Humans = Cancer

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Ho w M any T im es Hasthe H um an Population Doubled?Com parisons w ith C ancerW a r r e n M . H e mUniversi ty of Colorado

A long w i th decreasing d ou b l ing t imes as a func t ion o f inc reas ing ra tes o f popu la-t ion g row th ove r the pa s t severa l thousand years , the hum an spec ies has shownst riking para lle ls w i th a ma l ignant g row th . S om e cancers a lso d isp lay decreas ingdou b l i ng t imes o f ce l l p ro l if e ra ti on du r ing the m os t rap id l y g row ing phase . A t 6b i l li on , t he num ber o f doub l ings reached by the hum an p opu la t i on as o f 1998 i s32.5 , wi th the 33rd do ub l ing (8 .59 b i l l ion) expected ear ly in the nex t century . Inte rms o f to ta l a n im al b iomass, inc lud in g tha t o f domest ic an im als unde r humancon t ro l , the 33rd do ub l ing o f hum an-re la ted b iomass has been passed. In te rms o fenergy use, w h ic h is a more accura te index o f the g loba l eco log ica l imp act o fhumans, the hum an spec ies has passe d its 36 th d oub l ing . Th ese ca lcu la t ions areimpor tan t because , i n add i t i on to the number o f doub l i ngs , the human popu la t i onis sho w ing severa l im por tan t s imi la r i ties wi th a mal ignan t o rgan ismic tumor , wh ic hresu l ts in death o f the hos t o rgan ism a t be tween 37 and 40 doub l ings . At cur ren tg row th ra tes , t he num ber o f i nd i v idua l humans w i l l r each those leve ls w i th in 20 0 -400 years f rom the present , bu t the eco log ica l impact wi l l be fe l t much sooners ince the num ber o f doub l ings o f ene rgy consum ed w i l l pass 37 ea r l y i n the nex tcentury . These observa tions supp or t the hypothes is tha t the hum an spec ies has be-com e a m al ignant p rocess on the p lan et tha t is li ke ly to resu l t in the equ iva len t, fo rhum ans, of ecosystem death, o r at least in a radical t ransformat ion of the ecosys-tem, the ear ly phases o f wh ich are be ing observed.

Please address correspondence to W arren M. H em , 113 0 Alp ine, Boulder, Colorado80304.Pop ulation and En vironm ent: A Journal of Interdisciplinary StudiesVolum e 21, Num ber I , September 19999 1999 Hu m an Sciences Press, Inc. 59


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60POPULATION AN D ENVIRONMENT

I N T R O D U C T I O NR a p i d g r o w t h o f t h e h u m a n p o p u l a t i o n h a s r e s u l t e d i n d o u b l i n g t i m e sas low as 35 years f o r t he g loba l popu la t ion and 20 years in some reg ions(Zacha r iah & V u , 198 8) . D ou b l in g t imes o f l ess t han 20 years have beeno b s e r v e d a m o n g s o m e lo c a l p o p u l a t i o n s ( H e m , 1 9 7 7 , 1 9 92 ). U n t il t h e p as tf e w d e c a d e s , d o u b l i n g t i m e s o f t h e g l o b a l p o p u l a t i o n h a v e b e e n d e c r e a s -i n g b y 5 0 % o r m o r e w i t h e a c h d o u b l i n g s i n c e A . D . 0 ( v o n Fo e r s t e r e t a l . ,1960 , von Foers te r , 1966 ; Ump leby , 1990 ; F ischer 1993) . Assuming a pop-u l a t io n o f 2 5 0 m i l li o n a t A . D . 0 ( We e k s, 1 9 9 2 , p . 29 ) , t h e h u m a n p o p u l a t io nd o u b l e d 4 ti m e s f ro m A . D . 0 to 1 9 7 6 , w i t h t h e d o u b l i n g t im e s d r o p p i n g f ro m165 0 years (es t. 50 0 m i l l ion a t 165 0 A .D . ) t o 46 years ( from 2 b i l l ion in 19 30t o 4 . 2 9 b i l li o n i n 1 9 7 6 ) . P e o p l e w h o a re 4 0 y e a rs o l d o r m o r e in 1 9 9 8 a rea m o n g t h e fi rs t p e o p l e i n h i s to r y to h a ve liv e d t h r o u g h a d o u b l i n g o f w o r l dp o p u l a t i o n ; p e o p l e w h o a re 7 5 y e a rs o l d h a ve s ee n t h e h u m a n p o p u l a t i o nt r i p l e . H o w m a n y t i m e s has t h e h u m a n p o p u l a t i o n d o u b l e d ?Th e s p e c i f ic e v e n t t h a t p r o m p t e d m y a t te m p t to a n s w e r t h is q u e s -t i on was t he as ton ish ing comment severa l years ago by a ca re fu l , we l l -i n fo rmed , and h igh ly i n te l l i gen t na t iona l po l i t i ca l l eader i n a p r i va te mee t -i n g t h a t " . . . w e s h o u l d b e c o n c e r n e d a b o u t p o p u l a ti o n g r o w t h b ec au se ,a f t e r a l l , t he human popu la t ion has doub led f o r t he f i r s t t ime , and t h i s

h a p p e n e d s i n c e t h e t im e o f C h r i s t. "A f te r t h e m e e t in g , I i n fo r m e d t h e g e n t le m a n , w h o w a s o n e o f t h e h i g h e s t-r a n k i n g m e m b e r s o f t h e U . S . g o v e r n m e n t , t h a t t h e h u m a n p o p u l a t i o n h a dd o u b l e d s e ve ra l ti m e s s i n c e t h e t im e o f C h r is t a n d t h a t i t h a d d o u b l e d m a n yt ime s be fo re t ha t . U po n hea r ing th i s , he appeared s ta r t led a nd shaken by t h i sn e w s , a n d h e as ke d a n a id e t o f o l l o w u p o n it. Qu i t e a s id e fr o m p r o v i d i n gaccura te in fo rm at ion t o po l i t i ca l leaders , t he re a re co m pe l l i ng sc ien t if icreasons f o r ca lcu la t ing t he num ber o f times t he hum an pop u la t ion has dou b led .K n o w i n g t h e n e t n u m b e r o f t im e s t h e h u m a n p o p u l a ti o n h as d o u b l e dg i v e s u s i m p o r t a n t d a t a t h a t a r e h e l p f u l i n c o m p a r i n g h u m a n p o p u l a t i o ng r o w t h t o o t h e r p o p u l a t i o n s a n d b i o l o g i c a l p h e n o m e n a , i n d e t e r m i n i n glong- te rm ra tes o f g rowth , i n es t ima t ing t he t o ta l number o f human be ingswho have ever l i ved , and in es t ima t ing ne t i nc rease in human b iomass . Wem u s t k n o w t h e s e t h i n g s i n o r d e r t o u n d e r s t a n d o u r i n c r e a s i n g l y i m p o r t a n tr o l e i n n o t o n l y o c c u p y i n g t h e p l a n e t a r y e c o s y s t e m , b u t i n d o m i n a t i n g i t(V i t ousek e t a l . , 1997) . An even more u rgen t t ask i s t o unders tand the d i -m e n s i o n s a n d m e a n i n g o f h u m a n p o p u l a t i o n g r o w t h a s a p r i n c i p a l f a c t o rin ecosys tem ch an ge - -c r i t i ca l i n fo rm at ion t ha t sc ien tis ts can p rov ide to


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61WARREN M . HERN

po l i cymakers (B rund t land , 1997) . The paramete rs t ha t a re espec ia l l y im-por tan t a re the p resen t s i ze o f t he p op u la t ion and its presen t ra te o f g ro wth .Bu t human para l l e l s w i t h a ma l ignan t p rocess make i t necessary t o knowt h e n u m b e r o f d o u b l in g s , w h i c h a re i m p o r t a n t to u n d e r s t a n d in g t h e b e h a v -ior o f a cancer .

T O T A L N U M B E R O F N E T D O U B L I N G SI n t e rms o f t he t o ta l number o f popu la t ion doub l ings , i t does no t rea l l ym a t t e r w h e n w e s t a r t e d d o u b l i n g o r h o w l o n g t h e d o u b l i n g s h a v e t a k e n .Bu t w e may be reaso nab ly su re t ha t the f i rs t doub l ings , a t som e t im e los t t oh is to ry , w a s w h e n t h e n u m b e r o f h u m a n s , h o w e v e r d e fi n e d , w e n t f ro m o n et o t w o a n d f ro m t w o t o fo u r , a n d s o f o rt h . G i v e n o u r m e c h a n i s m o f re p r o -d u c t i o n , t h e i m p o s s i b i l i t y o f d e f i n i n g t h e " f i r s t h u m a n b e i n g " a t a n y p o i n ti n t i m e d u e t o t h e o v e r l a p p i n g a n d s i m u l t a n e o u s l y e v o l v i n g h o m i n i d s p e -c ies f rom 3 .5 t o 1 .5 m i l l i on years ago , an ac tua l s ta r t i ng po in t f o r t he dou-

b l i n g o f t h e h u m a n p o p u l a t i o n i s o n l y a t h e o r e t i c a l c o n s t r u c t . A t s o m epo in t , we became in te rb reed ing members o f a s ing le b io log ica l spec ies ,a n d w e c a n n o t d e t e r m i n e w i t h a n y p r e c i s i o n w h e n t h a t o c c u r r e d . I na d d i t i o n , t h e r e i s a b u n d a n t e v i d e n c e t h a t h u m a n p o p u l a t i o n s w a x e d a n dw a n e d o v e r t i m e s , p e r h a p s c r a s h i n g t o n e a r - e x t i n c t i o n d u r i n g t e m p o r a r i l yun favorab le c l ima t i c cond i t i ons in t he la te P le i s tocene th rough ear l y Ho lo -cene (from 10 0 ,00 0 th roug h 10 ,0 00 years B .P .; Ha rpen d ing e t a l., 1 99 3 ;M c C o r r i s t o n & H o l e , 1 9 9 1 ; H o l e , 1 9 9 4 ) . M c N e i l l ( 1 9 7 4 ) d o c u m e n t s s o m eof t he innumerab le ep idemics t ha t resu l t ed in shor t - t e rm popu la t ion losseso f 50 t o 90 pe rcen t . I n t he ea r l y ex is tence o f ou r spec ies , t he popu la t ionm a y h a v e d o u b l e d a n d h a l v e d m a n y t i m e s b e f o r e r e a c h i n g a n y n e t d o u -b l in g . P o p u l a ti o n g r o w t h h a s n o t b e e n c o n s i s te n t o r m o n o t o n i c .For t he sake o f exa m in ing t h i s ques t ion and i ll us t ra t ing t he answer, I havecons t ruc ted a t ab le based on es tima tes f rom pa leon to log ica l a nd a rch eo log i -c a l s tu d ie s , b e g i n n i n g w i t h t h e a p p r o x i m a t e t im e w h e n Ho m o hab i li s existed(T a ble 1 w i t h N = 1 a n d e n d i n g w i t h 1 9 9 8 w h e n th e h u m a n p o p u l a ti o n w a ses tima ted t o have reached ap prox ima te ly 6 .0 b i l l i on (U .S . Census Bureau ,1998) . 1 Roug h es tima tes o f po pu la t ion g ro w th rates a re de r i ved f rom thedo ub l ing t ime in te rva l es tima tes. T he s imp les t ma them at ica l an sw er t o theq u e s t io n p o s e d h e r e is 6 . 0 x 1 0 9 = 2 x w h e r e x is t h e n u m b e r o f d o u b l in g s ,

In ( 6.0 x 1 0 9 ) 2 2 . 5 1 5x . . . . 3 2 .4 8 9 2 ( I )In 2 0 .69 3


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62P O P U L A T I O N A N D E N V I R O N M E N T

T A B L E 1Doubl ings of Human Popula t ion (wi th pro jec t ions) '

D o u b l i n g D o u b l i n gN u m b e r P o p u l a t i o n Y e a r R O N I % T i m e (Y ea rs )

0 I 3 ,000 ,00 0 BP 0 .0001I 2 2 ,50 0,00 0 BP 0 .00012 4 2 ,000 ,000 BP 0 .00033 8 1 , 7 5 0 , 0 0 0 BP 0 . 0 0 0 34 16 1 ,500 ,000 8P 0 .00055 32 1 , 2 5 0 , 0 0 0 BP 0 . 0 0 0 56 64 1 ,000 ,000 BP 0 .00077 128 900 ,000 BP 0 .00078 2 5 6 8 0 0 , 0 0 0 8P 0 . 0 0 0 79 5 1 2 7 0 0 , 0 0 0 B P 0 . 0 0 0 71 0 1 , 02 4 6 0 0 , 0 0 0 B P 0 . 0 0 0 711 2 ,048 500 ,000 8P 0 .000712 4 ,096 400 ,000 BP 0 .000713 8 ,192 300 ,000 BP 0 .001414 16 ,384 2 5 0 , 0 0 0 8 P 0 . 0 0 1 4

15 32 ,768 200 ,000 BP 0 .001416 65 ,536 150 ,000 BP 0 .001417 131 ,072 100 ,00 0 BP 0 .001418 262 ,144 5 0 , 0 0 0 8P 0 .00281 9 5 2 4 , 2 8 8 2 5 , 0 0 0 8 P 0 . 0 1 420 1 ,048 ,576 20 ,000 BP 0 .01421 2 ,097 ,152 15 ,000 BP 0 .028

5 0 0 0 0 05 0 0 0 0 0250 000250 0001 2 5 0001 2 5 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 O 0 0 0 01 O 0 0 0 01 0 0 0 0 05 0 , 0 0 050 ,000

5 0 , 0 0 05 0 , 0 0 05 0 , 0 0 025 ,0005 , 0 0 05 , 0 0 02 , 5 0 0

DEVELOPMENT OF AGRICULTURE22 4 ,194 ,304 12 ,500 BP 0 .02823 8 ,388 ,608 10 ,000 BP 0 .0352 4 16,777,216 8 ,000 BP 0 .03525 33 ,554 ,432 6 ,000 8P 0 .0352 6 6 7 , 1 0 8 , 8 6 4 4 , 0 0 0 8 P 0 . 0 727 134 ,217 ,720 3 ,000 BP 0 .10028 268 ,434 ,000 2 ,000 BP 0 .042 9 5 3 6 , 8 6 8 , 0 0 0 3 4 0 8 P 0 . 3 530 1 ,073 ,736 ,000 140 BP 0 .8731 2 ,147 ,472 ,000 68 BP 1 .532 4 ,294 ,944 ,000 22 BP 1 .932 .5 6 ,000 ,000 ,000 0 8P 1 .833 8 ,589 ,888 ,000 15 + 1 .73 4 16,777,216,000 55 + 1.435 34 ,359 ,55 2 ,000 105 + 1 .036 68 ,719 ,10 4 ,000 175 + 1 .037 137 ,438 ,208 ,000 245 + 1 .03 8 2 7 4 , 8 7 6 , 4 1 6 , 0 0 0 3 1 5 + 1 . 039 549 ,75 2 ,832 ,00 0 385 + 1 .04 0 1 , 0 0 0 , 0 0 0 ,0 0 0 , 0 0 0 4 5 5 +

[A.D. O][165o][185Ol[1930][1976][2o131[2053][2103][2173][2243][2313][2383]* [2453]

2 , 5 0 02 , 0 0 02 , 0 0 02 , 0 0 01 , 0 0 0

7 0 01 , 6 5 0

2 0 08 04 63 74 05 07070707O70


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63WARREN M . HERN

or abou t 32 . 5 doub l i ngs . T he 32nd doub l i ng w as r eac hed i n 1976 , un l es sw e s ta rt c o u n t i n g w i t h " A d a m a n d E v e ," th e p o i n t a t w h i c h t h e re w e r e t w om em ber s o f t he H om o genus , i n w h i c h c ase t he 31 s t do ub l i ng w as r eac hedin 1976 . Th is i s no t a t r i v ia l d i f f e rence , bu t t he specu la t i ve na tu re o f t heen te rp r i se , t he d i f f i cu l t y o f de f in ing the f i r s t human among the va r iousc om pe t i ng hom in i d s pec ies , and t he t im e s pans be t w een ea r l y doub l i ngsmakes th i s po in t m oo t and i r re levan t . W ha t mat te rs i s t he num be r p resen tnow , and t ha t num be r m eans t ha t 32 . 5 doub l i ngs hav e oc c u r r ed .T he s im p les t a r i t hm e t i c a l w ay t o c oun t t he num be r o f doub l i ngs i s t os ta rt w i t h 1 and c on t i nue w i t h a do ub l i ng un t i l on e pas s es t he c u r ren tpop u la t i on lev el ( abou t 6 b i l li on i n 199 8 and add ing abou t 80 m i l li on ne tincrease each year ) . On th is bas is , a lso, a l lowing for ser ious repor t ing er -rors and a 10% co n f ide nce in te rva l i n pop u la t ion es timates, we have com -p le ted 32 .5 doub l ings f rom a s ing le ances to r .

M A L I G N A N T PR O PER TIES O F H U M A N P O P U L A T I O N G R O W T HT h e n u m b e r o f d o u b l i n g s o f t h e h u m a n p o p u l a t i o n , t h e d i m i n i s h i n gdoub l i ng t im es , and c onc om i t an t i n c r eas i ng r a t e o f g l oba l popu la t i ongrowth over p reh is to r i c and h is to r i c t ime , a re o f i n te res t because rap idg r ow t h o f t he hum an popu la t i on i s as s oc ia t ed w i t h a w ide v a r i e t y o f phe -nom ena d is rup t i ve o f the p lane ta ry ecosys tem, a mat te r w h ic h is o f con-ce rn to som e, bu t not a l l , sc ientis ts (Keyf itz , 19 93 ). In part icula r , I havedes c r i bed t he im po r t an t pa r a l l e l s be t w een t he ac t i v i t y o f t he hum an s pe -

c ies and a ma l ignan t p rocess . The para l le l s a re so s t rong and cons is ten tthat I have of fered the hypothes is (d iagnos is ) that the human spec ies hasi ts e lf bec om e a " m a l i gnan t ep i ec o pa t ho log i c p r oc ess 2 engaged in c on v e r t-ing a l l p lan t , an ima l , o rgan ic , and ino rgan ic mate r ia l on the p lane t in tohum an b i om as s o r i ts adap t iv e ad junc t s ( H e r n , 1990 ) and t ha t t he agen t o ft h i s m a l i gnan t t r ans f o r m a t i on i s hum an c u l t u r e ( H em , 1993 ) .T he m os t d i rec t w ay t o s up po r t the hy po t hes is t ha t t he hum an s pec ieshas bec om e a c anc e r on t he p l ane t i s t o s ho w t ha t t he ov e r a ll c ha r ac te r is -t ic s o f t he hum an s pecies , i n c l ud i ng t he m a t hem a t ic s o f po pu la t i on g r ow t h ,hav e equ i v a l enc e o r s im i l a r i t y w i t h t he g r ow t h o f m a l i gnan t t um or s .One o f t he f i ve ma jo r charac te r i s t i cs o f a ma l ignan t p rocess i s rap id ,unc on t r o l l ed g r ow t h ) and t h i s s eem s an ac c u r a t e des c r i p t i on o f hum anpopu la t i on g r ow t h ov e r t he pas t m i l l enn ia , es pec ia l l y du r i ng t he pas t f ew

cen tu r ies . Th is i s l a rge ly due to t he e l im ina t ion o r con t ro l o f p reda to rs andc om pe t i to r s i n c l ud i ng t hos e t ha t a r e m i c r ob ia l and pa r as it ic .


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64POPULATION AN D ENVIRONM ENT

It is n e c e s s a ry t o a sk w h a t o t h e r o r g a n is m , b i o l o g i c a l p h e n o m e n o n , o rs p e c i e s p o p u l a t i o n e x h i b i t s sus ta ined g r o w t h c o u p l e d w i t h e x t e n s i v e d i s -r u p t io n o r d e s t ru c t io n o f s u r r o u n d i n g s ys te m s a n d w i th d i s ta n t c o l o n i z a -t i o n . A n o b v i o u s a n s w e r is c a n c e r, w h i c h u s u a l ly b e c o m e s e v i d e n t e n o u g hf o r d i a g n o s i s i n a n o r g a n i s m w h e n i t h as 1 g m o f t u m o r m a s s m e a s u r i n g 1c m i n d i a m e t e r r e p r e s e n t i n g 3 0 d o u b l i n g s f r o m a s i n g l e c e l l a n d c o n t a i n i n ga b o u t 1 b i l l i o n (1 0 9 ) c e l l s ( T a n n o c k , 1 9 8 9 ) . F r o m t h i s p o i n t , g r o w t h t o at u m o r m a s s o f 1 k g r e q u ir e s o n l y 1 0 fu r t h e r d o u b l i n g s ( ib i d .) . D e a t h o f th eh o s t o r g a n i s m o c c u r s a t 3 7 - 4 0 d o u b l i n g s ( 1 , 0 0 0 b i l l i o n o r 10 12 c e l ls (T a n-n o c k , 1 9 9 2 ) . A t o u r c u r r e n t o f f i c i a l l y e s t im a t e d r a te o f g r o w t h o f n u m b e r so f p e o p l e ( a b o u t 1 . 4 % p e r y e a r) , w e w o u l d r e a ch 3 7 d o u b l in g s in a b o u t2 0 0 y e a r s ( 1 . 3 7 x 1 0 1 1 p o p u l a t i o n ) a n d 4 0 d o u b l i n g s (1 .1 x 1 01 2 p o p u -l a t i o n ) i n a b o u t 4 0 0 y e a r s .

T a n n o c k ( 1 9 8 9 ) p o in t s o u t t h a t, " . . . t h e p e r i o d o f tu m o r g r o w t h t h a t isc l i n i c a l l y e v i d e n t r e p r e s e n t s a r a t h e r s h o r t p e r i o d i n t h e to t a l l i fe h i s t o r y o fa t u m o r . " T a n n o c k a l s o n o t e s t h a t t u m o r s d o n o t g r o w b e c a u s e t h e r a t e o fc e l l p r o l if e r a t i o n is f a st e r t h a n in n o r m a l t is s u e s ; " . . . t h e y g r o w b e c a u s et h e r a te o f c e l l p r o d u c t i o n e x c e e d s t h e r a te o f c e l l d e a t h . " T h i s is t ru e e v e na s t h e tu m o r a p p r o a c h e s 4 0 d o u b l i n g s a n d t h e g r o w t h r ate is d i m i n i s h in gd u e t o d e c l i n i n g c e l l s u r v iv a l . W h i l e c a n c e r c e l l p r o l if e r a t io n o c c u r s a ti n c r e a s i n g l y r a p i d ( h y p e r e x p o n e n t i a l ) ra te s in t h e e a r l y sta g es o f s o m e c a n -c e r s , m o s t c a n c e r s i n c r e a s e a t a n e x p o n e n t i a l r a t e , w i t h a c o n s t a n t d o u -b l i n g t i m e , d u r i n g m o s t o f t h e i r h i s to r ie s ( F ig u r e 1 , S l i n g e r la n d & T a n n o c k ,1 9 9 8 ) . A de c l in ing g ro w th ra te does no t m ean tha t the cancer has s toppedbe ing a cancer . O n t h e c o n t r a r y , i t m a y m e a n t h a t t h e p o i n t h a s b e e nr e a c h e d i n t h e g r o w t h c u r v e w h e n it le v e ls o u t , w h i c h o c c u r s a s t h e m a l ig -n a n c y a p p r o a c h e s t h e la s t f e w d o u b l i n g s ( F ig u r e 2 , S l i n g e r l a n d & T a n n o c k ,1 9 9 8 ) .I n 1 9 6 0 , v o n F o e r st e r e t a l . (1 9 6 0 ) , p u b l i s h e d a f o r m u l a t h a t d e s c r i b e dt h e g r o w t h o f th e h u m a n p o p u l a t i o n t h a t w a s d e r iv e d f ro m a le a s t- sq u a re sr eg r es s io n a n a ly s is o f d o u b l i n g t i m e s o f th e h u m a n p o p u l a t io n . W i th a c o n -f id e n c e i n te r v a l o f + 5 . 5 ye a r s , t h e a u th o r s f o u n d t h a t t h e d o u b l i n g t im e sa p p r o a c h e d z e r o a t A . D . 2 0 2 6 . 8 7 . V o n F o e rs te r 's f o r m u l a , o r i g i n a l ly d e -r iv e d t o d e s c r i b e a p a t t e rn o f h y p e r e x p o n e n t i a l ( i. e. fa s te r t h a n e x p o n e n t ia l )g r o w t h in c a n c e r c e l ls , i s g i v e n i n t h e g e n e r a l f o r m o f

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cancer. A, Plotted on l inear axes; B, Same da ta plotted using alogarithm ic scale for tum or volum e. (Data of RP H il l and RS Bush,unpubl ished. Included w i th permission.) A grow th curve for a rapid lygrowing transplantable tumo r in a m ouse is included in B for compa rison.TD = volum e. [From Slingerland and Tan nock (1998). Reprinted withpermission of The M cG raw -Hi l l C ompanies.]


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I 2 5 4 .5 6 7 8 9T i m eF I G U R E 2 . H y p o t h e t i c a l g r o w t h c u r v e f o r a h u m a n t u m o r , s h o w i n g t h el o n g l a t e n t p e r i o d p r i o r t o d e t e c t i o n . Tu m o r s m a y s h o w a n e a r l y l a g p h a s ea n d p r o g r e s s i v e s l o w i n g o f g r o w t h a t l a r g e s i z e .[F rom S l i nge r l and and Tannock (1998) . ]

h i s t o ri c a l h u m a n p o p u l a t i o n s iz e . Th e s i m p l if i e d e q u a t i o n h a s t h e fi n a l fo r mN in b i l l i ons = 180 / (2027 - t ) ( 3 )

w h e r e t is t h e a c t u a l y e a r o f h i s t o r ic a l t i m e i n q u e s t io n . Fo r t h e y e a r 1 9 9 3 ,f o r e x a m p l e , th i s c a l c u l a t i o n y i e l d s a n e s t im a t e d w o r l d p o p u l a t i o n o f 5 . 2 9 4b i l li o n , w h e r e a s t h e a c tu a l n u m b e r is a p p r o x i m a t e l y 5 . 5 2 6 b i l li o n a c c o r d -i ng to the m os t recen t es t ima tes (U .S . Census Bureau , 1998) . Fo r the year1 9 9 4 , t h e c a l c u l a t i o n y i e l d s a n e s t i m a t e d w o r l d p o p u l a t i o n o f 5 . 4 5 5 b i l -l io n , w h e r e a s th e a c t ua l n u m b e r o b s e r v e d w a s a p p r o x i m a t e l y 5 . 6 0 7 b i l l i o naccord ing to the mos t recen t es t ima tes (U .S . Census Bureau , 1998) . Recen te s t i m a t e s o f t h e 1 9 9 8 w o r l d p o p u l a t i o n b y t h e U S B u r e a u o f t h e C e n s u spu t i t a t 5 .93 b i l l i on , whereas von Foers te r ' s f o rmu la p red i c t s a popu la t i ono f 6 .2 b i l l i o n i n 19 98 . A t t h i s po in t , t he l ines c ross, w i t h vo n Foers te r 's


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67WARREN M . HERN

fo rmu la cons i s ten t l y p red i c t i ng l a rge r popu la t i on l eve l s than those an t i c i -pa ted .V o n Fo e rs te r's f o r m u l a , w h i c h h a s u n d e r - e s ti m a t e d w o r l d p o p u l a t io nle v els s i n c e 1 9 6 0 ( U m p l e b y 1 9 9 0 ) , p r e d i c t s t h e 4 0 t h d o u b l i n g w i l l o c c u r a ta b o u t N o v e m b e r 1 3 , 2 0 2 6 A . D . , a t w h i c h t im e d o u b l in g t im e s w i l l a p -p r o a c h z e r o . E m i li a n i h a s m a d e n e w c a l c u l a t io n s w h i c h y i e l d a d a t e o fa r o u n d 2 0 2 3 A . D . ( E m i li a n i, 1 9 8 8 , p . 2 2 4 ) . C a l c u l a t io n s w i t h t h e f o r m u l au s in g 1 9 9 4 p o p u l a t i o n e s t im a t e s o f a p p r o x i m a t e l y 5 . 6 b i l l i o n y i e l d a p r o j -ec ted year o f t h i s ca tas t roph i c even t o f 2030 . Von Foers te r ' s f i na l equa t i onis d e r i v e d f r o m t h e sa m e g e n e r a l f o r m u l a u s ed f o r t u m o r g r o w t h b y Ta n-nock (N = Noexp [(Kp-KL)t ]; 199 2 , p . 155) , w he re N = n um be r o f e l e -m e n t s a t t h e e n d o f t i m e t, N o = n u m b e r o f e l em e n t s a t b e g i n n i n g o fg r o w t h , K p = r ate o f p r o d u c t i o n o f e le m e n t s , KL = ra te o f loss o f e le-men ts , and t = t ime e lapsed . Th i s i s no t su rp r i s i ng s i nce von Foers te r ' sw o r k l a id t h e fo u n d a t i o n f o r t h e f o r m u l a u s ed b y Ta n n o c k . V o n Fo e rs te rresponded to the Na t i ona l Cancer Ins t i t u te ' s reques t t ha t he deve lop amathemat i ca l desc r i p t i on o f t he p ro l i f e ra t i on o f t umor ce l l s ( von Foers te r ,1 9 5 9 , p . 3 9 1 ). H i s a p p l i c a t io n t o h u m a n p o p u l a t io n s w a s s im p l y a w a y o ftes t ing the equ a t i on (von Foers te r e t a l. , 1 960) .The m athem at i ca l " s i n gu la r i t y "4 desc r i bed i n von Foers te r 's pape r( 1 9 6 6 ) i n w h i c h d o u b l i n g t im e s a p p r o a c h z e r o (A e --> 0 ) a n d t h e p o p u l a -t ion goes to in f in i ty (N --> oo) i s the resu l t o f the p ro je c t ion o f the l inea rd e cre a se i n h u m a n p o p u l a t i o n d o u b l i n g t i m e s b y 1 /2 y e a r p e r y e a r d u r i n gthe pas t 20 00 years (F igure 3) . Vo n Foers ter and h is co -au thors po in t outtha t i n the phys i ca l sc i ences , a " s i ngu la r i t y " means tha t t he sys tem inw h i c h i t o c c u r s e x p e r i e n c e s g r e a t i n s t a b i l it y i n th e v i c i n i t y o f th i s p o i n t a n di s fun da m en ta l l y a l te red i n som e w a y a f te r t h i s po in t has been passed (vonFoers te r e t a l ., 1961) . Tha t p o in t i n t ime as ca l cu la ted by vo n Foers te r andh i s co l league s is less than 30 years f rom no w.

R A T E S O F G R O W T H O F T H E H U M A N P O P U L A T I O NT h e p o i n t a t w h i c h w e b e g i n c o u n t i n g a n d th e to ta l n u m b e r o f d o u -

b l in g s a re i m p o r t a n t i f w e w i s h t o s tu d y a n y r a t e o f g r o w t h o f t h e h u m a np o p u l a t i o n . U n t i l r e c e n t ly , d o u b l i n g t im e s w e r e g e t t in g s h o r te r as a c o r o l -l a ry o f i nc reas ing ra tes o f g row th ; t hey a re i nve rse l y re l a ted . I n the Pa leo -l i t h i c p e r i o d , t h e d o u b l i n g t i m e s w e r e p r o b a b l y c l o s e t o 1 0 0 , 0 0 0 y e a r s( H as sa n , 1 9 8 0 ) . I n d i v i d u a l l i v e s w e r e s h o r t a n d r e p r o d u c t io n w a s l i m i t e db y s h o rt li fe s p an s . I n t h e N e o l i t h i c p e r i o d , f o l l o w i n g t h e d e v e l o p m e n t o fa g r ic u lt u re , t h e re w a s a " p o p u l a t i o n e x p l o s i o n , " w i t h d o u b l i n g t im e s d r o p -


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69WARREN M . HERN

c u r r e n t ra te w o u l d m e a n t h a t t h e f ir s t h u m a n c o u p l e w o u l d h a v e li v e d o n l ya b o u t 1 6 0 0 y e a r s a g o . E v en f u n d a m e n t a l is t s b e l i e v e t h a t A d a m a n d E v el iv e d e a r l ie r t h a n t h a t . Q u i t e o b v i o u s l y , th e c u r r e n t h i g h g r o w t h ra te s o f th eg l o b a l p o p u l a t i o n a re r e l a t iv e l y r e c e n t i n t h e h u m a n e v o l u t i o n a r y e x p e r i -e n c e .V a r i o u s a u t h o r s h a v e p o i n t e d o u t t h a t t h e r a t e o f g r o w t h o f t h e h u m a npo pu la t i on has s tea d i l y i nc reased as fa r back as can be m easured o r es t i-mated un t i l the last fe w years (Pearl , 193 9; Me yer , 19 59 ; Bar t le t t, 1993 ) .Von Foers te r (1966) has shown tha t exponen t i a l g row th ra tes desc r i bed fo rt h e h u m a n p o p u l a t i o n a r e , i n f a c t , t a n g e n t s t o a h y p e r b o l i c c u r v e o n as e m i lo g a r i th m i c s ca le , i n d i c a t i n g t h a t g r o w t h c a n b e d e s c r ib e d a s e x p o -n e n t i a l o n l y i n t h e v i c i n i t y o f t h e i n s t a n t o b s e r v a t i o n , a n d t h a t , o v e r a l l ,i t i s hyperexponen t i a l (F igu re 4 ) . Un t i l recen t l y , t he ove ra l l t rend has beenfo r inc rea s ing ra tes o f inc rease . Fo r exa m p le , t he hum an po pu la t i on w en tf ro m a b o u t 2 5 0 m i l l io n a t A . D . 0 to 5 0 0 m i ll io n in 1 6 5 0 , s lo w e d d o w no n l y b y th e B l a c k D e a t h , w i t h a d o u b l i n g t i m e o f 1 6 5 0 y ea rs a n d a n a v e r-a g e g r o w t h ra te o f a b o u t 0 . 0 4 % , b u t t h e n e x t d o u b l i n g t o 1 b i l l io n in 1 8 5 0t o o k o n l y 2 0 0 y e a r s w i t h a n a v e r a g e g r o w t h r a t e o f 0 . 3 5 % p e r y e a r . Th en e x t d o u b l i n g t o o k o n l y 8 0 y ea rs (2 b i l l io n in 1 9 3 0 ) , g i v i n g a n a v e ra g eg r o w t h ra te o f a b o u t 1 % p e r y e ar, a n d t h e n e x t d o u b l i n g t o 4 b i l l io n t o o ko n l y u n t i l a b o u t 1 9 7 6 w i t h a n a v e r a g e g r o w t h r a t e o f 1 . 5 % p e r y e a r .Con t ra ry to repor t s o r asse r t i ons tha t t he g loba l human popu la t i ong row th rates have de c rea sed i n recen t yea rs , t he re is ev id en ce tha t t he ra tem a y b e a b o u t 1 . 8 % o r m o r e. Fo r e x a m p l e , th e g l o b a l h u m a n p o p u l a t i o nd o u b l e d b e t w e e n 1 9 5 0 a n d 1 9 8 7 , g o i n g f r o m 2 . 5 t o 5 . 0 b i l l i o n ( 3 7 y e a r s ) ;i t d o u b l e d b e t w e e n 1 9 5 6 a n d 1 9 9 4 f r o m 2 . 8 to 5 . 6 b i l l io n ( 3 8 y ea rs ); a n di t w i l l h a v e d o u b l e d b e t w e e n 1 9 6 0 a n d 1 9 9 8 f ro m 3 . 0 t o 6 .0 b i l li o n ( 3 8years ) . These i n te rva l s a l l y i e l d a 1 .8 -1 .9% ra te o f g row th (69 .3 /37= 1 .87% ) . These 37 - and 38 -ye ar ave rages a re i nsen s i t i ve to sho r t -t e rmvar i a t i ons , such as d ram at i c recen t dec l ines i n loca l o r reg iona l f e r t i l i t yra tes (Bongaarts, 19 93 , 199 4) , b ut the y are a t leas t as re l iab le as o f f i c ia le s t i m a t e s o f c u r r e n t g r o w t h r a t e s , w h i c h o f t e n e x c l u d e t h e m o s t r a p i d l yg r o w i n g m a r g in a l p o p u l a t i o n s f r o m c en s us . C u r r e n t e s ti m a t e s h a v e f re -q u e n t l y p r o v e n t o b e e r r o n e o u s l y l o w . U m p l e b y ( 1 9 9 0 ) , f o r e x a m p l e ,p o i n t s o u t th a t o f f ic i a r d e m o g r a p h i c p r o j e c t i o n s ( su c h a s f ro m t h e U n i t e dNat i ons ) a re based on be l ie f s abou t dec l i n i ng fu tu re g row th rates , w i th theresu l t t ha t underes t ima tes a re cons tan t l y rev i sed upwards . The a r t i f i c i a l l yn a r r o w e d d i f f e r e n c e s a r e t h u s t h e b a s i s f o r n e w e r r o n e o u s l y l o w p r o j -ec t i ons . I t is i nd i sp u ta b le , how eve r , t ha t t he ave rage g row th rates fo r theset w o p e r i o d s w e r e a t l e a s t 1 . 8 % p e r y e a r .O ne o f t he sources o f e r ro rs i n o f f ic i a l es t ima tes i s t ha t some o f t he


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71WARREN M . HERN

d e c l i n i n g g r o w t h ra te s . A n i n a c c u r a t e l y l o w e s t i m a t e o f c u r r e n t p o p u l a t i o nfo r the base a t cu r ren t t im e (T 2 ) is used aga ins t w h i ch to measure the d i ff e r -e n c e b e t w e e n t h a t a n d t h e p r e v i o u s p o p u l a t i o n l e ve l a t T 1, w h i c h is n o wk n o w n t o b e h i g h e r th a n i t w a s t h o u g h t a t t i m e T1 to b e ; a t t i m e T 1 , t h es a m e e r r o r w a s m a d e s i n c e t h e p o p u l a t i o n w a s p e r c e i v e d t o h a v e g r o w nf r o m t h e p r e v i o u s ( a n d n o w a c c u r a t e l y k n o w n ) le v e l o f T o i n X ye a rs t o th e( i naccu ra te l y un deres t ima ted ) po pu la t i on a t T1 . Th i s g i ves a fa l se ly l o w ra teo f g r o w t h z , w h i c h t u r n s o u t t o b e t h e s a m e f a l s e l y l o w r a t e o f g r o w t h n o wbe ing es t ima ted a t t ime T 2 fo r t he same reasons (U n i ted Na t i ons , 199 2 ;U m p l e b y , 1 9 9 0 ) . T h e d e m o g r a p h e r s u s e a n a c c u r a te n u m b e r f o r t h e p r e -v i o u s p o p u l a t io n b a s e - - s i n c e i t w a s c o l le c t e d t en y ea rs a g o a n d n o w w ek n o w t h a t it w a s h i g h e r th a n w e t h o u g h t - - a n d a n i n a cc u r a te , fa ls e ly l o we s t im a t e f o r t h e c u r r e n t ( t o d a y 's ) p o p u l a t i o n , g i v i n g a g a i n a fa l s e ly l o w o f f i-c i a l e s tim a t e o f g r o w t h ra te . T h i s c o n t i n u a l l y c o m p o u n d e d e r r o r is u s ed top ro jec t the fa l l ing g ro w th ra tes fo r t he fu tu re . I t is c i r cu la r reason ing , bu t i tis e n s h r in e d a s c o n v e n t i o n a l a n d t h e r e fo r e i n d i s p u t a b l e w i s d o m .An o the r i l lus t ra t i on tha t d raw s o f f i c i a l es t im a tes i n to que s t i on is thee s t i m a t e t h a t a p p r o x i m a t e l y 8 0 m i l l i o n p e o p l e a r e b e i n g a d d e d t o t h e 1 9 9 8w o r l d p o p u l a t i o n o f 6 . 0 1 09 e a c h y e a r f o r a g r o w t h ra te o f 1 . 4 % . H o w -ever, i f t he pop u la t i o n g rew f rom 5 .0 x 109 i n 198 7 to 5 .6 109 i n1 9 9 4 , a n d t o 6 . 0 = 1 0 9 i n 1 9 9 8 , th a t i s a b o u t 1 0 0 m i l li o n p e r y e a r n e ti nc rease fo r an ave rage ra te o f a t l eas t 1 .8% per yea r , and the mos t recen te s ti m a te s o f 5 . 6 1 0 9 f o r 1 9 9 4 a n d 6 . 0 x 1 09 i n 1 9 9 8 m a y p r o v e to b et o o l o w .I t v e r y w e l l m a y b e t h a t g r o w t h ra te s h a v e d e c l in e d i n th e la s t f e wyears f rom 1 .9% to 1 .8% o r even 1 .4% per yea r . I n the l ong pe rspec t i ve ,h o w e v e r , i t is c o n t r a r y t o a ll o f h u m a n h i s t o r y a n d m a y b e b a se d o n e s ti -m a t e s t h a t s e r i o u s l y u n d e r s t a t e t r u e p o p u l a t i o n n u m b e r s . A n a p p a r e n t o rr ea l d e c l in e i n g r o w t h ra te s f it s c o n v e n t i o n a l n o t i o n s o f s t a b i l iz i n g d e n s i t y -d e p e n d e n t l o g i s ti c p o p u l a t i o n c u r v e s s u c h a s t h e c la s s ic a l a s y m p t o t i c p r o j -e c t i o n f ir s t d e s c r i b e d b y R a y m o n d P e a rl ( P e a r l, 1 9 2 2 , p . 2 4 8 ; 1 9 2 4 , p . 6 5 3 ;1 9 3 9 , p . 2 5 8 ) a n d c la s s ic a l d e m o g r a p h i c t r a n s i t io n t h e o r y . A t t h e t im e ,P e a rl, i n fi t ti n g a lo g i s t ic c u r v e t o t h e a v a i l a b l e h u m a n p o p u l a t i o n n u m b e r sa n d t h e g r o w t h o f Drosophi la ( 1 9 2 2 , p . 2 5 4 ) , o f f e r e d t h e o p i n i o n t h a t h u -m a n p o p u l a t io n g r o w t h ra te s w e r e s l o w i n g d o w n d r a m a t ic a l ly ( 1 9 3 9 , p.2 5 4 ), th a t t h e t o ta l p o p u l a t i o n o f th e w o r l d w o u l d n e v e r b e d o u b l e w h a t i tw a s i n th e e a r l y 1 9 3 0 ' s (2 , 1 0 4 , 8 0 0 , 0 0 0 ) , a n d t h a t t h e " co l o s s a l l i m i t " o f2 , 6 4 5 , 5 0 0 , 0 0 0 p o p u l a t io n a s p r o je c t e d b y t h e l o g is t ic c u r v e w o u l d n o tl i k e l y b e a p p r o a c h e d u n t i l th e y e a r 2 1 0 0 A . D . N o n e t h e le s s , P e a rl a d d e dt h e o b s e r v a ti o n t h a t " . . . T h e e a rt h o n a n d f ro m w h i c h m a n m u s t l iv e is n o t


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73WARREN M . HERN

9 The rate o f w o r l d pop u l a t ion g row th m ay be dec l in i ng , pa r tl y due tode c l in ing b i r th ra te s in some pop ula t ions . How ever , wh i le th is i s reas-sur ing for some, i t has a paral le l wi th large mal ignant tumors, whicha lso exper ience a d imin ished growth ra te in the termina l phases. In atumor, the ce l l death ra te beg ins to exceed ce l l p roduct ion ra te becausethe tum or ' s m etabo l i c ne eds exceed the d im in ish ing capa c i ty o f thehost organism. In hum ans, increasing death rates co uld plau sibly ref lectan ag ing popula t ion, increas ing leve ls o f po l lu t ion, dec l in ing nut r i t ion,and a g loba l a tmosphere d im in ish ing ly su itab le for hum an life .M os t m a l ignan t tum ors d i sp lay exponen t i a l g row th ra tes w i th cons tan tt um or v o l um e dou b l i ng t imes and dec l in i ng g row th ra tes in t he te rm i na ls tages. U nt i l recently , the hu m an p op ula t ion has show n increas ing (hyper-expo nen t ia l ) g row th ra tes . In sp ite o f overa l l decreases in gro w th ra tes , the"g ro w th fac to r " o f the hum an pop u la t ion con tinues to d i sp lay exceed ing l yh igh ra tes o f g row th . U .S . Ce nsu s Bureau (1998) w or ld popu la t ion es ti-mates ind i ca te an overa ll pop u la t ion g row th ra te o f 1 .4% and a rate o f0 .1 % in deve loped count ries , bu t ove r on e-h a l f the popu la t ion has a ra te o fpopu l a t ion g row th o f 2 . 0% and a popu l a ti on doub l ing t i me o f 35 y ea rs. A

l i t t l e a r i thmet i c shows tha t the doub l i ng t ime o f the mos t qu i ck l y -g row ingpop u la t i on w i l l ge t us to 8 .6 b i l li on , the 34 th doub l ing o f the human pop u-la tion, long before 20 35 A.D . , w he n i t is pro jec ted to occ ur b y the U.S.Census Bureau. Th is mi les tone appears to be scheduled to occur not muchla te r than 2013 o r 2015 A .D.

P A RA LL E L IN C R EA S E S I N H U M A N B I O M A S S A N D H U M A N -R E LA T E D B IO M A S S

The numbers o f humans , i nc lud ing the num ber o f pop u la t ion dou -b l i ngs , may no t fu l l y convey the eco log i ca l consequences o f human popu-la ti on g ro w th . Ano ther w ay is to ca lcu la te the eco log ica l impa c t o f hum anpop u la t ion g row th by de te rm in ing the m ass o f the humans w h o a re l iv i ngin the ecosys tem at an y time . H um an b ioma ss increases m ay be ca lcu la tedby tak ing some m ed ian numbers such as med ian a du l t m ass , ma le andfemale, and m edian masses for ch i ld re n. Us ing an ear ly P le is tocene es t i-mate o f 55 kg fo r the average ad u l t m a le and 45 kg fo r the a verage adu l tfemale (Rele th ford , 1990, p . 309) and 25 kg for the average ch i ld , w e s tartw i th 100 kg for the f irs t s tone age cou ple . W i th four surv iv ing ch i ldren no tye t o f rep roduc t i ve a ge , they have doub led the i r biomass . The mo derncoun te rpar ts o f the P leis tocene cou p le w ou ld ha ve the masses o f 75 kg(male) and 60 kg (female) w i th 25 kg for the ave rage (7 year-o ld) c h i ld


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(Frisancho , 1990) . U s ing an assum pt ion o f t hese m asses w i t h 60 % o f thea v e r a g e h u m a n p o p u l a t i o n o v e r t i m e b e i n g c o m p o s e d o f a d u l t s ( 5 0 %males, 5 0% fema les ) an d 40 % ch i ld re n w i t h average m asses o f 25 kg , f o ra n a p p r o x i m a t e h u m a n b i o m a s s o f 3 x 1 0 1 1 k g , w e h a v e re a ch e d a d o u -b l i n g o f 31 .5 i n h u m a n b i o m a s s a l o n e f o r t h e g l o b a l p o p u l a t i o n f r o m t h eo r i g i n a l c o u p l e . I f w e a l s o in c l u d e d o m e s t i c a n i m a l s a s h u m a n a n i m a l b i o -mass , s ince t hey a re pa r t o f t he human occupa t ion o f t he p lane t (Crosby ,1 9 8 6 ; H a m m o n d , 1 9 9 2 ) , a d d i n g a p p r o x i m a t e l y 1 1 0 1 2 k g ( Ta b le 2 ), w ehave reached 33 .6 d o u b l i n g s .V i t ousek e t a l. , es tima ted in 1 986 tha t the hu m an species i s us ing 40%of a l l te rres tr ia l ne t pr im ary p rod uc t ion (TNPP) on the p lanet . In 199 7,V i t ousek and h is co -au thors es t ima ted t ha t up t o 50% o f t he land su r facearea o f the E ar th is used by hu m an be ings in som e manner , t ha t huma nsare us ing up t o 50% o f t he access ib le f resh wa te r resources , t ha t humanscause ab ou t 5 0% o f a l l te rres tr ia l n i t rogen f i xa t ion , and t ha t 66 % o f a llf i sher ies are overexp lo i ted, dep le ted, or a t the l im i t o f exp lo i ta t ion (V i -t ousek e t a l. , 1 997) .There i s a l ready a ser ious de f i c ienc y o r dec l ine in nu t r it ion f o r som eg r o u p s . B y t h e t im e w e re a ch th e 4 0 t h d o u b l i n g , h u m a n n u t r it io n w i l l e i -t he r be sub-ma rg ina l , as i t a l ready is f o r m an y pe op le , o r au to t roph ic ( can-n iba l i sm) .

P AR ALLE L IN CR EA SE S I N H U M A N E N E R G Y C O N S U M P T I O NI nc reases in human numbers and in human an ima l b iomass ( inc lud ingdomes t i c an ima ls ) a re s ign i f i can t . Bu t t he g loba l eco log ica l impac t o f hu -m a n a c t i v i t y i s m o r e a c c u r a t e l y m e a s u r e d b y t h e c o n s u m p t i o n o f e n e r g y .Few th ings mod i f y eco log ica l sys tems as much as t he use o f energy f o rh u m a n e x p l o i t a t i o n o f t h e e n v i r o n m e n t i n c l u d i n g t h e e x t r a c t i o n o f m i n -era ls , the use o f m ater ia ls such as foss il fue ls , the cu l t iva t ion o f food c ropsand o the r p lan t s , and t he p roduc t ion o f g reenhouse gases .Wh i le i nd iv idua l ca lo r i c needs va ry accord ing t o ac t i v i t y pa t t e rns , wemay reasonab ly assume tha t t he average P le i s tocene adu l t i nd iv idua lbu rned abou t 3500 k i l oca lo r ies (Kca l ) pe r day . Our ances to rs su rv i ved byscavenging, hu nt ing , and gather ing, a l l o f w h ic h are ac t iv i ties tha t requ i reh igh leve ls o f energy .W i th a con vers ion f ac to r o f 4 BTU per Kca l (Cook , 197 6 ; L indeb urg ,1 9 9 5 ; C o l e m a n & D e w a r , 1 9 9 7 ) , t h e r o u g h e q u i v a l e n t o f 3 5 0 0 K c a l i s

(4 ) (3500 ) = 14 ,000 ; t he fi rs t hypo the t ica l P le i s tocene h um an burn ed


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75WARREN M. HERN

TA B LE 2Est imation of D om estic Animal Biomass

A nim al # Av. Wt . B iomass (kg)Cattle 1.271,279 X 109 1 ,1 5 0 b 663,149,950,000Sheep & goats 1.716 ,749 x 109 100 lb 77,871,734,000Pigs .845,108 X 109 250 Ib 95,835,247,000Horses .118,302 X 109 1 ,0 0 0 b 53 ,797,867,000Buffalo & cam els .157,967 X 109 1 ,0 0 0 b 71 ,653,831,000Chickens, ducks, Turkeys 11.5 x 109 5 Ib 26,082,000,000Catfish .385 x 109 I Ib 174,636,000Total dom estic anima l bioma ss, kg* 988,565,250,000*Does not include domestic pets, sm all food an imals, zoo animals. For purposes of this paper,the num ber used w ill be I x 1012 kg.Sources: U.S. Department of Agriculture, Inventory And Average Liveweight, 1993, U.S.,mimeo; W inRock International Reports, Litt le Rock, Arkansas, and W orld Resources 19 92 -1993 (Hamm ond, 1992)abou t (14 ,000 )(365 ) = 5 .1 x 106 BTU pe r yea r o r wha t we m ay ca l l a"P le is tocene Energy Co nsum pt ion U n i t " (PECU).

In 1995, w or ld co nsu m pt ion o f energy was est imated a t 3 .63 1017BTU per year (U.S. Dept o f Energy, 1998) . D iv id ing th is number by theannua l per cap i ta energy con sum pt ion o f 5 .1 106 BTU in the ear lyP le is tocene (one "PECU") y ie lds a re la t i ve wor ld ene rgy consumpt ion o f7.1 x 10 ~ (adjusted) BT U's (or 7.1 x 10 ~ PECU's). Using form ula (1) toes t ima te the number o f doub l ings (x ) o f human ene rgy use s ince ou r f i r s tancestor, the result is

7.1 x 101~ = 2 (4)In(7.1 x 101~x = (5)In 225x = - = 36 (6).693

In te rms o f energy use by human be ings, there had been 36 doub l ingsas o f 1995. Globa l energy use is doub l ing every 30 years a t the ra te o f2 .3% per year (U.S. Dept o f Energy, ib id . ) . We may expect the 37 th dou-


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b l i n g o f e n e r g y u se t o o c c u r in o r a b o u t th e y e a r 2 0 2 5 a s s u m i n g th e r e is n oinc rease o r dec rease in t he rate o f i nc rease in t he consumpt ion o f energy .

C O M P E T I N G O B S E R V A TIO N S A N D H Y P OT H ES E SC o m p e l l in g a s t h e m a t h e m a t ic s o f h u m a n p o p u l a t i o n in c re a se m a y b e ,

t h e re a r e re a so n s t o q u e s t i o n w h e t h e r t h e p ro c es s o f d o u b l i n g o f th e p o p u -l a t i o n w i l l c o n t i n u e t o t h e p o i n t s p r o j e c t e d b y t h e c a l c u l a t i o n s i n t h i s p a -per . Fo r examp le , Bongaar t s (1998) p ro jec t s a dec l in ing popu la t ion in Eu-r o p e a n d i n t h e U . S . a n d a d e v e l o p e d - w o r l d p o p u l a t i o n e q u a l t o t h ep r e s e n t i n t h e y e a r 2 0 5 0 . Th e e p i d e m i c o f H I V / A I D S i n A f r i c a r a i s e s c o n -c e r n s a b o u t a d e c l i n i n g p o p u l a t i o n i n t h a t c o n t i n e n t , a n d t h e d e v e l o p m e n to f an t ib io t i c - res is tan t bac te r ia ra i ses t he spec te r o f o the r k inds o f g loba lp a n d e m i cs th a t c o u l d s e r io u s ly d im i n i s h t h e h u m a n p o p u l a t io n . W e d o n o tk n o w w h a t g l o b a l w a r m i n g w i l l d o t o w o r l d f o o d p r o d u c t i o n o r s to ra ge , o rt o la rge p op u la t ion s l iv ing a t sea leve l, bu t the con sequ ence s o f se r iousa n d r a p i d g l o b a l w a r m i n g o r o t h e r a n t h r o p o g e n i c a t m o s p h e r i c d i s t u r -b a n c e s c o u l d b e c a t a s tr o p h i c .H u m a n h i s to r y te l ls u s n o t h i n g s o m u c h a s t h e u n c e r t a in t y o f p r e d i c -t i o n s a b o u t h u m a n p o p u l a t i o n d y n a m i c s . A s n o t e d , p o p u l a t i o n s c i e n t i s t sd i d n o t i m a g i n e in t h e e a r l y 2 0 t h c e n t u r y th a t t h e h u m a n p o p u l a t io n w o u l dreach the leve ls tha t i t has a l rea dy reached.There a re no rea l pa ra l l e l s w i t h t he human exper ience in t he an ima lw o r l d . C e r t a i n l i f e f o r m s h a v e g r o w n i n p o p u l a t i o n a n d e v e n g a i n e d ac e r t a i n d o m i n a n c e f o r p e r i o d s o f t i m e , b u t p o p u l a t i o n e r u p t i o n s i n n a t u r et e n d t o b e l i m i t e d b y f o o d s u p p l y a n d o t h e r e n v i r o n m e n t a l c o n s t r a i n t s(M acL u l i ch , 193 7 ; An dre wa r tha & B i rch , 195 4) . Serious ou tb reaks o fh igh ly des t ruc t i ve spec ies t ha t d im in ish t he numbers o f o the r spec ies andd is rup t ecosys tems a re a lm os t a lway s the resu l t o f h um an in te rven t ion andare more i l l us t ra t ions o f t he hypo thes is o f t he human spec ies as a ma l ig -nan t p rocess t han con t ras t ing o r compara t i ve examp les (Ehr l i ch & Rough-garden , 1987) . H um an s a re t he on ly species tha t possesses cu l t u ra l adap ta -t ions tha t ma ke the env i ronm enta l a l t e ra t ions pe rvas ive and pe rma nen t andwh ich have a record o f d i rec t l y caus ing t he ex t inc t ion o f o the r spec ies .

I t i s poss ib le t ha t t he numbers o f t he human spec ies w i l l s t op g row ingc o m p l e t e l y o r t h a t t h e g r o w t h r a t e w i l l s u d d e n l y d r o p t o e x t r e m e l y s m a l lP le is tocene leve ls as the resu l t o f de l ibe ra te so c ia l de c is ion s or de ns i ty -dependen t mechan isms p r io r t o genera l ecosys tem fa i l u re . I t i s poss ib letha t na t ions w i t h re la t i ve ly l ow popu la t ion dens i t i es , abundan t na tu ra l re -sources , and low rates o f g row th w i l l be spared the g loba l con sequ ence s o f


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77W ARREN M. HERN

hu m an - indu ce d g loba l w arm ing , access to cheap energy , and the e ffec ts o fr a p id p o p u l a t i o n g r o w t h i n o t h e r p a r ts o f t h e w o r l d . B u t it d o e s n ' t s e e m t obe ve ry l i ke l y .

C O N C L U S I O NTh e c l o s e p a r a l l e l s b e t w e e n t h e t o t a l n u m b e r o f d o u b l i n g s o f t h e h u -m a n p o p u l a t i o n i n t e rm s o f n u m b e r s , b i o m a s s , a n d e n e r g y u s e a c c o m -p a n i e d b y i n c r e a s in g r ate s o f g r o w t h a n d t h e c h a r a c t e r is t ic s o f a m a l ig n a n tp rocess ra i se d i s tu rb ing ques t i ons abou t t he re la t i onsh ip be tween the hu -

m a n p o p u l a t i o n a n d t h e g l o b a l e n v i r o n m e n t . F ir st, it s u p p o r t s t h e h y p o t h -es i s (d i agnos i s ) t ha t t he human spec ies has become a ma l i gnan t p rocess onthe p lane t . Second , because o f t he fac t t ha t we a re ve ry c l ose to the num~ber o f do ub l i ngs a t w h i ch a m a l i gna n t p rocess reaches i ts m ax im um le tha lp o t e n t i a l , w e a r e f o r c e d t o c o n t e m p l a t e t h e f a c t t h a t a m a l i g n a n c y i n a ni n d i v i d u a l o r g a n i sm c o n t i n u e s u n t i l t h e h o s t o r g a n i sm h a s c ea s ed t o fu n c -t i o n - i t d i e s .Hu m ans can k i l l ne i the r the Earth no r the g loba l ecosys tem . Bu t w ec a n m o d i f y th e e c o s y st e m i n w h i c h w e l iv e to th e p o i n t t h a t it w i l l n olo n g e r s u p p o r t u s o r o t h e r c o m p l e x f o rm s o f l if e . W h e t h e r t h is p o i n t is e v e rr ea ch e d, o r w h e t h e r i t is r e a c h e d b e f o re t h e h u m a n p o p u l a t i o n h a s d o u -b led as many t imes as a ma l i gnan t t umor a t t he t ime o f hos t o rgan i smdea th , rema ins to be seen .

A C K NOWL EDGMEN T SI w i sh to tha nk H e inz vo n Foers te r, A lbe r t A . B ar t le t t, S tua rt Um p leby ,

P r i sc i l l a Re in ing , Gabr i e l Lasker , Char l es Sou thw ick and anonymous re -v i e w e r s f o r r e v i e w i n g e a r l y v e r s i o n s o f t h i s m a n u s c r i p t a n d m a k i n g v a l u -ab le sug gest ions . M y ass is tant , Er ica Schafer, had an eag le eye for im por-tan t bu t eas i l y m issed e r ro rs . I esp ec ia l l y w i sh to than k P ro fesso r Bar t le t t f o rde ta i l ed sugges t i ons and mathemat i ca l gu idance . A l l e r ro rs tha t rema in a rem y o w n .

ENDNOTES1. The Un i ted N at ions Pop u la t ion Fund (UNPF) has se t Oc tobe r 12 , 1999 fo r com me m ora-t ion o f the "Da y o f 6 B i l l io n . " W heth er o ne accepts the ear l ie r es timates by the U.S.


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C e n s u s B u r e a u o f r e a c h i n g 6 b i l l i o n i n 1 9 9 8 , a s m a n y d o , o r a l a t e r c o m m e m o r a t i v e d a tei s ir r e levan t to the con c lus ions o f th i s pape r .2 . T h e te r m " e p i e c o p a th o l o g i c p ro c e ss " is o n e I h a v e c o i n e d t o d e s c r i b e a " p a th o l o g i c "p rocess (d i sease s ta te ) tha t i s ope ra t i ng upon ( "ep i - " ) the ecosys tem ( "eco - " ) ; a l l r oo ts i nt h e w o r d h a v e a G r e e k o r i g i n . S e e L i d d e l l a n d S c o tt 's Greek-Engl ish Lex icon (1958) Lon-d o n : O x fo r d /C l a r e n d o n P r e s s .3 . T h e f iv e a r e : 1 ) r a p i d , u n c o n t r o l l e d g r o w th ; 2 ) i n v a s i o n a n d d e s tr u c t io n o f a d j a c e n t n o r-ma l t i ssues ; 3 ) me tas tas i s , o r d i s tan t co lon i za t i on ; 4 ) de -d i f fe ren t i a t i on , o r l oss o f d i s -t i n c t i v e n e s s i n i n d i v i d u a l c e l l s a n d t i s s u e s ; a n d 5 ) t h e p r o d u c t i o n o r e x c r e t i o n o f t o x i cm e ta b o l i te s . T h e d e v e l o p m e n t a n d m e d i a t i o n o f th e s e c h a ra c te ris tic s i n h u m a n s o c i e t y b yh u m a n c u l t u r e i s d e s c r i b e d i n tw o p r e v i o u s p u b l i c a t i o n s ( H e m , 1 9 9 0 , 1 9 9 3 ) .4 . " S i n g u l a r i ty " a s d e f i n e d b y v o n F o e r ster e t a l. (1 9 6 1 ) i s t h e c o n d i t i o n

5.

l i m y = oo, x- -> xow h e r e y = p o p u l a t i o n o r n u m b e r o f e le m e n t s , x = d o u b l i n g ti m e a n d Xo = z e r o d o u -b l i n g t i m e .E s tim a te s o f d o u b l i n g t i m e s a n d r ates o f p o p u l a t i o n g r o w th p r i o r t o 2 , 0 0 0 y e a rs B .P . a r eb a s ed o n t h e s t u die s a n d r ep o rt s o f a n th r o p o l o g i c a l d e m o g r a p h e r s a n d p a l e o d e m o g r a -phe rs such as Hassan , Bou rgeo is -P icha t, and o the rs. An y p ro jec t i on o f fe red h e re fo r they e a r s b e y o n d 2 0 1 3 i s p u r e s p e c u l a t i o n , b u t I h a v e a t t e m p te d t o b a s e m y e s t i m a te s o nc u r r e n t d a ta a n d l i k e l y p a t te rn s f o r t h e s a k e o f g i v i n g t h e r e a d e r a t h o u g h t f u l f r a m e w o r kfo r t h e l o n g p e r s p e c t iv e a n d f o r t h e p o s s i b i l it ie s f o r t h e f ut ur e.

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