© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington MSc Student Supervisors : Dr Stephen Hartley, Dr Marcus Frean Victoria University, Wellington Jim Barritt Combining random search and deterministic attraction in simulations of animal foraging behaviour

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 1 Talk Outline Background Field results Simulation Random walks Simulation Results Future work

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 2 Background Project investigating effects of scale on egg distributions of Pieris rapae Dr. Stephen Hartley, Marc Hasenbank Simulation alongside field studies

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 3 Foraging for an oviposition site Which cabbage ?

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 4 Resource concentration ? Measure how many eggs per plant are laid Correlation between plant density and eggs per plant BUT … Density depends on scale … Resource concentration Resource dilutionIdeal free distribution

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 5 Density depends on scale 10 m 1 plant 20 plants, density = 0.2 plants / m 2

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 6 Density Depends on scale 30 m 1 plant 54 plants, density = 0.06 plants / m 2

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 7 Density Depends on scale 432 plants, density = plants / m 2 90 m 1 plant

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 8 Research Question Resource concentration Resource dilutionIdeal free distribution Can we observe different responses to plant density at different scales of measurement ?

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 9 Field results Observe resource dilution

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 10 Are there theoretical movement patterns that show different responses to scale? Provide a Null model to aid interpretation of field data Asses potential mechanisms affecting egg distribution Explore multi species / generation interactions Why Simulate ?

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 11 Simulation methods Random walkers - Simple and widely used - Abstraction of continuous movement Deterministic attraction - Perception - Information gradients / matrix Random walk influenced by environment - Parameters of Random Walk - Environmental feedback

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 12 Random Walks A L

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 13 Correlated Random walks Angle of turn drawn from a normal distribution Creates a more directional path than pure random Cain (1986), Byers (2001)

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 14 Simulation In Action - Step 0

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 15 Simulation In Action - Step 1

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 16 Simulation In Action - Step 2

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 17 Simulation In Action - Step 3

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 18 Simulation In Action - Step 4

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 19 Simulation In Action - Step 6

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 20 Simulation In Action - Step 8

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 21 Simulation In Action - Step 10

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 22 Simulation In Action - Step 11

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 23 Simulation In Action - Step 12

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 24 Simulation Experiment Parameters - A = Angle of turn (20 to 100 degrees) - L = Step Length (0.5m to 2m) - 10, 000 butterflies - 10 replicants - Densities 6x6m 1x1m

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 25 Results Simulation vs Field

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 26 Results Log Linear Regression

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 27 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 2005School of Biological Sciences, Victoria University, Wellington 28 Conclusions Observed resource dilution - In both simulation and field results Simple random walk does not represent field results exactly Shows no significant difference of responses in gradient of dilution

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 29 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 Can we produce changes at different scales? Lifecycle: migration and birth Multi species - Co-existance?

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 30 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 2005School of Biological Sciences, Victoria University, Wellington 31 Questions ? Simulation of insect foraging - Random Walks Observed similar trends to field data - Further refinement of model - Include deterministic attraction - Can we observe different responses at different scales ?

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 32 Appendix 1

© Jim Barritt 2005School of Biological Sciences, Victoria University, Wellington 33