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© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington MSc Student Supervisors : Dr Stephen Hartley, Dr Marcus Frean Victoria.

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Presentation on theme: "© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington MSc Student Supervisors : Dr Stephen Hartley, Dr Marcus Frean Victoria."— Presentation transcript:

1 © Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington MSc Student Supervisors : Dr Stephen Hartley, Dr Marcus Frean Victoria University, Wellington Jim Barritt Using a Random Walk to simulate animal foraging behaviour

2 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 1 Talk outline Background - Field results What is a Random walk? Results so far Future work

3 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 2 Background Part of a project investigating insect foraging interactions (Pieris rapae) Dr. Stephen Hartley, Marc Hasenbank Simulation in conjunction with field studies

4 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 3 Foraging for an Oviposition site Which cabbage ?

5 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 4 Resource concentration ? Is there a relationship between plant density and eggs per plant ? - Concentration: Higher plant density - more information e.g. olfactory cues animals expected to locate easily and remain within dense patches. - Dilution: Animals may encounter widely spread plants more frequently and not remain within dense patches which leads to more eggs per plant on low density plants. - Ideal free distribution: Complete information / access - Depends on patterns of movement Resource concentration Resource dilutionIdeal free distribution

6 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 5 Field results Dilution Concentration Free Distribution

7 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 6 Dilution Concentration Free Distribution Field results - log transformation

8 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 7 Why simulate ? Wide range of existing research modelling behaviour of Pieris rapae - Jones (1970), Cain (1985), Kareiva (???) - Are these a good fit to our field observations? - Validation of current theory Provide a conceptual model to aid interpretation of field data - Use simple model and compare to field data - Reveal intrinsic patterns Asses potential behaviour mechanisms affecting egg distribution - How do the butterflies move ?

9 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 8 Quantifying movement paths Start Animal moves continuously in space

10 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 9 Quantifying movement paths Start Sample location in space over time 1 2 3 4 5 6 7 8

11 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 10 Quantifying movement paths Start Join the dots to create Steps - an abstraction of the real path

12 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 11 Quantifying movement paths Start Measurements

13 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 12 Random walks Can use same parameters to recreate paths in a simulation Do an example of a simple random walk Pure random vs Correlated random Parameters A and L

14 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 13 Random walks - correlated moves Do an example of a simple random walk Pure random vs Correlated random Parameters A and L

15 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 14 Simulation Demonstration with simple layout Experimental layout - Same as the field layout Parameters Results

16 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 15 Simulation in action - Step 0 L=10 A=20

17 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 16 Simulation in action - Step 1 L=10 A=20

18 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 17 Simulation in action - Step 2 L=10 A=20

19 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 18 Simulation in action - Step 3 L=10 A=20

20 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 19 Simulation in action - Step 4 L=10 A=20

21 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 20 Simulation in action - Step 6 L=10 A=20

22 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 21 Simulation in action - Step 8 L=10 A=20

23 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 22 Simulation in action - Step 10 L=10 A=20

24 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 23 Simulation in action - Step 11 L=10 A=20

25 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 24 Simulation in action - Step 12 (End) L=10 A=20

26 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 25 Experimental layout

27 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 26 Experiment Parameters L = Step Length (0.5m to 2m) A = SD Angle of turn (20 to 100 degrees) 10, 000 butterflies 10 replicates Published: Root(xxxx) - A - 90 degrees - L - Varies

28 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 27 Simulation Results

29 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 28 Simulation Results

30 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 29 Results Simulation vs Field

31 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 30 Results Simulation vs Field

32 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 31 Results Log Linear Regression Dilution Concentration Free Distribution

33 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 32 Results Log Linear Regression Dilution Concentration Free Distribution

34 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 33 Statistical tests Chi Squared to compare egg distributions - All significantly different to field (p<0.001) Log Linear regression analysis to compare slope of response - No significant differences to field - All show resource dilution

35 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 34 Conclusions Observed resource dilution - In both simulation and field results Simple random walk does not represent field results exactly - Saw change in effect for lower step length - Change parameters - Change behaviour algorithm - More than 1 egg - Space agents

36 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 35 Future Work Deterministic attraction - Force of attraction (similar to gravity) - Perceptual ranges - Information gradients / matrix Random walk influenced by Environment - Move length and Angle of turn as functions of information gradients Lifecycle: migration, multiple eggs and birth Multi species - Co-existance? Different responses at different scales?

37 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 36 Acknowledgements Thanks to - Dr Stephen Hartley - Dr Marcus Frean - Marc Hasenbank - Victoria University Bug Group - Special thanks to John Clark and the staff of Woodhaven Farm (Levin) http://www.oulu.fi/

38 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 37 Questions ? Simulation of insect foraging - Random Walks - Observed similar trends to field data Future work - Include deterministic attraction - Can we observe different responses at different scales ? jim@planet-ix.com

39 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 38 References Aldrich, J. (1997). R.A. Fisher and the making of maximum likelihood 1912-1922. Statistical Science 12, pp.162-176. Bukovinszky, T., R. P. J. Potting, Y. Clough, J. C. van Lenteren, and L. E. M. Vet. (2005). The role of pre- and post-alighting detection mechanisms in the responses to patch size by specialist herbivores. Oikos 109, pp. 435-446. Byers, J. A. (2001). Correlated random walk equations of animal dispersal resolved by simulation. Ecology 82, pp.1680-1690. Cain, M. L. (1985). Random Search by Herbivorous Insects: A Simulation Model. Ecology 66, pp. 876-888. Finch, S., and R. H. Collier. (2000). Host-plant selection by insects - a theory based on 'appropriate/inappropriate landings' by pest insects of cruciferous plants. Entomologia Experimentalis Et Applicata 96, pp. 91-102. Fretwell, S. D., and H. L. Lucas. (1970). On territorial behaviour and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, pp. 16-36. Grez, A. A., and R. H. Gonzalez. (1995). Resource Concentration Hypothesis - Effect of Host-Plant Patch Size on Density of Herbivorous Insects. Oecologia 103, pp. 471-474. Holmgren, N. M. A., and W. M. WGetz. (2000). Evolution of host plant selection in insect under perceptual constraints: A simulation study. Evolutionary Ecology Research 2, pp. 81-106. Jones, R. E. (1977). Movement Patterns and Egg Distribution in Cabbage Butterflies. The Journal of Animal Ecology 46, pp. 195-212. Olden, J. D., R. L. Schooley, J. B. Monroe, and N. L. Poff. ( 2004). Context-dependent perceptual ranges and their relevance to animal movements in landscapes. Journal of Animal Ecology 73, pp. 1190-1194. Otway, S. J., A. Hector, and J. H. Lawton. (2005). Resource dilution effects on specialist insect herbivores in a grassland biodiversity experiment. Journal of Animal Ecology 74, pp. 234-240. Root, R. B. (1973). Organization of a Plant-Arthropod Association in Simple and Diverse Habitats: The Fauna of Collards (Brassica Oleracea). Ecological Monographs 43, pp. 95-124. Tilman, D., and P. M. Kareiva. (1997). Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. Monographs In Population Biology 30

40 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 39

41 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 40 Correlated Random Walk


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