Why locusts start to feed: A comparison of causal factors

Anim. Behav., 1986, 34, 480496

Why locusts start to feed: a comparison of causal factors

S. J. SIMPSON* & A. R. L U D L O W t *Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, U.K.

tAFRC Insect Physiology Group, Department of Pure and Applied Biology, Imperial College at Silwood Park, Ascot, Berks, SL5 7DE, U.K.

Abstract. New statistical methods have allowed a quantitative comparison of a number of causal factors affecting feeding in fifth-instar nymphs of the migratory locust (Locusta migratoria). The methods allow one to measure the way the probability of feeding changes with time since the last meal, and how it is affected by previous meal-size, light, food-stimuli, recent defaecation and a short-term rhythm. Since all these factors are measured on the same scale (the extent to which they multiply the probability of feeding) their relative importance can be assessed. Such measures can then be related to the known physiology that underlies the initiation of feeding. For example, the effect of recent defaecation was unexpectedly large, increasing the probability of feeding seven-fold. It is likely that the size of this effect is due to a sudden change in firing rate of the stretch receptors which monitor the shape and fullness of the hindgut.

Locusts tend to feed in bouts of several minutes' duration, separated by periods of quiescence, aver- aging abut 40-60 min (Blaney et al. 1973; Simpson t982a). The regulation of food intake in fifth instar Locusta migratoria nymphs has received much attention and the factors determining the amount eaten during a meal are now well known (Bernays & Chapman 1974; Bernays & Simpson 1982; Simpson & Bernays 1983). The present paper examines and compares the factors which cause a locust to start feeding.

In a series of experiments, Simpson (1981, 1982a,,b) has recorded the temporal pattern of feeding in locust nymphs with easy access to palatable, nutritious food. The experiments measured the effects of a number of factors on the gap between meals. Recent developments in statistics allow us to examine the way the probability of feeding changes with time since the last meal. One can also determine the way this probability is affected by any causal factors measured. We have therefore reanalysed the data to measure changes in feeding probability so that causal factors may be more easily compared.

Thus, we are interested in measuring the change in probability of feeding with time since the last meal, and in measuring the effect of various causal factors on that changing probability. A variety of methods are available (see Whitehead 1983 for a review) most of which derive from medical statistics, where it is necessary to measure the effect of treatments on the life expectancy of patients, and

where the probability of dying often changes through the course of the disease.

Using medical terminology, a gap between meals is equivalent to a 'survival time' and the start of the meal is equivalent to a 'death'. The survival times of a number of patients can be used to calculate the probability of dying at any stage in the disease. This probability is usually expressed in terms of the 'hazard', which is not a probability but a 'probability density'. The distinction arises because the probability of dying is a ratio measured over a definite very short time interval, while the hazard is that ratio scaled up into convenient time units. Formally, the probability of dying in the short time interval following time t is given by

P(t) = prob(t < T < t + 6tit < T)

where T is the survival time, 6t is the time interval, and the expression I t < T should be read as 'given that the patient has survived until time t'.

The hazard at time t is given by

prob(t < T <_ t + 6tit < 73 h(t) : 6)imo -t-

6t (1)

where lim~t~0+ means the limit as fit approaches z e r o ' ,

In words, the 'hazard' at time t is proportional to the probability of a meal starting in the next small time interval, given that the last meal ended exactly t min before. In other contexts, the hazard is known as the failure rate, age-specific death rate or force of mortality, and a behavioural equivalent would be

480

Simpson & Ludlow: Why locusts start to feed 481

useful. The term 'starting ra.te' would be analogous to failure but could be mistaken for the rate at which food is taken in during the first few seconds of a meal. It could be more confusing in the context of walking or flying. We shall therefore use the term 'starting tendency'.

The classical term 'tendency' was defined by Hinde (1970) in the following way: ' In everyday speech, to say an animal has a tendency to behave in a particular way means that we have evidence that it is likely to do so'.

Used in this sense, the term tendency includes both the probability of starting a meal (while the animal is not feeding) and the probability of continuing the meal once started. The terms 'starting tendency' and 'continuing tendency' might be used to distinguish these two cases, although starting and stopping tendencies are in some ways a more natural pair.

We shall use the term starting tendency to mean exactly the same as the hazard and, like the hazard, it can rise above 1.0. The crucial point is that the starting tendency is proportional to the probability of a meal starting in the next short time interval; any factor which doubles that probability will double the starting tendency, and vice versa. Thus, it is always correct to speak of changes in feeding probability, or of a factor multiplying the probability, but the quantity shown in Figs 3-9 is the starting tendency for feeding.

As noted by Ludlow (1976) the probability of starting an activity may be influenced by a very large set of causal factors, because any factor that promotes one activity will make others less probable. Hence, the starting tendency is simply a measure of observed behaviour. We do not use it to mean the combination of causal factors for feeding at a given instant, as McFarland and his colleagues have done (see McFarland & Houston 1981). The precise measurement of starting and stopping tendencies for each activity makes it possible to quantify the effects of causal factors on each activity, but we use the term tendency as a rigorously defined measure of behavioural output; it is not a term describing the animal's internal state.

Another key point about the starting tendency for feeding is that it can depend on time since the last meal. Moreover, gaps will be longer under some treatments than others, and the problem in the present study is to control statistically for changes following a meal, so that the effect of

different treatments on the starting tendency can be measured.

M A T E R I A L S A N D M E T H O D S

The data come from three experiments. The locusts (Locusta migrator& L.) used in each of these were taken immediately after moulting to the fifth (penultimate) instar and placed individually into containers that were screened from each other. Insects had ample seedling wheat at all times and were kept at a constant temperature of 30~ under a 12 h: 12 h light-dark cycle.

Effect of Previous Meal

Ten locusts were observed continuously from the time of moulting (the morning of day 0) until the morning of day 6, a period of 130 h (experiment 1). The starting time, length and size of every meal taken by each insect during this period was recorded. Gaps between meals were measured from the end of one meal to the start of the next (Simpson 1982a). Data from the 12-h light phase of day 1 are used in the present analysis.

Effect of External Food Stimuli

In order to investigate the effect of the presence or absence of food stimuli on the time between meals, 20 locusts were observed from lights-on, day 1, until the end of the first meal of that day (experiment 2). As each insect stopped feeding, it was removed from its container and either placed in a fresh container with seedling wheat or in an empty container. After the insects had become quiescent in their new containers, the time until the first period of locomotion was recorded for both groups. Nine of the 10 locusts with access to food fed within 60 s of starting locomotion, so this period gives a good estimate of time between meals.

Effect of Light Regime

The effect of the light regime on the time between meals was measured by comparing the data for light and dark phases from experiment 1 (Simpson 1982a).

In the present analysis the 12-h light and dark phases of day 1 are used.

482 Animal Behaviour, 34, 2

Effect of Short-term Rhythm and Defaecation

Eight locusts were observed in detail over the light phase of day 1 (experiment 3). Simultaneous records of feeding and a number of other behaviours were made. Simpson (1981) showed from such records that the start of feeding, and a variety of other behaviours, occurs in relation to an endogenous rhythm running at about 15 min per cycle; the exact period varying between individuals from 12 to 17 rain. Feeding does not occur on every cycle but almost always begins at a constant phase.

Nearly 50% of all meals were also found to begin within 4 rain of the locust defaecating. Defaeca- tions occur, on average, every 30 min when the insect is feeding ad libitum (Simpson 1982b).

Preliminary Hypothesis

Having established experimentally that feeding was influenced by the size and time of the previous meal, the presence of food stimuli, the effect of the light regime, a short-term rhythm and recent defaecation, Simpson (1982b) discussed the way these factors were combined. Simpson postulated that the short-term rhythm reflects an oscillating causal factor, a certain threshold level of which is required to trigger feeding or to increase the probability of its occurrence. This threshold level declines with time after a meal as the inhibitory effects due to the previous meal decline. Meals of different sizes result in differently shaped threshold curves, bigger meals giving a higher initial threshold than smaller ones. Factors such as light, the presence of food and defaecation are added to the oscillating causal factor bringing the sum of excitatory factors closer to the threshold and so increasing the probability of feeding (see Fig. 1).

In Simpson's model, the threshold is set partly by the inhibitory effects of the previous meal and partly by competition from other activities. Lud- low (1982) however, has described a model in which the start-threshold for each activity is set exclusi- vely by inhibition from the ongoing activity; inhibition from the previous meal would then be regarded as an inhibitory factor affecting feeding. There is no incompatibility between these two models although they group causal factors in different ways. Any particular causal factor would have the same effect in both models.

In either model, feeding is more probable when the inhibitory effects of the previous meal are low,

or factors such as light, food and the short term oscillation are high. The methods of analysis used in the present study allow us to measure the way that probability is affected by each causal factor and hence to compare the strength of various factors.

S T A T I S T I C A L ANALYSIS

Our analysis attempts to measure the way that the probability of feeding is affected by various causal factors. The methods are widely used in medical statistics, although they may be new to students of behaviour. The mathematical justification is given by Aitkin & Clayton (1980) and the approach is reviewed in the book by McCullagh & Nelder (1983). The computer programs were published by Aitkin & Francis (1980) but an updated version of the software, together with a practical guide to the analysis, is included in Aitkin et al. (1986). Our aim here is to give readers a clear understanding of the power of the analysis and the ideas behind it, but they will need to consult the above references before embarking on similar analyses themselves.

Effect of Previous Meal

The preceding analysis of this experiment (Simp- son 1982a) employed log survivor curves (Fig. 2) in which the slope at any point is proportional to the starting tendency. As Fig. 2 shows, the slope becomes increasingly steep with time, indicating that the starting tendency increases with time since the last meal. Simpson (1982a) used Kolmogoro~ Smirnov one-sample tests to see whether the change in feeding probability indicated in Fig. 2 was significant. Similar tests were made on all insects.

Using that approach it is not easy to see whether the probability of feeding changes in the same way in different insects, nor to measure the size of the change so that its importance can be compared with other factors, such as the presence of food stimuli or the size of the preceding meal. In this section we reanalyse the data, using methods that allow us to measure the contribution of several different causal factors simultaneously.

The central idea was introduced by Cox (1972) and involves fitting a 'proportional hazards' model. Such a model is appropriate if the hazard changes in the same way under different treatments and if


A feeding threshold af ter :

~large ?eal ~ N,~ small meal

U

.._1

B FP TIME

first time when f. th. probability, of

feeding enhanced :

food stimuli food stimuli

A FP TIME

Figure 1. Preliminary hypothesis from Simpson (1982b). Feeding threshold (f.th.) lines represent the level of causal factors required before feeding is likely to begin. The oscillating line represents the level of causal factors present at any moment and underlies the feeding rhythm. The rhythm has a period of about 15 min, the exact value varying between individual nymphs. Shaded areas represent times in the cycle when the probability of feeding is high. FP: first peak after the end of a meal. (A) The effect of meals of different size; (B) the effect of raising or lowering other factors.

the effect of the treatment is to multiply the hazard. Fo r example, we may assume that feeding is inhibited by the effects of the previous meal, but that this inhibition declines with time in much the same way in all insects. As a consequence the starting tendency rises with time. However, other factors will affect the starting tendency so that it is twice as high, say, in the light as in the dark. The essential feature of a proport ional hazards model is that light multiplies the starting tendency by the same amount whether it is 10 or 100 rain since the last meal. This assumption can be tested.

A complication that arises in behavioural studies is that gaps extend beyond the end of the observation period or beyond the change from light to dark. Since long gaps are most likely to be affected in this way, their exclusion would bias the analysis. Fortunately, patients also survive beyond the end

of the study and the statistical problems they pose have been solved.

Gaps which go on beyond the end of the observation period, or into the next treatment, are said to be 'censored' or 'right censored'. A gap which began before the start of the observation period is also right censored because it too is an underestimate of the survival time. A 'left censored' observation is a gap which ended when you were not looking, and is therefore overestimated. The method used here does not allow left censored observations (Aitkin & Clayton 1980).

There have been several papers showing how one can fit proport ional hazard models using the statistical package G L I M (Baker & Nelder 1978), and these are reviewed by Whitehead (1983). F r o m the curve in Fig. 2 it looks as though the starting tendency (the slope of the line) increases with time

484 A n i m a l B e h a v i o u r , 34, 2

80

.r

,,=, ~1 i L i i o~' a lo

100~

i

0 40 80 120

B

0~6

0.04

i 0~2 ~ 1 .6010

TIME 81NCE LAST MEAL (min)

N=IO

Figure 3. Fitted line showing the starting tendency for feeding (hazard) plotted against the time since the last meal, using the method of Aitkin & Clayton (1980) and assuming that gaps between meals have a Weibull distribution. Individual data points cannot be shown because the hazard cannot be calculated directly from a single point. The value 1.6010 indicates the shape parameter (c~ in equation 2).

GAP LENGTH (0 (rain)

Figure 2 Log-survivor function for gaps between meals from a typical locust. (A) expands the portion shaded in (B) and shows the bout criterion chosen for that insect.

from the last meal in a fairly smooth way. For such cases the method described by Aitkin & Clayton (1980) should work well.

The basic idea is to assume that the gaps have a particular distribution with particular parameter values and then, for each gap, you can calculate the ' l ikelihood' of a gap of that length occurring in a populat ion with that distribution. You can also calculate the likelihood of a gap being longer than t, so you can find the likelihood of a censored gap. Then you can combine the likelihoods from all the gaps to find the likelihood of the observed distribution (assuming the particular parameter values).

You then alter the parameters and calculate the new likelihoods. The best fit is the one for which the data have the 'maximum likelihood'. The great advantage of this method is that you treat each gap independently, so you can measure the effect of other explanatory variables on the likelihood of each gap, and so get parameter estimates of the effect of each of these causal factors. What Aitkin & Clayton showed was that you could do this very easily in G L I M for exponential, Weibull and extreme value distributions. Of these, the Weibull

distribution gave the best fit to the present data, as expected when the probability of feeding rises (or falls) smoothly with time since the last meal (e.g. Figs 2,3).

The approach, then, is to fit a Weibull distribution to the observed gap lengths, and Fig. 3 shows the results for the first locust. It is, unfortunately, not possible to show data points in Fig. 3 (or subsequent figures) because the hazard cannot be calculated from a single observation. Differentiat- ing log-survivorship curves such as that in Fig. 2 would also give misleading results because a tie would imply that the hazard was infinite at that point on the curve.

The model shown in Fig. 3 has two parameters: a shape parameter (c 0 and a parameter (q) discussed below.

h(t) = ~t ~ - ~e "l (2)

For this insect, the shape parameter, c~, had the value 1.6010 and the hazard increased with time since the last meal. If the shape parameter were 1'0 the gaps would have an exponential distribution and the probability of feeding would be unaffected by time since the last meal. Curves with differing shape parameters are illustrated in Fig. 4. Shape parameters less than 1-0 give falling hazards with the curvature increasing as c~ diminishes.

The parameter (r/) may be a single constant or it

S i mpson & L ud l ow . W h y locusts s tar t to J e e d 485

may represent a complex regression model of the form

1"] = flO "3w f l l X l ~ - f 1 2 X 2 .3r . . . _{ f l k X k (3)

Thus, measuring the effect of given causal factors involves measuring the coefficients, fl, in equation (3).

Substituting equation (3) in equation (2) gives

h(t) = c t t ~ l e f l~ .+&xk (4)

o r

h(t) = c t t ~ l BoB~l . . .B~ ~ (5)

where Bi = e~i. Thus, the term ~t ~-1 gives the basic shape of the

curve, while the rest of the model determines how much this curve is multiplied by. When plotted on a logarithmic scale (as in Fig. 4) multiplication is equivalent to raising or lowering the curve.

One can test the statistical significance of the shape parameter by fitting an exponential distribution first, and then a Weibull. The Weibull model has one more parameter (assumption) than the exponential, so using it consumes one extra degree of freedom. One tests whether extra assumptions (parameters) are justified by seeing how much variation they explain per degree of freedom. The variation has a Z 2 distribution and is called the 'deviance' to distinguish it from the variance of classical models. Comparing the amount of variation (deviance) explained by exponential and Wei- bull models indicates whether the improvement in fit is significant. In this case the deviance drops by 2.37, for one degree of freedom, and consulting the X 2 tables indicates that the change is not significant. However, only 10 gaps were recorded for this insect, and it is not surprising that statistical significance cannot be established. Fortunately, Aitkin & Clayton's method allows One to combine the data from all of the 10 insects, provided that there are no drastic differences between them.

One can imagine two ways in which individuals might differ. The shape parameters (~) might be different, giving a differently shaped hazard function for each insect. In that case, a proportional hazards model would be inappropriate. In addition, or alternatively, the overall hazard (q) might be higher in some insects than others, while the shape of the curve is similar. By fitting Weibull distributions to each insect separately, the shape parameters were found to lie between 0-918 and 2.169, and these extremes are plotted (on a logar-

0,1

L9

,,=

>- z ~ 0.01

z

C--

2.619 N=IO

1.601 N=IO

/ ~ --0.918 N=5

0.001 0 40 80 120

TIME SINCE LAST MEAL (min)

Figure 4. Fitted lines showing starting tendency for feeding plotted (on a logarithmic scale) against the time since last the meal for three separate insects. The values shown by each curve give the shape parameters (ct in equation 2).

ithmic scale) in Fig. 4, together with the curve from the first locust. Because of the logarithmic scale, differences in the height of the curves represent multiplication.

The extremes certainly differ, but one of the curves is based on only five gaps. Fortunately, one can test for differences in shape parameter by fitting a sequence of models in which data from all insects are combined. One should normally fit the fullest model first, and then find which of its components is least significant. If that component can be dropped without loss of explanatory power, it is excluded and the next least significant component is tested. However, it is easier to explain the notation if we move from the simple to the complex.

The sequence of models and the subsequent calculations are shown in Table I. The terms should be read as in a regression equation. Fitting the 'Exponential' model is equivalent to assuming that the starting tendency is the same for all insects, and does not change with time since the last meal. Adding the term 'Weibull' fits a Weibull shape parameter, so that the starting tendency is the same for all insects, but changes with time since the last meal. This is equivalent to fitting a single curve


Table I. Analysis of deviance table showing effect of adding separate Weibull shape parameters to each insect

Residual deviance Difference from of current model previous model

Current model df Deviance Term df Deviance

Exponential 81 871.77 Weibull 80 864-89 Weibu11 1 6.88** Weibull + Insect 71 846.79 Insect 9 18.10" Weibull + Insect +Weibull.Insect 62 833.43 Weibull-Insect 9 13.36

Residual 62 833.43

Total 81 871.77

*P<0.05; **P< 0.01.

through all the points (a constant giving the intercept of the Y-axis is assumed). The fall in deviance between this and the exponential model is 6.88, for one degree of freedom, which is significant at the 1~ level. Hence, we conclude that the probability of feeding changes with time since the last meal.

Fitting the model 'Weibu l l+Insec t ' allows a separate Y-intercept for each insect, and therefore fits 'parallel ' curves, each with the same shape parameter, e, but a different overall hazard, t/. The fall in deviance of 18.10 is made at the expense of nine degrees of freedom, because nine extra parameters are included in the model. However, the Z 2 tables show that this is cost-effective, so we conclude that insects differ signficantly in their starting tendency.

Adding the term 'Weibull-Insect ' fits separate shape parameters for each insect, and this reduces the deviance still more. However, a fall of 13.36 in deviance is not enough to justify the expense of nine more degrees o f freedom, so we adopt the more parsimonious model of Weibull + Insect and conclude that the shape parameter is similar in each insect. In other words, that the probability of feeding changes in broadly the same way in each insect. This is a fortunate result because it means that the assumptions behind the proport ional hazards model are not violated.

In the course o f this analysis the term 'Sex' was also fitted, to see if the locust's sex had any effect on the probability of feeding, but the model 'Sex +Weibu l l ' had a deviance of 864.18 which was only 0-71 (and one degree of freedom) lower than Weibull alone, so sex appears to have no significant effect. It would, of course, be pointless to leave Sex

in after adding 'Insect' , because the term Insect contains all the information contained in the term Sex and more.

In many G L I M analyses, the residual deviance of the final model gives an estimate of absolute goodness of fit, but this measure cannot be used when fitting a Weibull distribution because of the fitting method. Goodness of fit of the final model has therefore to be judged by checking that there is no systematic pattern in the 'residuals' (see Aitkin & Clayton 1980) and by comparing the Weibull model with others. In this case, a Weibull model gave a better fit than either an exponential or an extreme value model.

As mentioned above, the best approach is to begin with the fullest model the data allows, then eliminate terms that are not significant. There are a number of reasons for this, the most important, perhaps, is that factors are often correlated so that removing one from a full model may have little effect on the deviance, while fitting the same factor alone explains a great deal. The opposite can also happen, if factors cancel out each other 's effects, and removing a factor can improve the fit. In the present case, the difference between Exponential and Weibull models increases as more factors are added. Thus, when we drop the Weibull shape parameter after first fitting Insect, the change in deviance is 17.03 (Table II) rathe r than 6-88 (Table I). This means that pooling data from separate insects, without allowing for differences between them would lead us to underestimate the way the probability changes with time since the last meal. All future comparisons are therefore based on removing factors from a full model.

When correlations occur it is not always possible


to distinguish statistically between competing models and it may be necessary to describe them all.

Meal size In the previous analysis (Simpson 1982a) the

effect of meal size on the following inter-meal interval was not easily discerned. Correlations between meal size and the time to the next meal were small and differed between insects~ In the present analysis we merely add meal size as an explanatory variable and note the reduction in deviance. Adding meal size to the model Weibull +Insect reduces the deviance by 4.71 (Table II) and consumes one degree of freedom. This is significant at the 5~ level, so we conclude that meal size has a statistically significant effect.

Is the effect of meal size different in different insects? When fitting meal size in the previous model it was assumed that meal size multiplied the starting tendency by the same amount for all insects. We may allow the multiples to differ for different insects by fitting the interaction between insect and meal size (Insect.Size), noting the change in deviance. When this is done the deviance falls to 837.57 which is a drop of 4.51 (Table II) but this is certainly not worth the nine degrees of freedom consumed by the extra parameters. Thus, we conclude that meal size has a significant effect on the probability of feeding, and that the effect is broadly similar in different insects.

It seems very likely that the starting tendency rises with time after a meal because the inhibitory effects decline during that time. If so, we should expect little change after a very small meal, and a substantial change after a large one. Thus, we should expect the shape parameter to be close to 1.0 (an exponential fit) after a small meal and substan- tially above 1.0 after a large one. To test this, the gaps were grouped into two classes: those following a meal of 45 mg or less, and those following one of more than 45 mg (the mean meal size was 45.8 mg).

The program was re-run for each group and, as expected, there was a substantial difference in shape parameters between the two groups. Figure 5 sfaows the resulting starting tendencies. F o r gaps following a small meal (mean meal size = 20.2 mg) the shape parameter was 1.25 and did not differ significantly from 1.0 (an exponential fit). For gaps following a large meal (mean meal size = 78.4 mg) the shape parameter was 2.71, and the difference between this and 1.0 was highly significant.

0.1 MEAN MEAL SIZE -mg ~ 7 8 , 4 N=36

45 8 ( 9 . N = 8 2

z 20.2 N=46 ,,=, LI.

U. >- ~0.01 LU

0.001 0 40 80 120

TIME SINCE LAST MEAL (rain)

Figure 5. Fitted lines showing the starting tendency for feeding plotted (on a logarithmic scale) against the time since the last meal. The middle line is fitted to all the data, the other two to meals greater or less than 45.8 mg, respectively.

The finding that the shape parameter depends on meal size does not invalidate the use of a proportional hazards model to investigate the importance of other factors, provided that the distribution of meal sizes is comparable in all experiments.

Thus, the final model has the terms Weibull + In- sect + Size. Hence, it has the same shape parameter for all insects (value 1.5314), but the starting tendency differs between insects and is affected by meal size. The estimated coefficient/} for meal size was 0.9919 which means that every milligram of the preceding meal reduced the starting tendency by about 0-8~. This model, however, describes the situation for a particular distribution of meal sizes. Where the mean meal size is less, the subsequent inhibition is less and ceases sooner, while after large meals the inhibition is greater and lasts longer, as shown in Fig. 5.

Effect of External Food Stimuli

The aim of the second experiment was to measure the effect of external food stimuli on feeding-related activities. Since locusts usually climbed onto the wall of the cage, and remained quiescent between meals, the time to first locomotion was approximately the same as the time


Table II. Analysis of deviance for experiment 1

Term df Deviance

Sex (with Weibull) I 0.71 Insect (with Weibull)t 9 18.10" Weibull (with Insect);~ 1 17.03"* Insect.Weibull (with Insect) 9 13.36 Size (with Insect +Weibull) 1 4.71" Insect. Size (with Insect + Weibull) 9 4.51

t Insect (with Weibull) measures the effect of adding a term for Insect while controlling for changes in the starting tendency for feeding with time since the last meal.

:~ Weibull (with Insect) measures the difference between exponential and Weibult models while controlling for differences between insects.

* P<0.05; **P<0-01.

between meals. The time to first locomotion was therefore measured for 10 locusts with food and 10 without. Only one gap was measured for each insect.

In spite of the differences between this and other experiments, the results are not very different from those of experiment 1. The Weibull shape parameter was 2'874, indicating that the starting tendency rose with time after the meal (Fig. 6) and this change was highly significant (Table III). The presence of food increased the probability of locomotion by nearly six times (coefficient /~= 5.942). Finally, the shape parameters did not depend on the presence or absence of food (Table III).

Table III. Analysis of deviance for experiment 2

1 . 0

FOOD PRESENT N= 10

7- 0

0 0.1 0 o,

u_ >~ N = I O 0 Z

z w

_z

,,< 0.01

0.001 0 40 80 120

TIME SINCE LAST MEAL (rain)

Figure 6. Fitted lines showing the starting tendency for locomotion plotted (on a logarithmic scale) against the time since the last meal. The presence of food multiplies the probability of locomotion by about six-fold.

Term df Deviance

Weibull (with Food)~ 1 22.90* Food (with Weibull):~ 1 11-04" Food .Weibull l 0.42

I" Weibull (with Food) measures the difference between exponential and Weibull models while controlling for the presence or absence of food.

:~ Food (with Weibull) measures the effect of adding a term for Food while controlling for changes in the starting tendency for locomotion with time since the last meal.

* P<0.01.

Effect of Light Regime

The aim of this analysis was to compare feeding behaviour in light and dark phases of the daily cycle. Locusts were observed continuously for 12 h in light and 12 h in darkness. Using an analysis similar to that for the effect of the previous meal led to the analysis of deviance shown in Table IV.

Although the variation between insects was not significant in this experiment, the term Insect was included in the model to control for any variation there may have been, and so to increase the accuracy of the parameter estimates. The starting tendency changed with time from the meal, and it changed in the same way in the light as in the dark (Light 'Weibul l was not significant). The Weibull shape parameter was 1.4144 for light and dark combined, and was 15~ higher in the light than in the dark.


Table IV. Analysis of deviance for experiment 3

Table V. Analysis of deviance for experiment 4, using a Weibull fit

Term df Deviance

Sex (with Weibull) I 0.0 Insect (with Weibull) 9 9.8 Weibull (with Insect) 1 16.5" Light (with Insect + Weibull) 1 14.5" Light. Weibull (with Insect) 1 0.57 Insect. Light (with Weibull

+Insect+Light) 9 12.1

Term df Deviance

Insect (with Weibull) 7 24.00* Weibull (with Insect) 1 31.37" Phase (with Weibull+ Insect) 1 0.06 Relief (with Weibull

+ Insect + Phase) 1 0.08

*P<0.01.

* P<0"0t.

The probability of feeding was about twice as high in the light as in the dark (coefficient /~=2.016).

Effect of Short-term Rhythm and Defaecation

Simpson (1981) found that each insect showed a short-term cycle of between 12 and 17 min, and that meals were likely to start in the peak half of the cycle. He also found that defaecation increased the probability of feeding, so that meals were likely to occur within 4 rain of a defaecation.

For statistical purposes, these two short-term factors are rather different from long-term ones such as light, or the presence of food, or even the size of the preceding meal. Each of the long-term factors affects the whole of the gap between two meals, and consequently we would expect it to have a significant effect on gap length. The short-term factors, however, will not have an appreciable effect on gap length if they fluctuate in the same way between all meals. Defaecation may cause a meal to start slightly earlier than it would otherwise, and a meal may start late if the locust does not defaecate, but one would have to take the timing of all defaecations into account to predict their effect on gap length. Hence, one cannot easily use the Aitkin & Clayton method to reveal the effect of the short-term cycle or of defaecation. We have therefore used a two-stage approach.

The first step was to fit a Weibull distribution to the observed gap lengths. This showed that the starting tendency rose with time from the last meal (shape parameter 1-684) and that there was a significant difference between insects (Table V). This confirms the conclusions from experiment 1, and the agreement between the two estimates of the shape parameter are remarkably good (1' 5134 and 1.684). The effect of the short-term cycle (Phase)

and of defaecation (Relief) were, of course, negligible.

The next step was to examine the starting tendency less than, or more than, 4 min from a defaecation and, simultaneously, to examine the starting tendency in the peak or trough half of the short-term cycle for that insect. This was done using GENSTAT to analyse a four-dimensional contingency table.

The first dimension (Relief) indicated whether or not the insect had defaecated in the last 4 min. The second (Phase) indicated whether it was in the trough or peak half of its cycle. The third dimension (Insect) allowed us to treat each of the eight insects separately, while the fourth dimension (Hunger) was used to group gaps into four length classes: those between 0 and 30, 31 and 60, 61 and 90 and 91 and 120 min respectively. In effect, the last two dimensions were controlling for differences between insects and for differences in the time since the last meal.

For each cell in the contingency table we calculated the total 'risk time', that is the number of minutes a locust spent in the state indicated by the cell. This number of minutes was used to calculate the expected frequency using the OFFSET facility in GENSTAT (See Baker & Nelder 1978).

There was a degree of approximation in calculat- ing the risk time; we assumed that half the time was spent in the peak and half in the trough of the insect's short-term cycle, and we found the propor- tion of non-feeding time spent within 4 min of defaecation, separately for each insect, but we did not treat the gap classes separately. It is possible, for example, that defaecations tend to follow meals in some predictable way. However, that would have caused a significant interaction between defaecation and gap length (Hunger) but the interaction was not significant.


Table VI. Analysis of deviance based on contingency table (see text)

Term df Deviance

Insect 7 14.4" Hunger 3 22.5** Phase 1 34.6** Relief 1 72.3" * Insect. Hunger 20 28.5 Insect. Phase 7 7.8 Insect. Relief 7 13.0 Hunger. Phase 3 0.5 Hunger. Relief 3 4.2 Phase. Relief 1 0.7

All terms are dropped from or added to the main-effects model: Insect + Hunger + Phase + Re- lief. * P < 0.05; **P<0.01.

The analysis of deviance (Table VI) shows that all of the four main effects were highly significant, but none of the interactions were. Apar t from being much more cumbersome to program, the method is rather less sensitive to changes with time since the last meal, and presumably less sensitive overall. Its value lies in the fact that it tests whether the number of meals starting within 4 min o f a defaecation were more, or less, than one would expect, given the time each locust spent within 4 min of a defaecation. Moreover , we can estimate the size of the defaecation and phase effects. Thus, being within 4 min of defaecation increased the starting tendency by about seven times (coefficient /~=7.142). The amplitude of the short-term cycle was slightly smaller; a locust was four times more likely to start feeding during the peak half, than during the trough half of the cycle (coefficient /~=4-116). Since none of the interactions was significant, we may conclude that defaecation and the short-term cycle multiplied the hazard by the same amount, whether the insect was within 15 min or 105 min from the last meal.

The coefficients for Hunger allow us to compare this method with the Weibull fit, since this method estimates the mean probability of feeding in each of four time classes. The agreement is reasonable (Fig. 7) given the approximations involved in the contingency-table analysis and the fact that the last estimate in that analysis is based on only eight meals from five insects.

1.0

C~ _z

0.1

n- O LL >- 0 z

I -

O z_ F- n- ~ 0 . 0 1

0.00 1

/ - J

I J

f

N = 1 2 4

40 80 120 TIME SINGE L A S T M E A L (min)

Figure 7. Fitted line showing the starting tendency for feeding plotted (on a logarithmic scale) against the time since the last meal. The horizontal lines are based on a contingency-table analysis (described in text) in which the probability of feeding is assumed constant during each 30-min interval.

R E S U L T S

The methods described in the preceding section allowed us to fit a model in which the starting tendency for feeding increased with time since the last meal, and this probability was multiplied by other causal factors measured. In the preceding section we were concerned with the statistical significance of each factor but, here, our aim is to measure their biological significance. This is made possible because we can compare all the factors on the same scale: the extent to which they multiply the probability of feeding. The multiplying effect of all factors may be visualized directly if their effects on the starting tendency are plotted on the same logarithmic scale (as in Fig. 8).

Simpson & Ludlow." Why locusts start to feed 491

A z • o.1

,,=

u.

0.04

CE

~ o.oo. r o 40 80 120

TIME SING te LAST MEAL (min)

J

f

B FOOD PRESENT

FOOD ABSENT

C LIGHT

DARK j

E DEFAECATION D SHORT-TERM RHYTHM ~

FTEAK

ROUGH 15 rain 30 mln

Figure 8. Summary of results. (A) The starting tendency for feeding plotted (on a logarithmic scale) against the time since the last meal. (B) The effect of food on the starting tendency for locomotion (food-searching). (C-E) The effect of other factors on the starting tendency (also on a logarithmic scale). Each factor was found to multiply the probability of feeding (or food-searching) and this is equivalent to shifting the curve in (A) up or down by the amount indicated in (B-E). Light causes a two-fold and defaecation a seven-fold increase in probability of feeding. Some of these factors are combined in Fig. 9.

The results are summarized in Fig. 8. Figure 8A represents a 'control' locust observed during the light phase after a meal of mean size. The rest of Fig. 8 shows how much this curve would be affected by changing the experimental conditions, or by causal factors which depart from the mean.

The main feature of Fig. 8A is the way the starting tendency increased with time since the last meal. The shape of Fig. 8A would be altered by differences in meal size (see Fig. 5). Large meals reduced the probability of feeding more than small ones but they also changed the shape of the curve, so that the inhibiting effect of a large meal persisted longer than that of a small meal. In the limit, one would expect the probability of feeding to be unaffected by a meal of negligible size.

Locusts usually rested between meals and the

onset of locomotion was a good indication that feeding was about to begin. Thus, the starting tendency for locomotion reflects the probability of feeding rather well, and Fig. 8B shows that the quiescent period was almost six times less likely to end in the next minute when food was removed from the cage than when it was present. Removing food, then, should shift the curves in Fig. 8A down by the amount shown in Fig. 8B.

Feeding was half as probable in the dark as in the light (Fig. 8C) and one would therefore expect the curves in Fig. 8A to be shifted down by the amount shown in Fig. 8C.

During the light phase there was a short-term cycle of 12-17 min (constant in any locust) and feeding was about four times more probable during the peak than the trough half of this cycle (Fig. 8D). The short-term cycle was not so clear in the dark phase, possibly because of the small number of meals taken.

Finally, the probability of feeding was seven times higher during the 4 min after a defaecation than at any other time. Defaecations were irregu- larly spaced but, on average, 30 rain apart (Fig. 8E). Since there was no statistical interaction between the effects of defaeeation and the short- term rhythm, we can conclude that defaecation had the same effect on the probability of feeding whether it occurred in the peak or trough half of the short-term cycle.

All of the factors shown in Fig. 8 are on the same scale, including the change in probability with time after a meal. Thus, one may compare their effect on feeding probability rather easily. For example, the probability of feeding rises ten-fold between 5 and 100 min after a meal of average size, which suggests that inhibitory signals following the meal are only slightly larger than the effect of defaecation and the fluctuations of the short-term cycle. The differences between light and dark phase are rather smaller.

A further advantage of showing the factors on a logarithmic scale is that one can 'calculate' the starting tendency in other conditions by simply shifting the curves up or down by the appropriate amount, or by superimposing the short-term cycle or the effects of defaecation on the 'control' curve of Fig. 8A. Such a combination is shown in Fig. 9.

D I S C U S S I O N

Figure 8 allows us to compare the relative impor-


1 . 0

z

w w

0.1 re

z w I.-

_z I,-

0 . 0 1

0 . 0 0 1 J i i 0 40 80 120

TIME SINCE LAST MEAL (min)

Figure 9. The starting tendency for feeding plotted (on a logarithmic scale) against the time since the last meal. The starting tendency fluctuates because of the short-term rhythm and the effect of defaecation.

tance of various causal factors on the probability of feeding and it was a great surprise to find so little difference between the various factors measured.

Although Fig. 8 gives an estimate of the change in probability of feeding, following a meal, the estimate should not be vested with spurious accuracy. Any statistical method is approximate and there are particular dangers in applying new methods to new fields. Nevertheless, separate estimates of the hazard and shape constants are consistent with each other, and the effect of meal size on the shape of the hazard curve is exactly what one would expect from the events within the gut and haemo- lymph. It would be useful to use data on the time course of the effects following a meal to check the change in feeding probability; a deterministic

model combining known information would be a valuable adjunct to this analysis.

While a quantitative description of the changes following a meal is an important aim of the present study, an additional aim is to measure the relative effects of different factors. For this comparison the appropriateness of a Weibull model may not be critical. Clayton (1983) fitted models with poly- nomial hazards to data on leukaemia remissions and found that linear, quadratic, cubic and quartic models differed in their description of the hazard functions, but agreed well in their estimates of the effect of clinical treatment on survival times. By analogy we may expect that the effect of factors such as food stimuli or light regime will be well estimated even if the Weibull model does not faithfully represent the changes with time from the last meal. McCullagh & Nelder (1983) also observed that the structure of the model makes surprisingly little difference to estimates and infer- ences.

The approach assumes that factors multiply the probability of feeding in the next minute. This is clearly not true for meal size which, as explained above, changes the shape of the fitted curve. However, it seems to be true for the other factors since none of them altered the shape of the Weibull curve, nor were any of the interaction terms tested significant. While there is no quantitative estimate of statistical power for these methods, the fact that a multiplicative effect can be rejected decisively for one factor implies that the other factors are genuinely multiplicative. It also implies that a proportional hazards model is appropriate for these other factors.

This does not imply that the animal multiplies factors in any simple way (see Houston & McFar- land 1976, for a discussion) because the probability of feeding is a measure of observed behaviour. It presumably results from competition between activities, and hence between sets of causal factors, but the way factors are combined before such competition occurs will not usually have a simple relationship with the probability of feeding. Never- theless, it is encouraging that the data do not violate any of the statistical assumptions of the approach.

It is encouraging too to find that the results of these analyses corroborate the basic features of the preliminary hypothesis, despite the fact that this was based on less powerful statistical techniques.

Now that we have quantitative measures for the


effect of a number of factors oh the probability that a locust will begin to feed, it is valuable to consider how such measures relate to known physiology.

The Effect of Meal Size

The results of the present behavioural analyses with respect to meal size tie in well with what is known of the underlying physiology.

The ingestion of food has a variety of effects which not only lead to short-term inhibition of feeding but also persist for some time after a meal and reduce the likelihood of further feeding. Increased input from stretch receptors on the gut is important in terminating a meal and also leads to the release of neuroendocrine substances which have a longer-term influence. Such substances act both peripherally, for example by reducing the sensitivity of taste receptors, and centrally, for example by inhibiting locomotor activity. In addition, absorption of nutrients from the gut alters blood composition. This in turn influences the rate of gut emptying and reduces the responsiveness of the locust to stimuli (for review see Simpson & Bernays 1983).

By 1 ~ h after feeding, various inhibitory effects have largely declined. Their amplitude and rate of decline are proportional to meal size, although the exact relationships are not known. Thus, in the locust at least, it is unnecessary to postulate 'increasing hunger' with food deprivation. Curves such as those presented in Fig. 5 should allow precise characterization of the relevant physiologi- cal mechanisms.

The Effect of External Food Stimuli

Visual and/or olfactory stimuli provided by seedling wheat could be the relevant stimuli which cause a six-fold increase in the probability that a recently fed, quiescent locust will move and feed (Fig. 8B). The fact that the probability of feeding in the dark (when there is obviously no visual stimulation from the food) is only half that in the light (Fig. 8C) suggests that olfactory cues may be the more iruportant. " Mordue (Luntz) (1979) showed that grass odour increased the responsiveness of nymphs of the locust Schistocerca gregaria to a suboptimal food (filter-paper soaked in 0" 1M sucrose).

The influence of the sight or smell of food is not specific to feeding, however, as demonstrated by

the fact that while a locust is quiescent it exhibits a variety of non-locomotor behaviours (shuffling, shuddering, small leg movements, etc.) more frequently when food is present than when it is absent (Simpson 1982b). It seems that such behaviours share a common causal factor with feeding and that the presence of food shifts the level of causal factors closer to their various thresholds (see Fig. 1).

The Effect of Light Regime

Light increases the probability of feeding and this effect can be explained at a number of levels. Most obviously, locusts cannot see the food in the dark. They can of course smell it and, under the experimental conditions, food was never more than 5 cm from the insect at any time.

Light, apart from enabling the insect to see food, can also act as an arousing stimulus per se. Photokinetic responses to light have been well documented in locusts (Cassier 1965), the effect being due to stimulation of the ocelli and antennae (Cassier 1965; Bayramoglu-Ergene 1966). Respon- siveness changes with light intensity and may be modified by other activating factors such as temperature and mechanical stimuli.

Blaney et al. (1973) showed that variation in light intensity and temperature, produced by a 25-W bulb switching on and off every 15 rain, decreased the gap between meals taken by locusts kept in otherwise constant light. Similarly, bursts of light from a stroboscope tend to stimulate a quiescent locust to move and feed (Simpson, unpublished data).

Another possibility is that the effect of photore- gime on the probability of feeding occurs, not solely because of the presence or absence of light, but because of circadian changes in activity. A circadian rhythm of activity apparently does occur in locusts, although it is weak and does not persist very long under constant conditions (Edney 1937). The fact that the efficiency of food and water utilization is lower during dark phases (Simpson 1982c) and that foregut emptying is slower (Simp- son 1983a) suggests a more general depression of metabolic activity during dark phases than would be expected simply because of the absence of light.

The representation of the effect of light on feeding, as shown in Fig. 8C, is somewhat misleading. Feeding activity actually changes during a dark phase, being relatively constant for the first 8 h and declining to a low level in the last 4 h


(Simpson 1982a). From the previous analysis, 3.0 using Kolmogorov-Smirnov tests, and pooling w data from the first 8 h of several dark phases for e~

I-- individual locusts, the probability of starting to Z

feed in the dark, unlike in the light, remains I.u 2.0

constant with time since the last meal (Simpson U 1982a). The present analysis uses the whole 12-h hd dark phase from only day 1, and the more sensitive analysis shows that the probability of feeding ua Ix. increases with time since the last meal, both in the 1.0 dark and the light. The Weibull shape parameter is O

I-- slightly (15%) lower in the dark than in the light, however, and this may reflect the fact that the gut Z empties 7% more slowly during an average gap in the dark (Simpson 1983a).

The Effect of the Rhythm

The role of the short-term rhythm in feeding has been discussed by Simpson (1981). Its nature is unknown, other than that it is endogenous and phase-set by the instantaneous transition from dark to light each morning.

The effect of the short-term rhythm was measured by comparing the number of meals starting in the peak and trough half of the cycle, and the rhythm is shown as a square wave in Figs 8 and 9. In fact, the rhythm is approximately sinusoidal (Simpson 1981) and meals were quite closely clustered around the peak as shown in Fig. 10. Moreover, the clustering is closer to the peak centre after short gaps than after longer ones. Hence, meals began at the highest point in the cycle when the preceding gap was short, but over a greater range of the cycle after longer gaps, as predicted in Fig. I. This effect reaches a plateau after about 80 rain and thus parallels the decline in inhibitory feedback from the last meal.

In common with the effects of food and light, the influence of the rhythm is not restricted to feeding. Other behaviours such as locomotor activity (without feeding) and a variety of non-locomotor activities, which are performed by a locust while resting between meals, also follow the same rhythm and, indeed, occur more frequently than feeding.

The Effect of Defaecation

Defaecation had a remarkably large effect on the probability of feeding. An investigation of the hindgut of the locust pro,)ides clues as to why this should be.

22

15 [

4 -20 21-40

PRECEDING

18 13

18

v /

v / v / v /

v /

v / v / v / V / g /

P'/A 41-60 61-80 > 80

INTERFEED(min ) Figure 10. The average time from the peak centre at which feeding begins for different inter-feed lengths. The shorter the inter-feed lengths, the closer to the peak the average meal starts. Data are pooled from the 12-h, day-1 records of the eight insects in Simpson (1981). Vertical lines represent standard errors, while the number above each histogram gives the number of data for each value.

The hindgut accounts for about one-third of the total gut length. It consists of an ileum and a rectum. When empty, the ileum is S-shaped and lies suspended within six bands of longitudinal muscle, along which run the nerves that innervate the hindgut. Prior to defaecation, the ileum of a locust that is feeding ad libitum is full and the S-shaped fold is at least partially straightened. The longitudinal muscle bands then contract and part of the ileal contents are forced back to the rectum, from which they are voided as a faecal pellet (Goodhue 1963).

These dramatic changes in the shape of the hindgut and associated muscle bands stimulate populations of stretch receptors (Simpson 1983b). Such receptors are strongly phasic in their response to changes in the shape of the hindgut and also respond tonically at a lower level when a particular shape is maintained. In addition, touch sensitive hairs surround the anus and these arc almost certainly stimulated as the pellet is voided.

Thus, during defaecation there is a high level of sensory input to the central nervous system, signal- ling that a significant section of the alimentary canal is emptying. The strongest of these inputs are transitory and so the influence of defaecation on the probability of feeding only lasts for about 4 rain after the voiding of a faecal pellet.


Again the question arises as to whether the effect of defaecation is specific to feeding or is acting in the same way as any other transitory, excitatory stimulus, such as light flashes or mechanical distur- bance. That the latter may be the case is suggested by the occurrence of other non-locomotor behaviours immediately before and after defaecation (Simpson 1981). Also, defaecation may lead to locomotion without feeding.

This raises the difficult issue of interactions between locomotion and feeding. Locomot ion is necessary in most cases to reach the food. Observa- tions suggest that two basic types of locomotor activity precede feeding. The most common type is exhibited when the insect leaves the resting position and moves directly towards the food with its head lowered and its palps tapping the substrate. Imme- diately on contact, the forelegs grasp the food and feeding commences. On other occasions an insect will initiate locomotion but not move directly towards the food, and feeding may not occur until the food has been contacted several times in the course of moving about the container. This type of locomotion is more common in relation to defaecation-induced than to non-defaecation-induced meals (Simpson 1982b).

The former behaviour seems to imply that both feeding and locomotion are strongly excited prior to initiating locomotion and that this leads to directed movement towards the food, whereas the latter suggests that just the locomotion threshold is crossed on leaving the resting position, and activity and random contact with the food subsequently elevate the level of the causal factor above the feeding threshold.

The clearest evidence for directed locomotor activity in locusts comes from the work of Kennedy & Moorhouse (1969) and Moorhouse (1971). They found that S. gregaria nymphs which were deprived of food would move upwind if exposed to grass odour in a wind tunnel. This positive anemo- tactic response was inhibited for some time after the locust had fed, but a variety of stimuli could overcome this inhibition. Thus, recently-fed nymphs would exhibit strong, upwind locomotion if they were roughly handled first.

In summary then, a number of factors affect the probabili ty of feeding to varying degrees. Of these, light, food stimuli, the short-term rhythm and defaecation are not specific to feeding behaviour, since they also influence the occurrence of a variety of non- locomotor behaviours as well as undirected

(kinetic) locomotor activity. Of those factors inves- tigated, the most specific in effect would appear to be the inhibitory consequences of a previous meal. While the probability of feeding increases with time since a meal, the probability of occurrence of at least some of the non- locomotor behaviours does not change (Simpson 1981). This is interesting as it implies that, although such behaviours share common causality with feeding, their thresholds are disassociated from that for feeding. A more detailed investigation of non-locomotor behaviours will be the subject of a future paper.

A C K N O W L E D G M E N T S

We owe much to Drs Reg Chapman and Liz Bernays for discussions during the course of the work. Many thanks are also due to Drs Brian Francis and Trevor Sweeting for expert statistical advice.

R E F E R E N C E S Aitkin, M. A., Anderson, D. A., Francis, B. & Hinde, J. P.

1986. Statistical Modelling in GLIM 3. Oxford: Oxford University Press.

Aitkin, M. & Clayton, D. 1980. The fitting of exponential, Weibu11 and extreme value distributions to complex censored survival data using GLIM. Appl. Statist., 29, 156 163.

Aitkin, M. & Francis, B. 1980. A GLIM macro for fitting the exponential or Weibull distribution to censored survival data. GLIM Newsl., 2, 19-25.

Baker, R. J. & Nelder, J. A. 1978. The GLIM System, Release 3, Generalized Linear Interactive Modelling. Oxford: Numerical Algorithms Group.

Bayramoglu-Ergene, S. 1966. Untersuchungen fiber die dynamogene Funktion der Antennen bei Anacridium aegyptium. Z. vergl. Physiol., 52, 362-369.

Bernays, E. A. & Chapman, R. F. 1974. The regulation of food intake by acridids. In: Experimental Analysis of Insect Behaviour (Ed. by L. Barton Browne), pp. 48-59. Berlin: Springer Verlag.

Bernays, E. A. & Simpson, S. J. 1982. Control of food intake. Adv. Insect Physiol., 16, 59 118.

Blaney, W. M., Chapman, R. F. & Wilson, A. 1973. The pattern of feeding of Locusta migratoria (Orthoptera, Acrididae). Acrida, 2, 119-137.

Cassier P. 1965. Le comportement phototropique due criquet migrateur (Locusta migratoria migratorioides R. et F.): bases sensorielles et endocrines. Annls Sci. nat. Zool., 7, 213 358.

Clayton, D. G. 1983. Fitting a general family of failure- time distributions using GLIM. Appl. Statist., 32, 10~ 109.

Cox, D. R. 1972. Regression models and life tables (with discussion). J. R. statist. Soc., B, 74, 197 220.


Edney, E. B. 1937. A study of spontaneous locomotor activity in Locusta migratoria migratorioides (R. & F.) by actograph method. Bull. entomol. Res., 28, 243-278.

Goodhue, D. 1963. Some differences in the passage of food through the intestines of the desert and migratory locusts. Nature, Lond., 200, 288-289.

Hinde, R. A. 1970. Animal Behaviour: A Synthesis of Ethology and Comparative Psychology. 2nd edn. New York: McGraw-Hill.

Houston, A. & McFarland, D. 1976. On the measurement of motivational variables. Anim. Behav., 24, 459-475.

Kennedy, J. S. & Moorhouse, J. E. 1969. Laboratory observations on locust responses to windborne grass odour. Entomologia exp. Appl., 12, 487-503.

Ludlow, A. R. 1976. The behaviour of a model animal. Behaviour, 58, 131-172.

Ludlow, A. R. 1982. Towards a theory of thresholds. Anim. Behav., 30, 253 267.

McCullagh P. & Nelder, J. A. 1983. Generalized Linear Models. London: Chapman & Hall.

McFarland, D. & Houston, A. 1981. Quantitative Etho- logy." The State Space Approach. London: Pitman.

Moorhouse, J. E. 1971. Experimental analysis of the locomotor behavio ur of Schistocerca gregaria induced by odour. J. Insect Physiol,, 17, 913-920.

Mordue (Luntz), A. J. 1979. The role of the maxillary and labial palps in the feeding behaviour of Schistocerca gregaria. Entomologia exp. Appl., 25, 279-288.

Simpson, S. J. 1981. An oscillation underlying feeding and a number of other behaviours in fifth-instar

Locusta migratoria nymphs. Physiol. Entomol., 6, 315 324.

Simpson, S. J. 1982a. Patterns in feeding: a behavioural analysis using Locusta migratoria nymphs. Physiol. Entomol., 7, 325-336.

Simpson, S. J. 1982b. The control of food intake in fifth- instar Locusta migratoria L. nymphs. Ph.D. thesis, University of London.

Simpson, S. J. 1982c. Changes in the efficiency of utilisation of food throughout the fifth-instar nymphs of Locusta migratoria. Entomologia exp. Appl., 31,265 275.

Simpson, S. J. 1983a. Changes in the rate of crop emptying during the fifth-instar of Locusta migratoria and their relationship to feeding and food utilisation. Entomologia exp. Appl.~ 33, 235-243.

Simpson, S. J. 1983b. The role of volumetric feedback from the hindgut in the regulation of meal size in fifth- instar Locusta migratoria nymphs. Physiol. Entomol., 8, 451-467.

Simpson, S. J. & Bernays, E. A. 1983. The regulation of feeding: locusts and blowflies are not so different from mammals. Appetite, 4, 313-346.

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(Received 26 April 1982; revised 30 January 1985; MS. number." 2244)

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Why locusts start to feed: A comparison of causal factors