Modelling mechanisms of animal behaviour

1. Modelling mechanisms of animal behaviour Tony Ludlow tony.ludlow@modelresearch.com www.modelresearch.com 12th January 2006

2. An important question • Why does a dog have a wet nose?

3. Definition and purpose of models • A model is a working version of a theory or hypothesis • To work, the model must be complete and unambiguous • It is therefore a reliable way of working out the consequences of our ideas • It may consist purely of equations but is usually a computer program

4. Aims of session To focus on one particular research program to illustrate: • The kind of questions that needed further experiment • Those that were helped by modelling • The new questions that were raised by modelling • Something of the steps in the modelling process

5. Review of moth orientation • A brief account of the way our ideas developed • Identify the modelling questions • Try, as a group, to find answers to these questions • Brief presentation of my answers and tests of the models

6. Development of ideas • Kennedy (1940) Mosquitoes turning `upwind' • Kellogg, Frizel and Wright (1962) upwind orientation in Drosophila • Kennedy and Marsh (1974) upwind zigzag flight of moths in a wind tunnel; reversed by floor movement • Marsh, Kennedy and Ludlow (1978, 1981) Control of track angle and groundspeed in three windspeeds

7. Tracks in three windspeeds

8. Development of ideas (cont) • Ludlow and Marsh (1978) proposed that moths resolve image movement into longitudinal and transverse components • Kennedy, Ludlow and Sanders (1980, 1981, 1982) used uniform pheromone and a single female superimposed on uniform pheromone. Complete theory of anemotaxis now published. • David, Kennedy, Ludlow, Perry and Wall (1982) recorded parcels of smoke moving in straight lines for several metres in turbulent wind. First time we recognised the efficiency of the anemotactic mechanism

9. Smoke in straight lines

10. Development of ideas (cont.) • David, Kennedy and Ludlow (1983) confirmed theory developed in wind tunnels, and the efficiency of the system, by recording moths in the field.

11. Pheromone and bubbles in the field

12. Points of surprise • Upwind turning expected (by us) but not the zig-zagging or casting • Control of groundspeed and track angle a surprise • Behaviour in uniform pheromone a surprise. We expected smooth upwind flight or jamming. • In hindsight, the male has to find the nearest female when there are thousands • Straight-line movement of odours was a stunning surprise. It changed our whole view of the efficiency of the system (wet-nosed dogs) • Confirmation in the field was expected

13. Generalising to other insects • The surprises show how often we were wrong; how well could we now predict the behaviour of other species? • Wasps • Do forest insects use same mechanism in more difficult place? • Do Tsetse fly too fast to wait for the wind? It is the females that get caught • What difference does a large target make to Drosophila and mosquitoes? Why don't they need to race? • Do aphids drift down wind and land when they get an odour? Modelling the system can help us understand these issues.

14. Modelling the strategies of different insects • What inputs would a model insect need? • What responses would we have to build in? • What calculations would be needed? • What questions might such a model answer? • Belanger et al (1998) did just that

15. Questions the AFRC were paying us to answer • How does a male moth find a female emmitting sex pheromone? • Can we jam the system? • If so how far apart do sources of artificial pheromone have to be? • Is it better to try and kill the males with poison bait? • Will it work with Tsetse? • Monitoring helps

16. How does the nervous system work? • How does a moth turn upwind? • How does it achieve a similar ground track in winds of different speed? • Why does it keep the same groundspeed in different windspeeds? • Why not fly as fast as you can to the female? • We will model biology you already know

17. Triangle of velocities

18. Wind drift and triangle of velocities • Image movement in opposite direction to movement over the ground • Track angle: q = a + d • Image movements could be resolved into L and TR • Moths cannot measure W, a or q directly • To control them it must calculate them from A, G and d or A, L and TR

19. How does a moth turn upwind? • What ideas can you come up with?

20. A simple model of upwind turning

21. DARE P program (part 1) $D1 * * UPWIND TURNING MECHANISM * ************************ * * Let ALPHA be the angle, in degrees, between the insect's long axis * and the upwind direction (wind from left to right is positive). * ALPHA' is the turning rate (degrees per second, right positive) * ALPHA' = DELAY(TORQUE, TORLAG, 1, 0.0 ) * * where DELAY(...) is a function which makes ALPHA' equal to the * value that TORQUE had exactly TORLAG seconds before * TORQUE = C1*(THRUSTL - THRUSTR) * * where C1 is a constant of proportionality, and where THRUSTL and * THRUSTR are left and right wing-thrust respectively. These are * given by *

22. DARE P program (part 2) THRUSTL = P - TR THRUSTR = P - TL * * where P is a signal increasing wing-thrust on both sides. TR and TL are the rates of right-left and * left-right image movement. (NOTE: it could be THRUSTL = P + TL; THRUSTR = P + TR. * What difference would that make and how could we test the model? * * Right-left image movement is proportional to the transverse wind drift (WIND*SIN(ALPHA)) * but the neurons carrying this signal cannot go negative, so the signals carrying TR and TL are * given by: * TR = WIND*MAX( SIN(ALPHA*RADIAN), 0.0) TL = WIND*MAX( SIN( -ALPHA* RADIAN), 0.0) * * where MAX(...) is a function that ensures that TL and TR never go negative. * * An initial value for ALPHA must be set elsewhere in the program, * as must values for the parameters TORLAG, C1, P, WIND and RADIAN * END *-------------------------------------------------------------------------------------------------------

23. Output from model

24. Cross-wind casting

25. Track angle (q) in three windspeeds

26. Triangles of velocities at two track angles

27. Baker & Kuenen (1982) • Used hanging plumes • They stopped the wind flow suddenly • The moths continued up the plume in the same direction and casting as before

28. Maintaining a course with no wind • Jander (1963) proposed a Compensation Theory for maintaining an angle to a stimulus using cos g • Mittelstaedt (1964) proposed his bicomponent theory (sin g, cos g) • Ludlow (1983) proposed a “radial theory” of orientation based on ommatidia looking in different directions

29. Track angle (q) in three windspeeds

30. True groundspeed, G

31. A theory of track angle control • Moth identifies upwind direction by zero transverse movement • ‘Commands' a given track angle by sending different degrees of excitation to the right and left wings PLPR • Command signal is opposed by two feedback loops: • Optomotor signal increases as moth turns from upwind direction • Upwind turning mechanism is `left on' • This system needs moth to divide by groundspeed or keep groundspeed constant • This system needs the moth to maintain roughly constant height

32. The full model

33. DARE P Program of the model The central idea of the program is that left and right wing thrust is given by: THRUSTL = PL - ALPHAL - TR - L/2.0 THRUSTR = PL - ALPHAR - TL - L/2.0

34. Predictions from the model • The moth will need sufficient cues in visual field for the optomotor signal to work • There should be less variation in L + T across windspeeds than there is in G or L2 + T 2= G 2 • There should be less variation in A + L across windspeeds than there is in track angle, q • These predictions are testable

35. True groundspeed, G

36. Aproximate groundspeed, L + T

37. Pythagoras theorem, L2 + T2

38. Table of statistics

39. Track angle, q

40. Table of statistics

41. Conclusion • Modelling forces you to define all assumptions • It allows you to work out consequences of these assumptions • Modelling raises new questions • The model won’t work if it is not complete