Lévy processes and stochastic von Bertalanffy models of growth, with application to fish population analysis

Journal of Theoretical Biology

Volumn 258, Issue 4, 2009, Pages 521-529

  Russo, Tommaso ^a   Baldi, Paolo ^a   Parisi, Antonio ^a   Magnifico, Giuseppe ^b   Mariani, Stefano ^c   Cataudella, Stefano ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b CNR   (Italy)

^c UNIVERSITY COLLEGE DUBLIN   (Ireland)

Author keywords

Clupea harengus; Fish growth; Fisheries; Individual based models; Subordinators

Indexed keywords

CLUPEOID; GROWTH MODELING; POPULATION DYNAMICS; POPULATION MODELING; STOCHASTICITY;

ANALYTIC METHOD; ARTICLE; ATLANTIC HERRING; GROWTH; NONHUMAN; PHYSICAL DEVELOPMENT; PRIORITY JOURNAL; STOCHASTIC MODEL; THEORETICAL MODEL;

AGING; ANIMALS; DATA INTERPRETATION, STATISTICAL; FISHES; MODELS, BIOLOGICAL; STOCHASTIC PROCESSES;

ANIMALIA; CLUPEA HARENGUS;

EID: 67349094498     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2009.01.033     Document Type: Article

References (36)

1. AA., VV., 2007. Report of Herring Assessment Working Group for the Area South of 628 N. ICES CM 2007/ACFM: 11.
2. Arino O., Shin Y., and Mullon C. A mathematical derivation of size spectra in fish populations. C.R. Biol. 327 (2004) 245-254
3. Bennett W., Ostrach D., and Hinton D. Condition of larval striped bass in a draught-stricken estuary: evaluating pelagic food web limitation. Ecol. Appl. 5 (1995) 680-692
4. Beverton R., Hylen A., Østvedt O.-J., Alvsvaag J., and Iles T. Growth, maturation, and longevity of maturation cohorts of Norwegian spring-spawning herring. ICES J. Mar. Sci. 61 (2004) 165-175
5. Brett J. Environmental factors and growth. In: Fish Physiology. Bioenergetics and Growth vol. III (1979), Academic Press Inc., New York
6. Caswell, H., 2001. Matrix Population Models: Construction, Analysis, and Interpretation. Sinauder Associated, Sunderland, Massachusetts, USA.
7. Conover D., and Munch S. Sustaining fisheries yields over evolutionary time scales. Science 297 5578 (2002) 94-96
8. Cont, R., Tankov, P., 2004. Financial Modelling with Jump Processes. Chapman & Hall/CRC Financial Mathematics Series, Chapman & Hall/CRC, Boca Raton, FL.
9. DeAngelis D., Rose K., Crowder L., Marshall E., and Lika D. Fish cohort dynamics: application of complementary modelling approaches. Am. Nat. 142 4 (1993) 604-622
10. Edwards A., Phillips R., Watkins N., Freeman M., Murphy E., Afanasyev V., Buldyrev S., da Luz M., Raposo E., and Stanley H. Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature 449 (2007) 1044-1049
11. Ernande B., Dieckmann U., and Heino M. Adaptive changes in harvested populations: plasticity and evolution of age and size at maturation. Proc. R. Soc. Lond. 271 1537 (2004) 415-423
12. Essington T., Kitchell J., and Walters C. The von Bertalanffy growth function, bioenergetics, and the consumption rates of fish. Can. J. Fish. Aquat. Sci. 58 (2001) 2129-2138
13. Fujiwara M., Kendall B., and Nisbet R. Growth autocorrelation and animal size variation. Ecol. Lett. 7 (2004) 106-113
14. Gudmundsson G. Stochastic growth. Can. J. Fish. Aquat. Sci. 62 (2005) 1746-1755
15. Hinrichsen H.-H., Buehler V., and Clemmesen C. An individual-based model for direct conversion of otolith into somatic growth rates. Fish. Oceanogr. 16 3 (2007) 207-215
16. Imsland A., Jonassen T., Langston A., Hoare R., Wergeland H., FitzGerald R., Mulcahy M., and Stefansson S. The interrelation of growth performance and disease resistance of juvenile Atlantic halibut (hippoglossus hippoglossus L.) from different populations. Aquaculture 204 (2002) 167-177
17. Imsland A., Nilsen T., and Folkvord A. Stochastic simulation of size variation in turbot: possible causes analysed with an individual based-model. J. Fish. Biol. 53 (1998) 237-258
18. Jorgensen C., Enberg K., Dunlop E., Arlinghaus R., Boukal S., Brander K., Ernande K., Gardmark A., Johnston F., Matsumura S., Pardoe H., Raab K., Silva A., Vainikka A., Dieckmann U., Heino M., and Rijnsdorp A. Managing evolving fish stocks. Science 318 (2007) 1247-1248
19. Karlin S., and Taylor H.M. A Second Course in Stochastic Processes (1981), Academic Press Inc. (Harcourt Brace Jovanovich Publishers), New York
20. Kendall B., and Fox G. Variation among individuals and reduced demographic stochasticity. Cons. Biol. 16 1 (2002) 109-116
21. Kooijman S. Dynamic Energy and Mass Budgets in Biological Systems. second ed. (2000), Cambridge University Press, Cambridge, UK
22. Lv Q., and Pitchford J.W. Stochastic von Bertalanffy models, with applications to fish recruitment. J. Theoret. Biol. 244 4 (2007) 640-655
23. Mariani S., Hutchinson W., Hatfield E.M.C., Ruzzante D., Simmonds E.J., Dahlgren T.A.C., Brigham J., Torstensen E., and Carvalho G. Biocomplexity in a highly migratory marine pelagic fish, Atlantic herring. Mar. Ecol. Progr. Ser. 303 (2005) 245-257
24. Mulligan T., and Leaman B. Length-at-age analysis: can you get what you see?. Can. J. Fish. Aquat. Sci. 49 (1992) 632-643
25. Rilling G., and Houde E. Regional and temporal variability in the distribution and abundance of bay anchovy (anchoa mitchilli) eggs, larvae, and adult biomass in the Chesapeake bay. Estuaries 22 (1999) 1096-1109
26. Ruzzante D., Mariani S., Bekkevold D., Andre C., Mosegaard H., Clausen L., Dahlgren T., Hutchinson W., Hatfield E., Torstensen E., Brigham J., Simmonds E., Laikre L., Larsson L., Stet R., Ryman N., and Carvalho G. Biocomplexity in a highly migratory marine pelagic fish, Atlantic herring. Proc. R. Soc. Lond. 273 (2006) 1459-1464
27. Sainsbury K. Effect of individual variability on the von Bertalanffy growth equation. Can. J. Fish. Aquat. Sci. 37 (1980) 241-247
28. Sato K.-I. Lévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics vol. 68 (1999), Cambridge University Press, Cambridge (Translated from the 1990 Japanese original, revised by the author)
29. Sumpter J. Control of growth of rainbow trout (oncorhynchus mykiss). Aquaculture 100 (1992) 299-320
30. Uchmanski J. Individual variability and population regulation: an individual-based model. Oikos 9 (2000) 539-548
31. von Bertalanffy L. A quantitative theory of organic growth. Human Biol. 10 (1938) 181-213
32. von Bertalanffy L. Quantitative laws in metabolism and growth. Quart. Rev. Biol. 32 3 (1957) 217-231
33. Wang Y. Estimating equations for parameters in stochastic growth models from tag-recapture data. Biometrics 55 (1999) 900-903
34. Wang Y., and Thomas M. Accounting for individual variability in the von Bertalanffy growth model. Can. J. Fish. Aquat. Sci. 52 (2003) 1368-1375
35. Weatherley A., and Gill H. The Biology of Fish Growth (1987), Academic Press Inc. (Harcourt Brace Jovanovich Publishers), New York
36. Winters G., and Wheeler J. Clupeoid fishes of the world (suborder clupeioidei). An annotated and illustrated catalogue of the herrings, sardines, pilchards, sprats, shads, anchovies and wolf-herrings. Can. J. Fish. Aquat. Sci. 44 (1987) 882-900