Periodism and Energy Summation with Special Reference to Flight Rhythms in Aphids

Diurnal rhythms, as in insect flight or in plant movement, are often due to the periodic repetition of an act by the same individual. Some organisms, however, perform an act only once in their lives (such as hatching from the egg), yet this single act repeated by different individuals is synchronized to show a periodicity in the population. Here lies a fundamental difference between population periodicity per se, which can never occur in an individual, and individual periodicity which is reflected in populations.

But periodic acts by the same individuals and single acts by a succession of different individuals both require synchronization for a periodicity to be manifested in the population. This synchronization of the only act on the one hand and of the initial act on the other, may be due to the same cause ; namely, to a differential rate of development preceding the act which, in different individuals, brings the acts together.

In the same way, it is possible also to regard periodic behaviour in a single organism as due to the periodic changes in the rates of its developmental processes.

This general principle is applied in this paper to the daily bimodal flight rhythms in populations of Aphis fabae Scop.

Winged aphids, produced on a crop, fly away when only a few hours old, never to return; the action is not repeated.

Nevertheless, a bimodal curve of numbers departing during the day (Fig. 1) with no flight at night is a common feature of such populations (Johnson, 1954)-It is shown in this paper that such a periodicity is primarily due to the alternate contraction and lengthening of the period of maturation preceding flight (the teneral period) as the temperature during the day and night fluctuates. A limited number of rather simplified examples is given; they do not cover all possible variations on the general pattern. For example, on different days the two peaks may differ widely in relative height, amplitude and time of occurrence; one may be suppressed or merged into the other. Such variations depend on the temperature and on the organisms’ relations to it ; they are of interest mainly to specialists and will be further analysed for aphids elsewhere (Johnson, Taylor & Haine, 1957).

There are three elements contributing to the periodicity of flight in aphid populations. These are: the rate of moulting into the winged adults; the length of the teneral period from moulting to flight; the environmental factors inhibiting flight.

All these elements vary in a complex way especially with temperature; and in nature they are integrated to produce a flight curve. In order to illustrate this process and the method for reconstructing flight curves from the variable and complex data obtained in the field it is convenient first to consider a simplified example (case i) to bring out the basic interactions between the above three elements in relation to temperature.

In temperate countries the mean hourly temperature during the 24 hr. often somewhat resembles a sine curve. Consider therefore a simple example (Fig. 2) in which the temperature during the day and night follows a sinusoidal curve (θ ₁ θ ₆) which is repeated on two successive days and never falls below a developmental threshold of 0° C. on the empirical temperature scale ; the moulting rate is constant at 10 per hr. and the velocity of development during the teneral period is linearly related to temperature (see pp. 213 and 215). Flight occurs immediately after maturation.

The teneral period But because $θ¯$⁠, the mean temperature, varies with time of moulting, and therefore with ⁠, the teneral period, will also vary with the time of moulting.

An area, for moulting at t₁ and maturation at t₂, is heavily outlined on the sine curve in Fig. 2. For moulting 1 hr. later at t₃, the cross-hatched area is subtracted from the left and added on to the right-hand side of the original area, so maintaining a constant area but shifting the maturation time relatively farther to the right. Similarly for moulting at t₅ (dotted area) and so on. Thus as the temperature at the time of moulting moves along the sine curve, so the period of development t₁t₂, t₃t₄, t₅t₆, etc., also shortens and lengthens rhythmically as the mean temperature rises and falls.

As each successive batch of ten insects moults at mean intervals of 1 hr., so they mature at longer or shorter intervals according to the mean temperature. The moulting rate, with the accumulated number of moults along curve k₁l₁(Fig. 2) is thus translated to a curve k₂l₂ for accumulated mature insects. If the insect flies off immediately on maturation then the numbers departing each hour will be the successive hourly differences along the accumulated maturation curve k₂l₂; this is represented by a single-peaked curve, xy.

The manner in which the single-peaked curve, xy, is produced, however, is applicable to any energy-controlled developmental process (whether in a population or an individual) where the energy fluctuates and complete development is attained approximately in a single cycle.

However, flight in aphids may be inhibited by factors such as light intensity and temperature. For example, aphids do not fly at night and, if completing their development during the night, will wait until dawn when they should depart, not all at once, but distributed over a certain period. These would produce a first peak in the morning in addition to the second, later peak. Also as light diminishes at night the rate of take-off also diminishes serially; arbitrary values of 75 and 50% for the take-off of mature individuals have therefore been given respectively for the 2 and 1 hr. preceding sunset in case 1. The individuals remaining, though mature, would not fly ; they are added on to the next morning peak. The final result is a doublepeaked curve, the heavy line uv in Fig. 2.

This is the theoretical basis for the curve of bimodal flight in aphid populations. Obviously the shape of the accumulative maturation curve and thus of the first differential or maturation rate curve, xy, will depend on the extent of the constant area under the temperature curve ; that is, it will depend on the thermal constant of the organism.

It is now possible to analyse the more complex process which actually occurs with A. fabae in nature.

In July 1952 a suction trap (Taylor, 1951) was operated in a bean crop heavily infested with A. fabae, measuring the aerial aphid density (C. G. Johnson & Taylor, 1955), and on 6 July showed a typical bimodal curve (Fig. 4c); the greater proportion of all aphids caught by this trap had just left the crop on their first flight (see p. 213).

Temperature was recorded continuously in the crop and was always above the threshold for the maturation of winged aphids. The rate at which alatae were produced by moulting (the moulting rate, case 1) was also recorded approximately once an hour. A complete description of the experimental procedure is given elsewhere (Johnson, Haine & Cockbain, 1957; Johnson, Taylor & Haine, 1957).

The natural example with alienicolae of A. fabae in summer differs from the formalized example in case 1, in the following ways.

The temperature curve is not sinusoidal, but steeper on the ascent than on the descent; there are slight irregularities from hour to hour, and it passes above the developmental optimum of 28° C. (Fig. 3).

Winged aphids are produced when the 4th larval instar moults. In nature the moulting rate is not constant as in case 1 but has a well-marked periodicity of its own (Johnson, Haine & Cockbain, 1957).

After moulting from the 4th larval instar, the alate adult passes through a period of maturation (the teneral period) before flight. This takes several hours.

The length of the teneral period varies with temperature, in the manner typical of most developmental processes ; its threshold may be taken as 9° C. and its optimum is 28° C. The development-velocity curve against temperature is semi-logistic, not linear as in case 1 (see p. 210). A full description of the temperature relations of the teneral period is given in Taylor (1957), and temperature is the only factor we need consider as affecting the duration of the teneral period.

In nature the aphid flies away immediately at the end of the teneral period (indeed this may be used to define its length) only if weather and light permit.

Experience in the field shows that approximately 1‒2 hr. after sunrise or 1‒2 hr. before sunset may be regarded as the equivalent of the light threshold for take-off for the purposes of this paper (see p. 212).

Aphids begin to take off when the temperature rises above a threshold. In this example the temperature threshold comes after the light threshold has been passed both in the morning and in the evening; this is typical. We may therefore regard temperature as the effective releaser to flight in the morning and light, 1‒2 hr. before sunset, as the inhibitor in the evening.

The threshold for aphid take-off was determined both in the field and in the laboratory; the lowest temperature at which any aphid was seen to take off was 15·5° C. But the lowest temperature for take-off, like any other attribute of an organism, is not the same for each individual nor perhaps for the same individual on different occasions ; and this attribute will be distributed about a mean value.

Provided the temperature is always above the upper limit of this distribution any aphid will take off as with a take-off after landing from a previous flight. But when the temperature is rising through the range covered by the distribution and we are considering initial take-off, then a few aphids will take off at 15·5° C., more at 16·5° C. and so on until the optimum is reached, after which there will be a decline in the initial take-off rate. As the remarks above indicate this does not imply an inhibition of take-off above the upper limit of the distribution.

The frequency distribution of take-off obtained in the laboratory is slightly skew, with a mode at approximately 17-3° C. (Table 1). This agrees with a distribution obtained from A.fabae in the field by Müller & Unger (1951) in Germany.

These remarks apply to the single act of take-off. Total numbers in active flight will be the sum of the successive numbers taking off (i.e. the integral of the frequency distribution) and, rising to a maximum, will be followed by a plateau until landing produces a decline in the numbers flying. This gives the familiar activity curve which may be confused with the threshold distribution.

In nature the trap samples aphids as they leave the crop and so reflects the takeoff rate. Consequently the first peak of flight is a frequency distribution of take-off.

A moderate wind blowing directly on an aphid delays take-off but does not prevent it, for the aphid tries repeatedly, eventually taking-off in spite of the wind (Haine, 1955 a, b). The experiments on 5‒6 July 1952 were made in a sheltered garden and the effect of wind speed in delaying take-off can be neglected (Taylor, 1957) ; this view is also justified by the accuracy of the reconstructed curves in this paper (Fig. 4).

To sum up therefore, it may be said that the aphids in this example take flight immediately they are flight-mature except in the early morning before the temperature has risen to 15·5° C. and after 1‒2 hr. before sunset; and that this is typical of summer conditions in the south of England.

Given the moulting rates and the temperatures throughout the night and day of 5 and 6 July (Fig. 3), together with the flight thresholds and the temperature velocity curve for the teneral period (Taylor, 1957), it is possible to reconstruct an expected flight curve for 6 July using the method described in case 1. This can then be matched with the actual observed flight curve (Fig. 4) obtained from the suction trap in the same crop and on the same occasion.

Each hour of the teneral period spent at a certain mean temperature adds an increment to development. In case 1 the temperature × development-velocity curve was linear, and an hour at any temperature added the same increment ; the empirical temperature curve itself could therefore be used for summation. The temperaturevelocity curve for the teneral period in nature is semi-logistic, and an hour at different temperatures adds different increments ; a certain developmental increment must therefore be assigned specifically to the mean temperature for each hour during a day. In other words the actual temperature curve must be transformed into a curve for developmental increments; we have called this the temperatureequivalent curve (Table 2, Taylor, 1957), and it is used in the constructions shown in Fig. 4a, b. The actual temperature curve is shown in Fig. 3.

It is advisable first to construct an expected flight curve based on a constant moulting rate.

This shows that in spite of departures of temperature from a sine curve, the use of a semi-logistic temperature-velocity curve, the inclusion of a temperature threshold for take-off and in spite of other out-of-doors conditions, the basic bimodality is established as in case 1 (compare Fig. 4a, c).

A second curve reconstructed with the variable moulting rate observed on 5‒6 July (Fig. 3) gives a still closer agreement of expected and observed curves (cf. Fig. 46, c). Thus the depression in numbers 1300 and 1600 hr. in case 3 is caused by the reduction in moulting overnight. This depression is commonly seen in aphid flight curves (Müller & Unger, 1952).

There are, however, several discrepancies to consider. The first peak in case 3 (Fig. 46) was obtained by arranging the number of mature insects estimated to have accumulated overnight in a frequency of flight according to a curve fitted to the distribution in Table 1 ; it is, in fact, identical in form to the observed peak (Fig. 4c), but it appears 30 min. too early and is too small. A slight discrepancy in its position is not surprising, for the position is decided by the actual temperatures at that time of the day; these are rising so rapidly that differences between air and leaf temperatures or an incorrect placing of the thermograph could produce such an effect. The size of the first peak depends also on the contribution made by insects maturing but not flying late on the previous evening; this cannot be estimated satisfactorily at present, on account of errors in estimating moulting rates from one day to another and in the effect of waning light on take-off.

The actual moulting rate was not observed exactly at hourly intervals (for details see Johnson, Haine & Cockbain, 1957); interpolated values at hourly intervals had therefore to be estimated and 3 hr. running means taken to obtain the moulting rate curve in the reconstruction of case 3. The slight depression immediately following the first reconstructed peak is caused by an unusual reduction in the moulting rate of the insects on the sample leaves at about 13-00 hr. on the day before. Such a discrepancy in the fit between observed and expected flight curves in case 3 (Fig. 4), especially for the first peak, is thus not surprising in view of sampling errors in estimating the moulting rate, apart from those of the suction trap itself.

Variations of the bimodal flight curve of aphids are extremely numerous; they are caused mainly by variation in the daily temperature curve of the same or previous day affecting the duration of the teneral period, in association with a wide variability in moulting rates. Temperature has the greater effect, particularly in the timing of peaks ; variation in moulting rate affects the height of peaks and the occurrence of subsidiary peaks.

Two examples are given here to illustrate the kind of modifications likely to occur with temperature curves of different character to those already considered; these two examples are based on actual temperature records observed in the field but with minor variations smoothed out (Fig. 5). A constant moulting rate will be used together with the temperature-velocity curve and flight thresholds for A. fabae. In the illustrations to these two examples (Figs. 6, 7), the flight curve differs very little from the hourly maturation curve, and the latter alone is drawn.

The mean temperature for 24 hr. is 16-4° C. with a range of 7-24° C. The temperature passes below the developmental threshold for nearly 6 hr. (Fig. 5 a).

Insects which fail to complete the teneral period in time for the second peak are further delayed in their development by the sub-threshold temperatures at night. Maturation is then completed very rapidly as the temperature rises next morning and the different individuals, all maturing in a short time, fly off as a steep first peak in the morning. The second peak is flattened to virtual extinction.

Thus, if the temperature within one cycle (in this case 24 hr.) does not allow development to be completed (the sum of the increments being less than the thermal constant), the second peak will disappear and become part of the first peak in the next period.

The mean temperature for 24 hr. is 18-2° C. with a range of 4-30-5° C. The temperature passes below the developmental threshold for 6$12$ hr. and above the optimum for 6 hr.

When the temperature rises above the optimum for teneral development the teneral period is lengthened, and a sufficient rise above the optimum could virtually inhibit development, though this has not been observed in nature. A more common effect is a slight excess of temperature and a retardation of development.

If the teneral period is lengthened both by sub-threshold temperatures and by temperatures above the optimum a shift of the second peak into the following day might occur as in case 4. If, however, the mean temperature for the day is also high, so allowing completion of the teneral period within the same day, the second peak will occur normally but the first peak will diminish: this is the effect in case 5.

In cases 1, 4 and 5 it has been assumed that the temperature curves are similar for two successive days. Obviously, modifications will occur when the temperature is different on successive days.

This paper has considered the specific problem of aphid flight rhythms, but the principles have a general application. The role of differential development rates in conjunction with threshold effects in causing rhythms of other actions, on different time scales and in other organisms, is obvious. It is tacitly accepted in the seasonal growth of insect populations which has its equivalent in the accumulative maturation curve in Figs. 2, 6 and 7. In seasonal population change it is the reproductive rather than the developmental element which is commonly stressed, but as shown in this paper, changes in reproductive rates (which are equivalent to the moulting rates in Figs. 2, 6 and 7) may only modify a basic pattern due primarily to variable periods of development.

In fact the seasonal and bimodal periodicity of emergence of the dragon fly, Anax imperator Leach, between May and July appears to be an example (Corbet, 1954, 1955). There the period for cessation of development during diapause represents the period below the temperature threshold for development. It would seem, however, that the annual temperature curve itself, rather than diapause, might produce the effects observed as an almost exact parallel to case 4 in this paper; as with the dragon fly, case 4 has a very much flattened second peak. There are numerous similar examples throughout the literature.

But apart from seasonal population growth many short-term periodicities which might tacitly be assumed as behavioural in character could be due to a synchronization of development in the individuals of a population and not susceptible to an interpretation primarily in terms of behaviour alone.

This paper has dealt mainly with an insect, but apart from other poikilotherms, where a similar effect is likely, it is theoretically possible that a similar mechanism may apply even in a homoiotherm if a summation of increments with some environmental factor operates on a regulatory mechanism.