Evolutionary optimality in stochastic search problems

Journal of the Royal Society Interface

Volumn 7, Issue 50, 2010, Pages 1301-1310

  Preston, Mark D ^a   Pitchford, Jonathan W ^a   Wood, A Jamie ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

Evolution; Fish recruitment; L vy flights; Optimal foraging; Stochastic models

Indexed keywords

BIOLOGY; ECOLOGY; FUNCTION EVALUATION; OPTIMIZATION; POPULATION DYNAMICS; STOCHASTIC SYSTEMS;

COMPUTATIONAL MODEL; ECOLOGICAL SCENARIOS; ENVIRONMENTAL STOCHASTICITY; EVOLUTION; FITNESS FUNCTIONS; HEAVY-TAILS; LEVEL CHARACTERISTIC; OPTIMAL FORAGING; OPTIMALITY; STOCHASTIC SEARCH;

STOCHASTIC MODELS;

ARTICLE; EVOLUTION; OPTIMAL FORAGING; STOCHASTIC MODEL; VARIANCE;

EID: 77956583079     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2010.0090     Document Type: Article

References (31)

1. Bartumeus, F., Catalan, J., Fulco, U. L., Lyra, M. L. & Viswanathan, G. M. 2002 Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. Phys. Rev. Lett. 88, 097901. (doi:10.1103/ PhysRevLett.88.097901)
2. Benhamou, S. 2007 How many animals really do the Lévy walk? Ecology 88, 1962-1969. (doi:10.1890/06-1769.1)
3. Burrow, J. F., Baxter, P. D. & Pitchford, J. W. 2008 Lévy processes, saltatory foraging, and superdiffusion. Math. Model. Nat. Phenom. 3, 115-130. (doi:10.1051/mmnp:2008060)
4. Chambers, R. C. & Trippel, E. A. 1997 Early life history and recruitment in fish populations. London, UK: Chapman & Hall.
5. Codling, E. A. 2008 Individual-based movement behaviour in a simple marine reserve fishery system: why predictive models should be handled with care. Hydrobiologica 606, 55-61. (doi:10.1007/s10750-008-9345-9)
6. Codling, E. A., Plank, M. J. & Benhamou, S. 2008 Random walk models in biology. J. R. Soc. Interface 5, 813-834. (doi:10.1098/rsif.2008.0014)
7. Currey, J. D., Pitchford, J. W. & Baxter, P. D. 2007 Variability of the mechanical properties of bone and its evolutionary consequences. J. R. Soc. Interface 4, 127-135. (doi:10.1098/rsif.2006.0166)
8. Darwin, C. R. 1859 The origin of the species. London, UK: John Murray.
9. Durham, W. M., Kessler, J. O. & Stocker, R. 2009 Disruption of vertical motility by shear triggers formation of thin phytoplankton layers. Science 323, 1067-1070. (doi:10.1126/science.1167334)
10. Dytham, C. & Simpson, S. D. 2007 Evolutionary models of active movement by larval coral reef fishes in response to mortality rates on the reef. Mar. Ecol. Prog. Ser. 346, 255-264. (doi:10.3354/meps07039)
11. Edwards, A. M. 2008 Using likelihood to test for Lévy flight search patterns and for general power-law distributions in nature. J. Animal Ecol. 77, 1212-1222. (doi:10.1111/j.1365-2656.2008.01428.x)
12. Edwards, A. M. et al. 2007 Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature 449, 1044-1047. (doi:10.1038/nature06199)
13. James, A., Plank, M. J. & Brown, R. 2008 Optimizing the encounter rate in biological interactions: ballistic versus Lévy versus Brownian strategies. Phys. Rev. E 78, 051128. (doi:10.1103/PhysRevE.78.051128)
14. James, A., Pitchford, J. W. & Plank, M. J. In press. Efficient or inaccurate? Analytical and numerical modelling of random search strategies. Bull. Math. Biol. (doi:10.1007/s11538-009-9473-z)
15. Kopelman, R. 1988 Fractal reaction kinetics. Science 241, 1620-1626. (doi:10.1126/science.241.4873.1620)
16. Minto, C., Myers, R. A. & Blanchard, W. 2008 Survival variability and population density in fish populations. Nature 452, 344-348. (doi:10.1038/nature06605)
17. Pitchford, J. W. & Brindley, J. 2001 Prey patchiness, predator survival and fish recruitment. Bull. Math. Biol. 63, 527-546. (doi:10.1006/bulm.2001.0230)
18. Pitchford, J. W., James, A. & Brindley, J. 2003 Optimal foraging in patchy turbulent environments. Mar. Ecol. Prog. Ser. 256, 99-110. (doi:10.3354/meps256099)
19. Pitchford, J. W., James, A. & Brindley, J. 2005 Quantifying the effects of individual and environmental variability in fish recruitment. Fish. Oceanogr. 14, 156-160. (doi:10.1111/j.1365-2419.2004.00299.x)
20. Pitchford, J. W., Codling, E. A. & Psarra, D. 2007 Uncertainty and sustainability in fisheries and the benefit of marine protected areas. Ecol. Model. 207, 286-292. (doi:10.1016/j.ecolmodel.2007.05.006)
21. Plank, M. J. & James, A. 2008 Optimal foraging: Lévy pattern or process? J. R. Soc. Interface 5, 1077-1086. (doi:10.1098/rsif.2008.0006)
22. Real, L. A. 1980 Fitness, uncertainty, and the role of diversification in evolution and behaviour. Am. Nat. 115, 623-638. (doi:10.1086/283588)
23. Sims, D. W., Righton, D. & Pitchford, J. W. 2007 Minimizing errors in identifying Lévy flight behaviour of organisms. J. Animal Ecol. 76, 222-229. (doi:10.1111/j.1365-2656.2006.01208.x)
24. Sims, D. W. et al. 2008 Metcalfe: scaling laws of marine predator search behaviour. Nature 451, 1098-1102. (doi:10.1038/nature06518)
25. Steinke, M., Stefels, J. & Stamhuis, E. J. 2006 Dimethyl sulfide triggers search behavior in copepods. Limnol. Oceanogr. 51, 1925-1930.
26. Viswanathan, G. M., Buldyrev, S. V., Havlin, S., da Luz, M. G. E., Raposo, E. P. & Stanley, H. E. 1999 Optimizing the success of random searches. Nature 401, 911-914. (doi:10.1038/44831)
27. Viswanathan, G. M., Afanasyev, V., Buldyrev, S. V., Havlin, S., da Luz, M. G. E., Raposo, E. P. & Stanley, H. E. 2000 Lévy flights in random searches. Physica A 282, 1-12. (doi:10.1016/S0378-4371(00)00071-6)
28. Wood, A. J. & Ackland, G. J. 2007 Evolving the selfish herd: emergence of distinct aggregating strategies in an individual-based model. Proc. R. Soc. B 274, 1637-1642. (doi:10.1098/rspb.2007.0306)
29. Yoshimura, J. & Clark, C. W. 1991 Individual adaptations in stochastic environments. Evol. Ecol. 5, 173-192. (doi:10.1007/BF02270833)
30. Yoshimura, J. & Shields, W. M. 1987 Probabilistic optimization of phenotype distributions: a general solution for the effects of uncertainty on natural selection. Evol. Ecol. 1, 125-138. (doi:10.1007/BF02067396)
31. Zollner, P. A. & Lima, S. L. 1999 Search strategies for landscape-level interpatch movements. Ecology 80, 1019-1030. (doi:10.1890/0012-9658(1999)080[1019:SSFLLI]2.0.CO;2)