–biological functions outlined above; perhaps allowing the assessment of large scale patterns. The influence of N regeneration on a food web The role of protozoan N-regeneration was assessed in a microbial food web model (Davidson et al., 2005); this was an extension of the model by Fasham et al.(Fasham FUTURE DIRECTIONS OF et al., 1990) that included a multiple currency of C and O. MARINA-BASED MODELLING N, and hence variation in the C:N ratio of both phytoplankton and their protozoan predators. The protozoan compartment of the model was parameterized from lab- Better parameterization oratory experiments on O. marina. Nutrient regeneration Response relationships such as those presented in was related to the relative C:N ratios of prey and preda- Table I are increasingly being derived for O. marina, and tor using three alternative functions all capable of repre- these studies provide a valuable resource for model con- senting, to some degree, the N regeneration efficiency of struction. Modellers need to be made aware of the exist- O. marina: a constant nitrogen regeneration efficiency ing data sets for O. marina, which have yet to be fully (NRE); a stepwise switching function between low exploited for model parameterization (e.g. Fuller, 1990; and high NRE, termed threshold elemental ratio Jeong et al., 2001, 2004; Kimmance et al., 2006). [Table I, equation (16)]; and a dynamic nutrient Hopefully this paper has helped fulfil that role.

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Fig. 1. An indication of how further population dynamics might be obtained for comparison with model output: abundance of Oxyrrhis marina and the prey ﬂagellate Dunaliella primolecta, grown at 168C in 32 PSU seawater enriched with f/2 media (Sigma). (a)–(c) are 18-day time-course incubations of predator (open circle) and prey (closed circle) in triplicate ﬂasks. (d) and (e) are phase plots: (d) is a plot of the three 18-day time-course incubations (a–c); (e) is a plot of a series of short (5–11 days) incubations, indicating a semblance of population cycling.

However, many of the existing studies have been related environmental conditions are, therefore, required to to the grazing impact on harmful or aquaculture- better validate these and future models. As guidance, relevant prey species (e.g. Jeong et al., 2001), and we we present an example of such a data set for model suggest that further study of cosmopolitan and benign comparison (Fig. 1). This represents a subset of numer- prey and the role of abiotic factors in modulating these ous time course experiments beginning at many initial relationships are required. predator and prey concentrations. Such an approach, while generating time-course data, may minimize the bottle effects (e.g. accumulation of toxins and fouling on Independent time-series for comparison surfaces) that can bias long-term incubations. Population Models also require test data, independent to the obser- models, independently derived from O. marina functional vations on which they are derived. Considering the and numerical response and prey growth data may be number of studies conducted using O. marina, surpris- tested using the resultant phase-plot data. ingly few have proved to be amenable for this purpose. One of the reasons that the O. marina–I. galbana data For example, studies that analyse the selective grazing set of Flynn and Davidson (Flynn and Davidson, properties of O. marina are particularly prominent in the 1993b) has been so often used as a comparison with works we have reviewed. However, a disproportionally simulations is the availability of a robust model that pre- high fraction of these have applied their model to the dicts prey growth in non-steady state conditions data of Flynn and Davidson (Flynn and Davidson, (Davidson et al., 1993; Davidson and Cunningham, 1993b). Further time course experiments following 1996). Hence, the experimental study and modelling of O. marina and one, or more, prey items in differing O. marina, in particular, and protozoa in general must be

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conducted in parallel with that of their prey, to allow in size under such conditions (Flynn et al., 1993). both trophic levels to be simulated to the same level Understanding and modelling the response of micro- of complexity. This requires experimental studies to zooplankton grazers to alternative prey following simple measure a sufficient array of parameters including changes in environmental conditions will be a necessary numbers, biomass, ingestion, grazing, respiration and step to the development of robust models in the future. nutrient cycling rates to allow appropriate model parameterization and testing, to minimize the need to “fit” Plankton functional type models free model parameters. Plankton functional type (PFT) models are increasingly being employed in ocean biogeochemistry, and here again using O. marina may be instructive. The use of Improving model structure, using PFT models is somewhat controversial, with some Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 O. marina authors (e.g. Anderson, 2005) suggesting that their appli- Doney (Doney, 1999) highlighted the need for succinct cation may be premature. However, notwithstanding but realistic mathematical models capable of simulating this debate, there is consensus that better model para- the cycling of multiple nutrients within microbial food meterization is required. This is particularly pertinent at webs. These are necessary to simulate the transfer of the microzooplankton level. For example, the dynamic production to higher trophic levels and the export flux green ocean model (Le Que´re´ et al., 2005) contains five of C to the ocean floor. Within this context parameteri- separate autotrophic functional types, but only a single zation of zooplankton or microzooplankton response in composite, protozooplankton compartment to represent a range of different model structures is increasingly a heterotrophic flagellates and ciliates. While this is topic of debate. To this end, below, we provide an indi- understandable in terms of model tractability, the para- cation of how O. marina might be used in a range of meterization of the equations used to represent this models to help resolve this debate. “functional group” requires deeper consideration in the light of the wealth of behaviour that different species Nutrient–phytoplankton–zooplankton models and genera are capable of (Montagnes et al., 2008a) and In general, the classical nutrient–phytoplankton– observations of temporal succession of different microzooplankton (NPZ) models (e.g. the widely used model zooplankton groups (Davidson et al., 2007). of Fasham et al., 1990) use a simple closure term to rep- Analysis of the functional response of O. marina in resent grazing. The potential deficiency in this approach comparison with other heterotrophic marine micro- or was highlighted by Mitra (Mitra, 2009) who discussed dinoflagellates, expanding on initial studies such as the difference between the theoretical response of NPZ those of Jeong et al.(Jeong et al., 2008), and with mul- models that employ generic “closure” functions and tiple prey items ( John and Davidson, 2001), would add those that include specific representation of carnivory confidence to single functional group parameterization, and cannibalism, finding that these generated differ- or provide definitive evidence that multiple micro- ences in simulated primary production and f-ratio. In a zooplankton functional groups are required in models. similar vein, Gentleman et al.(Gentleman et al., 2003) The application of developing techniques such as lectin comprehensively reviews the mathematical formulation labelling (Wootton et al., 2007), flow cytometric separ- and use of a range of different multiple resource func- ation of prey and predators (Montagnes et al., 2008a), tional response relationships for zooplankton. Again, the analysis of stable isotope signatures (Flynn and her comparison of response was based on theoretical Davidson, 1993a) or stable isotope probing (Radajewski simulations. Hence, while studies such as these highlight et al., 2000), will hopefully provide the data sets from the potential pitfalls for modellers from an erroneous which to progress this field. choice of functional response, experimental verification of the most appropriate functions is still required. Individual-based models Considering the relative wealth of information on Individual-based models (IBMs) provide an alternative O. marina revealed in this review, it seems a very suitable modelling strategy to those that seek to represent the organism with which to test the suitability of alternative ecosystem as a whole, and O. marina is an ideal candi- functional relationships to represent grazing processes. date for these. IBMs calculate biological variables while For example, Isochrysis galbana, the prey species on which following individual (or meta-) particles in space. These much of the O. marina-based predator–prey modelling is models may then be of particular use for the study of based, becomes smaller during N depravation advective populations and/or species that form only a (Davidson et al., 1992; Flynn et al., 1994). However, small fraction of the biomass of a trophic level but are other phytoplankters, e.g. Nannochloropsis oculata, increase important for other reasons. A number of important

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biotoxin producing phytoplankton species such as the manuscript. We would also like to thank two anon- advective Dinophysis spp. (Hart et al., 2007) or the low- ymous reviewers for their suggestions. biomass high-toxicity dinoflagellate Alexandrium tamarense (Touzet et al., 2010) fit these criteria. As O. marina ingests biotoxin producing dinoflagellates (Jeong et al., 2001, 2003), it may be a suitable candidate organism for FUNDING developing grazing terms within such models. This work was supported by the SAMS/NERC Oceans Furthermore, in rare cases, it forms large blooms of up 2025 programme (K.D.) and a UK NERC grant NE/ 5 21 to 10 cells mL (Begun et al., 2004) and thus its own F005237/1 awarded to P. C. Watts, C. D. Lowe and may be important in short-term rapid fluxes of nutri- D.J.S.M. ents in some ecosystems. Thus, O. marina-IBMs may too Downloaded from https://academic.oup.com/plankt/article/33/4/651/1473431 by guest on 28 September 2021 be justified in the future.

REFERENCES SUMMARY Anderson, T. R. (2005) Plankton functional type modeling: running What has O. marina modelling delivered to the scientific before we can walk? J. Plankton Res., 27, 1073–1081. community? Of the autecological models reviewed, the Azam, F., Fenchel, T., Field, J. G. et al. (1983) The ecological role of majority deal with some aspect of prey selectivity; the water-column microbes in the sea. Mar. Ecol. Prog. Ser., 10, 257–263. combined body of work in this area is particularly Bartumeus, F., Peters, F., Pueyo, S. et al. (2003) Helical Levy walks: useful in demonstrating that prey selectivity by micro- adjusting searching statistics to resource availability in microzoo- heterotrophs is, indeed, capable of influencing the trophic plankton. Proc. Natl Acad. Sci., 100, 12771–12775. transfer of phytoplankton biomass (e.g. Strom, 1993; Begun, A. A., Orlova, T. Y. u. and Selina, M. S. (2004) A “bloom” in Flynn et al., 1996; Davidson et al., 1995a, b) and that func- the water of Amursky Bay (Sea of Japan) caused by the dinoflagel- tional form used to simulate this selectivity will influence late Oxyrrhis marina Dujardin, 1841. Russ. J. Mar. Biol., 30, 51–55. model results (Mitra et al., 2003; Mitra, 2006; Mitra and Boakes, D. E., Codling, E. A., Thorn, G. J. et al. (2011) Analysis and Flynn, 2006). In this light, there is a somewhat surprising modelling of swimming behaviour in Oxyrrhis marina. J. Plankton Res., relative lack of more basic combined experimental- 33, 641–649. modelling studies based around O. marina that specifically Bresnan, E., Hay, S., Hughes, S. L. et al. (2009) Seasonal and inter- seek to model the response to particular environmental annual variation in the phytoplankton community in the north east of Scotland. J. Sea Res., 61, 17–25. drivers (an exception being the temperature based study Capriulo, G. M. (1990) Ecology of Marine Protozoa. Oxford University of Kimmance et al., 2006). This is an obvious area for Press, New York, pp. 366. further fruitful study. The relative lack of synecological Caron, D. A. (1991) Evolving roles of protozoa in aquatic nutrient studies employing O. marina-based model parameteriza- cycles. In Reid, P. C., Turley, C. M. and Burkill, P. H. (eds), Protozoa tion perhaps reflects this need, with the more sophisti- and their role in Marine Processes, NATO ASI Series G: Ecological cated models of prey selectivity requiring a fundamental sciences, Vol. 25. Springer-Verlag, Heidelberg, pp. 387–416. underpinning prior to their wider application. Caron, D. A. and Goldman, J. C. (1988) Dynamics of protistan In conclusion, as O. marina is not often abundant in carbon and nutrient cycling. J. Protozool., 35, 247–249. open water samples, it might not be the organism of first Davidson, K. (1996) Modelling the components of the microbial loop. choice to parameterize the protozoan component of such Mar. Ecol. Prog. Ser., 145, 279–296. models. However, as indicated above, available evidence Davidson, K. and Cunningham, A. (1996) Accounting for nutrient suggests its use is appropriate, and the relative wealth of processing time in mathematical models of phytoplankton growth. Limnol. Oceanogr., 41, 779–783. O. marina studies makes it a pragmatic choice. Furthermore, there are ecosystems where O. marina may be abundant, Davidson, K., Flynn, K. J. and Cunningham, A. (1992) Non-steady state ammonium-limited growth of the marine phytoflagellate, and in these regions using O. marina-derived parameters Isochrysis galbana Parke. New Phytol., 122, 433–438. would be entirely appropriate. Therefore, we support its Davidson, K., Cunningham, A. and Flynn, K. J. (1993) Modelling continued use as a model organism to parameterize temporal decoupling between biomass and numbers during the simple and more complex population models. transient nitrogen-limited growth of a marine phytoflagellate. J. Plankton Res., 15, 351–359. Davidson, K., Flynn, K. J. and Cunningham, A. (1995a) A first ACKNOWLEDGEMENTS attempt of model factors affecting the ingestion of prey by the dinoflagellate Oxyrrhis marina. Cytology, 37, 969–977. The Authors would like to thank Edd Codling and Davidson, K., Cunningham, A. and Flynn, K. J. (1995b) Predator– Emily Roberts for their constructive comments on this prey interactions between Isochrysis galbana and Oxyrrhis marina III.

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