IL NUOVO CIMENTO VOL. 16 D, N. 6 Giugno 1994

Energetics oí Social Phenomena: Physics Appliedto Evolutionary Biology.

K. JAFFÉ and C. FONCK

Departamento Biologia de Organismos, Universidad Simón BolivarApartado 89000, Caracas 1080, Venezuela

(ricevuto il 18 Gennaio 1994; approvato il 20 Luglio 1994)

Surnrnary. - The potential usefulness of applications of two physical concepts toevolutionary biology was evaluated on ant societies. The optimization principIe,which predicts a more efficient use of energy by more sophisticated societies, wascontrasted to that of irreversible thermodynamics, predicting an increase inorderliness and thus an increase in energy consumption per unit of biomass. Ourresults on oxygen consumption measurements of ant colonies showed a complex andnon-linear relationship between colony size and energy consumption per unit mass,that can be explained by irreversible thermodynamics and catastrophe theory,whereas an additional exponential inverse relationship may be explained byoptimization'principles. Thus, social complexity is related to energy consumption ina discontinuous manner, and seems to be bound by both negentropy content of asociety and social-optimization mechanisms.

PACS 87.10 - General, theoretical, and mathematical biophysics (including logic ofbiosystems, quantum biology, and relevant aspects of thermodynamics, informationtheory, cybernetics, and bionics).

1. - Introduction.

Several attempts to base the biological-evolution principIe on physical lawsinclude assumptions that natural selection has led to the optimization of living beingsaccording to various principIes, such as average fitness [1], maximal efficiency inresource utilization [2], minimal metabolized energy per unit of biomass [3],maximum energetic power [4], minimaI rate of entropy dissipation [5], etc. AlI thesecriteria assume that Darwin's principIe transIates into optimaI regimes of operationalong metabolic pathways in a biologicaI system. This implies that evoIution tends tomake energy use by organisms more efficient and thus, all else being equaI, energyconsumption per unit mass should be reduced over evoIutionary time.

An opposing view derives from the approach put forward by irreversiblethermodynamics analysing seIf-organizing systems [5], which assumes an increase inorder and thus in energy consumption per unit mass as a thermodynamic necessity of

543

544 K. JAFFÉ and c. FONCK

evolution[6]. Although Nicolis and Prigogine [5] suggest that contact betweenirreversible thermodynamics and Darwin's idea of the survival of the fittest canprobably be made because a low rate of dissipation is likely to give an organism aselective advantage, Lamprecht and Zotin [6] and specially Zotin and Konoplev[7]and Zotin et al. [8,9] work out the idea more carefully and conclude that theprobability state for living organisms may be associated with the respirationintensity value. Only in the course of biological evolution have organisms withincreasing high levels of orderliness appeared step by step. Consequently, thedissipation function is related to the distance of the organism from equilibrium state.This theoretical contradiction allows for experiments which eventually could solvethe disjunctive if quantitative measures of order or of energy consumption are used tocompare organisms along a phylogenetic tree.

A quantitative measurement of order in living systems has always beendifficult[10]. With the advent of irreversible thermodynamics [5], order can beassessed through estimates of entropy. This assumption is based on the fact that thehigher the order or complexity of an organism, the lower the probability state of thesystem, the longer the evolutionary time to produce the given state, the farther thethermodynamic system is from the stationary state or equilibrium, the higher thevalue of bond dissipation function, the higher the basal metabolic rate, the larger theenergy consumption per unit mass [6-9,11].

Zotin and Konoplev[7] proposed a negentropy measurement through anorderliness criterion (Cr), based on basal metabolic rates, measured through oxygenconsumption (Qo) normalized by body weight (W), as an index of order for livingorganisms; where

and Cr = k·aIT,

where a and b are species specific constants, a being the oxygen consumption at unitweight and b describes the variation in oxygen consumption due to variations inweight, T is the absolute temperature and k = 3490 h K/cal. This index assumes thatheat production in adult animals is equivalent to respiratory intensity [9].

Zotin and Konoplev[7], using data from around 100 different species summed upby Hemmingsen [12], showed that Cr gives values which reflect the phylogenetichistory among vertebrates and among invertebrates, if comparisons are made at thelevel of classes, or at the genus level [8]. One limitation of this work is that it wasdeveloped having solitary organisms in mind, and adaptations to this approach arerequired if we want to apply it to social systems.

In ants, an equivalent approach, measuring the degree of order through theinformation content of the communication system used for recruitment to food[11],showed that an orderliness criterion (negentropy content of the chemicalcommunication systems) correlates positively with social complexity, and thus couldbe used in phylogenetic analysis. In another study [13], optimization of energy use byevolving organisms predicted by some theoretical extensions of the neo-Darwiniantheory was contrasted to that of irreversible thermodynamics predicting an increasein orderliness and thus an increase in energy consumption per unit of biomass. Theresults showed that simple optimization models cannot explain experimental data andthat social complexity correlates differently with negentropy, depending on the levelof analysis. Comparing the genera among Formicidae, workers (not colonies) fromgenera with highly social species were less negentropic than those of socially

ENERGETICS OF SOCIAL PHENOMENA: PHYSICS APPLIED TO EVOLUTIONARY BIOLOGY 545

primitive ones. At the subgeneric level, social complexity correlated positively withnegentropy among species for specific worker castes, revealing the existence of twodifferent evolutionary routes to complex Attini ant societes. This work allowed todefine more concrete predictions in order to solve the dilemma stated: in socialspecies, energy consumption of colonies (not individuals) should have a specificevolutionary pattern, increasing as the societies get more complex (i.e.negentropic).

In spite of these works, many biologists do not seem convinced that physicalapproaches such as irreversible thermodynamics have anything relevant to say in thestudy of biological systems and their evolution[14,15], perhaps because theapproaches mentioned so far are too general and applications to specific problemshave been lacking.

This study attempts to focus on the subject tackling a concrete problem: therelationship between social life and energy consumption (the thermodynamics ofsociality). The question posed is: is the increase in social complexity (i.e. number ofindividuals or degree of sophistication) in a given society correlated to an increase inefficiencyof energy use by the society (optimization principIe), or is it rather relatedto an increase in energy consumption per unit mass (thermodynamic prediction)? Theoptimization theory principIe supposes that evolution tends to create ever betteradapted organisms (or societies). If sociality is considered to be a higher form ofexpression of life and thus a highly sophisticated product of evolution, societiesshould optimize the use of energy. Irreversible thermodynamics predicts that associal systems represent a higher level of complexity than non-social systems, theyare further away from a stationary state, and consequently require more energy fortheir maintenance.

The ants constitute a practical experimental system for the evaluation of thebioenergetics of a society. It seems that social insects, especially ants, have a higherenergy demand when compared to other insects [16]. It is a matter of debate whetherthis peculiarity is due to the social nature of these insects [17-19]. Studies haveconcentrated on the energy consumption of isolated individuals, but very little isknown about the energetics of social units, i.e. groups of ants or colonies.

2. - Formulation oí the problem.

Essentially, three hypotheses should be considered when investigating thepossible relationship between the social organization of a species and its energyconsumption.

a) Optimization hypothesis: social life is energetically more efficient, resultingin a reduction of energy expenditure per biomass unit. Given that solitary lifeprecedes sociallife in the evolutionary history of the group, social organization shouldresult .in energy use optimization, as societies adapt to environmental constraints.

b) Thermodynamic hypothesis: social life implies an increment in energy costsper individual. In this sense, the social unit would be more than the sum of its parts.Such an outcome would be a prediction of the Irreversible Thermodynamics Theoryapplied to dissipative structures, i.e. living system [5]. The ant society with itsmembers and their interactions forms a complex system that maintains a certainorganization, thus requiring external energy proportional to the degree of«orderliness» or negentropy of the society.

546 K. JAFFÉ and c. FONCK

e) Neutral hypothesis: sociallife has no effect on the energy consumed by thesociety's members; the energy intake of the whole society equals the sum of theconsumption of each isolated individual.This is normally assumed for estimates of theenergy expenditure of social insect colonies([17-20],for example).

In aerobic organisms such as ants, the oxidation of foodstuff (respiration) is themain source of energy required for metabolismoThus, oxygen consumption is a goodestimate of energy consumption.

3. - Materials and methods.

We examined the relationship between colony size and its energy consumption inthree sympatric but phylogenetically distant ant species: Camponotus rufipes(subfamily Formicinae) is dimorphic and is considered a socially complex species withlarge colonies, Odontomachus bauri (subfamily Ponerinae) is monomorphic and isregarded as having a simple society with smaller colonies[21]; and Zacryptocerusdepressus (subfamily Myrmicinae) is highly polymorphic and belongs to the morederived Formicidae [11,13].

In order to estimate energy consumption, respiratory rates were measured with aWarburg respirometer. An absorbent containing barium hydroxide was used to trapthe carbon dioxide produced by the insects inside a closed glass flask. The recipientcontaining the ants was connected to a manometer. Changes in pressure were used toestimate the volume of oxygen consumed by compensating the pressure changesintroducing a known volume of water, equivalent to the amount of oxygen consumedby the ants. The temperature of the experimental system was maintained at 24°C(annual mean temperature in the habitat where the ants were sampled), using athermostatic water bath. Groups of workers were placed in the respirators 24 hoursbefore the experimentoAt least 3 measurements of 2 h each were performed for eachdata point.

Colonies were collected in the field using a portable vacuum cleaner; theycontained workers, queen(s), larvae and eggs, although workers represented alwaysover 95% of the biomass. The «history» of the colonies could vary: when used ascollected from the field they were called «colonies».Some colonieswere split to formsmaller «ant groups», most of them without larvae andjor queen. In order toaccommodate ant groups of different sizes, it was necessary to use desiccators of 0.5(small containers) and 2.0 liters (large containers) of volume. Individuals were placedinside specially built 5 mI tubes. During the experiments, the amount of oxygen wasnot allowed to vary more than 2 percent of the atmospheric content by regularlyreplacing the air. Controls involving the same experimental set-up measuringrespiration of ant refuses after ants had been removed, showed an oxygenconsumption less than 3% of that of experimental groups.

Colonies of Camponotus rufipes and Odontomachus bauri were collected atSartenejas, Estado Miranda, Venezuela. Zacryptocerus depressus, although presentin the former location in small numbers, was collected at Chaguaramas, EstadoMonagas, Venezuela. The colonies were kept in the laboratory using artificial nestsmade out of plaster of Paris, inside glass desiccators. A minimum of five-day period ofacclimatization was established prior to the respirometric bioassays. Light,temperature and humidity conditions were controlled during the experimentalperiodo Except Z. depressus (which feeds on sugar solutions and honey alone), all

ENERGETICS OF SOCIAL PHENOMENA: PHYSICS APPLIED TO EVOLUTIONARY BIOLOGY 547

1.8

1.6

1.4 l.:bD 1.2

---

~ r~ 1.0 :~~ .'" 0.8 ••.

0.6

•

..~ ..

a)

0.4

0.2

10-2

2.5

2.0

::§ 1.5..c:---

a';' 1.0

0.5

0.0.10-2

10-1 10° 101

n (g): 19=66 ants

10-1 10° 101

n (g): 19=55 ants

b)

2.5

2.0

::§ 1.5..c:---

a';' 1.0

0.5

0.0

10-3

'.

..•

10-2 10-1 10°~ n (g): 19=303 ants

e)

Fig. 1. - Energy use (rate of oxygen consumption per unit mass) of ant groups or colonies ofdifferent sizes. Data are from individual ant workers (dots), ant groups in small containers(triangles), in large containers (squares), or from colonies in large containers (diamonds). Thesize of the colony or group is indicated in g of total weight of the colony. The two lines show theadjustment to eqs. (1) and (2), respectively. a) Odontomachus bauri, b) Camponotus rufipes,e) Zacryptocerus depressus.

species are insectivorous, although their diet may also include sugars. Feedingconsisted of diluted honey and dead crickets, which were administered ad libitum.

Oxygen of colonieswas measured every two hours during 24 h in order to estimatedaily variations. Each data point in fig. 1 is the mean of three 2 h long oxygenconsumption measures taken at different moments of the daily cycle.

Activity of individuals was assessed by observing ants every 10min during the2 h oxygen consumption measurement period and the movements of the ants wererecorded. Percentage· of time showing activity was calculated as the fraction ofobservations where the ant was moving.

548

4. - Results.

K. JAFFÉ and c. FONCK

The colonies oxygen consumption varied slightly during the daily cycle. O. bauricolonies were more active and consumed more oxygen during the day compared withthe night, but the maximal daily difference in oxygen consumption measures was of18% (among 4 replicate colonies); where as C. rufipes was more active at night,showing a maximal daily difference in oxygen consumption of 36%. Variations in theoxygen consumption of colonies according to size were orders of magnitud e larger (upto 10000 times) than those oberved for single colonies at different times of theday.

In fig. 1 we plotted the amount of oxygen consumed by colonies of various sizes,divided by their biomass. The relationship between energy use (expressed as oxygenconsumption of the colony per unit time and unit mass: e) and colony size (expressedas the fresh weight of ant groups: n) shows a discontinuous function typical of acatastrophic event around a bifurcation. The curves can be divided into two distinctfunctions separated by a singularity or catastrophic evento At small colony sizes, thecolony oxygen consumption (E) increases arithmetically as colony size increases,fitting the equation

E=e'n,

where e is dependent on the size of the colony, relative to a certain critical colony sizees, so that for small colonies or groups

(1) e = e' = const , when n < es,

where e' is equivalent to the consumption per unit mas s of an average worker incolonies which have not reached a critical size.

For colonies larger than es, e is a function of colony size, so that

E = e(n)n.

An arbitrarily selected simple function which fits our experimental datareasonably well is

(2) e(n) = el! = a - b log(n), when n> es,

where E is expressed in mI of 02/h, e in mI of Odh/ g, and n in g of fresh weight. a andb are constants.

One of the values of el! can be estimated extrapolating it from eq. (2) so that

e; = a - b log(nl)'

where

nl = n/N.

N represents the number of individuals in the colony or group, so that nl is equivalentto the weight of an average ant. e; reflects the theoretical cost to establish a givensociety formed by a single individual; or formulated differently, it measures themaximum average amount of energy consumed by individuals engaged in organizinga colony. Using the estimated value e;, we may define a species specific constant

ENERGETICS OF SOCIAL PHENOMENA: PHYSICS APPLIED TO EVOLUTIONARY BIOLOGY 549

TABLE 1. - Values of the funetion deseribing eqs. (1) and (2), taken from fig. 1.

O. bauriC. rufipesZ. depressus

nI (mg) (N = 1)

15.2 ± 2.218.1 ± 15.93.3 ± 0.9

e' ± sd (mIOdh/g)0.59 ± 0.090.53 ± 0.090.52 ± 0.2

el!:a ± sd

3.47 ± 0.104.85 ± 0.1212.93 ± 0.08b ± sd

0.68 ± 0.150.97 ± 0.084.00 ± 0.37r2

0.660.980.98

ea

2.673.6310.86e

4.56.920.9

es (g)1.92.60.8

es (N)125144242

size range oí10-102102-103102-104

normal colonies (N)

e' was calculated using eq. (1). Values for, a, b, r2 and el! were calculated with a linear regression analysis using log(n)(see eq. (2». es was estimated from fig. 1. nI was calculated using data from a minimum of 20 individual ants. N indicatesthe number of ants.

describing the singularity point

e = eo le' ;

e measures the amount of energy required to form an ant aggregate which intherlpodynamic terms functions like a normal healthy colony. This amount of energyis expressed as the number of times individual energy consumption is increased in thesingularity with respect to individual energy consumption at aggregates smallerthan cs.

The energetic cost of establishing a society was correlated to the social complexityof the species. The socially more complex species showed larger values of eo , e and esforming a gradient starting from the primitive Ponerinae, following the moreadvanced Formicinae, and ending at the most derived Myrmicinae (table I).

Individuals in small colonies showed an oxygen consumption that wasintermediate to that of isolated individuals at rest and that of active isolatedindividuals (fig. 1). Oxygen consumption of individuals was not correlated with theweight of the individual (r2 = 0.009 for O. bauri and 0.12 for C. rufipes, p > 0.1); butwas rather correlated with activity (% of time showing activity; r2 = 0.42 for O. bauriand 0.74 for C. rufipes, p < 0.01 and 0.001, respectively). Maximal individual oxygenconsumption reached similar levels as maximum average individual oxygenconsumption (e) in active colonies (fig.1).

The. value of E (or e) was not determined by the history of the group. Grouphistory refers to whether artificial colonies were formed by splitting field coloniesinto smaller groups or whether colonies were used as collected from the field (groupsand colonies in fig.1). In addition, energy consumption of the colony was not relatedto the ant density in the groups, i.e. number of individuals per unit area. The use ofrecipients of different sizes containing groups of the same size permitted theevaluation of this variable (fig. 1). In all three species the size of the recipient, andthus the ant density of the colonies, did not affect the oxygen consumptíon functíon.

550

5. - Discussion.

K. JAFFÉ and c. FONCK

We know that individuals of highly social ant species are less complex thanindividuals from simpler ant societies [13]. This is in agreement with previousfindings of studies on the complexity of the ants nervous system [22]. This impliesthat social complexity may be achieved by simplifying individual constituents,through individual specialization, reaching a more harmonious integration ofindividuals into the society. Thus, in order to comply with thermodynamic rules,colonies (not individuals) of highly social species have to have higher metabolic ratesper unit mass than colonies from less complex ant societies. This can achieved only ifworkers of highly complex ant societies are more active (due to increased socialinteractions) than workers from less complex societies, consuming more energyduring a normal social life than workers from socially primitive species.

Increase in energy requirements of social systems, predicted by irreversiblethermodynamics, is not contradictory with the fact that individuals in a colony maybe made by evolution more simple and thus less exigent in energy, as this lastadaptation has to do with specialization of parts of a system: the colony;whereas theformer one has to do with evolutionary constraints: increase in the negentropycontent of the system. Thermodynamic rules predict that colonies of highly socialspecies should have higher metabolic rates, i.e. consume more oxygen, compared tothose of less complex societies [13]. This may be achieved through increased socialinteractions, even if individual workers have lower basal metabolismo

Our results confirm the prediction described above and clearly show that thegenerally accepted assumption that colony's energy consumption represents the sumof the energy requirement of an average individual worker [17,23,24] does not hold.Our results show that large ant colonies may consume more energy per individualthan small ones (i.e. the colony is more than the sum of its parts), and that therelationship between colony size and energy consumption of the colony isnon-continuous and non-linear.

The fact that the relationship between group size and mean individual oxygenconsumption shows a singularity, i.e. has two stationary states, showing abifurcation, suggests that colonies are complex dissipative structures [5]. Thisphenomenon can be correlated with those of coupled oscillators reported forLeptothorax allardycei [25] and simulated for virtual ant colonies[26,27]. In theseworks the authors showed that individual ants 01' workers in small groups show fewerbursts of activity compared to workers in groups of large size, where workers showsynchronic activity with other workers and thus have longer periods of activity, suchas predicted for chaotic systems composed of coupled oscillators; the transitionbetween coupled and non-coupled states is also marked by a singularity. Ourobservations on the behaviour of the coloniesconfrrmthis finding as we observed thatindividuals, when kept isolated in a closed container, tried to escape, occasionallybecoming very active 01' from time to time entering a cryptic phase, whereindividuals showed no activity. This activity was significantly correlated with therange in e of individual ants. Once workers were grouped, they aggregated withoutshowing any conspicuous activity. This phase coincidedwith the portian of the curveexplained by eq. (1). In active colonies, workers were seen performing diverseactivities such as foraging, brood care, nest building, grooming, antenating, wastecarrying, etc. This phase coincidedwith the portion of the curve described by eq. (2).We thus propose that the trigger from one phase to the other is related to a critical

ENERGETICS OF SOCIAL PHENOMENA: PHYSICS APPLIED TO EVOLUTIONARY BIOLOGY 551

mass of workers necessary to achieve coupling of the various activities among theworkers. The presence of a queen may be important but on many occasions, queenlesscolonies showed both types of behaviour.

The jump in oxygen consumption, after a certain critical colony size (es) isreached, is analogous to a physico-chemical system of phase transitions, compatiblewith thermodynamic predictions on the energy required for the organization ofcomplex open systems [6]. Thus, the results can be interpreted as a discontinuousincrement in the energy consumption of individuals in the colony (an abrupt changefrom rest to activity) when a social structure is established, marking a singularitywhich defines a bifurcation, characteristic of a dissipative system.

The larger scatter in the data around the bifurcation is also a thermodynamicprediction [5]. A biological interpretation of this phenomenon could be that theworker composition of a colony is critical at small colony sizes. As ants are known tobe highly polyethic (i.e. individual workers, dependent on caste, age or previousexperience, perform specific tasks in a colony), an artificially created colony may lackspecific worker castes and thus be unable to establish a functioning society. Thisphenomenon could explain the large scatter of the values of e around cs.

Once the society has been established, ants seem to optimize the energyconsumption of the colony, where larger colonies consume less oxygen per unitweight than relatively smaller ones (eq. (2». In colonies with the highest averageindividual oxygen consumption, e is comparable to the maximum values obtained forvery active individual workers, indicating that in these colonies, all or a majority ofworkers are highly active. As colonies get larger, the values of e drop, suggesting alower individual activity or a lower proportion of ants being active. Lachaud andFresneau [28], working with different ant species, observed that in large colonies anumber of individuals contribute little or nothing to the nest chores. Some authorsbelieve that these workers may play a role as worker reserves [29]. This kind ofgradient in activity and behaviour could partially explain mechanisms by which asociety is able to reduce its energy consumption per unit mass as the society increasesin size. Species vary in the rate they reduce energy consumption per unit mass atincreasing colony sizes (constant b in table 1), where more advanced species showmore negative slopes of the function e", which is predicted by the optimizationprincipIe.

On the other hand, the differences in the values of eo, es or e are compatible withthe thermodynamic prediction that more complex systems require more energy fortheir maintenance: ants from the subfamily Ponerinae are considered to be moreprimitive than the Formicinae, whereas the Myrmicinae are considered to be themost derived ants among Formicidae [11,21,22]. This gradient correlates with thevalue of these constants (table 1).

It is important to note that although the experiments were undertaken usingphylogenetically distant species (from different subfamilies of Formicidae), buildingdifferent types of nest, having different feeding habits, and showing differentbehaviours [21], the general pattern observed in the results was surprisingly similar,excluding the possibility that we are measuring a trivial phenomenon relevant tospecific ant species. Comparisons of thermodynamic constants among closely relatedant species showed similar trends of evolutionary gradients [13].

Considering the whole of the results, we propose a new hypothesis, resulting froma combination of the thermodynamic and the optimization principIes, which couldexplain the energetics of ant societies. The hypothesis assumes the following:

552 K. JAFFÉ and c. FONCK

1) The generally assumed neutral hypothesis is not valido2) The energetic cost of assemblages of organisms is a discontinuous function of

the size of the system.

3) There is an energetic cost of sociality which depends mainly on the degree ofsophistication of the system. This cost is thermodynamically related to the energyrequired by individuals to perform the activity necessary to establish a functioningsociety.

4) Established societies optimize the .average energy consumption perindividual as the society increases in size, where more advanced species are moreefficient in optimizing energy use.

Although much research remains to be done to uncover the biosocial causes of theirregular behaviour of the energy-colony-size relationship, we believe we haveuncovered a general phenomenon, which is not specific to ants, and which allows toestimate the energetic cost of sociality in a given system. As our predictions arebased on well-established general physical laws, the finding that ant colonies show acomplex relationship between energy consumption and size, could have a moregeneral application. Thus, similar complex catastrophic patterns may be evidencedamong other social organisms, among complex ecosystems and among socioeconomicphenomena in human societies.

This work demonstrates the heuristic value of applications or irreversiblethermodynamics and physical dynamics to biological and social systems for thedetection of new biosocial phenomena. These approaches should be considered ascomplementary to neo-Darwinian approaches in the study of biological systems.

* * *

We acknowledge critical discussions with Drs. B. Scharifker, J. Lecuna, C.Bosque and E. Herrera. Help with English writing carne from F. Osborn andDr. A. Ribbi. Financial support carne from project BID-CONICIT QF-36.

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