Lévy flights and the search behaviour of marine top predators
David Sims Marine Biological Association Laboratory, Plymouth, UK & Biological Sciences, University of Plymouth, UK Royal Society, 2006
Collaborators Julian Metcalfe, David Righton (Cefas, Lowestoft) Graeme Hays, Rory Wilson (University of Wales Swansea) David Morritt (U. London) MBA Behavioural Ecology Research Group Corey Bradshaw (Adelaide, Australia) Leader: David Sims Anthony Richardson (U. Queensland, Australia) Emily Southall, Viki Wearmouth, Steve Cotterell, Nick Mohammed Z. Ahmed (U. Plymouth) Humphries, Andrew Griffiths, Matt McHugh, Josh Filer, Andy Brierley (U. St Andrews) Jenny Dyer, Joel Kimber, Nuno Queiroz, Nick Pade, Jon Pitchford (U. York), Alex James (U. Canterbury, NZ) Chrysoula Gubili, Tristan Guttridge, Edd Brooks (in Mike Musyl (U. Hawaii, USA), Kurt Schaefer (IATTC La Jolla) Bahamas), Zoe Brooke, John Rundle, Pete Rendle Mark Hindell (U. Tasmania), John Stevens (CSIRO, Hobart) & EUTOPIA partners Biological search problem
How to find objects at unknown locations
For hunters - what search strategy to employ:
• To maximise likelihood of encounter rate • In environments that are complex, heterogeneous • With incomplete knowledge
Deterministic - probabilistic Fine-scale clues…
Video clip: Owen Bruce, Save Our Seas Foundation Geographical scale…
Mucientes et al, & Sims (2009) Biol. Lett. 5, 156-159 See Nature Research Highlights
0.5 m SearchSearch decisionsdecisions
Movements ??
Resource
time Empirical Approach
Fully aquatic marine predators are useful model species to test such ideas
•Prey – extreme spatio-temporal variability
•Seawater medium reduces detection distances
•Incomplete knowledge over large range of meso-scales
•Prey fields can be measured, in some cases
•Large predators, risk of predation lower
•But, predator movements largely hidden from direct observation QuestionsQuestions aboutabout searchsearch behaviourbehaviour
(1) What are the patterns of prey abundance and distribution?
(2) What movements do predators show in relation to different prey densities?
(3) How might chances be maximised when knowledge is incomplete?
(4) Are there general principles? Basking shark Cetorhinus maximus
Zooplankton: copepods, crab zoea, fish eggs, fish larvae… 1. What are the patterns of prey abundance and distribution?
Variability in zooplankton abundance Zooplankton: sparsely distributed, high- density micro patches
20 18 16 14 12
10 8 6 4 Zooplankton abundance(g/m3) 2 0 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 Days
Sims & Quayle (1998) Nature 393: 460-464 2. What movements do predators show in relation to different prey densities?
Fine-scale foraging movements
Intensive and extensive movements
Shark tracks
Zooplankton density (g m-3)
Sims & Quayle (1998) Nature 393: 460-464 Sims (1999) Proc. R. Soc. B 266: 1437-1443 Sims et al. (2006) Proc. R. Soc. B 273: 1195-1201 Remain in rich patches that are transported by tidal currents
Group-feeding track
Current direction and speed
Sims & Quayle (1998) Nature 393: 460-464 Decline in patch density
4
) 3.5 -3 3
2.5
2
1.5
1
Zooplankton density (g m 0.5
0 0 100 200 300 400 Time (h) Sims (1999) Proc. R. Soc. B Sims (1999) Proc. R. Soc. B 266: 1437-1443 Swimming speed increases in low zooplankton densities and at the threshold level….feeding stops
1.4 ) -1 1.2
1* Feeding 0.8
0.6
0.4 Swimming speed (m s (m speed Swimming 0.2 Non-feeding 0123Threshold
-3 * mean cruising Zooplankton density (g m ) speed
Sims (1999) Proc. R. Soc. B 266: 1437-1443 Plymouth, U.K.
1
2
Front
SST AVHRR satellite image: NERC RSDAS Sims (2008) Adv. Mar. Biol. 54, 171-220 Sims & Quayle (1998) Nature 393, 464600-464 Optimal foraging and the Lévy flight hypothesis
How do open organisms find sparsely distributed, ephemeral prey?
Random searching is more effective if the movement step lengths follow an inverse power law : ‐μμ Where 1 < μ ≤ 3 ‐ and is optimised when μ = 2.0 PP((ll)) ~~ ll i.e. New prey patch encounters are maximised
Hypothesised organisms evolved to exploit optimal Lévy flight search patterns
Simple Lévy random walk Lévy random walk Lévy random walk random walk μ = 2.0 μ = 1.5 μ = 3.0
Shlesinger & Klafter 1986, 1993; Viswanathan et al. 1996 Nature 381:413-415; 1999 Nature 401:911-914 Lévy flight foraging hypothesis by 2007: much empirical support…
Microbes, zooplankton, bumblebees, deer, jackals, seals, monkeys, even humans (fishing boats, hunter-gatherers)…
Everywhere researchers looked they found Lévy patterns…
A new principle in ecology; a universal law? What about the large-scale movements of oceanic predators? Tracking behaviour Satellite-linked data loggers Argos satellite transmitters Mobile telephone tags Video clip: Emily Southall, MBA 31 Oct 7 Aug 15 Aug 28 Jul 11 Jul 11 Aug
5 Jan 24 May 1 Aug 18 Jul 22 Jun 10 Oct
1 Jun 24 Nov Basking shark
Blue shark
Porbeagle shark CPR- derived prey field (copepod)
Sims et al. (2006) Proc. R. Soc. B 273: 1195-1201 Testing success of movement structure
‘Prey landscape’
Sims et al. (2006) Proc. R. Soc. B. 273, 1195-1201 Testing success of movement structure
‘Prey landscape’ biomass time
Sims et al. (2006) Proc. R. Soc. B. 273, 1195-1201 Compare real sharks with random ‘walking’ model sharks
200
150 100 50 Frequency 0 200 300 400 500 600
Zooplankton (mg g-3)
Real shark Model shark
Sims et al. (2006) Proc. R. Soc. B. 273, 1195-1201 Ocean sunfish Mola mola
Towed Fastloc GPS-Argos transmitter for high spatial accuracy tracks (24 - 64 m)
Sims et al. (2009) PLoS One 4: e7351 Bradshaw, Sims, Hays (2007) Ecol. Applic. 453: 714-716 1 0
50
100
150
200 May 24 Jun 1 Jun 8 Jun 15 Jun 22 Jun 29 Jul 6 Jul 13 Jul 20 Jul 27 ArchivalArchival depthdepth datadata 2 0
50
100
150
200 Jun Jul Aug Sep Oct Nov • Spatially accurate pressure sensor 3 0 50
100
150 • High frequency (down to 1 Hz)
200 Jul 31 Aug 7 Aug 14 Aug 21 Aug 28 Sep 4 Sep 11 Sep 18 Depth,Depth,Depth, m m m 4 0 50 • Long-term records at high frequency 100
150 (weeks to months)
200 Aug Sep Oct Nov Dec Jan Feb
5 0 20 • Sample a move distribution thoroughly 40 60 with very few gaps 80 100 Jun 18 Jun 19 Jun 20 Jun 21 Jun 22 Jun 23 Jun 24 6 0 20 • Good data for testing Lévy flight 40 60 80 hypothesis 100 Jun 1 Jun 7 Jun 14 Jun 21 Jun 28
Date Fine-scale vertical movement at the long-term limit
Lévy walk (flight) -μ P(lj) ~ lj with 1 < μ ≥ 3 μopt ~ 2.0
Sims, Righton, Pitchford (2007) J. Anim. Ecol. 76: 222-229 Sims et al. (2008) Nature 451: 1098-1102. 4. Are there general principles?
Assembled large dataset: 1.2 million move steps of 31 individuals from 7 species
0
50 Depth (m)
1st June 8th June 15th June 22nd June 29th June
0 50 100 150 Depth (m)
24th May 7th June 21st June 5th July 18th July 30th July
0 50 100
Depth (m) 150 195 25th May 29th June 2nd Aug 6th Sept 11th Oct 14th Nov Tested for Lévy patterns
Scaling laws of search behaviour among fish x) (normalised ( N frequency) 10 Log
Log10 x (move step, m)
Sims, D.W. et al. (2008) Nature 451: 1098-1102. Graeme Hays Swansea University Rory Wilson Swansea University Scaling laws among marine predators x) (normalised ( N frequency) 10 Log
Log10 x (move step, m)
Sims, D.W. et al. (2008) Nature 451, 1098-1102. What about prey patterns?
Sims, D.W. et al. (2008) Nature 451, 1098-1102. Data from Andy Brierley Scaling laws among marine predators and prey… x) (normalised ( N frequency) 10 Log
Log10 x (move step, m)
Sims, D.W. et al. (2008) Nature 451, 1098-1102. Scaling laws among marine predators but not a juvenile shark… x) (normalised ( N frequency) 10 Log
Log10 x (move step, m)
Sims, D.W. et al. (2008) Nature 451, 1098-1102.
Lévy flight foraging hypothesis by 2007: much empirical support…
Microbes, zooplankton, bumblebees, deer, jackals, seals, monkeys, even humans (fishing boats, hunter-gatherers)…
Everywhere researchers looked they found Lévy patterns…
A new principle in ecology; a universal law?
Sims et al. (Mar, 2007) J. Anim. Ecol. Edwards et al. (Oct, 2007) Nature Newman (2005) Contemporary Physics Clauset et al. (2007) arXiv.0706.1062v1 White et al. (2008) Ecology 89: 905-912 Complex movements in relation to environment: single pattern may not dominate
Frontal Stratifed r DVM ‘switch’ n DVM 4. 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 whitetip shark
Bigeye tuna Yellowfin tuna
Swordfish Blue marlin Black marlin
Ocean sunfish
Collaborators: Mike Musyl (Hawaii), Kurt Schaeffer, Dan Fuller (La Jolla), Juerg Brunnschweiler (Zurich), Graeme Hays (Swansea), Tom Doyle (Cork), Jon Houghton (Belfast), Cathy Jones, Les Noble (Aberdeen)
Silky shark Truncated Pareto (power law) distribution
3.5 Silky 46588M
3
2.5 22 Observed 2 Hypothesised
21 1.5 MLE μ = 1.97 Log10(Rank) 1 X = 5.379 20 min X = 156.0 0.5 max
19 0
0 0.5 1 1.5 2 2.5 Log10(step length) 18
Latitude (deg N) 0 17 20 Time (in 15 min intervals)
40 16 60
15 80 Depth (m) 100
120 14 204 203 202 201 200 199 198 197 196 195 194 140 Longitude (deg W) 160
180 Track data from Mike Musyl (Hawaii)
)
) shows shows
) ) longimanus longimanus patterns patterns
falciformis falciformis forager? forager?
Carcharhinus Carcharhinus ( (
movement movement
tip optimum tip optimum
Carcharhinus Carcharhinus an an ( (
white white diverse diverse
shark shark
Silky Silky Oceanic Oceanic
of of well well
as as diversity diversity 34
species species individuals individuals
values μ 2 within
μ within
between between
considerable considerable
and and Species show show
1
patterns patterns between between
results results as as
0 The The movement movement Considerable diversity in patterns Mako Sunfish Swordfish Porbeagle Blue shark Silky shark Blue marlin Bigeye tuna Black marlin Whale shark Yellowfin tuna Basking shark Bigeye thresher Oceanic whitetip shark More reasons for diversity: Diel vertical migration masks foraging movements
Species μ values
Bigeye thresher
Blue marlin
Black marlin
Swordfish
0 1 2 34 μ
Swordfish a
Bigeye thresher b Depth Black marlin c
Blue marlin d Time (approx 12 days in each case)
The long step lengths caused by diel vertical migration result in lower exponents • Pelagic predators show complex movements
• Some patterns consistent with Lévy flight foraging hypothesis
• Not universal under all conditions; diverse patterns within and between spp
• Interspersing of random and Lévy processes?
Key questions: Are Lévy movements adaptive or an emergent property? Have they evolved? If so, when?
Sims Lab Funding: NERC Oceans 2025, NERC Responsive mode, DEFRA, Leverhulme Trust, The Royal Society, FSBI, Esmée Fairbairn Foundation, SOS Foundation, FCT Portugal, US Nat Geo Society, English Nature, EUTOPIA & EuroCoML