Elsevier

Ecological Modelling

Volume 391, 10 January 2019, Pages 16-28
Ecological Modelling

A simulation study on how the resource competition and anti-predator cooperation impact the motile-phytoplankton groups’ formation under predation stress

https://doi.org/10.1016/j.ecolmodel.2018.10.019Get rights and content

Highlights

  • Predator-induced aggregation in motile phytoplankton.

  • Modelling resource competition and anti-predator cooperation in phytoplankton.

  • Individual-based modelling for motile phytoplankton cells.

  • IBMs conception and numerical simulations.

  • Impact of competition and cooperation on the aggregation process.

Abstract

The phytoplankton's spatial aggregation is a very important phenomenon that can give responses to many questions such as the passage from the unicellularity to the multicellularity. In this work, we are interested by predator-induced aggregations in motile phytoplankton. Our aim is to bring, through a simulation study, some explanations on how these groups form and analyze the simultaneous effect of both resource competition and anti-predation cooperation on the groups’ formation process. For this purpose, we developed a 3D individual-based model (IBM) that takes into account small-scale biological processes for the phytoplankton cells that are: (1) motion, described by a stochastic differential equation in which the drift term is density-dependent to take into account the attraction mechanism between cells due to their chemosensory abilities and the dispersal term representing the diffusion of cells in water, (2) a density-dependent birth–death process to describe the demographical process in phytoplankton cells. In the latter, division and death rates were considered density-dependent to include a local competition for resources that slows up the cell's division and a local cooperation in phytoplankton that reduces the cell's predation death. We implemented the IBM and considered several scenarios that combine three different levels of resource competition with three different intensities of cooperation. The different scenarios were tested using real parameter values for phytoplankton.

The simulation of the IBM showed that phytoplankton cells form aggregations via the “coming together” mechanism driven by the cell's motion process in which, the attraction mechanism is enhanced by the cooperation behavior (the latter is a response to the predation stress). After that, groups grow through the “remaining together” mechanism which is a consequence of the division–death process and also the attraction mechanism which prevents the daughter cells from leaving the group after division. Also, the simulation of the different scenarios highlights the role of cooperation in the formation of aggregates and shows that although resource competition impairs the aggregation process and the group size, cooperation plays an important role in sustaining the aggregating process and when it is strong, the induced aggregation process is so successful that it completely prevents cells being grazed; and both group and population sizes are maintained at a good level.

Introduction

Phytoplankton aggregation is a complex biological phenomena that plays a significant role in the primary production and the marine life cycle. The understanding of the mechanisms underlying the aggregations’ formation is very important and can give response to many questions such those related to the development and the evolution of the multicellularity (Ratcliff et al., 2013, Sathe and Durand, 2016, Kapsetaki et al., 2017, van Gestel and Tarnita, 2017). The reasons behind groups’ formation in phytoplankton can be social such as protection from predator (Smayda, 1997, Boraas et al., 1998, Lurling and Beekman, 2006, Long et al., 2007, Sathe and Durand, 2016), the search of prey (Spero and Morée, 1981), the performance of sexual reproduction through gametes fission (Hadjivasiliou et al., 2015), or environmental (the process of turbulence (Durham et al., 2013) and the non-homogeneous distribution of the resources (Mellard et al., 2012). Specifically, many works have demonstrated that motile phytoplankton species are more patchy than the non-motile ones (Mouritsen and Richardson, 2003, Durham et al., 2013), but very few works were made to describe or/and understand the mechanism generating this patchiness and to explain how these cells interact with each other and with their micro-environment (Hutchinson, 1961, Durham et al., 2013, Sathe and Durand, 2016). In this work, we focus particularly on the study of the aggregation mechanism induced by the predation risks for motile phytoplankton cells.

The search of protection from predators is generally considered one of the most important reasons of group formation (Hamilton, 1971, Krause and Ruxton, 2002, Spieler, 2003, Johannesen et al., 2014). Some experimental studies have shown that the survival rate increases with the increase of the aggregation size (Foster and Treherne, 1981, Spieler, 2003). Indeed, individuals inside groups can have the benefit either from the avoidance effect since the predators have less chances to find a group of preys than one of many single preys (Turner and Pitcher, 1986, Krause and Ruxton, 2002), or from the dilution effect, because the predator can only eat a fraction of a group of preys, so the larger the group, the lower is the chance that a particular individual will be the attacked one (Krause and Ruxton, 2002). Turner and Pitcher (1986) explained that the two precedent effects must be in combination to have a real positive effect (called the attack-abatement effect) on the prey survival.

Some experimental works were made to demonstrate the anti-predation aggregation strategies for phytoplankton cells (Smayda, 1997, Boraas et al., 1998, Lurling and Beekman, 2006, Lürling and Van Donk, 2000, Ratcliff et al., 2013, Sathe and Durand, 2016, Kapsetaki et al., 2016, Kapsetaki et al., 2017). It was observed that many species of motile and non-motile phytoplankton form multicellular groups in response to predators, however, it is not well known if these groups form by daughter cells remaining together after division, or by potentially unrelated cells aggregating together. For example, Boraas et al. (1998) and Lürling and Van Donk (2000) suggested that group formation in the non-motile species Chlorella vulgaris and Scenedesmus obliquus was via daughter cells remaining together after division. In contrast, Sathe and Durand (2016) demonstrated that the motile species Chlamydomonas come together when they are under predation stress. These authors suggest that these species of phytoplankton cells respond to the chemicals released by the predator (kairomones) that give them the green light to aggregate (Fig. 1) . In their experimental study, the predator is a flagellated protist called Peranema that can predate on small single cells but not on large cell aggregations. Recently, Kapsetaki and co-authors (Kapsetaki et al., 2016, Kapsetaki et al., 2017) showed a clear and direct fitness benefit of forming groups to avoid predation for some non-motile species as a combination between coming together and remaining together after division. They observed that the non-motile cells S. obliquus form predator-induced groups within 1 h, which is faster than their division time, indicating that in a first stage, cells aggregate by coming together.

On the other hand, competition for resources also plays a central role on the spatial distribution of phytoplankton cells either at the macroscopic level (Klausmeier and Litchman, 2001, Huisman et al., 2006, Litchman, 2007, Yoshiyama et al., 2009, Mellard et al., 2012) or at the individual-level (see for instance, Hellweger and Kianirad (2007), Fredrick et al. (2013), Bouderbala et al. (2018)) and when the group size starts to increase, the competition inside the group increases as well (Bouderbala et al., 2018). In general, very few experiments were made to study the compromise between the benefits of being in aggregations through the anti-predation strategies and the costs of competition inside aggregations (Boraas et al., 1998, Grand and Dill, 1999, Bednekoff and Lima, 2004), and to our knowledge, no model on phytoplankton cells was made to address this ecological question and to show the mutual impact of resource competition and anti-predator cooperation and its effect on the predator-induced spatial aggregations.

In this work, we propose to study the process of groups’ formation in motile phytoplankton cells under predation stress and to analyze the impact of the simultaneous effect of competition and cooperation in phytoplankton cells, on the predator-induced spatial aggregations. For this purpose, we adopt the individual-based modelling approach (Grimm, 1999, Grimm et al., 2006, Grimm et al., 2010, DeAngelis and Grimm, 2013). Individual-based models (IBM's) are models that describe characteristics and dynamics observed at the level of individual organisms and describe the changes in their state. They are considered as one of the most useful tools for modelling complex systems since they permit to simulate the simultaneous operations and interactions of multiple individuals in an attempt to re-create and predict the appearance of complex phenomena. Also, they can be applicable to many problems for which the mathematical treatment is hard. Despite their usefulness, only few IBMs were conceived to study phytoplankton dynamics in general and phytoplankton aggregation in particular (El Saadi, 2004, El Saadi and Arino, 2006, El Saadi and Bah, 2006, El Saadi and Bah, 2007, Rudnicki and Wieczorek, 2006, Bouderbala et al., 2018).

So, in this work, we develop a 3-dimensional individual-based model (IBM) that takes into account small scale biological processes for the phytoplankton cells such as motion and the demographical process. The motion is described by the fundamental principle of dynamics (Grünbaum and Okubo, 1994, Niwa, 1994, Okubo and Levin, 2013) that has been applied to phytoplankton cells by El Saadi (2004), El Saadi and Arino (2006), El Saadi and Bah (2006, 2007) using a stochastic differential equation in which, the drift term describes the spatial attraction toward the surrounding cells while the dispersal term represents the cell diffusion. To describe the attraction mechanism between phytoplankton cells, we use the chemotaxis approach that emphasizes biological small scale mechanisms. This approach states that motile-algae such as Dinoflagellates and many other protists flagellates have chemosensory abilities that would be useless if the oceanic environment was chemically homogeneous (Levandowsky and Hauser, 1978, Spero and Morée, 1981, Fitt, 1985, Spero, 1985, Jackson, 1987). Bell and Mitchell (1972) and Azam and Ammerman (1984) reported that phytoplankton cells excrete some extracellular-products and defined the concept of the phycosphere (a highly concentrated region in extracellular products that forms around the phytoplankton cell). Via the chemo-attraction induced by its phycosphere, a phytoplankton cell attracts its neighboring cells that move towards it (El Saadi, 2004, Adioui et al., 2005, El Saadi and Arino, 2006, El Saadi and Bah, 2006, 2007). For the demographical process, we consider a stochastic birth–death process. The division rate is considered density-dependent to include the competition effect in such a way that a cell with higher number of neighbors will have a lower division rate. This means that a competitive environment will slow down the division process. For the death rate, we present two variants: the first one, by considering the death rate constant and the second, by considering the death rate density-dependent to include the cooperation behavior between cells as an anti-predation strategy. We should mention that the cooperation effect is quantified through the death rate which is considered as a decreasing function of the local density. This means that a higher number of neighbors will reduce the death rate. To simulate our IBM, we use Monte Carlo Acceptance-Rejection algorithm that was initiated by Fournier and Méléard (2004) to simulate a stochastic IBM that includes a competition effect.

We organize the paper as follows: in Section 2, we present a detailed description of the IBM using the ODD's protocol (Overview, Design concepts, Details). In Section 3, the stochastic algorithm is proposed and in Section 4, the different scenarios to be tested and parameter values are presented and discussed. Section 5 is devoted to the simulation results and in Section 6, we discuss the results and conclude with some remarks.

Section snippets

The IBM ODD's protocol

In this section, we adopt the ODD protocol (Overview, Design concepts, Details) (Grimm et al., 2006, Grimm et al., 2010) to develop our IBM and for the simulations, we use GAMA-platform version GAMA 1.8 Release Candidate 1 (RC1) that is a modelling and simulation development environment for building spatially explicit agent-based simulations, developed by the International Research Unit UMMISCO.

The used stochastic algorithm

We use the Acceptance–Rejection algorithm to simulate the model. Initiated by Fournier and Méléard (2004), it has been used in many studies (Champagnat and Méléard, 2007, Campillo and Joannides, 2009, Fritsch et al., 2015, Khader, 2015). We define the upper bound event rate over the population, which represents the sum of the upper division D¯ and death M¯ rates as follows:λ¯=D¯+M¯=ND0+M0Let t be the date of the last event and N the population size at time t. For the next branching time, we do:

  • 1.

The parameter values and tested scenarios

Table 2 presents the 12 different scenarios to be tested in this study. To simulate the demographical process of our IBM, we considered real values of phytoplankton for the maximum division rate D0 and the global death rate M0 (see Table 1). On the other hand, since the main cause of phytoplankton death is predation and as grazing represents the main process for loss of phytoplankton (Gutiérrez-Rodríguez et al., 2011, Law et al., 2018, Wohlrab, 2013, Cuesta et al., 2018), we considered that the

Simulation results and statistical analysis

In this part, we present the results obtained from the simulation of the 12 scenarios.

Discussion and concluding remarks

The aim of this work was to understand how motile phytoplankton cells form groups under predation stress and how resource competition and the anti-predation cooperation impact on the aggregating process, the group size and the phytoplankton population. For this purpose, we developed an IBM that take into account small scale biological processes for the phytoplankton cells that are cells’ motion and cells’ division and death. The cells’ motion includes two components: a molecular diffusion and a

Acknowledgements

We would like to thank the editor and the two anonymous reviewers for their valuable comments which helped us to improve the manuscript's quality. We thank Stefania Kapsetaki and Santosh Sathe to their precious biological explanations. We are also grateful to GAMA community to their availability and help in the programming part.

References (76)

  • V. Grimm

    Ten years of individual-based modelling in ecology: what have we learned and what could we learn in the future?

    Ecol. Model.

    (1999)
  • A. Gutiérrez-Rodríguez et al.

    Growth and grazing rate dynamics of major phytoplankton groups in an oligotrophic coastal site, Estuarine

    Coast. Shelf Sci.

    (2011)
  • W.D. Hamilton

    Geometry for the selfish herd

    J. Theor. Biol.

    (1971)
  • F.L. Hellweger et al.

    A bunch of tiny individuals – individual-based modeling for microbes

    Ecol. Model.

    (2009)
  • F.L. Hellweger et al.

    Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

    J. Theor. Biol.

    (2007)
  • G.A. Jackson

    A model of the formation of marine algal flocs by physical coagulation processes

    Deep Sea Res. A: Oceanogr. Res. Pap.

    (1990)
  • M. Levandowsky et al.

    Chemosensory responses of swimming algae and protozoa

    Int. Rev. Cytol.

    (1978)
  • E. Litchman

    Resource Competition and the Ecological Success of Phytoplankton

  • H.-S. Niwa

    Self-organizing dynamic model of fish schooling

    J. Theor. Biol.

    (1994)
  • M. Spieler

    Risk of predation affects aggregation size: a study with tadpoles of Phrynomantis microps (Anura: Microhylidae)

    Anim. Behav.

    (2003)
  • A. Abada et al.

    Multicellular features of phytoplankton

    Frontiers Mar. Sci.

    (2018)
  • F. Azam et al.

    Cycling of organic matter by bacterioplankton in pelagic marine ecosystems: microenvironmental considerations

  • P.A. Bednekoff et al.

    Risk allocation and competition in foraging groups: reversed effects of competition if group size varies under risk of predation

    Proc. R. Soc. Lond. B: Biol. Sci.

    (2004)
  • W. Bell et al.

    Chemotactic and growth responses of marine bacteria to algal extracellular products

    Biol. Bull.

    (1972)
  • R.N. Binny et al.

    Spatial structure arising from neighbour-dependent bias in collective cell movement

    PeerJ

    (2016)
  • M.E. Boraas et al.

    Phagotrophy by a flagellate selects for colonial prey: a possible origin of multicellularity

    Evol. Ecol.

    (1998)
  • I. Bouderbala et al.

    A 3D individual-based model to study effects of chemotaxis, competition and diffusion on the motile-phytoplankton aggregation

    Acta Biotheor.

    (2018)
  • G.L. Bowie et al.
    (1985)
  • F. Campillo et al.

    A spatially explicit Markovian individual-based model for terrestrial plant dynamics

    (2009)
  • N. Champagnat et al.

    Invasion and adaptive evolution for individual-based spatially structured populations

    J. Math. Biol.

    (2007)
  • P.J. Clark et al.

    Generalization of a nearest neighbor measure of dispersion for use in K dimensions

    Ecology

    (1979)
  • J.A. Cuesta et al.

    Sheldon spectrum and the plankton paradox: two sides of the same coin-a trait-based plankton size-spectrum model

    J. Math. Biol.

    (2018)
  • D.L. DeAngelis et al.

    Individual-based models in ecology after four decades

    F1000prime Rep.

    (2013)
  • U. Dieckmann et al.

    The Geometry of Ecological Interactions: Simplifying Spatial Complexity

    (2000)
  • W.W. Driscoll et al.

    Synergistic cooperation promotes multicellular performance and unicellular free-rider persistence

    Nat. Commun.

    (2017)
  • S. Duran-Nebreda et al.

    Emergence of multicellularity in a model of cell growth, death and aggregation under size-dependent selection

    J. R. Soc. Interface

    (2015)
  • W.M. Durham et al.

    Turbulence drives microscale patches of motile phytoplankton

    Nat. Commun.

    (2013)
  • N. El Saadi et al.

    A stochastic modelling of phytoplankton aggregation

    ARIMA

    (2006)
  • Cited by (2)

    • Moment approximation of individual-based models. Application to the study of the spatial dynamics of phytoplankton populations

      2022, Applied Mathematics and Computation
      Citation Excerpt :

      Nevertheless, this model considers constant rates of division and death, which is not very realistic from a biological point of view, since many factors affect these demographic rates, including competition over resources. In a recent work, Bouderbala et al. [12,13] extended the IBM of El Saadi [20–23], by introducing the effect of competition for resources in the death process [12], and, in a second work [13], in addition to considering competition on resources in the division process, the same authors extended the IBM of El Saadi [20–23] by introducing a cooperation process between phytoplankton cells in the death process. The analysis of the effect of the competition process isolated from the cooperation process was only evoked, very briefly and not in detail.

    • Understanding how the collective behaviour of phytoflagellates is affected by light attenuation and diel vertical migration using individual-based modelling

      2020, Journal of Theoretical Biology
      Citation Excerpt :

      One of the evolutionary strategies developed by the motile cells is the formation of spatial groups that can cover many of the strategies cited above such as the reduction of the predation stress and the mixotrophy. The groups take their shape from microscopic interactions such as the chemo-attraction process (Bouderbala et al., 2018, 2019; El Saadi, 2004; El Saadi and Bah, 2006, 2007) where the cells are attracted toward each other due to social reasons such as : the protection from predators (Sathe and Durand, 2016, Kapsetaki et al., 2016, Kapsetaki et al., 2017), the search for preys when they are under heterotrophic regime (Spero, 1985) or even to perform the sexual reproduction (Hadjivasiliou et al., 2015). The environment also plays an important role through the process of turbulence (Durham et al., 2013) or due to the non-uniformity of the resources distribution in the water column where the cells form patches vertically as a function of light and nutrients distribution (Mellard et al., 2011, Huisman et al., 2006).

    View full text