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Supervised and helped by Dr Stephen Hartley, Dr Marcus Frean, Marc Hasenbank Victoria University, Wellington Jim Barritt © Jim Barritt 2006School of Biological.

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Presentation on theme: "Supervised and helped by Dr Stephen Hartley, Dr Marcus Frean, Marc Hasenbank Victoria University, Wellington Jim Barritt © Jim Barritt 2006School of Biological."— Presentation transcript:

1 Supervised and helped by Dr Stephen Hartley, Dr Marcus Frean, Marc Hasenbank Victoria University, Wellington Jim Barritt © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington Using a Random Walk to simulate the foraging behaviour of Pieris rapae http://www.oulu.fi/

2 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 1 Talk outline Background Theory Simulation Results Conclusion / Future work http://www.oulu.fi/

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 - Session 15 - Egg laying on patchy resources and the importance of spatial scale Simulation in conjunction with field studies

4 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 3 Theory - the Oviposition Question Which cabbage ? Pieris rapae

5 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 4 Theory - Resource concentration ? Is there a relationship between eggs per plant and plant density ? - Concentration: Higher plant density should provide more information (e.g. olfactory cues) so animals are expected to locate dense patches easily and remain within them. This would lead to more eggs per plant on high density patches - Root (1973) - Dilution: Foraging animals may not remain in high density stands, instead moving around at a constant rate irrespective of plant density. This produces more eggs per plant on low density plants or egg spreading behaviour - Yamamura (1999) - Ideal free distribution: Complete information / access leads to the eggs being distributed evenly - Depends on patterns of movement Resource concentration Resource dilution Ideal free distribution Low DensityHigh Density

6 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 5 Theory - Resource concentration ? Is there a relationship between eggs per plant and plant density ? - Concentration: Higher plant density should provide more information (e.g. olfactory cues) so animals are expected to locate dense patches easily and remain within them. This would lead to more eggs per plant on high density patches - Root (1973) - Dilution: Foraging animals may not remain in high density stands, instead moving around at a constant rate irrespective of plant density. This produces more eggs per plant on low density plants or egg spreading behaviour - Yamamura (1999) - Ideal free distribution: Complete information / access leads to the eggs being distributed evenly - Depends on patterns of movement Resource concentration Resource dilution Ideal free distribution Low DensityHigh Density

7 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 6 Theory - Resource dilution ? Is there a relationship between eggs per plant and plant density ? - Concentration: Higher plant density should provide more information (e.g. olfactory cues) so animals are expected to locate dense patches easily and remain within them. This would lead to more eggs per plant on high density patches - Root (1973) - Dilution: Foraging animals may not remain in high density stands, instead moving around at a constant rate irrespective of plant density. This produces more eggs per plant on low density plants or egg spreading behaviour - Yamamura (1999) - Ideal free distribution: Complete information / access leads to the eggs being distributed evenly - Depends on patterns of movement Resource concentration Resource dilution Ideal free distribution High DensityLow Density

8 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 7 Theory - Ideal free distribution ? Is there a relationship between eggs per plant and plant density ? - Concentration: Higher plant density should provide more information (e.g. olfactory cues) so animals are expected to locate dense patches easily and remain within them. This would lead to more eggs per plant on high density patches - Root (1973) - Dilution: Foraging animals may not remain in high density stands, instead moving around at a constant rate irrespective of plant density. This produces more eggs per plant on low density plants or egg spreading behaviour - Yamamura (1999) - Ideal free distribution: Complete information / access leads to the eggs being distributed evenly It depends on patterns of movement Resource concentration Resource dilution Ideal free distribution

9 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 8 Simulation Two seasons of field observations (Marc Hasenbank) How do patterns of movement create the observed response ? - Published simulations: Jones (1977), Cain (1985), Byers (2001) - Random vs force of attraction (incorporate perceptual information?) How do we simulate ? - Quantify movement paths - Create conceptual model - what is a random walk ? - Run simulation experiment!

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

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

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

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

14 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 13 Random walks - Step 1 We can simulate the path: - Choose θ (angle of turn) at random (+/- 180°) - Move 1 step length in that direction... +90° 0° -90° +/-180°

15 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 14 Random walks - Step 2 We can simulate the path: - Choose θ (angle of turn) at random (+/- 180°) - Move 1 step length in that direction - Repeat +90° 0° -90° +/-180°

16 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 15 Random walks - Step 3 We can simulate the path: - Choose an heading at random (+/- 180°) - Move 1 step length in that direction - Repeat +90° 0° -90° +/-180°

17 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 16 Random walks - Step 10 This is a Random Walk (or flight!) - It does not imply that the animal is behaving randomly but that there is a random element involved in the interaction with the environment - Root & Kareiva (1984) Start

18 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 17 Random walks - correlated steps Some animals may exhibit pure random walks - e.g. Whirligig Beetles (Gyrinus sp.) Butterflies have a direction of travel and so are more likely to turn with θ around 0° Correlated http://insects.tamu.edu +90° 0° -90° +/-180°

19 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 18 Random walks - correlated steps We can simulate correlation of angle of turn by selecting θ from a probability distribution... +90° 0° -90° +/-180° Cain (1985) - demonstrated similar distribution for observed Pieris angles of turn

20 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 19 Random walks - Correlated steps After 10 steps... Start

21 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 20 Correlated random walk More directional than pure random walk Start

22 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 21 From theory to simulation Take the standard deviation (s.d.) of the probability distribution and the step length... 0° -90° +/- 180° +90°

23 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 22 From theory to simulation Provides two simulation parameters, L and A +90° 0° -90° +/- 180° A L

24 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 23 Simulation Visual demonstration with simple cabbage layout Experiment Parameters Results

25 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 24 Visual demonstration - Step 0 L=10 A=20 Cabbage Butterfly Release boundary

26 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 25 Visual demonstration - Step 1 L=10 A=20 When move outside world, removed

27 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 26 Visual demonstration - Step 2 L=10 A=20

28 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 27 Visual demonstration - Step 3 L=10 A=20

29 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 28 Visual demonstration - Step 4 L=10 A=20

30 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 29 Visual demonstration - Step 6 L=10 A=20

31 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 30 Visual demonstration - Step 8 L=10 A=20

32 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 31 Visual demonstration - Step 10 L=10 A=20

33 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 32 Visual demonstration - Step 11 L=10 A=20 When intersect a cabbage, lay egg and die

34 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 33 Visual demonstration - Step 12 (End) L=10 A=20

35 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 34 Experiment Parameters L = step length (0.5m to 2m) A = s.d angle of turn (20° to 100°) Cabbage radius = 20cm, spacing = 25cm Large L / Small A = more directional Small L / Large A = more wiggle 12, 000 butterflies 10 replicates DirectionalWiggle

36 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 35 Experimental Cabbage layout

37 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 36 Results Simulation

38 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 37 Results Simulation vs Field

39 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 38 Results Simulation vs Field

40 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 39 Resource concentration Resource dilution Ideal free distribution Results Log Linear Regression H 0 - β=0 Field p-value = 0.037 Simulation p-value = 0.0425 r 2 (Field+Simulation) = 0.9 Simulation Field Ideal free distribution

41 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 40 Resource concentration Resource dilution Results Log Linear Regression H 0 - β=0 Field p-value = 0.037 Simulation p-value = 0.0425 r 2 (Field+Simulation) = 0.9 Simulation Field Ideal free distribution Consistent with literature (Yamamura, 1999)

42 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 41 Results - varying parameters L=50L=100L=150L=200 Plant Density Eggs Per Plant (mean +/stderr) A=20 A=60 A=100

43 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 42 Results - varying parameters L=50L=100L=150L=200 Plant Density Eggs Per Plant (mean +/stderr) A=20 A=60 A=100 L=200 A=100

44 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 43 Conclusions With a simple correlated random walk we can predict egg distributions for Pieris - No attractive force With no attractive force we observe resource dilution Attractive force could potentially produce resource concentration... ?

45 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 44 Conclusions With a simple correlated random walk we can predict egg distributions for Pieris - No attractive force With no attractive force we observe resource dilution Attractive force could potentially produce resource concentration... ?

46 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 45 Conclusions With a simple correlated random walk we can predict egg distributions for Pieris - No attractive force With no attractive force we observe resource dilution Attractive force could potentially produce resource concentration... ?

47 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 46 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 Lifecycle: multiple eggs, migration vs birth Multi-species - Co-existance by having different movement patterns? Fractal (Levy) Walks and landscape

48 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 47 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) - Funded by a Royal Society Marsden grant http://www.oulu.fi/

49 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 48 Questions ? With a simple correlated random walk we can predict egg distributions for Pieris With no attractive force we observe resource dilution Attractive force could potentially produce resource concentration... ?

50 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 49 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. Root, R. B., and P. M. Kareiva. (1984). The search for resources by cabbage butterflies (Pieris rapae): ecological consequences and adaptive significance of markovian movements in a patchy environment. Ecology 65:147-165. Tilman, D., and P. M. Kareiva. (1997). Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. Monographs In Population Biology 30 Yamamura, K. 1999. Relation between plant density and arthropod density in cabbage. Researches on Population Ecology 41:177- 182.

51 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 50 Mean Squared Displacement

52 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 51 Why simulate ? Wide range of existing research modelling behaviour of Pieris rapae - Jones (1970), Cain (1985), Byers(2001) - 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 Assess potential behaviour mechanisms affecting egg distribution - How do the butterflies move ?

53 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 52 Logr regression details

54 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 53 Published Parameters Published data: - Byers(2001) - derived from Root & Kareiva (1984) - A 50 degrees - L 2.5 m

55 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 54 Statistical tests H 0 Field egg distribution = Simulation - observed field, expected simulation H 0 Field regression slope (β) = Simulation

56 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 55 Statistical tests H 0 Field egg distribution = Simulation - observed field, expected simulation - X 2 H 0 - observed = expected : p<0.001 (3e-11) significant difference H 0 Field regression slope (β) = Simulation - t-test H 0 - β simulation = β field : p=0.839 no significant difference All results show resource dilution - Negative β - p<0.05 that β = 0 (Ideal free distribution)

57 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 56 Conclusions Simulation reproduces effects observed in the field - Resource dilution In both simulation and field results - Suggests random walk is good basis for representing Pieris movement - Consistent with literature But... Does not yet represent field results accurately - Saw change in effect for lower step length - Need to explore more parameters - Change behaviour algorithm e.g. more than 1 egg - Future work...

58 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 57 Field results Which do we observe in our field experiments ? Resource concentration Resource dilution Ideal free distribution

59 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 58 Field results Resource concentration Resource dilution Ideal free distribution

60 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 59 Resource concentration Resource dilution Ideal free distribution Field results - log transformation H 0 - β=0 p-value = 0.037 r 2 = 0.9 Field Ideal free distribution

61 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 60 Resource dilution Field results - log transformation H 0 - β=0 p-value = 0.037 r 2 = 0.9 Field Ideal free distribution Consistent with literature (Yamamura, 1999)

62 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 61 Theory Is there a relationship between plant density and eggs per plant ? 1 plant 20 plants, density = 0.2 High Density 5 plants, density = 0.05 Low Density

63 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 62 Theory - Response to plant density Three possible responses 1 plant 20 plants, density = 0.2 High Density 5 plants, density = 0.05 Low Density

64 © Jim Barritt 2006School of Biological Sciences, Victoria University, Wellington 63 Yamamura 1999 Results


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