Tri-trophic Plankton Models Revised: Importance of Space, Food Web Structure and Functional Response Parametrisation

H.I. Egilmez¹ ; A.Yu. Morozov^1, 2

¹ Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK
² Shirshov Institute of Oceanology, Moscow, 117997, Russia

Mathematical modelling of natural phenomena, Tome 11 (2016) no. 4, pp. 16-33

Résumé

Revealing mechanisms of efficient top-down control in eutrophic ecosystems remains a long term challenge in theoretical ecology. In this paper, we revisit the role of environmental heterogeneity, food web structure and shape of the predator functional response in persistence and stabilization of a planktonic system with high nutrient supply. We consider a 1D vertically resolved tri-trophic planktonic food web composed of a primary producer, an intermediate predator and a highly mobile top predator, such as a system of phytoplankton, microzooplankton and copepods. We explore the realistic scenario in which the top predator is omnivorous, i.e. when copepods can feed both on phytoplankton and microzooplankton. We show that the interplay between heterogeneity of the environment due to for instance, a light gradient in the water column, and trophic interaction between species can result in an efficient top-down control which would otherwise be impossible in the corresponding well-mixed system. We also find that allowing the top predator to feed on the primary producer may dramatically impede the coexistence of the three trophic levels, with only two levels generally surviving. The coexistence of all three trophic levels within a wide range of parameters becomes possible only when the top predator exhibits active food source switching behaviour. We also show the phenomenon of bistability in the considered tri-trophic food web: a small initial amount of the top predator should lead to its extinction whereas introduction of a supercritical initial amount will eventually result in establishment of the population. The demonstrated mechanism of top-down control seems to be rather generic and might be a good candidate to explain stability in some other non-planktonic tri-trophic ecosystems.

Détail

DOI : 10.1051/mmnp/201611403

Bibliographie

[1] M.W. Adamson, A. Yu. Morozov When can we trust our model predictions? Unearthing structural sensitivity in biological systems Proc. R. Soc. A 2012

[2] P.A. Abrams, C.J. Walters Invulnerable prey and the paradox of enrichment Ecology 1996 1125 1133

[3] A. Beckmann, I. Hense Beneath the surface: characteristics of oceanic ecosystems under weak mixing conditions - a theoretical investigation Prog. Oceanogr. 2007 771 796

[4] M. N. Breckels, N. W. F. Bode, E. A. Codling, M. Steinke The effect of grazing-mediated DMS production on the behaviour of the copepod Calanus helgolandicus Mar. Drugs 2013 2486 2500

[5] P.W. Boyd Environmental factors controlling phytoplankton processes in the Southern Ocean J. Phycol. 2002 844 861

[6] P.W. Boyd, S.M. Smith, T. Cowles Grazing patterns of copepods in the upwelling system off Peru Limnol. Oceanogr. 1980 583 596

[7] A. Calbet, F. Carlotti, R. Gaudy The feeding ecology of the copepod Centropages typicus (Kroyer) Prog. Oceanogr. 2007 137 150

[8] F. Carlotti, S. Nival Moulting and mortality rates of copepods related to age within stage: Experimental results Mar. Ecol. Prog. Ser. 1992 235 243

[9] F.P. Chavez, K.R. Buck, R.T. Barber Phytoplankton taxa in relation to primary production in the equatorial Pacific Deep Sea Res. 1990 1733 1752

[10] P. Chow-Fraser, W.G. Sprules Type-3 functional response in limnetic suspension-feeders, as demonstrated by in situ grazing rates Hydrobiologia 1992 175 191

[11] F. Cordoleani, D. Nerini, M. Gauduchon, A. Morozov, J-C. Poggiale Structural sensitivity of biological models revisited J. Theor. Biol. 2011 82 91

[12] F. Courchamp, L. Berec, J. Gascoigne. Allee Effects in Ecology and Conservation. Oxford Uni. Press, Oxford, 2006.

[13] J.J. Cullen, M.R. Lewis, C.O. Davis, R.T. Barber Photosynthetic characteristics and estimated growth rates indicate that grazing is the proximate control of primary production in the equatorial Pacific J. Geophys. Res. 1992 639 654

[14] B. Dennis Allee effect: population growth, critical density, and chance of extinction Nat. Resour. Model. 1989 481 538

[15] E.G. Durbin, A.G. Durbin Effects of temperature and food abundance on grazing and short-term weight change in the marine copepod Acartia hudsonica Limnol. Oceanogr. 1996 361 378

[16] A. M. Edwards, J. Brindley Zooplankton mortality and the dynamical behaviour of plankton population models Bull. Math. Biol. 1999 303 339

[17] C. A. Edwards, H. P. Batchelder, T. M. Powell Modeling microzooplankton and macrozooplankton dynamics within a coastal upwelling system J. Plankton Res. 2000a 1619 1648

[18] C. A. Edwards, T. A. Powell, H. P. Batchelder The stability of an NPZ model subject to realistic levels of vertical mixing J. Mar. Res. 2000b 37 60

[19] A.M. Edwards, A Yool The role of higher predation in plankton population models J. Plankton Res. 2000 1085 1112

[20] K. F. Edwards, M. K. Thomas, C. A. Klausmeier, E. Litchman Light and growth in marine phytoplankton: Allometric, taxonomic, and environmental variation Limnol. Oceanogr. 2015 540 552

[21] J.Z. Farkas, A. Yu. Morozov, E.G. Arashkevich, A. Nikishina Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication Bull. Math. Biol. 2015 1886 1908

[22] B.W. Frost Grazing control of phytoplankton stock in the open subarctic Pacific Ocean: a model assessing the role of mesozooplankton, particularly the large calanoid copepods Neocalanus spp Mar. Ecol. Prog. Ser. 1987 49 68

[23] G.F. Fussmann, B. Blasius Community response to enrichment is highly sensitive to model structure Biol. Lett. 2005 9 12

[24] A. Gabric, N. Murray, L. Stone, M. Kohl Modelling the production of dimethylsulfide during a phytoplankton bloom J. Geophys. Res. 1993 22805 22816

[25] M. Genkai-Kato, N. Yamamura Unpalatable prey resolves the paradox of enrichment P. Roy. Soc. Lond. B. Bio. 1999 1215 1219

[26] W. Gentleman, A. Leising, B. Frost, S. Storm, J. Murray Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics Deep-sea Res. Pt. II 2003 2847 2875

[27] I. Gismervik Top-down impact by copepods on ciliate numbers and persistence depends on copepod and ciliate species composition J. Plankton Res. 2006 499 507

[28] I. Gismervik, T. Andersen Prey switching by Acartia clausi: experimental evidence and implications of intraguild predation assessed by a model Mar. Ecol. Prog. Ser. 1997 247 259

[29] P. J. Hansen, P.K. Bjornsen, B.W Hansen Zooplankton grazing and growth: Scaling within the 2-2000 μm body size range Limnol. Oceanogr. 1997 687 704

[30] F. C. Hansen, M. Reckermann, W. C. M. Klein Breteler Phaeocystis blooming enhanced by copepod predation on protozoa: evidence from incubation experiments Mar. Ecol. Prog. Ser. 1993 51 57

[31] C.X.J. Jensen, L.R. Ginzburg Paradoxes or theoretical failures? The jury is still out Ecol. Model. 2005 3 14

[32] A. Kharab, R. B. Guenther. An Introduction to Numerical Methods: A MATLAB Approach. Third edition. CRC Press, Boca Raton, 2012.

[33] T. Kierboe, Saiz, M. Viitasalo Prey switching behaviour in the planktonic copepod Acartia tonsa Mar. Ecol. Prog. Ser. 1996 65 75

[34] W. Lampert Vertical distribution of zooplankton: density dependence and evidence for an ideal free distribution with costs BMC Biol. 2005 10

[35] N. Lewis, A. Morozov, M. Breckels, M. Steinke, E. Codling Multitrophic interactions in the sea: assessing the effect of infochemical-mediated foraging in a 1-d spatial model MMNP 2013 25 44

[36] K.M. Meyer, M. Vos, W. M. Mooij, W. H. G. Hol, A. J. Termorshuizen, W. H. Van Der Putten Testing the paradox of enrichment along a land use gradient in a multitrophic aboveground and belowground community PLoS ONE 2012 e49034

[37] A. Yu. Morozov, M. Sen, M. Banerje Top-down control in a patchy environment: Revisiting the stabilizing role of food-dependent predator dispersal Theor. Popul. Biol. 2012 9 19

[38] A. Yu. Morozov. Incorporating complex foraging of zooplankton in models: role of micro and mesoscale processes in macroscale patterns. In Dispersal, individual movement and spatial ecology: a mathematical perspective (eds M Lewis, P Maini S Petrovskii), pp. 1–10. New York, NY: Springer, 2011.

[39] A. Yu. Morozov, E.G. Arashkevich, A. Nikishina, K Solovyev Nutrient-rich plankton communities stabilized via predator-prey interactions: revisiting the role of vertical heterogeneity Math. Med. Biol. 2011 185 215

[40] A. Yu. Morozov, A. F. Pasternak, E. G. Arashkevich Revisiting the role of individual variability in population persistence and stability PLoS ONE 2013 e70576

[41] A. Yu. Morozov, S.V. Petrovskii Feeding on multiple sources: towards a universal parameterization of the functional response of a generalist predator allowing for switching PLoS ONE 2013 e74586

[42] A. Mougi, K. Nishimura A resolution of the paradox of enrichment J. Theor. Biol. 2007 194 201

[43] W.W. Murdoch The functional response of predators J. Appl. Ecol. 1973 335 342

[44] S. Petrovskii S, B. Li, H. Malchow Transition to spatiotemporal chaos can resolve the paradox of enrichment Ecol. Complex 2004 37 47

[45] G.A. Polis, R.D. Holt Intraguild predation: the dynamics of complex trophic interactions Trends. Ecol. Evol. 1992 151 155

[46] J.E.G. Raymont. Plankton and Productivity in the Oceans. Phytoplankton, Vol. 1 Pergamon. Oxford (1980)

[47] A. B. Ryabov, L. Rudolf, B. Blasius Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer J. Theor. Biol. 2010 120 133

[48] A. B. Ryabov, A. Morozov, B. Blasius Imperfect prey selectivity of predators promotes biodiversity and irregularity in food webs Ecol. Letts. 2015 1262 1269

[49] M. L. Rosenzweig Paradox of enrichment: destabilization of exploitation ecosystems in ecological time Science 1971 385 387

[50] M. L. Rosenzweig, R. H. Macarthur Graphical representation and stability conditions of predator-prey interactions Am. Nat. 1963 209 223

[51] S. Roy, J. Chattopadhyay The stability of ecosystems: a brief overview of the paradox of enrichment J. Bioscience 2007 421 428

[52] P.A. Stephens, W.J. Sutherland Consequences of the Allee effect for behaviour, ecology and conservation Trends. Ecol. Evol. 1999 401 405

[53] D.K. Stoecker, J.M. Capuzzo Predation on Protozoa: its importance to zooplankton J. Plankton Res. 1990 891 908

[54] W. K. Tang, M. Taal Trophic modification of food quality by heterotrophic protists: species-specific effects on copepod egg production and egg hatching J. Exp. Mar. Biol. Ecol. 2005 85 98

[55] P. Tiselius, P.R. Jonsson Foraging behaviour of six calanoid copepods: observations and hydrodynamic analysis Mar. Ecol. Prog. Ser. 1990 23 33

[56] S. M. Vallina, B. Ward, S. Dutkiewicz, M. Follows Maximal feeding with active preyswitching: A kill-the-winner functional response and its effect on global diversity and biogeography Prog. Oceanogr. 2014 93 109

[57] L. Van Duren, J. Videler Swimming behaviour of developmental stages of the calanoid copepod Temora longicornis at different food concentrations Mar. Ecol. Prog. Ser. 1995 153 161