Document Rpbrejb7Vnj20XV5vzbMKKJ48

784 t 7**. D- 7- OTWS, 9. 0., at CHMs. T. A.. IWTry Sri., Ml 1AM (IMA). > IV.tiaX, TV N., Mt (IMT). . C'aasy, A. B.. aai BMcfe, A, J. BM. Q%tm.,m. 1M1 (IMS). " *'IBHuShf'* WrtMk E' **4 k*** * " A* *-- ***". 1 " TWx, L Mi HM), 8., IVM M,,M. MV (IMS). " n Wifca. * L a4 h*. A.. J. BUM. Qiribst, A ST " a4 Ian, L A., V. rUrwmnt. Jbp. Hoq, MT, III Ortuta. P,, U*. Immrn.. U. MT (IMS). NATURE VOL IM NOVEMBER II 1*70 NATURE \ Btsk Connectance of Large Dynamic (Cybernetic) Systems: Critical Values for Stability Many systems being studied today are dynamic, large wi Complex: traffic at aa airport with 100 planes, shun areas with 104 persona or the human brain with 101* neuroma. In such systems, stability ia of oentral importance, for instability usually appears as a self-generating catastrophe. Unfortunately, present theoretical knowledge of stability V in large systems is meagre: the work described hers was intended to add to it. . Most of these large systems, often biological or social, are grossly non-linear, which increases the difficulties associated with them. Here we consider linear systems merely as a first step towards a more general treatment. We have attempted to answer: What is the chance that a large system will be stable T If a large system is assembled (connected) at random, or has grown haphazardly, should we expect it to be stable or unstable T And how does the expectation change as n, the number of variables, tends to infinity T Monte Carlo-type evidence1-1 had suggested that the probability ofstability decreased rapidly as s was increased, m some eases perhaps as fast ss !-*, mi exponentially-fast vanishing of the ohanoe that the system will be stable. This result, however, was for systems that were hilly connected, where every variable had an immediate effect on every other variable. While this case is obviously important in theory, it ia not the oase in most large systems in real life: not every person in a slum has an immediate effect on every other person, and not every oell in the brain directly affects every .other cell. The amount of connectedness ("oonnectanoe'') is often far bolow 100 . per omt. We have studied how such incomplete connect- snoe affects the probability of a system's stability. Let the linear system's' state be represented by the vector x (-- < x,, . . , x,, > , where each x< is a variable, a function of time), uni its changes in time by the matrix equation ' X-Ax \ . To "join the variables at random" ia to give the elements in A values taken from* some specified distribution. "Non-connexion from-Xi to x/' corresponds to giving the element ati the value zero. Thus, if the specified distribu tion has a peak at sera, sampling from it will give the equivalent pf a dynamic system with many non-connexions. The eonneotanee, C, of the system can then be conveniently defined aa the percentage of non-zero values in the distri bution. Thus, if the coefficients are drawn from a distribu tion with W per cent ssros, and if n - 1,000, then each line of the equation would contain about ten non-sera coeffi cients, corresponding to a system in which each variable is directly affected by about ten other variables. Because our work waa essentially exploratory, we used the distribution in whiah tbs non zero elements were distributed evenly between - 1-0 and + 1-0. The idemmla hi the mam diagonal, corresponding to the Intrinsic stabilises of tbs parka, were alt negative, distributed evenly between - M and - 0-1. Thus each samptad value M 40 SO Coosertssea (par oaal) 7%. l. VaxWtlos of aUMDtr with aonaseta ins of A corresponded to a system of individually stable parts, connected so that each part was affected directly by about C per cent of the other parts. On a digital computer, a value for n was given and a value for C. Random numbers appropriately distributed were then sampled to provide a matrix A. Hurwita'i criterion was applied to test whether the real parts of A's latent roots were all negative (the stable oase) and the result recorded. Further samples, giving further As, allowed the probabfiity of stability (*) to bo estimated. The probability was then re-estimated for another value of C, and so on, until the variation of P with C became dear. The results showed the feature -that we wish to report here. As the system was made larger, a now simplicity appeared. Fig. I shows a selection of the results, enough to illustrate the principal fact. When ni, the probability that the system would be stable depended on C in a somewhat oompiex curve (which could perhaps be predicted exactly). But as a increases, the curve changes shape rapidly towards a step-function, so that even when s is only 10, the shape might be so regarded, at least for some practical purposes. Thus, even at n 10, questions of stability can be answered simply by asking whether the oonnectanoe is above or below 13 per cent: 2 per cent deviation either way being sufficient to eonvert the answer from "almost certainly stable" to "almost certainly unstable". The matter is being investigated further, but it may be of general interest to notice that this work suggests that all large oompiex dynamic systems may be sxpeeted to show the property of being stable up to a critical level of oonnectanoe, and then, aa the oonnectanoe increases, to go suddenly unstable. This work was supported in part by the U8 Offioe of Scientific Research. Mask R. Oumm W. Ross Aim' Biological Computer Laboratory, University of IlliBoas, Urbana, Illinois 91901. Asrsat i. irm. Ui on ixl. 1 A*br. 8. Dmtf Jbr JVafe IMS). " p. So. PERS Population Issues in H H. Bhriich. man: San ) LMt Wltho A Journey Population 394 + 24 ph 1970.) 0. In spite of expoetption to aixAit si possibility < to rages /'< oontributioi This beauti in a jot-bla insuperable gross in th< leading. A! ably qualiftc might be c deeper over There is-a on demogra neutrally roj of the work level. It is i and project: judgment lx conjectural. The totoI to develop < globe, even dozens of m all inadequa care and inj containing lessons in fur thermodynai pollution hasuch as resi cooiogica] bai are apeoulati fanciful. In "growth mai distinctions i The sectioi suffer* most I purporting t< programmes oooveys an ii quoted for 1 started opera problems and DSW 332448 STLCOPCB4079024 Knmc~voi_ 229 rstpHTHpirw at 1070 70S (nr soritra inhibitor/ Mbatanor in the tiimd phagotytic Nativity after surgery. This work uy supported by tba American Ommw Society. Thomas M. Baba toutamtofPhjsiolap, Wwnity of Illinois Cawga of Madiame, CWesfo, Illinois A0680; . |mlil< Bgvcmber A IBSS; isvkrd Jab* 13, 1070. JUS. E. Bacas. B, intlfi. J.. Bass*. E, and Cnl. W. H., Art*. 0as,, M, SM(1M>. ' Lnrta. M. E. aa4 Onto. W. H., Art*, amt.. 71, 21 (lOM). '(M*. W. ,, JUJoaaM. O. O., RohsrM. II. 8., omt SoaUiwtek. B. W_ M . Dimrmimttim nt ftiwr UpjAtiB Cratary from. 8 Yonu lMlV. 'Saba, I.E,MD(Luts. , 807 (IMS). . . 1 Jtnaoraa. A. J.. ArrA. Swf-. 0A94T (10*7). Saba. T. IL. aad M taato. B. E. A'aur. J. MsrM.. SIS, 1ST (MSS). >hb^E aad M Lads, Jf. E. ba. Bn. Bar- JHd. AM* US, MS Jidda. C. E_ud Xroriir. D.. J. J. ATM., lit. IN (1SS1). Jidda C. E. and Kevlar. D,, A'darr. ISA 474 (ISM). ' gaba^T. B^mtlaa. J. p.. aad U Lado, H. X., J. JMtealamdaOUKal An., IN bads, V. E, aad 1W. A 7.. J. MrttnUmiM'tM Sat., 1.1SS (1SSS). . _ B.. BtoaM. O., Halaafa. E H.. asd ibSBjf CM MitttmmiSmil Apdtm (ME BUM. O. bj Hsfews. la E MliXeriMr- 0*8*4, USD. J. >,, asd PI LaHa, W. E. J. Bsftdn MUW am., A 987 (1SSS). and th* micrnaomal fraction was prepared and incubated as dtMiribnl by Oonnpy and Kluteh*. Radioactive oeet radio! and its metiibolitra wars extracted with di- ehloroinethanc and separated by paper chromat 'igraphy" . with ehangee in prooodwre aa reported previonnly,'*- Histological examination was carried out on kcstrsls fed 5 p.p.m. 'Arodor IBM' for 14 days. A oentrol portion of the liver was removed immediately alter death aad fixed in Carney's fluifl for 45 min. Section* were out at 5 pm. All sections were treated with deoxyribonuclease (0-1 mg/ml. in 0-1 M phosphate buffer (jH 7-5)-<M per cent gelatino-0-03 M MgSO,) for 3 h at room temperature to remove DNA which would otherwise stain with asm* B. All sections were then stained in acme B (0-1 per cent in 0-1 M citrate buffer, pH 4-0) for 2 h at 40 C, washod briefly with water and differentiated overnight with t-lmty! alcohol11. The density of the staining with asnro B was measured cytopbotomctrioally at 645 nra (ref. It). Ten readings of tbs per oent transmission of a standard area qf cytoplasm were made for each of five control and five experimental livers. The mean for control birds was 30-7 3-3 whereas for the experimental birds it was I(-8 3-6. An analysis of vsrianoe of both the individual values and the means gave calculated values which exceeded the 0-006 tabular fi we therefore conclude that the decrease hi percentage transmission is a oonseqnenoe of the presenoe of more eytoplaamie BNA in the 'Arodor'- treated kestrels. Metabolic Effects of Polychlorinated Biphenyls in the American Kestrel ( Polychlorinated biphenyls (FCB) have been widely 1 found in wildlife samples1-*. PCB a used as plasticisers m plastics, resin and chlorinated rubber*. They have been recommended for improving lindane residues1 and TsMe l. in dim MosoeoBAii atOAXsomr or ossnuiuns Asioemt at polar metiboHtm fnrwui Is mnlri/r mlonsoaul fTaettoa (ajspfa alas, 4 ft* tarh prosp) DMI Hun *4. Coatnri 0-S p.p.m. 'Arodor 12M* 6 0 p.p.m. `Arodor 1H4' 0 6 p.p.m. 'Arodor 1982' 6-0 p.p.m. 'Arodor 1282' / /lia 80-60 18-06 47 8* 0-00 7*5 1-20 tl-M 26 46 have been shown to increase the insecticidal properties of DDT and diddlin'. FCB are highly stable, insoluble A dose-dependent in vitro breakdown of oeetradiol to In water and soluble in lipids; so that they can persist a more polar metabolite occurred in livers from kestrels and undergo 'biological magnification in the environment. fed either `Arodor 1264' or 'Arodor 1862* (Table 1). Sax' reported the toxicity of chlorinated biphenyls as There was no apparent difference between the effects of moderate to high. One PCB has been shown to pro the two 'Arodors' nor was there any difference between duce chick hydroperioardial oedema and growth depres sexes. No such conversion took place in the livers from sed proportional to dietary levels (300 and 400 p.p.m.) bf the oontroi birds. . the toxicant*. These effect* were accompanied by such The increase of hepatic enzyme activity oan thus be pathological changes as:- aream-coloured pancreas, oonelated with an inoreaae of cytoplasmic BNA. Pro enlarged haemorrhagic kidney, enlarged adrenal gland, liferation of the endoplasmic reticulum of rat liver oells mall spleen, dermatitis, defeathering and transient following the administration of ohlordane1' and DDT" changes in Mood (duoone, haemoglobin and haematocrit has been noted although these changes were not quanti levels. Intramuscular injection of PCB has been shown to fied. Our findings suggest the physiological actions of ^ increase the rate of steroid metabolism 'in bird liver PCB are similar to those of DDT and its metabolites. homogenates1 as has been shown for organochlorine pesti - This industrial contaminant should be considered as an cides*. Although a oauoc> and1 effect relationship has not additional burden to the ecosystem comparable with that been demonstrated, FCB residues have been associated imposed by the organoohkmne pesticides. with decreasing populations of fish-eating birds and birds We thank Dr T. J. Cade for help fii providing the of prey1. . kestrels and Monsanto for supplying `jtoaoH 1264 and American kestrels wars' trapped, allowed to acclimatize 1262' and technical bulletins. This work was supported for a week, paired (one ipale and oae female per cage), by the National Institutes of Health, and earned oat , acclimatised for another week and then plaoed on cid while one of us (D. B. P.) was an established investi libitum experimental diets. 'Die kestrels' diet consisted gator, American Heart Association. of one day old dead cockerels. The dead oockerels were injected in tho breast legion at cither ,0-5 p.p.m. or 6-0 JxrtxxY L. Lnrcx* (w/w) of either 'Arodor 1364' 'Arodor 1363* ' David B. Psaxall onaanto trade names for PCB oontaining 64 per oent Langmuir Laboratory, chlorine and 63 per cent chlorine respectively) dissolved Section of Eoology and Systematica, h sesame oil. The higher dose is roughly equivalent to Cornell University, ^ t mg/kg PCB to each kestrel. Cockerels for control Ithaca, New York 14660. kestrels were injected with seesme oil only. It is assumed that the kestrels oonsumed essentially all of the dietary 'Arodor', for the onlyparts of the cockerel not eaten were the beaks aad feet, and the pellets regurgitated by the ' frastrda oonaisted of ooekeret down. Each pair was kept a burlap-covered 6x6x8 foot win sag* and fed wparfansfatal diet ones a dgy far 6 mouths. Ah tin and lmtml Much U; ml*4 J(T A ItTO. 1 Kinbrooch. E W,, Blsehs. r.. DostaA D. B., Hwwaa. A 0, sa4 Kims, M. liTltatm*, ISA IMS tlOM). Jaims^ A. Mask, A. 0,, Okies. A, aad OtUritad. 0* HdaraMA *'* linmmmU Tmk. ML, Ns. 0/TL-U1 A, M. , Hina)m. L. mi SaMsas. W. B.. J. JMa. Ibhml, A (ST (IMS). I c f the test period, the bird* were killed, Been removed. a B, b %i ft t DSVM 332449 STLCOPCB4079025