Em. exp. & appl. 25 (1979) 260-266. Ned. Entomol. Ver. Amsterdam

A CORRECTION FOR FOOD RESPIRATION IN BALANCING ENERGY BUDGETS

BY

B. AXELSSONr and G. I. AGREN Swedish Coniferous Forest Project, The Swedish University of Agricultural Sciences, P. 0. Fack, S-750

07 Uppsala, Sweden

A calculated correction factor due to food respiration is applied to the consumption term in energy

budgets for invertebrates. The factor is expressed as a function of the growth rate of the invertebrates,

the food respiration rate and the fraction of food remaining when changed. It is shown that applying

this correction factor to severaienergy budgets balances them.

Only a few of the studies on energy utilization by insects have independently evaluated each variable in the equation

C=P+R+FU (1)

where C= consumption, P= production, R= respiration and FU= egestion. Three of the reported budgets have disagreements between A,= C-FU and A,= P+R that are fairly large with A, invariably larger than A,. The difference between oxygen consumption calculated from Eq. (I) and estimated in a respirometer was 30%-70% for Platysamia cecropia and Pachysphinx modesta (Schroeder, 1972; 1973), and ca 250%*) for fifth-instar larvae of Danaus chrysippus (Mathavan & Pandian, 1975). These disagreements are always explained by stating that the gas exchange experiments did not measure the total maintenance costs. Exceptions are Woodland et al. (1968) working with Blatella germanica larvae and Axelsson (1977) studying Operophthera spp., where the imbalance is only four and three percent, respectively.

In this paper we suggest that the imbalance is caused by a serious overestimate of the consumption.

Estimation of consumption The overestimation of consumption seems to be the main explanation for the

imbalance in the studies performed at constant temperatures. The methods used to estimate consumption through direct weighing or measuring of consumed area

’ Permanent address: Department of Entomology, University, P.O. Box 561. S-751 22 Uppsala, Sweden

*) The value 250% is a recalculation of the imbalance which originally was reported to be 150%.

ENERGY UTILISATION IN INSECTS 261

do not account for the respiration of the food (fresh leaves) during the consumption period. Waldbauer (1968) states “The dry weight loss of excised leaves by metabolism is probably negligible”. We will here derive a formula permitting a precise estimate of the effect of leaf respiration.

Let F(t) be the amount of leaves at a given time, t, r the constant respiration rate of the leaves, C(t) the consumption rate, then F will obey the following differential equation

dF(t) - = -rF(t) -C(t)

dt

Before Eq. (2) can be integrated it is necessary to define C(t). However, as will be shown later, the specific form of the function C(t) is not very critical. A convenient approximation is therefore an exponential growth of the invertebrate

C(t) =coeat

where a is the specific growth rate of the invertebrate. Then Eq. (2) is easily integrated to (Fo= F(o))

F(t)=F,~-rt-~(eat-e’f) r+a

Let the duration of the consumption period be T, the amount of leaves remaining Fr, and the consumption during the whole period C,, then, Q, the fraction of the consumption out of the weight loss of the leaves is

% co CP- 1 rT+aT aaT- Q=-=--=-

e- rT- FT / Fo

F. - FT a Fo-FT aT ,aT _ ,-rT 1-FT/Fo

Thus, Q is the correction factor that applied to the weight loss of the leaves can account for their own respiration when calculating the consumption. The function Q depends on three readily measurable quantities, aT - the growth rate of the invertebrate times the duration of the experiment, I-T - the respiration rate times the duration of the experiment, and F and initial amount of leaves. The be i

Fo - the quotient between remaining leaves avrour of this function is displayed in Figs

l-3. One striking feature is the very weak dependence of Q on a-r, which means that the results can not depend very strongly on the specific assumption of an exponential growth rate of the consumption. In fact, as is shown in the appendix, for arbitrary consumption functions the direct effect of the consumption on Q is given by a factor between 1 and err, and since rr, as will be shown later, generally should be a small number, e rr is also close to I. Of course, this does not mean that the consumption rate has a negligible effect upon Q, but only that its effect upon Q is expressed indirectly through FT.

Another result is the very strong dependence of Q upon F Fr/Fo close to one, which can occur in experiments with f

F,, in particular for sma 1 specimens or where

food IS often changed. Although the absolute amount respired increases with the

262 B. AXELSSON AND G. I. AGREN

Q A 1.0 -

rT = 0.03

rT = 0.06

rT = 0.03 o,~5 --------------

rT = 0.12 ------ rT = 0.06 0.90

------_

---_ ,-_rT_= 0.12 ---A_

0.80

0 0.5 1.0 1.5 aT

Fig. I. The correction factor, Q, as a function of aT. a= growth rate of consumption; r= respiration

rate of food; T= interval between changes of food. Solid line F7/F,= 0 (all food eaten). Broken line FdF,= 0.5 (half the food eaten).

duration of the consumption period, this does not mean that its contribution to the required correction also increases. Actually, it can be shown that as long as r>-a, Q increases with the T (i.e., the consumption rate may not decrease too rapidly

0.2 L

* 0 0.05 0.10 0.15 rT

Fig. 2. The correction factor, Q, as a function of rT. aT= 0.75. Curves for other values ofaT would not be discernible from those displayed. Symbols as in Fig. I.

ENERGY UTILISATION IN INSECTS 263

0.6

0.L

0.2

0.06

,-rT = 0.12

0 0.5 1.0 FT’~

Fig. 3. The correction factor, Q, as a function of F,/Fo: aT.= 0.75. Curves for other values of aT would not be discernible from those displayed. Symbols as in Fig. I,

during the experiment). Therefore, if one wants as small a correction as possibie, one should not follow Waldbauer’s (1968, p. 240) recommendation to change food often but rather let the animals consume as much as possible. In this respect, the planimetric methods are ideal in that they correspond to FT/FO= 0 (non-eaten parts of the leaves do not enter the estimation procedure). However, they involve other difficulties which might be as serious (e.g. Axelsson et al., 1974, 1975).

The effect of rr upon Q is also quite strong. One particular factor that influences the value of r-r is the temperature at which the experiment is conducted. Expressed as dry weight loss the leaf respiration is of the order of 3%-5% per 24 hr (Michelini, 1958; Stiles & Leach, 1952; Schroeder, 1973). At 15” r= 0.03 d-’ for birch leaves (Bet& pen&u) (Axelsson, 1977) and with T= 1 d and assuming a Q,, of 2, r-r equals 0.06 and 0. I2 at 25” and 35”, respectively. This points to the special care that must be exercised when conducting experiments at high temperature.

DISCUSSION

Woodland et al. (1968) found a difference between A, and A, of only 4% for cockroach larvae. Because the food, wheat germ and cane sugar, certainly had very little respiration, if any at all, such a good agreement is to be expected.

In a study on the applicability of laboratory measurements to field populations of Uperophthera spp. Axelsson (1978), by taking into account the food respiration,

264 B. AXELSSON AND G. 1. AGREN

decreased the disagreement between the mean values of assimilation (A, and AJ to 3%. Without this correction the difference between A, and A, was more than 30%. The remaining small differences may even vanish if oxygen liberated during lipid anabolism was included (cf. Schroeder, 1973).

Applying the correction factor for leaf respiration also seems to yield good agreements in other cases. If the value 1.5 ml 0, g-r live wt h-l is taken as granted for the respiration rate at 32’ for D. chrysippus (Mathavan & Pandian, 1975) it is easily calculated that the assimilation at 32” should be 135 mg dw and the consumption 400 mg as compared to their 489 mg (average for males and females). The correction factor required to make the energy budget balance would therefore be 400/489= 0.82. Because all details about the experiment are not known we can only try to show that such a correction factor is reasonable. If we assume that food is changed once a day and that the respiration rate of Culotropis gigantea leaves equals that of birch leaves (probably an underestimate) we have rr 0.12. If then the leaves are exchanged when half eaten, the correction factor is precisely 0.82, Fig. 3.

A correction factor to the consumption term in the work by Schroeder (1973) can be estimated as follows. In this experiment the respiration rate of the leaves increased with time, but because the consumption is largest at the end of the experiment it seems reasonable to use a respiration rate of the leaves measured at the end of the experiment. Assume also that the leaves are exchanged every other day (not reported, but in accordance with Schroeder (1972)), then we have I-T 0.12. As the loss of plant material is estimated using a planimetric method, F,/F,= 0. Then, from Fig. 3 we find a correction factor of 0.94 giving an assimilation, A,, of 2.94 g dw compared to Schroeder’s A,= 2.9 g dw. The same correction factor, 0.94, should also apply to Schroeder (1972). Here the food is known to have been exchanged every other day but the respiration rate of the food is not measured. After the correction we have reduced A, from 5.1 to 4.1 g dw at 27” and A,= 4.0 g dw.

As can be seen from the above examples, taking the food respiration into account, can remove the imbalances in energy budgets to well within the measurement uncertainties. Although the correction of the consumption term can be only a few percent, its impact on the respiration term can be important because it is the absolute error in the consumption estimate that is carried over to’the respiration term where its relative importance, of course, is much increased. This suggests that in energy budget studies rather than looking for dubious explanations for why direct respiration measurements did not yield what was expected from data on consumption and growth, the procedure for estimating consumption must be carefully scrutinized.

We thank T. Fagerstriim for criticism. The work was partially financed by the Swedish Coniferous Forest Project supported by the Natural Science Research Council, the Environmental Protection Board, the Council of Forestry and Agricultural Research, and the Wallenberg Foundation.

ENERGYUTlLISATIONIN INSECTS 265

Appendix

Eq. 69

dF(t) - = -rF(t) -C(t) dt

which can be integrated to

F(t) =Foemrt-ewrt; dr e”C(t) = 0

=Foe-rt-esr(t-t’) ; dr C(t) 0

The last equality follows from the mean value theorem for integrals and 0 < t’ < t.

The correction factor Q now becomes T J dt C(t)

Q= O = ,r(T-t’) e -rT-FT IF0

F. -FT 1 -FT/Fo

The exact form of C(t) enters directly the expression for Q only through the value oft’ and since 0 < t’ < t its effect on Q is a factor between 1 and erT.

UN CORRECTIF, TENANT COMPTE DE LA RESPIRATION DE L’ALIMENT, A INTRODUIRE DANS LES BILANS ENERGETIQUES

II est bien connu que, dam les bilans Cnergttiques des inverttbres I’assimilation, calculee comme difference entre la consommation et la defecation, est suptrieure a celle calculte comme addition de la production et de la respiration. Un terme de correction tenant compte de la respiration de la nourriture a ete calcule pour Ctre utilise dans le calcul de ta consommation. II depend de la vitesse de croissance des invertebres, du taux de respiration de I’aliment et de la fraction qui en est consommie. Mais on constate que la vitesse de croissance des inverttbris n’influence que peu ce terme de correction, tandis que les deux autres facteurs, particulierement la fraction de nourriture consommee. peuvent itre trts importants. La vitesse de croissance peut done etre consider&e comme constante, ce qui permet un calcul exact du terme de correction. En I’appliquant a difftrents bilans tnergetiques, les differences entre les dew estimations qui atteignaient 30% et 250%, se trouvent reduites a moins de 4%.

REFERENCES

AXELSSON, B. 1977. Applicability of laboratory measurements of bioenergetic efficiencies to field populations of Operophthera fagata Scharf. and 0. brumara L. (Lep., Geometridae). Zoon 5: 147-156.

AXELSSON. B., BOSATTA, E., LOHM, U., PERSSON. T. & TENOW, 0. 1974. Energy flow through a larval population of Phyfodecra pallidus L. (Col., Chrysomelidae) on Corylus avellana L. I. Individual energy budget. Zoon 2 : 49-55.

266 B. AXELSSON AND G. 1. AGREN

AXELSSON, B., LOHM, U., NILSSON, A., PERSSON, T. & TENOW, 0. 1975. Energetics of a larval population of Operophthero spp. (Lep., Geometridae) in Central Sweden during a fluctuation low. Zoon 3 : 71-84.

MATHAVAN, S & PANDIAN, T. J. 1975. Effect of temperature on food utilization in the monarch butterfly Danaus chrysippus. Oikos 26: 60-64.

MICHELINI, F. J. 1958. The plastochron index in developmental studies of Xanthium ifalicum Moretti. Amer. Jour. Bat. 43 : 655-665.

SCHROEDER, L. A. 1972. Energy budget of the cecropia moths Plarysamia cecropia, (Lep., Saturniidae) fed lilac leaves. Ann. em. Sot. Am. 65 : 367-372.

- 1973. Energy budget of the larvae of the moth Pachysphinx modesta. Oikos 24 : 278-281. STILES, W. & LEACH, W. 1952. Respiration inplants, 3rd ed. New York, Wiley. WALDBAUER, G. P. 1968. The consumption and utilization of food by insects. Adv. Insect Physiol. 5 :

229-288. WOODLAND, D. J., HALL, B. K. & CALDER, J. 1968. Gross bioenergetics of B/ate//a germanica. Physiol.

Zool. 41 : 424-44 I.

Accepredforpublication: November 7, 1978