Moving on: modelling marine fish movements in relation to environment

Transcription

1 Moving on: modelling marine fish movements in relation to environment David Sims Marine Biological Association, Plymouth, UK Annual Science Meeting Liverpool 1-3 June 2009

2 Theme 6: Science for Sustainable Marine Resources MBA Contribution: Integrating individual to population processes in a changing marine environment WP 6.9 (MBA) - Examining regional differences in fish movements, behaviour and population structure People involved: David Sims, Martin Genner Nicolas Humphries, Matthew McHugh, Nuno Queiroz, Nicolas Pade Victoria Wearmouth, Jenny Dyer, Steve Cotterell Andrew Griffiths, Aliya El Nagar David Righton, Victoria Quayle (Cefas, Lowestoft)

3 W.P 6.9 Examining regional differences in fish movements, behaviour and population structure D6.9.1 Identify movement patterns of marine fish in relation to environment Determine movements: environment & scale Short- to long term functional distributions linked to environment Patterns: habitat selection, functional space use Understand population spatial dynamics Relevant to: parameterisation of spatially-structured fish population models Most use Random Motion, e.g. Guénette et al. (2000) Bull. Mar. Sci. 66,

4 Specialised random walks: Lévy flight Special class of random walk with displacements drawn from a probability distribution with a power law tail (the so-called Pareto-Lévy distribution) P(l j ) ~ l j -μ with 1 < μ 3 where l j is the flight length (move step length) μ the power law (Lévy) exponent Many small steps separated by longer jumps, with this pattern repeated at all scales Give rise to stochastic processes closely linked to fractal geometry and anomalous diffusion phenomena superdiffusion Shlesinger & Klafter 1985, 1993 Nature; Viswanathan et al Nature

5 Specialised random walks: Lévy flight Special class of random walk with displacements drawn from a probability distribution with a power law tail (the so-called Pareto-Lévy distribution) P(l j ) ~ l j -μ with 1 < μ 3 where l j is the flight length (move step length) μ the power law (Lévy) exponent Brownian motion, random walk Many small steps separated by longer jumps, with this pattern repeated at all scales Give rise to stochastic processes closely linked to fractal geometry and anomalous diffusion phenomena superdiffusion Shlesinger & Klafter 1985, 1993 Nature; Viswanathan et al Nature

6 Specialised random walks: Lévy flight Special class of random walk with displacements drawn from a probability distribution with a power law tail (the so-called Pareto-Lévy distribution) P(l j ) ~ l j -μ with 1 < μ 3 where l j is the flight length (move step length) μ the power law (Lévy) exponent Many small steps separated by longer jumps, with this pattern repeated at all scales Give rise to stochastic processes closely linked to fractal geometry and anomalous diffusion phenomena superdiffusion Shlesinger & Klafter 1985, 1993 Nature; Viswanathan et al Nature

7 How might chances be maximised when knowledge is incomplete? Lévy flight foraging hypothesis Viswanathan et al Nature Lévy flights: most efficient search for locating sparsely distributed prey Optimal search: Lévy exponent of μ 2 Hypothesis: organisms evolved to exploit optimal Lévy flight search patterns μ = 1.75 μ = 2.0 μ = 2.5

8 Fine-scale vertical movement at the long-term limit Lévy walk (flight) P(l j ) ~ l j -μ with 1 < μ 3 μ opt ~ 2.0 Sims, Righton, Pitchford (2007) J. Anim. Ecol. 76: Sims et al. (2008) Nature 451:

9 Do marine predators show Lévy-like patterns? Assembled large dataset: 1.2 million move steps of 31 individuals from 7 species Collaborators: Mike Musyl (Hawaii), Corey Bradshaw (Adelaide), Jon Pitchford (York), Alex James (Canterbury, NZ), Andy Brierley (St Andrews), Dave Morritt (London), Rory Wilson, Emily Shepard & Graeme Hays (Swansea), Dave Righton & Julian Metcalfe (Lowestoft)

10 Lévy-like scaling laws of predator movement and prey densities Log 10 N(x) (normalised frequency) Log 10 x (move step, m) Sims, D.W. et al. (2008) Nature 451,

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12 Are there general principles? Assembled new dataset: 12 million move steps, 55 individuals, 14 species, 5700 days Whale shark Basking shark Blue shark Porbeagle shark Bigeye thresher shark Mako shark Silky shark Oceanic white tip shark Bigeye tuna Yellowfin tuna Swordfish Blue marlin Black marlin Ocean sunfish Collaborators: Mike Musyl (Hawaii), Kurt Schaefer (La Jolla), Juerg Brunnschweiler (Zurich), Tom Doyle (Cork), Jon Houghton (Belfast), Graeme Hays (Swansea), Cathy Jones & Les Noble (Aberdeen)

13 Projection of 3D movements to 2D What will be the observed distribution of move steps be when 3D movement is projected into some fixed vertical 2D plane? Organism follows a Lévy flight in 3D, then the distribution of projected move steps is α α 1 x Γ( α / 2) h( x) = xmin xmin π Γ(( α + 1) / 2) provided x x min and where Γ(.) is the standard gamma function and is independent of x. Therefore, the projected move step distribution follows a power law with an unchanged exponent at all scales greater than the minimum move step x min. Sims, D.W. et al. (2008) Nature 451,

14 Model movements using specialised random walks entrained by temperature and population abundance centre Multiple centres reflect population structure/components Simulated pelagic fish tracks

15 GPS & Argos Fish and human predator overlap: map & quantify interaction strength

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