Pergamon Bulletin of Mathematical Biology, Vol. 57, No. 3, pp. 441460, 1995

Elsevier Science Ltd �9 1995 Society for Mathematical Biology

Printed in Great Britain. All rights reserved 0092-8240/95 $9.50+0.00

0092-8240(94)00048-4

B U I L D I N G A C T I V I T Y A N D L O N G E V I T Y O F Q U E E N L E S S G R O U P S O F T H E O R I E N T A L H O R N E T , VESPA ORIENTALIS

�9 J A C O B S. ISHAY,* A D A H. ABES,* H A R R Y L. C H E R N O B R O V , * V E R E D B A R E N H O L Z - P A N I R Y , * Y I S R A E L P A R M E T t and C A M I L F U C H S t *Depa r tmen t of Phys io logy and P h a r m a c o l o g y , Sackler Facu l t y of Medic ine and t D e p a r t m e n t of Statist ics and Ope ra t i ons Research, R a y m o n d and Beverly School of Exact Sciences, Tel-Aviv Univers i ty , R a m a t Aviv, 69978, Israel

(Fax: 972-3-6409113)

The effect of group size on behavioral parameters of the Oriental hornet, Vespa orientalis, was assessed experimentally under laboratory conditions. Hornet groups of various sizes (ranging from 1 to 100 individuals per group) comprised of young individuals (0-24 hr of age) devoid of a queen were placed in artificial breeding boxes (ABBs). The following three quantitative parameters were evaluated: the amount and rate of building as a function of the number of hornets in the group, the rate of oviposition as related to group size and the longevity of hornets as a function of their group size. The probability for the occurrence of these events was similarly considered and additional behavioral parameters were only assessed qualitatively.

Results of this investigation revealed a relation between the three mentioned quantitative behavioral parameters and the number of hornets per group. The number of hornets per group was positively related to the extent of building, the number of cells built by a group is 2n~/group size, but negatively related to the rate of building. As for the delay of building, a non-monotone relation was found. The relation between number of hornets per group and the oviposition delay was found to be non-monotone; the number of hornets per group and their longevity were found to be inversely related.

Discrepancies were recorded on the very small (1-2 individuals) or very large (100 individuals) hornet groups.

Introduction. Effect of crowding or group size on the physiology and behavior of animals has been investigated on numerous species. Studies of social insects by Grass6 (1946) were the first to yield the coining of such concepts as mass effect and group effect. In their attempts to elucidate social physiology in insects, Darchen (1957) and subsequently Martin (1963) raise the issue of "critical mass" in colonies of honeybees and discuss the importance of a queen's presence in such colonies for proper building of the comb. Yet in social hornets it was found (Ishay, 1973) that small groups of queenless workers raised in the

441

442 J. S. ISHAY et al.

Table 1. Hornet size groups used in the study

Size of group (no of hornets) 1 2 5 10 20 40 60 80 100 Total size of groups (per 10 9 8 9 9 6 2 2 5

group size) Total no. of hornets (per 10 18 40 90 180 240 120 160 500

group size) Total no. of hornets used in experiment--- 1358

laboratory construct a comb just the same as do queens or queenright colonies in the natural ambience (Iwata, 1971). Longevity of insects was similarly found to be affected by size of the group. Thus, Grass6 and Chauvin (1944) reported that the life span of termites and ants is shorter when they are isolated individually than when allowed to live in groups. A further finding relating to the ant species Neivamyrmex carolinensis is that the workers live longer in the presence of a queen (Watkins and Rettenmeyer, 1967). As for the hornet species Vespa orientalis, it was found that the mortality rate is affected by the population density, i.e. the greater the group (with the volume of the ABB kept constant) the greater the mortality (Ishay et al., 1980). Among these "problems" the pertinent ones are: (a) estimation of the minimal number of hornets needed to construct a comb or comb cells, and (b) estimation of the optimal population density for adequate building activity, oviposition and prolonged life span of the hornets. The present study addressed these questions.

Materials and Methods. Nests of the Oriental hornet were collected during the summer months (July-September) from the region of Ramat-Aviv in the Tel-Aviv metropolitan area. Once located in the field, the nests were exposed to diethyl ether and, shortly after, the population of anesthetized workers was extracted and the combs were collected (Ishay, 1964).

Each day, the hornets eclosing during the previous night were collected so that test hornets were 24 hr of age or less when used. Test hornets were introduced into breeding containers with a volume of 14,175 cm 3. This volume was chosen because it is similar to the volume of the natural cavity of a hornet nest at peak activity (Ishay, 1964). These containers comprised five wooden sides and a sixth glass side, with several holes bored into the side walls, through which vials containing sugar solution and protein nutrients as food could be inserted. As building materials, the hornets were offered a clump of soil and a paper towel which were placed in the container and also the wood of the container itself which they chewed off the walls. All hornets received sucrose solution at a 30% concentration and also protein food (fish or hornet pupae). The sugar solution was replenished every 2 days and also the protein food, both offered ad libitum. All the containers were identical in volume, shape and regime.

The hornets were arranged in groups of different size, as shown in Table 1.

BUILDING ACTIVITY AND LONGEVITY IN HORNETS 443

The density of hornets per ABB is expressed in terms of the number of hornets since the volume of the containers is constant.

Assignment of individual hornets into the various groups was totally random, using a "pool" of young (0-24 hr) hornets collected from numerous colonies. Equally random was the setting up of the various groups, so that on any one day the groups started were always different in size and never contained the same number of individuals. The ABBs Were placed on shelves that were illuminated with fluorescent light throughout the day (12 hr) and kept in the dark during the night. The temperature during the daytime ranged from 28 to 30~ and at night was 24 to 26~ In cases where significantly high hornet mortality occurred during the first 48 hr of the experiment, the entire hornet population of the "afflicted" ABB was replaced.

Observations and recordings on the various experimental groups were made once every 2 days during the morning hours (between 10 and 12 a.m.).

The qualitative and quantitative parameters examined and recorded in the different size groups of hornets were:

(a) comb building--when this occurred, data were collected regarding the onset of building, the number of cells built, the localization of the comb, the organization or orderliness of the comb cell building and the preference for building material;

(b) oviposition--conditional on cell building, the oviposition was evaluated in terms of duration until first egg was laid, number of eggs laid, and developmental stage of the brood;

(c) longevity--recorded in terms of time elapsed until death of the first hornet in the group, time elapsed until half the group population succumbed, and the time lapse until death of the last member of the group; and

(d) behavior---evaluated in terms of hornet aggregation, hornet organization into sub-groups in the large-sized groups, rapidity with which hornets reach the offered food, or retardation in reaching food.

The observational and other collected data were subjected to statistical evaluation, including the fitting of regression models. Regression models were fitted for estimating the relationship of one variable as a function of another, assuming cause and effect (Sokal and Rohlf, 1981). Various transformations were tested for both the dependent and independent variables. The Box-Cox power transformation (Box and Cox, 1964) served to determine the appropriate transformation for the dependent variable.

A family of transformations for the independent variables was then assessed as well. The selected models and transformations were based on maximization of the likelihood function. The resulting additive models (after the transforma- tion) were then compared with the relevant non-linear regression with respect to the distribution of the residuals generated by the two related models. When

444 J .S . ISHAY et al.

compared to the residuals obtained under the nonlinear regression we found, as a rule, that the distribution of the residuals from the transformed additive model resemble more closely the distribution assumed under the normal assumption.

For the sake of brevity we present in the next section only one illustrative example of this contention. The example also includes a discussion on the detection and treatment of outliers.

Whenever a polynomial regression was required, the selected degree was based on a backward elimination of terms (starting with a cubic equation). The critical p-value for excluding a term was c~ = 0.05. When the dependent variable was a dichotomous one (e.g. oviposition vs no oviposition or building vs failure to build) we used the logistic regression method.

Results (a) Relation between number of hornet per ABB and building capacity. Three

specific aspects were considered under heading: (1) the relation between total number of cells built (henceforth CELL per

ABB) and number of hornets in the ABB (henceforth H); (2) the relation between average number of cells built by each hornet

(henceforth cell per capita, or CPC) and the total number of hornets in the ABB; and

(3) the relation between the time elapsed from formation of the group to building of first cell by that group and the total number of hornets in the ABB.

The above three models are conditioned upon the event that comb building has occurred.

As per the first aspect, the question to be addressed was whether the relation between CELL and H was linear. From the scatter plot (Fig. 1A) we deduce that ln(H) is a better "explanatory variable" than H itself, and according to the Box-Cox method, the transformation of the square root of CELL is more suitable than the scale of CELL. The outcome, after two transformations, is shown in Fig. 1B, where a regression estimate is fitted between the square root of CELL and ln(H), and where:

33= 2.445 + 1.015X;

(SE=0.253) (SE =0.104)

R=0.828; n = 55. The significant positive relationship of this regression line testifies to the fact that the greater the number of hornets in the group the greater the number of cells built by that group. It was derived after removing two aberrant data points (Parmet, 1991). What characterized these aberrant data was that the number of hornets was high and the building consisted of a

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BUILDING ACTIVITY AND LONGEVITY IN HORNETS 445

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Figure 1. A: Scatter plot of the total number of cells built by a group (CELL) and the number of hornets (H) in the group. B: Display of root of CELL vs In(H) (H= number of hornets) so as to model the data. R of the regression line is 0.828. This correlation was derived after excluding the aberrant data (black circles). C: Scatter plot of mean number of cells built by one hornet of the group, i.e. cells per capita (CPC) vs number of hornets (H) in same group, D: Display of ln(CPC) vs In(H), so as to model the data. R of the regression line is 0.774. This correlation was derived after excluding the aberrant data (black circles). E: Display of residual plot for (CPC) without transformation. Black circles represent aberrant data. F: Same

results as in E but presented as ln(CPC). Black circles represent aberrant data,

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446 J .S . ISHAY et al.

single cell only, so perhaps it may be more appropriate to assign these cases to the category of boxes where no building took place at all.

As for the second aspect, we again addressed the question whether the relationship between the CPC and H in the ABB was linear.

From the scatter plot (Fig. 1C) we note that here, too, In(H) is a better "explanatory variable" than H itself. We see that In(CPC) is a better scale than the CPC scale proper. The outcome following the two transformations is given in Fig. 1D, where a regression line is fitted between ln(CPC) and ln(H), and where Y = l . 7 7 - 0 . 4 8 X ; R=0.77 and n=55 ; when P=0 .000 (against the postulate of no relationship between the parameters). This, then, is the model obtained after again excluding the two aberrant observations already mentioned in the elaboration of the previous question.

In this case, as mentioned in the previous section, we show an example of the preference for an additive model (after transformation) rather than the non- linear regression model. This is illustrated in Fig. 1E and F, where Fig. 1E is a residuals plot for the non-linear regression model and Fig. 1F is a residuals plot for the additive model. In Fig. IF, with the exception of the two aberrant points, the residuals are more homogenous and less related to the dependent and independent variables. F rom Fig. 1D and F we can clearly see the two aberrant points. Furthermore, the standardized residuals are greater than 2.5.

It follows that when there is building, then:

expected = E

E(CPC) = E(C/H) = e 1"7v" e- 0.480n m = el,Vv. H - 0.48

and when there is no building, the expected CPC is 0. We can therefore assess that E(CPC) is roughly proportional to the square

root of H, provided there is building. Quite surprisingly, the above formula can be approximated as follows:

e 1"77 ~ 2~t CELL = 2rc(H~

i.e. the total number of cells built by any specific group amounts to the perimeter of a circle whose radius is equal to the square root of the number of hornets in that group.

As for the third aspect, we addressed the question of a possible relation between H and the time difference from initiation of the group and the day of building of the first cell, or alternatively, the "delay" in building as a function of H. As in our previous computations, analysis of the data here presupposed that building did occur (inasmuch as the building "delay" become infinite when there is no building):

After perusing the appropriate scatter plot (Fig. 2A) we conclude that there is need to fit a regression curve between In(building delay) and H, and that the

B U I L D I N G ACTIVITY A N D LONGEVITY IN H O R N E T S 447

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Figure 2. A: Scatter plot of time elapsed from founding of group until building of first cell by that group (Building Delay) vs the number of hornets (H) in that group. B: Display of In (Building Delay) vs (H), so as to model the data. The regression line is at minimal 'Building Delay' time with H-= 17 and at maximal 'Building Delay'

time with H= 76.

most suitable here is a polynomial regression of the third order. The curve (Fig. 2B) is described by the equation:

E(building delay) = e (1.58 - 0 .063H+ 0.002H z - 1.549 • 10 - 5 H 3 )

(0.135) (0.02)(0.0006)(4.152 e -6)

From the presented model it is suggested that when H equals 17, there is minimal E(building delay) whereas when H equals 76, there is maximal E(building delay).

(B) Relation between number of hornets in the ABB and the oviposition capacity. Two aspects were evaluated here: (1) relation between the number of hornets (H) and the time interval from formation of the group until oviposition of the first egg (henceforth O D l = O v i p o s i t i o n Delay 1); (2) relation between number of hornets and the time interval from building of first comb cell until oviposition of the first egg (henceforth OD2).

Asfor the first aspect, the possible relation between OD1 and H, we note that it is better to work with ln(OD1) explainable by the fact that a third-order polynomial of ln(H) yields the most precise characterization. The third-degree polynomial model was chosen in Fig. 3A-1 and in Fig. 3B-1; in particular, one can see that there is a minimal point where the number of hornets is approximately 20 with feasilbility for a maximal point where the hornet number is approximately 2. The pertinent curve (Fig. 3B), is derived from the equation:

448 J.S. ISHAY et al.

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Figure 3. A: Scatter plot of time elapsed from founding of group until laying of the first egg (= Oviposition Delay I) vs number of hornets (H) in group. B: Display ofln (Oviposition Delay I) vs In(H), so as to model the data; regression line incorporating the data. According to the curve minimum oviposition delay will occur when H = 25, and maximum oviposition delay at H = 2. Abberant data are black circles. C: Scatter plot of time interval between formation of first cell by group and the oviposition delay (= Oviposition Delay II) vs number of hornets (H) in the group. D: Display of root (Oviposition Delay II) vs In(H), so as to model the data. R of the regression line is 0.332. E: Display of root (Oviposition Delay II) vs H, so as to model the data. The regression curve fitted to this plot is more accurate in the higher values of H than the linear model shown in D. F: The probability for Cell Building vs no of hornets, when the circles designate the measured results and the curve, the

expected ones.

BUILDING ACTIVITY AND LONGEVITY IN HORNETS 449

0.078 + 0.011 (In H) 2 - 0.002(ln H ) 3 E(Oviposition Delay 1) = e

(0.01) (0.0046) (0.001)

As can be seen, the curve in the Fig. 3B has the minimum and maximum points in the expected places in terms of In(H) except that the curve itself is somewhat flattened. A possible reason for that could be aberrant observations, and to correct for that we attempted to fit a model excluding the 4 aberrant results (standardized residuals were greater than 2.0). However, after exclusion of the exceptional values, we again tested for normality and this time the hypothesis was accepted. The equation for this "corrected" curve is:

E(O) = ln(OD1) = 2.617-- 0.121 ln(H) 2 + 0.025 ln(H) 3

(0.102) (0.043) (0.009)

E(OD 1) = e ~

and therefore the maximum of E(OD1) will occur at the point representing 14 days in group size of 2 hornets, while the minimum of E(OD 1) will be the point of 8 days in group size of 25 hornets. Again, we should reiterate that all the analyses are conditional to the occurrence of oviposition, else the OD becomes infinite.

As for possible relation between E(OD2) and 11, a preliminary scatter plot derived by us (Fig. 3C) is not very revealing. Upon applying the Box-Cox method, if we try to fit a model for (OD2) ~ on In(H), then it suffices to use a linear model (Fig. 3D):

where y = 3.024 - 0.247X. (0.240) (0.108)

If we wish to obtain higher precision at larger values of H, rather than use the simple linear model of In(H), there is need to use a more complex model employing squares and a third-order of magnitude (Fig. 3E).

E(Y) = 2.737 - 0.0009H 2 + 8.397 • 10 - 6 H 3

(0.176) (0.0003) (3.4 • 10-6).

Actually, whenever oviposition took place, there was invariably deposition of one egg per comb cell. The brood in such cells usually developed only until the third larval instar, i.e. a rather small larva. In fact, in the entire experiment, only six larvae reached pupation and these subsequently eclosed male imagoes.

Inasmuch as our analyses up to this point were instigated on the dual assumption that both comb building and oviposition took place, we should address separately the probabilities of these two events occurring:

(A) The probability (P) for comb-building--from our preliminary scatter plot

450 J.S. ISHAY et al.

it would seem that a linear model us ing H or ln(H) is inappropr ia te because both in the large-sized and small-sized hornet groups there were instances where no building was observed. However, if we use a polynomial model of a third order in which the ln(H) is a suitable explanatory variable (following examinat ion of the deviance of the fitted models), then we can obtain a good fit for the data from the equat ion (Fig. 3F):

Y = 1.75 + 2.76[ln(H)] 2 _ _ 0.62[in(H)]3

(0.084) (1.46) (0.07)

Y = 0 = l n [ p / ( 1 - p ) ]

P = e~ +e~

(B) The probabili ty for ovipos i t ion- -provided the oviposit ion is not dependent on the onset t ime of building, i.e. if the criterion is the day of onset of oviposit ion from the day the group was formed, i.e. not taking into considerat ion whether or not there was building, then the suitable model (after first examining the preliminary scatter plot and the deviance of the fitted models) will be the squared model , with the H consti tut ing the explanatory variable. The appropriate curve will be developed from the equation.:

Y = - 0 . 0 1 2 + 0 . 1 9 4 H - 0.002H 2

(0.475) (0.073) (0.0001)

Y = 0 = ln[P/(1 - P)]

P = e~ + e~

In cases where the oviposit ion is dependent on the onset t ime of building, i.e. when the criterion is the day of onset of oviposi t ion from the day of building the first cell (i.e. we select from the various groups those that did build asking whether they also oviposited): what is the probabili ty for such oviposit ion as a function of H? By examining the scatter plot and the deviance of the models fitted, we glean that the appropriate explanatory variable is ln(H) and the appropriate model is the following linear one:

Y = 0.11 + 0.78 ln(H)

(0 .53) (0 .30) ,

where Y = 0 = ln[P/(1 - P)]

P = e~ + e~

(C) Life expectancy of ho rne t s - - to assess the possible relation between longevity of hornets and number of hornets per group, three variables were measured: (1) min-t ime elapsed until death of first hornet in the group; (2) max-

BUILDING ACTIVITY AND LONGEVITY IN HORNETS 451

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Figure 4. A: Scatter plot of the times at which first hornet died in each group (min time) vs number of hornets (H) in the group. B: Display of ln (rain) vs ln(H), so as to model the data presented in A. C: Scatter plot of time at which half the population in the group died (median time) vs number of hornets in the group. D: Display of In

(median) vs ln(H), so as to model the data presented in C.

time elapsed until death of last hornet in the group; and (3) med-"half death" time of hornets in the group.

As per "min" time, the scatter plot (Fig. 4A) revealed that the suitable model here is a linear one with ln(min) and ln(H) as variables, and accordingly the model was set up (Fig. 4B) using the formula:

E[ln(min)] = 4.68 -- 1.19 ln(H)

(0.22) (0.08)

E(min) = e 4'68 - H - 1.19

From the above it was gleaned that the time of death of the first hornet in the group was roughly proportional to the number of hornets in the group.

As for the "max" time, the scatter plot failed to reveal any relation between it

452 J . S . I S H A Y et al.

and either H or In(H). Even when we tried to fit some sort of model for the data, we invariably found that the coefficient of H or In(H) equalled zero at the level of ~ = 0.05.

As for "med" time, the scattered plot (Fig. 4C) shows that the suitable model is the linear one, with ln(med) as variable, and after examining the deviance of fitted models, we found that In(H) is preferable to H. Hence we obtained (Fig. 4D):

ln(med) = 4.56 - 0.38 In(H)

(0.09) (0.015)

med = e 4 ' 5 6 �9 e -0"38In(H)

reed --- e 4 ' 5 6 . H - ~

med = e 4'5~ ( 1 / ~ ) .

(D) Hornet behavior--hornets placed in an ABB tend to congregate (positive thigmotaxis) on the ceiling of the box (negative geotropism) in the most shaded spot (negative phototropism), Several days later, comb building usually commences, as already described quantitatively. Qualitatively, the process is similar in the differently-sized hornet groups and is essentially as follows. The building commences on the ceiling of the ABB, the onset usually comprising a pedicel oriented vertically downwards and 0.7-1.5 cm long. Next to be built are the cells. First there are one or two cells which are built in the center (i.e. directly underneath the pedicel) and around these are built further circlets of cells, as already described by Ishay et al. (1982). This type of building is normal, i.e. it is exactly as those built by hornets in the wild. Aberrant building was, however, recorded in two instances: (a) in the small groups, comprised of one or two individuals, the built cells were either smaller or larger than normal, or lacked the typical hexagonal shape (Fig. 5). Furthermore, in most of these smaller-sized groups, the building of cells commenced without initial building of a pedicel, and not from the ceiling but rather on the vials containing the sugar solution (i.e. not from the zenith of the ABB). Even so, whenever there was building of cells, the outlet of the cells were still oriented directly downward, i.e. in the direction of the gravitational force, just as in the natural nest; (b) in the largest groups, comprised of 100 individuals, no building whatsoever was recorded.

In all cases where building took place, the preference for building materials was in the following decreasing order: mica, styrofoam, paper towels, wood, gypsum and Khamra soil. What all these materials have in common is that they are isolating materials with a high dielectric constant.

The extent of aggressive behavior by hornets in the differently-sized groups was gauged by nervous flights within the ABB or settling on its walls in a

BUILDING ACTIVITY AND LONGEVITY IN HORNETS 453

Fig. 5. (a) Non hexagonal cells built on a test tube containing sugar solution by a single hornet (V. orientalis) kept solitary in an ABB, thus comprising a one-hornet group, compared to a normal comb built by a group of 10 hornets in the same

conditions (b).

BUILDING ACTIVITY AND LONGEVITY IN HORNETS 455

threatening pose. In terms of the extent of aggression, the largest (100)-sized groups were again exceptional in that the individual hornets in these groups displayed a considerable degree of"apathy", standing motionless for 1-3 hr on the walls of the ABB, congregating around the food source with only few hornets showing any sign of aggression.

From the standpoint of approach to food or degree of hesitation in such an approach there were differences between the various hornet groups. In this connection, we should mention the phenomenon which we have named the "inspection dance", concerning the gradual approach to food. In the course of this "dance", usually performed by the first hornet to reach the food, the hornet intermittently approaches and withdraws, but with ever-increasing proximity to the food source. The same hornet also probes the food with its antennae and, very slowly, following this inspection, nears the food. Once the food source has passed such inspection by an initial hornet, it is no longer prohibited for the rest and is now freely approached by all the other hornets. This phenomenon is very clearly in evidence in the small hornet groups (1-20 hornets) but is practically never observed in the large hornet groups.

Discussion. In nature, the building of the hornet's (Vespinae) nest occurs in two main stages. The first stage, designated the pre-emergence stage, spans the time interval from foundation of the nest until eclosion of the first worker and during this period it is the queen which builds the embryonal comb. The second stage divides into several substages and represents the period during which the worker hornets eclose to take over the nest building. The first stage represents a haplometric system wherein we are deaing with a one-hornet group comprised of the queen which, having been fecundated, is therefore "motivated" to build in order to oviposit and found a colony. During the second stage we accordingy deal with groups of steadily increasing size, wherein the workers are the builders (and also fulfil other nest duties except the actual oviposition) in accordance with the ovipositional capacity of the queen, i.e. the workers build the comb cells at a rate which does not exceed the egg-laying rate of the queen.

The present study assessed the building and oviposition capacities of hornet groups but in doing so diverged in three significant ways from the previously described norms extant in nature: (1) the studied hornet groups were queenless; (2) our group of hornets was assembled from different colonies; and (3) the assembled hornets were not able to grow up under the normal rhythms of growth and activity extant in the natural colony because immediately upon eclosion they were removed into ABBs which they could not leave throughout the experimental period. The third difference implies that these "orphaned" hornets had to create de novo their own rhythms of activity. This difference notwithstanding, it was established long ago (Ishay, 1973) that worker hornets themselves are capable of both building and ovipositing, but what is innovative

456 J.S. ISHAY et al.

in the present study is the use of hornet groups of differing size ranging from 1 to 100 hornets per group.

Once we had modelled the probabilities of the building and oviposition by hornets, we utilized only those data attesting to these activities, so as to be able to assess a possible connection between group size and the amount and rate of building. In other words, after first ascertaining the probability that building and oviposition will at all occur in groups of a certain size, only then were groups displaying these activities assessed for the relationship between group size and the amount and rate of building and oviposition.

As for the building, our data show that the greater the number of hornets in the group, the larger the overall number of cells built. At the same time, the larger the number of hornets in the group, the smaller the mean number of cells built by any one hornet in that group (CPC). In other words, as the group size increases, the hornet workers fail to attain their maximum building capability (such as is manifested in groups of one or two hornets) and rather diminish gradually the number of cells built by each of them. It is not clear as yet what or who causes this regulation of cell number inasmuch as a hornet queen, which is naturally responsible for such regulation of cell building, has intentionally been lacking in our worker groups. Possibly it is the ovipositing workers who exercise these regulations, formulating their own hierarchy in the absence of a queen. Be that as it may, the fact that the CPC diminishes with increase in group size somewhat resembles the situation in pleometrotic systems formulated by other wasp species. For example, in wasps of subfamily Polistinae it has been shown that the number of cells built by a founding queen diminishes the greater the number of queens in the nest. Again in the hornet Vespa affinis, which founds in Sumatran pleometrotic nests (Matsuura, 1983), no differences in total number of cells were encountered between an embryonal comb in nests founded by a single queen and that in nests founded by several queens which means that in the latter case the number of cells built per queen was actually smaller.

The relationship between the number of cells built by a group and size of the group is interestingly defined by the formula for the circumference of a circle, which is 2rcr. Thus, from our size analyses it appears that the number of cells built by a group is dependent on the root of the group size (H) multiplied by 2~ that is CELL= 2rcx/H. We are not sure as yet whether this relationship is accidental or rather tied to the fact that the hornets build their combs in concentric fashion. Does this circular manner of building dictate a "commit- ment" on the part of a given-sized group to complete a given number of cells so as to close the circle? Nonetheless, under the laboratory conditions prevailing during the present study, this quantitative regularity of the building was retained up to groups of 80 individuals. In the largest-sized group (100 hornets), usually no building activities occurred whatsoever, at least in the

BUILDING ACTIVITY AND LONGEVITY IN HORNETS 457

given volume of our ABBs. In nature, the population "pressure", i.e. the massive increase in the number of hornets in the nest causes a proportional increase in the rate of building, and towards the end of the summer, when the nest contained the maximum number of individuals, there is also a peak amount of building. The activities and size of the colony are under control of the queen. On the other hand, in this study the conditions resembled those in an orphan nest, devoid of a queen, where the workers develop ovaries and commence cell building as well as oviposition. It is reasonable to conjecture that inability of the workers to leave the ABB and thereby "escape" an ambience saturated with oviposition-depressing pheromones, such as those probably released by the workers that had developed ovaries, is the primary reason for non-building in the very crowded groups of 100 hornets each--this despite the fact that the amount of building pheromones in such crowded ABBs is probably very high. In the less populated ABBs we can observe a group of building workers assembling around each ovipositing worker and accordingly a number of nascent building spots. Again we conjecture that in the 100- individual groups, owing to the crowing effect in the ABB, there is a reciprocal inhibitory effect by the ovipositing workers which prevents the assembling of workers around them and consequent building nidi. We noted with interest that in the groups of 100 individuals even after death of 50-60% of the population, i.e. even when there remained only 40-50 hornets in the ABB, no building commenced, despite the fact that in groups of hornets ab initio of this size there was invariably building activity. This implies either the persistence in the ABB of the factor initially responsible for inhibition of the building and thus the continuing repression of building or that hornets that had been suppressed from building while young cannot later restore their building capabilities.

A qualitative deviation from regular building was observed in the smaller groups comprised of one or two hornets. Herein the workers at times built cells that were not hexagonal and on many occasions built cells without first building a pedicel, albeit the orientation of the building--toward the gravitational force--was invariably retained as was the size of the built cells. The reason for this deviation could reside in the fact that in such small groups there is no "corrective" effect, such as the one exerted by one building hornet on its mate in terms of manner and accuracy of the building. In other words, we are missing here guidelines ensuring that the built cell will be precisely hexagonal, i.e. with six equal sides and six angles of exactly 120 ~ Evidently, there is a need for some corrective and regulatory mechanism which, apparently, is dependent on interaction or reciprocation by a larger number of hornets. Perhaps there is a need for a certain mass of hornets to achieve such safeguards of perfect building. It is interesting to point out that in experiments carried out with wasps of Paravespula and intended to assess the nest building capability of the queen (i.e. like groups of one hornet in the present study) under laboratory

458 J .S . ISHAY et al.

conditions, Ross (1982)found that 1.5% of queens of the species P. maculifrons and 9.1% of queens of P. vulgaris built combs devoid of pedicels. Such combs never exceeded a certain "embryonic" size and after 1-2 months degenerated altogether. Two possible explanations were offered for this phenomenon. The first was that a margin of error was created by the laboratory conditions under which the "aberrant" queens were maintained. The second assumed that in nature there is also faulty building to about the same extent as was observed in the laboratory except that such aberrant nests do not grow but rather degenerate and disappear so they are not detected by an observer examining an active nest.

In nature, however, the accuracy of the building of the hexagonal cells in the brood combs of the Oriental hornet built by the queen alone was never so impaired, nor did errors in cell building occur to any greater extent than in the combs built by the large-sized groups. This observation leads us to suspect that errors in the building of hexagonal cells in groups comprised of one or two hornets may stem from the nature of the substrate upon which the hornets opted to build, namely, the glass vials used to contain the sugar solution proffered as food for the hornets. The electric resistance of glass is higher than that of the soil or wood normally serving as the substrate for the incipience of building. Conceivably, in this case there was a disruption of the measuring systems of the hornets which are "programmed" to measure only small electrical resistances, so that this disruption was responsible for the ensuing errors in the final building product (Ishay et al., 1991).

Two different hormonal systems are responsible for building and oviposition in hornets. This has been deduced from experiments showing that building can occur without any subsequent oviposition (Ishay, 1975) and other experiments that revealed stimulation to oviposit and actual oviposition directly on the walls of an ABB in groups where no building occurred at all (Ishay et al., 1986). In line with this dichotomy, each hormonal system dictates its own behavioral pattern whether building or oviposition, and it is the coordination between the two systems which determines the rate of growth of the colony. In the natural, queenright colony, the queen induces such coordination and in so doing it also regulates the rate of growth of the colony. In our queenless experimental groups such central influence is absent and in its absence we have seen that the size of the group is apparently of critical importance. Our present data point to an opposing trend between inhibition of the building and inhibition of the oviposition in that when the group size is fairly small (10-20 individuals) there is a proclivity for minimal retardation of the building activity coupled to a maximal retardation of the oviposition, whereas at fairly large groups sizes (30-80 individuals) the situation is reversed (i.e. maximal retardation of building and minimal retardation of oviposition). The pattern with regard to the two events--building and oviposition--shows that when we are dealing

BUILDING ACTIVITY AND LONGEVITY IN HORNETS 459

with small groups of hornets, the two events are far removed but as the group size increases the proximity between the two events increases as well. However, at maximal group size (100 individuals)the two events again grow apart.

As for life span of the hornets in the different groups we found that time of death of the first hornet in a group as well as time of death of half the hornets in a group are both inversely proportional to the number of hornets in the group. In other words, the greater the group the smaller the mean life expectancy of its members. This bolsters previous findings with V. orientalis along the same lines (Ishay et al., 1980).

We are still in the dark regarding the reason for this inverse relation between group size and longevity. Perhaps this relation is attributable to a secretion of pheromones and/or toxic substances by the hornets in the various groups such as is elicited by each of the hornets toward its mate (Brian, 1983). The end result of such an occurrence would be a greater accumulation of toxic substances in the larger-sized groups, which would lead to a gradual, mutual intoxication of the group members and consequent disruption of the normal life span. This could also lead to a relative abbreviation of the life span in the natural nests of hornets.

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Received 10 April 1994 Accepted 28 September 1994