Open Access
| Issue |
Math. Model. Nat. Phenom.
Volume 21, 2026
|
|
|---|---|---|
| Article Number | 20 | |
| Number of page(s) | 29 | |
| Section | Population dynamics and epidemiology | |
| DOI | https://doi.org/10.1051/mmnp/2026012 | |
| Published online | 05 June 2026 | |
- E. Trudnowska, M. Gluchowska, A. Beszczynska-Moller, K. Blachowiak-Samolyk and S. Kwasniewski, Plankton patchiness in the polar front region of the west Spitsbergen shelf. Mar. Ecol. Progr. Ser. 560 (2016) 1–18. [Google Scholar]
- S. van Gennip, A.P. Martin, M.A. Srokosz, J. Allen, R. Pidcock, S.C. Painter and M.C. Stinchcombe, Plankton patchiness investigated using simultaneous nitrate and chlorophyll observations. J. Geophys. Res.: Oceans 121 (2016) 4149–4156. [Google Scholar]
- S.S. Urmy and J.D. Warren, Seasonal changes in the biomass, distribution, and patchiness of zooplankton and fish in four lakes in the Sierra Nevada, California. Freshwater Biol. 64 (2019) 1–18. [Google Scholar]
- M. Scheinin and E. Asmala, Ubiquitous patchiness in chlorophyll a concentration in coastal archipelago of Baltic Sea. Front. Mar. Sci. 7 (2020) 1–12. [Google Scholar]
- K.L. Robinson, S. Sponaugle, J.Y. Luo, M.R. Gleiber and R.K. Cowen, Big or small, patchy all: resolution of marine plankton patch structure at micro- to submesoscales for 36 taxa. Sci. Adv. 7 (2021) eabk2904. [Google Scholar]
- M. Levy, P.J.S. Franks and K.S. Smith, The role of submesoscale currents in structuring marine ecosystems. Nat. Commun. 9 (2018) 4758. [Google Scholar]
- E.R. Abraham, The generation of plankton patchiness by turbulent stirring. Nature 391 (1998) 577–580. [Google Scholar]
- R.E. Breier, C.C. Lalescu, D. Waas and M. Mazza, Emergence of phytoplankton patchiness at small scales in mild turbulence. PNAS 115 (2018) 12112–12117. [Google Scholar]
- K.L. Daly and W.O. Smith, Jr., Physical-biological interactions influencing marine plankton production. Annu. Rev. Ecol. Syst. 24 (1993) 555–585. [Google Scholar]
- J.C. Prairie, K.R. Sutherland, K.J. Nickols and A.M. Kaltenberg, Biophysical interactions in the plankton: a cross- scale review. Limnol. Oceanogr. Fluids Environ. 2 (2012) 121–145. [Google Scholar]
- D.J. McGillicuddy and P.J.S. Franks, Models of plankton patchiness, in: Encyclopedia of Ocean Sciences, edited by J.K. Cochran, H.J. Bokuniewicz and P.L. Yager, 3rd edn., Vol. 5. Elsevier, Oxford (2019) 536–546. [Google Scholar]
- C.L. Folt and C.W. Burns, Biological drivers of zooplankton patchiness. Trends Ecol. Evol. 14 (1999) 300–305. [Google Scholar]
- M. Bengfort, U. Feudel, E.M. Hilker and H. Malchow, Plankton blooms and patchiness generated by heterogeneous physical environments. Ecol. Complex. 20 (2014) 185–194. [Google Scholar]
- W.M. Durham, E. Climent, M. Barry, F. De Lillo, G. Boffetta, M. Cencini and R. Stocker, Turbulence drives microscale patches of motile phytoplankton. Nat. Commun. 4 (2013) 2148. [Google Scholar]
- E.A. Blukacz, W.G. Sprules, B.J. Shuter and J.P. Richards, Evaluating the effect of wind-driven patchiness on trophic interactions between zooplankton and phytoplankton. Limnol. Oceanogr. 55 (2010) 1590–1600. [Google Scholar]
- B. Chen, E. Masunaga, S.L. Smith and H. Yamazaki, Diel vertical migration promotes zooplankton horizontal patchiness. J. Oceanogr. 77 (2020) 123–135. [Google Scholar]
- A.T. Greer, C.B. Woodson, C.E. Smith, C.M. Guigand and R.K. Cowen, Examining mesozooplankton patch structure and its implications for trophic interactions in the northern Gulf of Mexico. J. Plankton Res. 38 (2016) 1115–1134. [Google Scholar]
- I. Hillmer, P. van Reenen, J. Imberger and T. Zohary, Phytoplankton patchiness and their role in the modelled productivity of a large, seasonally stratified lake. Ecol. Model. 218 (2008) 49–59. [Google Scholar]
- A.G. Degermendzhy, E.S. Zadereev, D. Yu. Rogozin, I.G. Prokopkin, Y.V. Barkhatov, A.P. Tolomeev, E.B. Khromechek, J.H. Janse, W. M. Mooij and R.D. Gulati, Vertical stratification of physical, chemical and biological components in two saline lakes Shira and Shunet (South Siberia, Russia). Aquat. Ecol. 44 (2010) 619–632. [Google Scholar]
- C. Schmoker and S. Hernandez-León, Stratification effects on the plankton of the subtropical Canary Current. Progr. Oceanogr. 119 (2013) 24–31. [Google Scholar]
- F. Ríos, R. Kilian and E. Mutschke, Chlorophyll-a thin layers in the Magellan fjord system: the role of the water column stratification. Continent. Shelf Res. 124 (2016) 1–12. [Google Scholar]
- B. Yang, M.G. Wells, J. Li and J. Young, Mixing, stratification, and plankton under lake-ice during winter in a large lake: implications for spring dissolved oxygen levels. Limnol. Oceanogr. 65 (2020) 2713–2719. [Google Scholar]
- V. Venkataramana, R.K. Mishra, P. Sabu, N. Anikumar, A. Sarkar, R.K. Naik, M.A. Soares and L. Gawade, Stratification governs the plankton community structure and trophic interaction in the Southwestern tropical Indian Ocean during boreal summer. Reg. Stud. Mar. Sci. 48 (2021) 101987. [Google Scholar]
- W.J. McKiver and Z. Neufeld, Resonant plankton patchiness induced by large-scale turbulent flow. Phys. Rev. E 83 (2011) 016303. [Google Scholar]
- S.A. Levin and L.A. Segel, Hypothesis for origin of planktonic patchiness. Nature 259 (1976) 659–659. [CrossRef] [PubMed] [Google Scholar]
- H. Malchow, B. Radtke, M. Kallache, A.B. Medvinsky, D.A. Tikhonov and S.V. Petrovskii, Spatio-temporal pattern formation in coupled models of plankton dynamics and fish school motion. Nonlinear Anal. Real World Appl. 1 (2000) 53–67. [Google Scholar]
- A.B. Medvinsky, S.V. Petrovskii, I.A. Tikhonova, H. Malchow and B.L. Li, Spatiotemporal complexity of plankton and fish dynamics. SIAM Rev. 44 (2002) 311–370. [CrossRef] [MathSciNet] [Google Scholar]
- Q.X. Liu, Z. Jin and B.L. Li, Resonance and frequency-locking phenomena in spatially extended phytoplankton- zooplankton system with additive noise and periodic forces. J. Stat. Mech. Theory Exp. 2008 (2008) P05011. [Google Scholar]
- T. Huang, C. Yu, K. Zhang, X. Liu, J. Zhen and L. Wang, Complex pattern dynamics and synchronization in a coupled spatiotemporal plankton system with zooplankton vertical migration. Chaos Solitons Fractals 175 (2023) 114063. [Google Scholar]
- T. Huang, C. Yu, Z. Lin, H. Zhang, R. Liu, R. Li, Y. Yang and Y. Tian, Self-organization of nested patterns in a coupled spatiotemporal phytoplankton-zooplankton system. Commun. Nonlinear Sci. Numer. Simul. 130 (2024) 107804. [Google Scholar]
- W. Wang, S. Liu and Z. Liu, Spatiotemporal dynamics near the Turing-Hopf bifurcation in a toxic-phytoplankton- zooplankton model with cross-diffusion. Nonlinear Dyn. 98 (2019) 27–37. [Google Scholar]
- G.M. Cohen and J.B. Shurin, Scale-dependence and mechanisms of dispersal in freshwater zooplankton. Oikos 103 (2003) 603–617. [Google Scholar]
- J.H. Steele and E.W. Henderson, A simple model for plankton patchiness. J. Plankton Res. 14 (1992) 1397–1403. [Google Scholar]
- S.J. Brentnall, K.J. Richards, J. Brindley and E. Murphy, Plankton patchiness and its effect on larger-scale productivity. J. Plankton Res. 25 (2003) 121–140. [Google Scholar]
- K. Bandara, O. Varpe, L. Wijewardene, V. Tverberg and K. Eiane, Two hundred years of zooplankton vertical migration research. Biol. Rev. 96 (2021) 1547–1589. [Google Scholar]
- L. Matthews and J. Brindley, Patchiness in plankton populations. Dyn. Stabil. Syst. 12 (1997) 39–59. [Google Scholar]
- J.M.G. Vilar, R.V. Sole and J.M. Rubi, On the origin of plankton patchiness. Physica A 317 (2003) 239–246. [Google Scholar]
- L.N. Hudson and D.C. Reuman, A cure for the plague of parameters: constraining models of complex population dynamics with allometries. Proc. Roy. Soc. B 280 (2013) 20131901. [Google Scholar]
- W. Tian, H. Zhang, Z. Wang, Y. Tian and T. Huang, Analysis on the stability of plankton in a food web with empirical organism body mass distribution. Environ. Sci. Pollut. Res. 30 (2022) 21327–21343. [Google Scholar]
- N.K. Thakur, A. Ojha and S.K. Tiwari, The role of adaptation in plankton system with Beddington-DeAngelis type functional response, in Mathematical Modelling and Scientific Computing 'with Applications: ICMMSC 2018, Indore, India, July 19-21, edited by S. Manna, B. Datta and S. Ahmad. Springer Proceedings in Mathematics & Statistics, Vol. 308. Springer, Singapore (2020) 21–33. [Google Scholar]
- X.C. Zhang, G.Q. Sun and Z. Jin, Spatial dynamics in a predator-prey model with Beddington-DeAngelis functional response. Phys. Rev. E 85 (2012) 021924. [Google Scholar]
- L. Xue, Pattern formation in a predator-prey model with spatial effect. Physica A 391 (2012) 5987–5996. [Google Scholar]
- Y.A. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd edn. Applied Mathematical Sciences, Vol. 112. Springer, New York, NY (1998). [Google Scholar]
- K. Manna and M. Banerjee, Stationary, non-stationary and invasive patterns for a prey-predator system with additive Allee effect in prey growth. Ecol. Complex. 36 (2018) 206–217. [Google Scholar]
- J. Shen and Y.M. Jung, Geometric and stochastic analysis of reaction-diffusion patterns. Int. J. Pure Appl. Math. 19 (2005) 195–244. [Google Scholar]
- L.N. Guin and H. Baek, Comparative analysis between prey-dependent and ratio-dependent predator-prey systems relating patterning phenomenon. Math. Comput. Simul. 146 (2018) 100–117. [Google Scholar]
- A. Calbet and M.R. Landry, Phytoplankton growth, microzooplankton grazing, and carbon cycling in marine systems. Limnol. Oceanogr. 49 (2004) 51–57. [Google Scholar]
- R.W. Eppley, Temperature and phytoplankton growth in the sea. Fishery Bull. 70 (1972) 1063–1085. [Google Scholar]
- J.E. Bissinger, D.J.S. Montagnes, J. Sharples and D. Atkinson, Predicting marine phytoplankton maximum growth rates from temperature: improving on the Eppley curve using quantile regression. Limnol. Oceanogr. 53 (2008) 487–493. [Google Scholar]
- Q.P. Li, P.J.S. Franks and M.R. Landry, Microzooplankton grazing dynamics: parameterizing grazing models with dilution experiment data from the California Current Ecosystem. Mar. Ecol. Progr. Ser. 438 (2011) 59–69. [Google Scholar]
- J.R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44 (1975) 331–340. [CrossRef] [Google Scholar]
- D. Straile, Gross growth efficiencies of protozoan and metazoan zooplankton and their dependence on food concentration, predator-prey weight ratio, and taxonomic group. Limnol. Oceanogr. 42 (1997) 1375–1385. [Google Scholar]
- L.D.J. Kuijper, T.R. Anderson and S.A.L.M. Kooijman, C and N gross growth efficiencies of copepod egg production studied using a dynamic energy budget model. J. Plankton Res. 26 (2004) 213–226. [Google Scholar]
- Y. Olsen, T. Andersen, I. Gismervik and O. Vadstein, Protozoan and metazoan zooplankton-mediated carbon flows in nutrient-enriched coastal planktonic communities. Mar. Ecol. Progr. Ser. 331 (2007) 67–83. [Google Scholar]
- A.G. Hirst and T. Kiorboe, Mortality of marine planktonic copepods: global rates and patterns. Mar. Ecol. Progr. Ser. 230 (2002) 195–209. [Google Scholar]
- A. Okubo, Oceanic diffusion diagrams. Deep-Sea Res. 18 (1971) 789–802. [Google Scholar]
- J.A. MacKinnon and M.C. Gregg, Spring mixing: turbulence and internal waves during restratification on the New England Shelf. J. Phys. Oceanogr. 35 (2005) 2425–2443. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.
