Open Access
Math. Model. Nat. Phenom.
Volume 19, 2024
Article Number 15
Number of page(s) 37
Section Population dynamics and epidemiology
Published online 20 June 2024
  1. R.D. Neuenhoff, D.P. Swain, S.P. Cox, M.K. McAllister, A.W. Trites, C.J. Walters and M.O. Hammill, Continued decline of a collapsed population of atlantic cod (gadus morhua) due to predation-driven allee effects. Can. J. Fisher. Aquat. Sci. 76 (2019) 168–184. [CrossRef] [Google Scholar]
  2. L. Akveld, The Cod: AC Jensen. Crowell, New York, NY (1972) 182 pp., US 7.95 (1974). [Google Scholar]
  3. S.M. Garcia, C. Newton et al., Current Situation, Trends and Prospects in World Capture Fisheries. FAO, Fisheries Department (1995). [Google Scholar]
  4. M. Kurlansky and R.M. Davidson, Cod: A Biography of the Fish that Changed the World. Phoenix Books (2006). [Google Scholar]
  5. C.C. on the Status of Endangered Wildlife in Canada), Cosewic Assessment and Status Report on Atlantic Cod (Gadus morhua) in Canada (2010). [Google Scholar]
  6. K.F. Drinkwater, The response of Atlantic cod (Gadus morhua) to future climate change. ICES J. Mar. Sci. 62 (2005) 1327–1337. [CrossRef] [Google Scholar]
  7. P.A. Shelton, A.F. Sinclair, G.A. Chouinard, R. Mohn and D.E. Duplisea, Fishing under low productivity conditions is further delaying recovery of northwest Atlantic cod (Gadus morhua). Can. J. Fisher. Aquat. Sci. 63 (2006) 235–238. [CrossRef] [Google Scholar]
  8. J.A. Brown, G. Minkoff and V. Puvanendran, Larviculture of Atlantic cod (Gadus morhua): progress, protocols and problems. Aquaculture 227 (2003) 357–372. [CrossRef] [Google Scholar]
  9. G. Rosenlund and Ó. Halldórsson, Cod juvenile production: research and commercial developments. Aquaculture 268 (2007) 188–194. [CrossRef] [Google Scholar]
  10. L.R. Fox, Cannibalism in natural populations. Annu. Rev. Ecol. Syst. 6 (1975) 87–106. [CrossRef] [Google Scholar]
  11. B. Bogstad, G.R. Lilly, S. Mehl, O.K. Palsson and G. Stefánsson, Cannibalism and year-class strength in Atlantic cod (Gadus morhua L.) in arcto-boreal ecosystems (Barents sea, Iceland, and Eastern Newfoundland). (1994). [Google Scholar]
  12. A. Folkvord, Growth, survival and cannibalism of cod juveniles (Gadus morhua): effects of feed type, starvation and fish size. Aquaculture 97 (1991) 41–59. [CrossRef] [Google Scholar]
  13. G. Blom and A. Folkvord, A snapshot of cannibalism in 0-group Atlantic cod (Gadus morhua) in a marine pond. J. Appl. Ichthyol. 13 (1997) 177–181. [CrossRef] [Google Scholar]
  14. A. Folkvord and H. Otterå, Effects of initial size distribution, day length, and feeding frequency on growth, survival, and cannibalism in juvenile Atlantic cod (Gadus morhua L.). Aquaculture 114 (1993) 243–260. [CrossRef] [Google Scholar]
  15. D. Austin, W. Bowen and J. McMillan, Intraspecific variation in movement patterns: modeling individual behaviour in a large marine predator. Oikos 105 (2004) 15–30. [CrossRef] [Google Scholar]
  16. W. Bowen, J. Lawson and B. Beck, Seasonal and geographic variation in the species composition and size of prey consumed by grey seals (Halichoerus grypus) on the Scotian shelf. Can. J. Fisher. Aquat. Sci. 50 (1993) 1768–1778. [CrossRef] [Google Scholar]
  17. R. Mohn and W. Bowen, Grey seal predation on the eastern Scotian shelf: modelling the impact on Atlantic cod. Can. J. Fisher. Aquat. Sci. 53 (1996) 2722–2738. [CrossRef] [Google Scholar]
  18. W.D. Bowen, J. McMillan and R. Mohn, Sustained exponential population growth of grey seals at sable island, Nova Scotia. ICES J. Mar. Sci. 60 (2003) 1265–1274. [CrossRef] [Google Scholar]
  19. P. Stephens, W. Sutherland and R. Freckleton, What is the Anee effect? Oikos 50 (199) 87. [Google Scholar]
  20. S.D. Gregory, C.J. Bradshaw, B.W. Brook and F. Courchamp, Limited evidence for the demographic Allee effect from numerous species across taxa. Ecology 91 (2010) 2151–2161. [CrossRef] [PubMed] [Google Scholar]
  21. A.M. Kramer, L. Berec and J.M. Drake, Allee effects in ecology and evolution. J. Anim. Ecol. 87 (2018) 7–10. [CrossRef] [PubMed] [Google Scholar]
  22. P.A. Stephens and W.J. Sutherland, Consequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol. Evol. 14 (1999) 401–405. [CrossRef] [Google Scholar]
  23. A. Veprauskas and J.M. Cushing, A juvenile–adult population model: climate change, cannibalism, reproductive synchrony, and strong Allee effects. J. Biol. Dyn. 11 (2017) 1–24. [CrossRef] [MathSciNet] [Google Scholar]
  24. M.K. Trzcinski, R. Mohn and W.D. Bowen, Continued decline of an Atlantic cod population: how important is gray seal predation? Ecol. Applic. 16 (2006) 2276–2292. [CrossRef] [PubMed] [Google Scholar]
  25. D.M. Keith and J.A. Hutchings, Population dynamics of marine fishes at low abundance. Can. J. Fisher. Aquat. Sci. 69 (2012) 1150–1163. [CrossRef] [Google Scholar]
  26. K.A. Vert-Pre, R.O. Amoroso, O.P. Jensen and R. Hilborn, Frequency and intensity of productivity regime shifts in marine fish stocks. Proc. Natl. Acad. Sci. U.S.A. 110 (2013) 1779–1784. [CrossRef] [PubMed] [Google Scholar]
  27. G. Chouinard, D. Swain, M. Hammill and G. Poirier, Covariation between grey seal (Halichoerus grypus) abundance and natural mortality of cod (Gadus morhua) in the southern gulf of St. Lawrence. Can. J. Fisher. Aquat. Sci. 62 (2005) 1991–2000. [CrossRef] [Google Scholar]
  28. C.S. Holling, Some characteristics of simple types of predation and parasitism. Can. Entomologist 91 (1959) 385–398. [CrossRef] [Google Scholar]
  29. A.M. Fisher, S.J. Cornell, G.I. Holwell and T.A. Price, Mate-finding Allee effects can be exacerbated or relieved by sexual cannibalism. J. Anim. Ecol. 89 (2020) 1581–1592. [CrossRef] [PubMed] [Google Scholar]
  30. V. Puvanendran, B.J. Laurel and J.A. Brown, Cannibalism of Atlantic cod Gadus morhua larvae and juveniles on first-week larvae. Aquat. Biol. 2 (2008) 113–118. [CrossRef] [Google Scholar]
  31. M.R. Rodriguez, N. Smith, T. Phan, J. Woodbury and Y. Kang, Interactions between leaf-cutter ants and fungus garden: effects of division of labor, age polyethism, and egg cannibalism. Math. Model. Natural Phenomena 13 (2018) 30. [CrossRef] [EDP Sciences] [Google Scholar]
  32. M.S. Shabbir, Q. Din, K. Ahmad, A. Tassaddiq, A.H. Soori and M.A. Khan, Stability, bifurcation, and chaos control of a novel discrete-time model involving Allee effect and cannibalism. Adv. Diff. Equ. 2020 (2020) 1–28. [CrossRef] [Google Scholar]
  33. M.S. Shabbir, Q. Din, R. Alabdan, A. Tassaddiq and K. Ahmad, Dynamical complexity in a class of novel discretetime predator-prey interaction with cannibalism. IEEE Access 8 (2020) 100226–100240. [CrossRef] [Google Scholar]
  34. P.R. Chowdhury, S. Petrovskii and M. Banerjee, Oscillations and pattern formation in a slow–fast prey–predator system. Bull. Math. Biol. 83 (2021) 1–41. [Google Scholar]
  35. A. Tassaddiq, M.S. Shabbir, Q. Din, K. Ahmad and S. Kazi, A ratio-dependent nonlinear predator-prey model with certain dynamical results. IEEE Access 8 (2020) 195074–195088. [CrossRef] [Google Scholar]
  36. W. Alharbi and S. Petrovskii, The impact of fragmented habitat’s size and shape on populations with allee effect. Math. Model. Natural Phenomena 11 (2016) 5–15. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  37. M.A. Lewis and P. Kareiva, Allee dynamics and the spread of invading organisms. Theor. Popul. Biol. 43 (1993) 141–158. [Google Scholar]
  38. G. Craciun, F. Nazarov and C. Pantea, Persistence and permanence of mass-action and power-law dynamical systems. SIAM J. Appl. Math. 73 (2013) 305–329. [CrossRef] [MathSciNet] [Google Scholar]
  39. H.L. Smith and H.R. Thieme, Dynamical Systems and Population Persistence, Vol. 118. American Mathematical Society (2011). [Google Scholar]
  40. P. Roy, S. Jain and M. Maama. Assessing the viability of tri-trophic food chain model in designing a conservation plan: the case of dwindling quokka population. Ecol. Complex. 41 (2020) 100811. [CrossRef] [Google Scholar]
  41. M. Garrione and C. Rebelo, Persistence in seasonally varying predator-prey systems via the basic reproduction number. Nonlinear Anal. Real World Applic. 30 (2016) 73–98. [CrossRef] [Google Scholar]
  42. P. Rebelo, S. Rosa and C.M. Silva, Modelling optimal pest control of non-autonomous predator-prey interaction. Math. Model. Natural Phenomena 17 (2022) 28. [CrossRef] [EDP Sciences] [Google Scholar]
  43. W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control, Vol. 1. Springer Science & Business Media (2012). [Google Scholar]
  44. L.S. Pontryagin, Mathematical Theory of Optimal Processes. Routledge (2018). [CrossRef] [Google Scholar]
  45. C. Freitas, E.M. Olsen, E. Moland, L. Ciannelli and H. Knutsen, Behavioral responses of Atlantic cod to sea temperature changes. Ecol. Evol. 5 (2015) 2070–2083. [CrossRef] [Google Scholar]
  46. X. Mao, Stochastic Differential Equations and Applications. Elsevier (2007). [Google Scholar]
  47. N. Dalal, D. Greenhalgh and X. Mao, A stochastic model for internal HIV dynamics. J. Math. Anal. Applic. 341 (2008) 1084–1101. [CrossRef] [Google Scholar]
  48. P.C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Vol. 28. Springer Science & Business Media (2013). [Google Scholar]
  49. W. Chen and M. Wang, Qualitative analysis of predator–prey models with Beddington-Deangelis functional response and diffusion. Math. Comput. Model. 42 (2005) 31–44. [CrossRef] [Google Scholar]
  50. G.A. Chouinard, L.G. Currie and G.A. Poirier, Assessment of Cod in the Southern Gulf of St. Lawrence, February 2000. Fisheries & Oceans, Science, Canadian Stock Assessment Secretariat (2000). [Google Scholar]
  51. R.M. Cook and V. Trijoulet, The effects of grey seal predation and commercial fishing on the recovery of a depleted cod stock. Can. J. Fisher. Aquat. Sci. 73 (2016) 1319–1329. [CrossRef] [Google Scholar]
  52. M. Crick and M. Hill, The role of sensitivity analysis in assessing uncertainty, in Uncertainty Analysis for Performance Assessments of Radioactive Waste Disposal Systems (1987). [Google Scholar]
  53. R.L. Iman and J.C. Helton, An investigation of uncertainty and sensitivity analysis techniques for computer models. Risk Anal. 8 (1988) 71–90. [CrossRef] [Google Scholar]
  54. R.L. Iman and J.C. Helton, The repeatability of uncertainty and sensitivity analyses for complex probabilistic risk assessments. Risk Anal. 11 (1991) 591–606. [CrossRef] [Google Scholar]
  55. D.J. Downing, R. Gardner and F. Hoffman, An examination of response-surface methodologies for uncertainty analysis in assessment models. Technometrics 27 (1985) 151–163. [Google Scholar]
  56. J.R. Butler, S.J. Middlemas, I.M. Graham and R.N. Harris, Perceptions and costs of seal impacts on Atlantic salmon fisheries in the moray firth, Scotland: implications for the adaptive co-management of seal-fishery conflict. Mar. Policy 35 (2011) 317–323. [CrossRef] [Google Scholar]
  57. K. Kauhala and M. Kurkilahti, Delayed effects of prey fish quality and winter temperature during the birth year on adult size and reproductive rate of Baltic grey seals. Mammal Res. 65 (2020) 117–126. [CrossRef] [Google Scholar]
  58. R.J. Lilley and R.K. Unsworth, Atlantic cod (Gadus morhua) benefits from the availability of seagrass (Zostera marina) nursery habitat. Global Ecol. Conserv. 2 (2014) 367–377. [CrossRef] [Google Scholar]
  59. D.J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43 (2001) 525–546. [NASA ADS] [CrossRef] [Google Scholar]
  60. R. Arditi and L.R. Ginzburg, Coupling in predator–prey dynamics: ratio-dependence. J. Theor. Biol. 139 (1989) 311–326. [CrossRef] [Google Scholar]
  61. M. Bandyopadhyay and C. Chakrabarti, Deterministic and stochastic analysis of a nonlinear prey-predator system. J. Biol. Syst. 11 (2003) 161–172. [CrossRef] [Google Scholar]
  62. M. Bandyopadhyay and J. Chattopadhyay, Ratio-dependent predator–prey model: effect of environmental fluctuation and stability. Nonlinearity 18 (2005) 913. [CrossRef] [MathSciNet] [Google Scholar]
  63. T. Perälä, J.A. Hutchings and A. Kuparinen, Allee effects and the allee-effect zone in northwest Atlantic cod. Biol. Lett. 18 (2022) 20210439. [CrossRef] [Google Scholar]
  64. J. Beirão, M. Boulais, V. Gallego, J.K. O’Brien, S. Peixoto, T.R. Robeck and E. Cabrita, Sperm handling in aquatic animals for artificial reproduction. Theriogenology 133 (2019) 161–178. [Google Scholar]
  65. K.E.T. Busch, I.-B. Falk-Petersen, S. Peruzzi, N.A. Rist and K. Hamre, Natural zooplankton as larval feed in intensive rearing systems for juvenile production of Atlantic cod (Gadus morhua L.). Aquacult. Res. 41 (2010) 1727–1740. [CrossRef] [Google Scholar]
  66. O.B. Samuelsen, A.H. Nerland, T. Jørgensen, M.B. Schrøder, T. Svåsand and Ø. Bergh, Viral and bacterial diseases of Atlantic cod Gadus morhua, their prophylaxis and treatment: a review. Dis. Aquat. Organ. 71 (2006) 239–254. [CrossRef] [PubMed] [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.