© 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

© 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

© 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

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

© 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

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

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

© 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 ?

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

© Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 9 Quantifying movement paths Start Sample location in space over time

© 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

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

© 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

© 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

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

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

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

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

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

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

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

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

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

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

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

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

© 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

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

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

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

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

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

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

© 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

© 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

© 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?

© 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)

© 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 Barritt 2006School of Biological Sciences, Victoria University, Wellington 38 References Aldrich, J. (1997). R.A. Fisher and the making of maximum likelihood Statistical Science 12, pp 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 Byers, J. A. (2001). Correlated random walk equations of animal dispersal resolved by simulation. Ecology 82, pp Cain, M. L. (1985). Random Search by Herbivorous Insects: A Simulation Model. Ecology 66, pp 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 Fretwell, S. D., and H. L. Lucas. (1970). On territorial behaviour and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, pp 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 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 Jones, R. E. (1977). Movement Patterns and Egg Distribution in Cabbage Butterflies. The Journal of Animal Ecology 46, pp 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 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 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 Tilman, D., and P. M. Kareiva. (1997). Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. Monographs In Population Biology 30

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

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