on the measurement of motivational variables

Anita. Behav., 1976, 24, 459-475

ON THE MEASUREMENT OF MOTIVATIONAL VARIABLES

BY ALASDAIR HOUSTON & DAVID M c F A R L A N D Animal Behaviour Research Group, Department of Zoology, Oxford

Abstract. This paper discusses some problems concerning the measurement of behaviour variables in general. However, to place the issues in context, discussion is centred on recent ethological work on the interaction of internal and external factors in determining behaviour. In particular, it is maintained that it is not meaningful to postulate that such factors add or multiply, but that the optimal ordering of causal states is the issue upon which attention should be focussed.

Ialtroduction The aim of this paper is to discuss some problems concerning the measurement of behavioural variables. The issue is placed in context by examples drawn from recent ethological work on the interaction of internal and external factors in determining behaviour. In general terms we describe two cases, one suggesting that these factors are multiplied, the other that they are added. It will be argued that this is not a genuine difference, in that the nature of the measurements determines the way in which the variables appear to combine. In particular, the preceding paper (Heiligenberg 1976) provides examples of precisely the issue that we wish to take up. The nexus of our argument is that what matters for an animal is that it orders its causal states in an optimal manner, designed to maxi- mize fitness (Sibly & McFarland 1976).

In order to illustrate the problem of interaction between the external stimuli and the internal states, we discuss two particular cases:

(a) the work of Baerends, Brouwer & Waterbolk (1955) which has often been cited as implying that internal and external factors are multiplied.

(b) Heiligenberg's (1974) investigations of aggression in cichlids which seem to suggest that the factors combine by addition.

Baerends et al. (1955) investigated the courtship behaviour of the male guppy (Lebistes reticulatus). Haskins & Haskins (1949) had established that males preferred large females to small ones. This suggests that size of female must be one of the factors that the male uses in deciding whether to court her. Another factor must be the male's sexual motivation. Baerends et al. (1955) used the various marking patterns of the male as an index of internal state. To this end, a 'calibration curve' was drawn up, as illustrated in Fig. 1. By observing the relative frequencies of various courtship activities when each of the marking patterns was present, they

were able to construct a rank order of internal states. Their main experiment involved establishing which size of female was required to elicit a given display from a male in a certain sexual state. In other words, the size of the female was titrated to obtain 'isoclines' in a two- dimensional space in which the motivational state of the animal can be represented. McFarland & Sibly (1975) call this space a 'causal factor space' and represent the 'motivational state' of the animal as a point in this space. They assume that every point uniquely determines a particular activity.

The shape of the isoclines obtained by Baerends et al. (1955) (Fig. 1) approximates to a hyperbola, which suggests that the internal and external factors are multiplied together to determine the tendency to perform the various courtship activities.

The other example of the effect of external stimuli on motivational state is provided by Heiligenberg's (1965) study of attack readiness of the cichlid fish (Pelmatochromis subocellatus). The strength of the attack readiness may be defined by the number of attacks the fish delivers per unit time in a standard situation. Specifically:

'An adult male fish is placed together with a group of young fish for several weeks. The male can attack the young fish at will. How- ever, the young fish always escape before being seriously bitten, so that a real fight-- which might exhaust the male--never occurs. The behaviour of the male is recorded for 15 rain; then a dummy of another male is presented behind a glass pane for half a minute, and the behaviour of the male is again recorded for the next 30 min. During the presentation of the dummy the male watches it, very rarely doing anything else than standing quietly in its place. Immediately after the removal of the dummy the male attacks the young fish much more than

459

460 A N I M A L B E H A V I O U R , 24, 2

before and then returns slowly to his previous level of aggression.' (Heiligenberg 1965).

Because the attack rate of the fish fluctuates considerably it ~s impossible to predict, f rom knowledge of its value in a given time interval, the exact ra te f o r the subsequent interval. However , the expected value y, of attack rate within a specific interval, can be estimated as a function of the observed attack rate x in the preceding interval. The attack rates observed within pairs of successive standardized time intervals, separated by a short intervening interval, were separated into classes on the basis of the level of attack observed in the first interval. Within each class the average values

and variances were calculated for the attack rate within the first interval x and within the following interval y. AS can be seen from Fig. 2, a straight-line relationship i s obtained. The same procedure is applied when a dummy is presented in the short intervening interval. Presentation of the dummy always alters the relationship between x and y by a constant amount (Fig. 2). In o ther words, the increment in attack rate caused by presentation of a dummy is independent of the pre-stimulatory attack rate, and the presentation is additive in its effect on the stimuli already existing.

Using Heiligenberg's method with the cichlid fish Hap!ochromis burtoni, Leong (1969) fouud

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/i

~ 7 4 5 6

4 s

~ 2 4 5

~ 6

t I i _ t I N T E R N A L S T I M U L A T I O N - - >

s 5 6 6

,iY J e . C A i

I .... 1 I t i __

5 IO IS ~0 ~ 35 40 RELATIV~ F ~ EQ~;~NCY ~'~

Fig. L Upper part: the influence of the strength of external stimulation (measured by the size of the female) and the internal state (measured by the colour pattern of the male) in determining the courtship behaviour of male guppies. Each curve represents the combination of external stimulus and internal state producing POsturing (P), sigmoid intention movements (Sl), and the fully developed sigmoid (S), respectively. Lower part: the 'calibration curve' for determining the place of the different marking patterns on the abscissa of the upper graph; (From Baerends et al. 1955)

HOUSTON & McFARLAND: THE MEASUREMENT OF MOTIVATIONAL VARIABLES 461

t~

m

I I I 8 6 9

actual attack rate (bites per minute)

Fig. 2. Expected values of attack rate yoo, (ordinate) within a subsequent 40O-s interval as a function of the attack rate x (abscissa) observed with a given 400-s interval (black circles). The expected value of y is ad- ditively increased (giving Ya,,,) if a dummy is presented between the given and subsequent 400-s interval (open circles). Data were divided into classes according to different levels of attack rate within the first 400-s interval. Within each group, average values (circles) and variances of the mean (bars) were calculated with respect to both co-ordinates. (From Leong 1969).

45 ~ 90*

Fig. 3. Black pattern marking head of territorial male (top) and dummy (bottom) showing only the black eye- bar represented by a piece of metal foil rotatable around the centre of the eye. The five eye-bar positions chosen in the experiments are indicated by dotted lines, the angle between the eye-bar and the eye-snout axis being0, 45, 90, 135 and 180 degrees respectively; the second position represents the natural location of the eye-bar. The body coloration of the dummy is yellowish grey matching the natural ground coloration of territorial males. All additional colour patterns are omitted. (From Heiligen- berg et al. 1972).

that different components o f the colour patterns o f territorial males, painted on dummies, were additive in their effects upon at tack rate. Similarly, Heiligenberg, Kramer & Schulz (1972) showed that different angular orientations o f the black eye-bar o f H. burtoni (Fig. 3) were additive in their effects upon at tack rate. Both these findings are in agreement with the rule o f heteo- geneous summat ion (Seitz 1940).

The pre-stimulatory at tack rate is presumably the result o f the combined effect o f the internal and external factors. The results o f these and subsequent experiments (Heiligenberg 1973), indicate that various external stimuli can increase or reduce attack rate in an additive manner. At first sight this seems to imply that internal and external factors combine in an additive manner. That is to say, if we were to draw isoclines in the manner o f Fig. 1, they would be straight lines, as shown in Fig. 4. This is not necessarily the case however. The fact that initial at tack rate does not alter the effect of a stimulus means that whichever isocline It t, we start from, we move to an isocline It 2, such that the change in at tack rate is constant, i.e.

Attack rate I t z - At tack rate Lx = const.

This relationship between Heiligenberg's data and the causal factor space is shown in Fig. 5. There are no t really enough points on the 'cue ' axis to enable the causal factor space to be constructed.

Despite the fact that an additive combinat ion rule is not required by the data, it is often assumed as one form o f representation (for example, see Heiligenberg's (1974) analogue model o f attack motivation). We wilt therefore

Internal factors >

Fig. 4. Straight-line isoclines in a two-dimensional causal- factor space.

462 A N I M A L B E I t A V I O U R , 2 4 , 2

use the cichlid experiments as a representative of the additive combination of internal and external factors. The apparent conflict between additive and multiplicative combination rules is not as hard to resolve as might be imagined. The key to the problem lies in the fact that the nature of the combination rule depends on the measurement of the variables. Baerends et al. (1955) touch on this when they write

'Hayes, Russell, Hayes & Kohsen (1953) and Russell, Mead & ttayes (1954) have used the shape of our curves . . . which is almost hyperbolic, as an argument for their opinion that interaction between interval and external variables--must be rnult ipl icative. . . Though we agree that much is to be said for this idea and that useful evidence could be obtained from experiments such as those we have undertaken, we should emphasize that our measurements are still very rough and that before much va lue is attributed to the actual shape of the curves more experimental work should be done to establish this detail ' (pp. 311-312).

In fact, we show below that measurements must be on art interval scale to make the shape of the curves meaningful. Baerends et al. (1955) admit that the colour patterns provide only ordinal measurements of the male's state:

'However, these and other criticisms (of the calibration procedure) are chiefly concerned with the exact distances between successive

markin5 patterns on the scale, not primarily with the order in which the patterns develop with increase of internal stimulation. This order, which is the principal basis for our further conclusions, seems fairly well established' (p. 306). As long as only ordinal measurement is obtained, the nature of the combination rule cannot be determined. Heiligenberg points out that his results could be transformed to produce multiplicative combination. In Appen- dix 1 we prove this result (theorem 1) and show how it depends on the nature of the scales.

As shown in theorem 2 of Appendix 1, if interval measurement cart be established then the question of how the variables combine becomes decidable.

Theorem 1 is the foundation of our argument for considering the ordering of the causal states rather than making assumptions about each of the state variables and how they combine. This approach is analogous to the abandonment of cardinal utility in economics. Indeed, the conditions established for the existence of indifference curves can be adapated as conditions for isoclines (see Wold 1953). We now give an example illustrating theorem 1.

The Behaviour of the Namib Desert Lizard Aporosaura anchietae

Of the many desert lizards which have been studied few have been found to have specific physiological adaptations to the desert environ- ment. The majority escape unfavourable con-

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b- | @. c - " ' | ~'|

"~I '~2 ~'3 '~ X1 X 2 X 3

Fig. 5. The relationship between Heiligenberg's (1965) data (left) and the causal-factor space (right). The y-axis represents post-stimulus attack rate (i.e. response). The x-axis represents pre-stimulus attack rate, an indication of internal state, a, b, and c are various stimuli arbitrarily spaced. As an isocline links points of equal response tendency, it is constructed by considering a fixed level of response. For example, the dashed isocline (xl, a) (x2, b) (x3, c) is obtained from the line y = Yl in the left-hand figure.

>


ditions by well defined adaptive behaviour (Mayhew 1968). Escape from thermal stress and desiccation by behavioural means usually involves hiding beneath sand or rocks. This behaviour has the disadvantage that it severely limits opportunities for feeding. This is particu- larly true of the sand-diving lizard A. anchietae. This species is found in the Namib desert in South-West Africa. It typically inhabits the slip face on the leeward side of sand dunes. The leeward side of the dune acts as a trap for wind-blown organic matter which accumulates at the foot of the slip face, where Aporosaura feeds upon grass seeds and insects. The physiological and behavioural adaptation of this lizard have been described in some detail by Louw & Holm (1972).

The lee side of the dunes is virtually wind- free and frequently faces the rising sun. Conse- quently, the surface temperature rises very

rapidly, as illustrated in Fig. 6. When the surface temperature reaches 30~ the lizard emerges from the sand and presses its ventral surface against the substrate. It takes up a special 'dished' posture which achieves the maximum contact between its body and the substrate. By this behaviour the animal achieves a rapid rise in body temperature and is soon able to move about and forage on the dune face. As the substrate temperature approaches 40~ the animal straightens its limbs to raise the body as far as possible above the substrate. It periodically raises the diagonally opposite limbs while the base of the tail is used for support. Above 40~ the lizards dive beneath the soft sand to reach the cooler depths. Tile behaviour of Aporosaura thus appears to be very much dictated by its thermo-regulatory requirements. These generally result in a bi- phasic period of activity during which the animal

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~ 271 i

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/ /

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Surface

0700 0900 1100 1300 1500 1700 Time

Fig. 6. Typical temperature conditions on the dune slip-face, which con- stitutes the micro-habitat of Aporosaura anchietae. Hatched blocks indicate the periods for which the lizard is above the surface of the sand (after Louw & Holm 1972).

464 A N I M A L B E H A V I O U R , 2 4 , 2

is able to forage on the slip face, as illustrated in Fig. 6. The work of Louw & Holm (1972) shows that these lizards are able to consume large amounts of food in a short period of time. After feeding in this manner, captive animals exhibit little or no interest in feeding and remain submerged beneath the sand for longer periods than usual. These workers also found that Aporosaura is able to store water in the digestive tract. I t is capable of ingesting 11 per cent of its bodyweight within 3 rain and can subsequently survive for more than 8 weeks without further opportunity to drink. These lizards obtain water primarily through eating insects; though they also have occasional opportunity to drink condensed water from periodic advective sea fog, which is typical of the area.

When the lizards are under the surface o f the sand, they are protected from climatic changes and from predation. However, they have no opportunity to obtain food or water. When weather conditions are favourable during the day, the animals emerge upon the slip face and feed upon detritus and arthropods. Here they suffer from a much in,creased rate of dehydration and are vulnerable to predation by the side- winding adder (Bitis peringueyi), the black- headed jackal (Canis mesornelas), the chanting goshawk (Melierax musicus), and the rock kestrel (Falco tinnunculus). The lizard's normal reaction to danger is a fast sprint followed by emergency diving beneath the sand. It is, however, only capable of this rapid anti-predator response when its body temperature is in the region of 30 to 40~ Below these temperatures the lizards

=o

o.

r

Lethal l imit ~

Warming behaviour

Below surface

S~ ng behaviour

J Lethal '1 i i "~1 limit

200 30 ~ 40oc Temperature

Fig. 7. Two-dimensional representation of the physiological states at which Aporosaura might be expected to be below the surface of the sand, or above the surface and involved in warming or cooling behaviour, or actively forag- ing. Boundary lines indicate transitions from one type of behaviour to tile other.

ttOUSTON & McFARLAND: THE MEASUREMENT OF MOTIVATIONAL VARIABLES 465

are less mobile, and on cold days they generally remain below the surface of the sand.

On the basis of these observed behaviour patterns of Aporosaura, and of their probable survival value, we can make a guess about the optimum survival strategy for this species. When the animal is replete with food and water we would expect it to spend less time on the surface of the sand and thus avoid predation and dehydration. When it has a negative energy or water balance, it can avoid eventual death only by venturing onto the surface of the sand to search for food and water. In cases of extreme hunger or thirst, we would expect the animal to run a greater risk of predation by emerging from the sand at a lower temperature than normal. In such circumstances a period of specialized warming behaviour would be necessary. Similarly, we would expect the animal to run greater risks of dehydration by remaining on the surface at ever-increasing temperatures and indulging in bouts of specialized cooling behaviour. These hypotheses are summarized in Fig. 7, which can be seen as a map of the behaviour upon a basis of physiological co- ordinates.

We now have the problem of accounting for the mechanisms by which the animal achieves such appropriate behaviour in changing en- vironmental circumstances, The traditional ap-

proach is to look for the sense organs through which information about the external env'.'ron- ment, and about internal physiological state, reaches the animal's brain. On the basis of work on other lizards, we have good reason to suppose that central thermoreceptors (Whitfield & Livezey 1973) and dehydration monitors (Fitzsimons & Kaufman 1974) exist in Aporo- saura. The representation of such information in the brain is commonly thought of as some kind of motivational tendency or potentiality to perform appropriate behaviour. The tenden, cies compete, or interact, in such a way that the observed behaviour is controlled by the strongest. A summary of this situation is illustrated in Fig. 8(a), in which the range of behaviour is restricted for the sake of simplicity.

Let us pretend that the animal merely has to make a decision to remain above, or below the surface. In accounting for the adaptiveness o f the lizard's behaviour, knowledge of the nature and strength of the relevant tendencies would not be sufficient. It is obvious that there must be some calibration of the tendencies, in terms of their relative importance, as indicated in Fig. 8(b). We would then have to specify how calibrated tendencies combine and interact. The necessity for both calibration and combination can be illustrated by reference to the stylised Aporosaura example, illustrated in Fig. 7.

t Drive (a) Physiol Monitors " state Behaviour control mechanism ----~Behaviour

(b) PhysiOI t '" i ~l I J Decisiol i ~lElehaviour state M~176 ! fl Calibrati~ ! ~ I I

Fig. 8. (a) Conventional representation of the influence of physiological state upon behaviour. (b) Modification of (a) to allow for division of the behaviour control mechanism into calibration and decision sub-systems.

466 A N I M A L B E H A V I O U R , 24 , 2

The rule for combining the calibrated variables (tendencies) produces an isocline, which can be thought o f as a threshold in this case. The problem with proceeding in this fashion is that we do not know how the tendencies are calibrated. I f all we know is the order in which a given calibrated tendency is ranked, then theorem 1 tells us that we cannot distinguish between an additive and a multiplicative combination rule.

To see how theorem 1 applies to this example, let two uncalibrated tendencies take values x l and x2, f rom the sets X1 and X2 respectively. N o w consider a ealibration tp~ (i.e. 'measurement ' by the animal) which assigns values to the uncalibrated tendencies X~, such that the response strength, r, cart be represented as an additive combinat ion o f the calibrated variables which we call vl and v2, f rom the sets V 1 and V 2 respectively.

~0, : x , -~ v, i = l, 2 (1)

r - - V l + v2 (2)

Under these circumstances, the threshold for surfacing (i.e. a line o f constant r )w i l l be a straight line. Figure 9 illustrates this for the case

V 1 ~ - V 2 - - 3 (3)

5~

4 -

2 -

1- ear

v~

Fig. 9. Causal factor space resulting from the calibration q0. The straight line is the threshold given by eqn (2), a~ = (1, 1), by = (1"5, 3).

and shows a point av below threshold and a point b~ above it. The calibration q) is, however, just a guess; all we know is the order the actual calibration imposes on the tendencies. Theorem 1 means that we can find an alternative calibration, ~g and a multiplicative combinat ion rule which will be equivalent to calibration q~ and a n additive combination. The existence of ~d follows f rom the t ransformat ion of T theorem 1 :

Tl : V~ ~ U~ i.e. u l - - Ttvl (4)

and as v~ = q0xi (5)

then W : Xl ~ U~ (6)

is given by ui ~ T d h x t (7)

We know, f rom theorem 2, that T is an exponential function, so eqn (7) cart be written as

u~ ~ betel (8)

where b and c are constants. This means that the threshold, previously

given by eqn (2) is now given by

u l u 2 = e 3 = 20.09 (9)

This is shown in Fig. 10, which also illustrates that au = T(av) is once again below threshold, while b, = T(b~) is above threshold. In other words, the same subsets o f X~ fall above and below threshold under both o f the calibrations.

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1 2 -

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8-

6-

4-

2-

Oau

,~ ~ ~ 1'o 1'= -'1~ U1

Fig. 10. Causal factor space resulting from the calibration ~. The hyperbola is the threshold given by equation (9), au = (e, e) = (2-72, 2.72), bu = (et" 5, e3) = (4.49, t2-18).

ttOUSTON & McFARLAND : THE MEASUREMENT OF MOTIVATIONAL VARIABLES 467

Putting the argument the other way round, if all we know is the ranking of the drive states, and their order on each axis, then we cannot distinguish between an additive and a multiplicative combination rule.

The Conjoint Measurement Approach Our argument so far might seem rather negative; we have been concerned solely with the limits of ordinal scales. There are, however, some positive results from the ordinal approach. In the next section, we outline the conjoint measurement approach to combination rules and from this we sketch how it is sometimes possible to derive interval scales. The ideas of concurrence and cancellation are shown to be central to both t/aese questions.

The conjoint measurement approach attempts to solve the measurement and the combination rule problem simultaneously, by constructing measurement scales in such a way that the proposed combination rule is satisfied. As Krantz & Tversky (1971) have said, 'The p r o b l e m . . , therefore is not whether a specified fimctional relation holds among several (in- dependently measured) variables, but rather whether there exist scales of measurement (for both the dependent and the independent variables) that satisfy the proposed composition r u l e . . . ' ' T h u s . . . one starts with an ordering of the dependent variable and investigates what properties this order should satisfy so that it can be represented numerically according to the proposed composition principle.' (We have called 'composition rules', 'combination rules' in this paper.)

Krantz & Tversky (1971) consider the four simple ways in which three variables, A, P, and U, can combine:

A + P - t - U (a + P)U A P + U APU

additive rule distributive rule dual-distributive rule multiplicative rule

We know, from theorem 1, that the additive and mutliplicative rules are ordinally equivalent. Krantz & Tversky show that the other rules can sometimes be distinguished on ordinal information alone. They also set out necessary conditions for the existence of a simple combination rule for positive variables. These conditions are called concurrence and double cancellation. We use A, P, U to denote sets of motivational tendencies such as the tendency to eat, with a, b, c, in the set A ; p , q, r in P; and u, v, w in

U; while A, P, and U are scales, i.e. numerical functions defined on A, P, and U respectively. The response to tendency (a, p, u) is denoted by r(a, p, u).

Concurrence* A variable is said to be concurrent if the

ordering of the responses that arise from changing the value of the variable is the same whatever the values of the other variables may be (the values of the other variables are held constant during each determination of an ordering).

Formally, A is concurrent with respect to P and U whenever

r(a,p, u) > r(b,p, u) if and only if

r(a, q, v) > r(b, q, v)

for all a, b in A, p, q in P, and u, v in U. In other words, if a results in a stronger response than b for one given set of tendencies, it will result in. a stronger tendency for all other sets.

On a graph like Fig. 5, the notion of concurrence corresponds to the solid lines not intersecting each other. It can be shown under certain circumstances that this is a sufficient condition for an additive representation (e.g. a motivational tendency x and a two-valued stimulus dimension y with x concurrent with respect to y).

Double Cancellation This condition concerns pairs of experimental

conditions and is illustrated graphically in Fig. 11. Formally A and P satisfy double cancellation if

r(a,q ,u) >~r(b,r,u) and r(b,p, u) >~ r(e, q, u) imply r (a, p, u) ~ r (c, r, u)

This has certain implications for indifference curves (see Luce & Tukey 1964 for a further discussion of this point) or motivational isoclines as illustrated in Fig. 12 which shows that cancellation holds for the curves determined by Baerends et al. (!955) (see Appendix 3).

*Krantz & Tversky (1971) call this condition 'independence', but this term might be confused with 'independent variable' (e.g. 'The essence of independence is that the ordering of the dependent variable can be used to order some of the independent variables.., in a manner that does not depend on the remaining variables' (Krantz & Tversky 1971.)


Another important point about double can- cellatiort is that it requires knowledge of at least three levels of each factor.

An Illustrative Example To demonstrate how the conjoint measurement approach compares with traditional methods~

(a,p,u) ~ -, �9 (a,r,u)

, \ \ ,% , , \ \ , \ i

( b,p, u) " i " " . . . . . ~'~1.~, -- . . . . . " ~ l ( b, r, u)

, \ \ \ : , \ , \ \ , , \ , \ \ ,

, ~ ~ \ \ , ! \ I \ \ t

rc.p, uj . : - ~ i _ ~- " rc,,,,,~ (c,q,u)

Fig. 11. Graphical illustration of the double cancellation axiom. The thin arrows represent the/> s of the premise; the thick arrow represents the >I of the implication.

I

8 . . . . i . . . . . . I

! I

%

| , ~

P

Fig. 12. The isoclines of Baerends et al. (1955) (see Fig. 1) considered with respect to double cancellation. The two outside isoclines provide starting points (black dots) for the double cancellation axiom. The dotted lines are construction lines at right angles to the axes. The points at which the outer construction lines cross (open circles) should lie on an isocline if double cancellation holds, which they do in this case.

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/

E

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3'~ ,'5 oc > Temperature

(a)

Tempera tu re

{b)

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==

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(c}

Fig. 13. Hypothetical functions relating temperature and survival for Aporosaura. (a) and (b) are cumulative probability functions, (c) is a calibration function derived from (a) and (b).


we return to the behaviour of the desert lizard A. anchietae.

In investigating calibration of the monitored internal states relevant to temperature and dehydration (see page 465), we would expect to find that the calibrated tendencies were related to the survival value of the physiological states. For example, the probability of death due to

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-10 o + 10 Uni ts Water balance

Fig. 14. Hypothetical calibration function relating water balance and tendency to surface.

thermal stress might well be a function of temperature, such as that illustrated in Fig. 13(a), and the probability of death by predation might also be a function of temperature for an animal on the surface, because the lizard, are less mobile at lower temperatures (Fig. 13(b)). On this basis we might expect the calibration of the thermal tendency to be somewhat like that illustrated in Fig. 13(c). Similarly, we might expect the calibration of dehydration to be something like the function illustrated in Fig. 14: the tendency to surface increases with dehydration, thus increasing the animal's chances of finding water; but at extreme dehydration this advantage is offset by the increased loss of water that results from being on the surface and exposed to the sun and wind. We now have a calibrated tendency to surface, based on temperature and a similar tendency based on dehydration. The question is, how do these combine to produce a single tendency to surface ?

We can calculate the consequences of assuming that the combination law is additive, and can separately calculate the consequences of assuming that the law is multiplicative. The additive rule implies that the isocline represent- ing a particular tendency to surface is a straight line, while the multiplication rule implies that the isocline is a hyperbola, as illustrated in Fig. 15. If we take these isoclines to represent the

I u l t ip l icat ive isocline

.r h-

I I I ,.a.-

H y d r a t i o n tendency

Fig. 15. Hypothetical motivational isoclines for Aporosaura, joining points of equal tendency to surface as a result of the combined thermal and hydra- tion tendencies.


threshold tendency to surface (i.e. the tendency which, on average, will be large enough to cause the animal to be above the surface), then we can represent the consequences of the hypotheses embodied in the two isoclines in terms of a map on the physiological co-ordinates (Fig. 7). In other words, on the basis of the (hypothetical) calibrations summarized in Figs 13 and 14, the additive hypothesis produces map A in Fig. 16, and the multiplieative hypothesis produces map M. The manner in which the calibrated drives are combined appears to make a large difference to the adaptiveness of the resulting behavioural strategies. However, an exponential transformation of the calibration curves (Figs 13 and 14), would produce new calibrations which, when combined

multiplicatively, would give the same map as that given by the additive rule in Fig. 16 (see Appendix 1). In general, if all we know is the order in which each drive is ranked, then theorem 1 tells us that we cannot distinguish between an additive and a multiplicative combination rule.

To apply the conjoint measurement approach in this case, we would perform the following experiments: Given the set of states of dehydration Wl, w2 . . . . wn and the set of body temperatures t l , tz . . . . tm, we would take a pair of points (w~, tj) and (wk, t3 from the causal factor space, and compare the behavioural tendencies they produced. (We suppose that there would be some experimental method of ordinally measuring the tendency to surface).

o

t -

O

c o

" 0 > .

at=

Lethal l imi t_

I

/ / \

\ \

\ \ \

/ /

7 j

•t Lethal I I t l im it

2 0 �9 3 0 �9 4 0 * C

Temperature

Fig. 16. Two-dimensional representation of the physiological states at which Aporosaura might be expected to be below or above the surface of the sand. The thin continuous boundary lines are transposed directly from Fig. 7. The thick line is based upon the additive isocline of Fig. 15 Map A. The dashed boundary line is based upon the multiplieative isocline Map M.


The results of an experiment would be represented as (wi, tj) ~ (wk, tt), if the magnitude of response to (w, tj) was at least as great as that of (wk, t,); and as (w,, tj) >! (Wk, tl), if the effect of (Wk, t,) was at least as great as that of (wl, tj).

The next step would be to check the data for concurrence. For each value of body temperature t~, we would order the states of dehydration in terms of their behavioural tendency. This is shown for two values of body temperature in Fig. 17. I f dehydration was concurrent with respect to temperature, the ordering would be the same as for each t , that is to say the lines joining points of a given w~ would not cross, as illustrated by Fig. 18. Body temperature would be checked for concurrence in a similar way. Note that the data shown in Fig. 18 would mean that body temperature would not be

A

.9 >

e ~

ew3 e %

t w 2

ew~ �9 w 1

tz t /

Fig. 17. The behavioural tendency resulting from various states of dehydration (w i, w2 and w 3) at two temperatures ti and tj.

W3

-~ w2 ,~ IA'3

> .~ W 2 W ' - -

m W 1

t~ t] t k

Fig. 18. The three states of dehydration (from Fig. 17) are shown as being concurrent: i.e. at any temperature, Wl ~ W2 ~ W3.

concurrent with respect to dehydration. Tiffs can be seen from Fig. 19, which is derived from Fig. 18.

I f both variables were concurrent we would go on to check for double cancellation. This involves testing the kind of implication shown in Fig. 11. I f both these conditions were satisfied then we would know that we could scale the axes of the causal factor space in such a way that either a multiplicative of an additive combination rule held.

~ t k

Fig. 19. The points in Fig. 18 are reorganized to illustrate the relationship of the temperatures. Because the lines joining points of a given temperature intersect, the temperatures are not concurrent with respect to states of dehydration.

/ f

"~ / " .,..,- ~Bar pressing / ' / / / ~ r

~15 ! i I I rain 1 hr 3 hr 6 hr

Interval between ireatment and test

Fig. 20. Three methods of assessing the 'thirst' of rats given 5 ml of 2 M saline by stomach tube. The ordinate indicates the amount by which the experimental test exceeded the control test, the nature of the units differing between the procedures used. (After Miller 1956). Apart from the levelling-off of the drinking curve, it would appear that the three measures of thirst are concurrent with respect to each other. If the levelling off of drinking were due to a ceiling (satiation) effect, it would be fair to discount the reading taken at 6 hr. The rankings imposed by each of the measures would then be concurrent.


Discussion Traditionally, the value of drive concepts has been seen in their role as 'intervening variables'. Difficulties arise when different empiricial methods are employed to measure drive variables. For example, Choy (cited by Miller 1956) gave rats 5 ml of 2 M saline by stomach tube, and assessed the resultant 'thirst' in terms of the amount of water drunk in 15 rain, the number of bar presses reinforced with water on a variable interval schedule given in 9 rain, and the concentration of quinine solution that the rats would tolerate. The three measures gave different results, as illustrated in Fig. 20. Hinde (1970) observed that 'In view of this lack of agreement among measures, we must con- clude that the postulation of a single intervening variable is too simple a hypothesis to account for all the changes in behaviour observed' (p. 197). In our opinion this conclusion is not justified, because the fault lies in the assumption that the measures of drive strength are being made on an interval scale. The necessity for some kind o f internal calibration, which we have discussed above, implies that such an assumption is invalid. I f we assume measurement on nothing stronger than an ordinal scale, then all we require is that the rankings imposed by each of the measures are concurrent, as explained in Fig. 20. As McFarland & Sibly (1972) point out 'Complexity alone is not sufficient grounds for dispensing with unitary drive concepts, since it may always be possible to choose a variable in the model system which behaves in a unitary manner by virtue of the way in which the system is defined'.

The advantage of the conjoint measurement approach is that we need make no initial assumptions about the drive calibrations, because they are incorporated in the final formulation; and this results from empirically determined rather than a priori relationship between motivational variables. This advantage is more apparent in a three-dimensional case (Krantz & Tversky 1971), but we have used a simple two-dimensional example to illustrate the principle involved.

An important distinction between this approach and that exemplified by Heiligenberg (1976) is that our combination rules refer to the animal's 'calibrated tendencies', which are envisaged as being 'subjective' from the animal's point of view. For example, Heiligenberg (1976) distinguishes between additive and multiplicative combination rules by means of an experiment

in which a particular aspect of the stimulus situation (namely the black eye-bar on the male cichlid fish H. burtoni) is removed.

Heiligenberg represents the eye-bar angle on an interval scale, a legitimate measure from the experimenter's point of view. However, he cannot assume that such a scale is used by the fish, and therefore he cannot establish which combination rules are used 'subjectively' by the fish. Furthermore, even when the value of the stimulus is measurable on art interval scale, it cannot be assumed that the absence of the stimulus gives zero value. Heiligenberg assumes, without evidence, that, when the eye-bar is absent, the contribution of eye-bar angle is zero. The problem is that his eqns (3) and (4) should have terms for the value of eye-bar presence in addition to terms for the value of eye-bar angle. Even supposing that eye-bar angle were measurable on an interval scale, the contribution of eye-bar presence would have to be evaluated experimentally.

Heiligenberg's conclusions are valid provided it is recognized that they refer only to the inter- actions between the experimenter's scales of measurement. Our aim is to develop a method of discovering how causal factors have been calibrated in the animal. We believe that this is a necessary step for further fruitful motivation analysis, and that models couched in terms of the experimenter's arbitrary scales of measurement are not very satisfactory, because they can always be transformed into other models.

It will be apparent that, because consideration of survival value enters into the formulation of calibration of tendencies, the same type of consideration must be inherent in the results of the conjoint measurement approach. This raises the possibility, which we intend to explore in a later paper, of relating the 'decision-rules', that result from the conjoint measurement approach, to the idea of a behavioural cost function put forward by Sibly & McFarland (1976) and by McFarland (1976). In this way we hope to be able to comment not only on the mechanisms controlling behaviour, but also on their design.

APPENDIX 1 This appendix contains the proofs of theorems 1 and 2.

Definitions Measurement involves finding a scale which assigns numbers to the objects of investigation.


Let the set of objects be Q and the real numbers be R, then a scale is a map m: Q -+ R.

Ordinal Scale A scale is an ordinal scale if and only if it is

unique up to monotone increasing and continuous maps of m(Q) into R.

Monotone Increasing Map A map of an ordered set A into an ordered

set B is monotone increasing if and only if a' <: a" impliesf(a') <f(a") for all a', a" in A.

Continuous Map A map h : R -~ R is continuous at the point

a in R if given ~ > 0; there is a~ > 0 such that

I f ( x ) - - f ( a ) l < whenever Ix -- a l < The map h is continuous if it is continuous at each point of R.

Interval and Ratio Scales A scale is an interval scale or ratio scale if it is

unique up to the positive linear transformations or dilations respectively.

Positive Linear Transformations The group Gp of positive linear transforma-

tions of R onto R consists of all transformations ga, b : x -+ ax q- b with a in R +, b in R.

Ga = {g,,, o) : a in R +} is the group of dilations.

Theorem I If the variables and the response they produce are measured on ordinal scales and take only positive values, then it is not possible to decide between an additive and a multiplic~ive combination rule.

Proof The proof is based on demonstrating that if

we find a scale which allows one of the combination rules to descxibe the data, then the scale values can be transformed'so that the other rule could be used.

Without loss of generality, assume that the measured response, r, can be represented as

r : V 1 -1- V 2 -[- . . . -~ V. (1)

where the v~ are the scale values of the variables x~. We now seek a transformation T such that

T ( r ) : T(Vl) X T ( v 2 ) . . . T(vn) (2)

and with the requirement that T be monatone increasing and continuous (this constraint

follows from the definition of ordinal scales). It is obvious that the exponential transformation

T ( r ) = e', T(v) = e"

is a suitable transformation.

Theorem 2 If measurement is on interval scales, it is not possible to find a transformation satisfyin~ equations (1) a~d (2).

Proof We can regard eqns (1) and (2) as establishing

a functional equation of the form

f ( x l + x2) = g(Yl), h(y2) (3)

It is known (Aczel 1966) that the only continuous solutions of (3) are of the form

f ( w ) -- abe cw

g(w) = ae c" (4) h(w) = becw

where a, b, c are constants. But as we are now considering interval scales the only permissible transformations (by definition) are positive linear ones. Thus transformations of the form of eqn (4) may not be used.

APPENDIX 2 It is sometimes possible to construct interval scales from ordinal data. There are arguments to suggest tha t it is impossible to obtain a finite set of necessary and sufficient conditions for this procedure (see Adams, Fagot & Robinson 1970, especially p. 381). The Luce--Tukey conditions, which we use below, are typical in that they include a non-necessary 'technical' axiom. (Their axiom 4, the Archimedian Axiom; Adams, et al. have shown that all the empirical content resides in axioms 1 to 3). The other axioms are as follows:

The Luce--Tnkey Axioms Axiom 1 (Well-ordering)

(a) Reflexivity: r (a ,p ) >~ r (a ,p )

for all a in. A, p in P. (b) Transitivity:

r (a ,p ) ~ r ( b , q )

and r (b ,q ) ~ r ( c , r )

imply r (a ,p ) >1 r(c, r )


(c) Connectedness: either r(a,p) >~ r(b,q)

or r(b,q) >1 r(a,p) orbo th , i.e. r(a,p) = r(b,q).

Axiom 2 (Solutions) For each a in A and p, q in P the equation

r(~p) = r(a,q) has a solution f i n A, and for each a, b in A and p in P, the equation

r ( a , x ) = r(b,p) has a solution x in P.

Axiom 3 (Double Cancellation) r(a,q) >~r(b,r)

and r(b,p) >~ r(c,q) imply r(a,p) >1 r(c, r)

The fourth axiom requires some definitions: A doubly infinite series of pairs (ai, pi), i = 0, -4- 1, • 2 . . . . . with az in A and p, in P i s a dual standard sequence (d.s.s.) provided that

r(am, Pn) = r(aq, pr) whenever m + n ----- q + r for positive, zero or negative integers m, n, q, and r.

A d.s.s, is trival if for all i either a~ = ao or Pt = po, in which ease both hold by transfer.

make them comparable with the double cancellation axiom. The outside isoclines provide the premises of the axiom in the following way.

As r(a,p) and r(b, r) lie on the same isocline,

r(a, p) = r(b, r) (1)

Therefore r (a, p) > / r (b, r) (2)

Similar ly r(b,p) = r(c,q) (3)

Therefore r (b, p) > / r (c, q) (4) Therefore r(a, p) >/r(c, r) if double cancellation holds (5) Equation (1) also gives us

r(b, r) >/r(a ,p) (6)

and eqn (3) also gives

r(c, q) ~ r(b, p) (7)

so double cancellation implies

r(c, r) >~ r(a, p) (8)

So, from eqns (5) and (8) we have

r(a,p) = r(c, r)

i.e. r (a, p) and r(c, r) should lie on the same isocline if double cancellation holds.

Axiom 4 (Arehimedean Axiom) I f (al, Pt) is a non-trivial d.s.s., b is in A, and

q is in P, then there exist (positive or negative) integers n and m such that

r(a,, Pn) >/r(b, q) >1 r(a,n, Pra) The existence theorem which follows from

axioms 1 to 4 is that there are real-valued functions f u n d g defined over A and P such that

(i) f(a) + g(p) >if(b) -}-g(q) if and only if (a, p) >/(b, q)

(ii) f(a) ~ f(b) if and only if a / > b (iii) g(p) >/g(q) if and only i fp >t q

Furthermore f measures the items of A and g the items of P on interval scales with a common unit.

APPENDIX 3 In this appendix an account is given of the way in which isoclines can be used to check double cancellation. Fig. 12 shows the isoclines of Baerends et al. (1955) (Fig. 1) relabelled to

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on the measurement of motivational variables

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