No-effect concentrations in algal growth inhibition tests

Wat. Re5. V01. 30, N0. 7, pp. 1625-1632, 1996

~

Per9am0n

P11:50043-1354(96)00056-5

N0-EFFEC7

C0pyr19ht • 1996 E15cv1er5c1ence Ltd Pr1nted 1n 6reat 8r1ta1n. A11 r19ht5 re5erved 0043-1354/96 $15.00 + 0.00

C0NCEN7RA710N5 1N A L 6 A L 6 R 0 W 7 H 1NH181710N 7E575

5. A. L. M. K 0 0 1 J M A N 1*, A. 0. HAN57VE172 and N. N Y H 0 L M 3 ~Department 0f 7he0ret1ca1 810109y, Vr1je Un1ver51te1t,de 80e1e1aan 1087, NL-1081 HV, Am5terdam and 2 1n5t1tute0f Env1r0n. 5c1., MW-7N0, P.0. 80x 6011, NL-2600 JA De1ft and 31n5t1tute0f Env1r0n. 5c1. • En9. D7U, 8y9n1n9 115, DK-2800 Lyn96y

(F1r5t rece1ved Ju1y 1995; accepted 1n rev15edf0rm Fe6ruary 1996) A65tract--We pr0p05e three 51mp1em0de15 f0r effect5 0f chem1ca1 c0mp0und5 0n the 9r0wth 0f 6atch cu1ture5 0f a19ae that a110wthe e5t1mat10n0f the n0-effectc0ncentrat10n.7he 9r0wth m0de1 a55ume5that the c05t5 f0r 9r0wth 15pr0p0rt10na1t0 the c0ncentrat10nthat exceed5 the n0-effect1eve1.7he ha2ard m0de1 a55ume5 that the ha2ard rate 15 pr0p0rt10na1 t0 the c0ncentrat10n that exceed5 the n0-effect 1eve1. 7he adaptat10n m0de1 15 51m11art0 the ha2ard m0de1, 6ut the effect5 0n1y 0ccur at the 5tart. 7he n0-effect c0ncentrat10n5 0f the three m0de15 turn 0ut t0 6e very 51m11ar.C0pyr19ht • 1996 E15ev1er5c1ence Ltd

Key w0rd5--N0EC, EC50, NEC, 9r0wth rate, k1111n9rate, adaptat10n

1N7R0DUC710N

7he effect5 0f chem1ca1 c0mp0und5 0n a4uat1c 6101091ca1 5y5tem5 are te5ted r0ut1ne1y w1th a 5et 0f 51mp1e t0x1c1ty te5t5, where 9r0up5 0f 1nd1v1dua15 f0r a 51n91e5pec1e5, u5ua11y0r191nat1n9 fr0m a 1a60rat0ry cu1ture, are exp05ed t0 a 5et 0f c0ncentrat10n5 0f a chem1ca1 dur1n9 50me 5tandard12ed per10d. 7he N0-065erved Effect C0ncentrat10n (N0EC) 15 def1ned a5 the h19he5t te5ted c0ncentrat10n that 91ve5 n0 519n1f1cant dev1at10n fr0m a c0ntr01 w1th0ut the chem1ca1 (8art1ett et a1., 1974, 8r1n9mann and K11hn, 1980). 7he u5efu1ne55 0f th15 fre4uent1y u5ed 5tat15t1c 5uffer5 fr0m 1ack 0f kn0w1ed9e a60ut the p0wer 0f the 5tat15t1ca1 te5t that 15 u5ed. 7h15 p0wer a150 depend5, 0f c0ur5e, 0n the pr06a6111ty 0f an err0r 0f the f1r5t k1nd (u5ua11y taken t0 6e 5%), wh1ch 15rather ar61trary. 1n add1t10n, the N 0 E C 15 h19h1y dependent 0n the te5t de519n, 51nce 1t can 0n1y a55ume va1ue5 0f te5ted c0ncentrat10n5. A c0mpr0m15e ex15t5 6etween the num6er 0f d1fferent c0ncentrat10n5 that are u5ed 1n the te5t and the num6er 0f rep11cate5 per c0ncentrat10n. Prec1510n 1ncrea5e5 w1th the num6er 0f d1fferent c0ncentrat10n5 and the p0wer 1ncrea5e5 w1th the num6er 0f rep11ca5. 1n the env1r0nmenta1 r15k a55e55ment 0f chem1ca15, the pred1ct10n 0f env1r0nmenta1 n0-effect c0ncentrat10n5 re11e5 heav11y 0n 1a60rat0ry te5t der1ved N 0 E C va1ue5. H0wever, m05t 5tandard ec0t0x1c1ty te5t5 were 0r191na11y de519ned f0r determ1n1n9 EC50 va1ue5. 1n an attempt t0 addre55 the pr061em5 1nherent t0 the N0EC, 1t 15 current pract1ce t0 der1ve PNEC5 (Pred1cted Env1r0nmenta1 N0-Effect C0ncentrat10n5) *Auth0r t0 wh0m c0rre5p0ndence 5h0u1d 6e addre55ed.

fr0m EC50 data U51n9 a 5Cheme 0f f1Xed app11Cat10n fact0r5. 7he draft MarCh 1995 ver510n 0f the EU teChn1Ca1 9U1danCe d0CUment f0r enV1r0nmenta1 r15k a55e55ment 0f new and eX15t1n9 5U65tanCe5 5U99e5t5 fact0r5 0f 10, 50, 100 and 1000, depend1n9 0n the am0Unt and 4Ua11ty 0f the data ava11a61e. 8eCau5e d05e-re5p0n5e 510pe5 Can 6e very C0mp0und-5peC1f1C, 50me w0rker5 pr0p05ed EC5, EC 10 0r 0ther ••5ma11••effect va1ue5.5uCh an appr0ach 15d1ff1cu1t t0 app1y t0 r15k a55e55ment, 6ecau5e 0f a 1ack 0f c0n5en5u5 a60ut the prec15e def1n1t10n 0f ••5ma11••. 7he 5ma11er the effect 512e 1n de5Cr1pt1ve m0de15 the 1ar9er the c0nf1dence 1nterva1 and the m0re the e5t1mate 6ec0me5 dependent 0n the 5pec1f1c m0de1 that ha5 6een u5ed t0 de5Cr16e the re5u1t5. 51nCethe emp1r1ca1109-10915t1c m0de1 d0e5 n0t have a 5c1ent1f1c6a515, th15 15 4u1te an 065taC1e. 7h15 pr061em 6ec0me5 1e55 1mp0rtant f0r the 1ar9er effect 512e5, 5uch a5 the EC15 0r EC20.7he pr061em then 6ec0me5 h0w ••5ma11•• effect5 1n the 1a60rat0ry tran51ate 1nt0 effect5 0utd00r5 and h0w the effect5 0f em15510n5 f0r var10u5 c0mp0und5 1n a certa1n area C0m61ne when each 15 a110wed t0 have a ••5ma11•• effect. 1n th15 art1c1e we d15cU55 the app11ca6111ty 0f a N0-Effect C0ncentrat10n (NEC) 1n a19a1 9r0wth 1nh161t10n te5t5. 7here are at 1ea5t f0ur 1nternat10na11y accepted 5tandard te5t de5cr1pt10n5, 1.e. the near1y 1dent1ca1 0 E C D 9u1de11ne 201 (0ECD, 1984), the 1nternat10na1 5tandard 150 8692 (150, 1989) and the EU 6u1de11ne C3 (EU, 1992) c0ver1n9 the fre5hwater env1r0nment, and the 1nternat10na1 5tandard, 150 10253 (150, 1994) c0ver1n9 the mar1ne env1r0nment. 7he a55e55ment 0f the N 0 E C va1ue 1n the5e meth0d5 15, 1n 1ack 0f 6etter, 0n1y 5uperf1c1a11y def1ned, and m05t1y 1eft t0 the jud9ement 0f the part1cu1ar 5c1ent15t

1625

1626

5. A. L. M. K001jman et a1.

whether a 5tandard 5tat15t1ca1 te5t 5h0u1d 6e app11ed 0r n0t. 7he weakne55 0f th15 appr0ach ha5 6een rec09n12ed 6y the w0rk1n9 9r0up5 deve10p1n9 the5e meth0d5. 7he N 0 E C va1ue w111depend 0n the var1at10n am0n9 rep11cate te5t ve55e15 and the dev1at10n5 0f treated a19a1 p0pu1at10n5 fr0m the c0ntr01. Re1at1ve1y h19h N 0 E C va1ue5 may theref0re re5u1t fr0m a 6ad1y perf0rmed te5t. 7he NEC d0e5 n0t 5uffer fr0m the 5tat15t1ca1 pr061em5 0f the N0EC, 6ecau5e the nu11 hyp0the515 15 that the NEC e4ua15 2er0. A p00r p0wer re5u1t5 1n an 1na6111tyt0 reject the nu11hyp0the515, and 1ead5 t0 the c0nc1u510n that the te5ted c0mp0und re4u1re5 further re5earch. 7he pre5ent art1c1e 15 0ne 0f a 5er1e5 (8edaux • K001jman, 1994; K001jman • 8edaux, 1996, 1996a, 19966) that dea15 w1th 51m11ar NEC5 1n the 0ther 0 E C D t0x1c1ty te5t meth0d5. A11 m0de15 6eh1nd the5e ana1y5e5 a55ume that the effect 512e 0n the var10u5 phy5101091ca1 tar9et pr0ce55e5 15 pr0p0rt10na1 t0 the c0ncentrat10n 0f the c0mp0und that exceed5 a n0effect c0ncentrat10n 1n the 0r9an15m5. 7he Dynam1c Ener9y 8ud9et5 (DE8) the0ry 15 u5ed t0 1dent1fy the tar9et pr0ce55e5. 7h15 the0ry 15 de5cr16ed 1n K001jman (1993). 7he ch01ce 0f a 11near re1at10n5h1p 6etween effect 512e and the t155ue-c0ncentrat10n re1ate5 t0 the 1dea 0f a 7ay10r-appr0x1mat10n t0 the •rea1• effect 512e. 50 the actua1 effect 512e m19ht 6e a c0mp1ex funct10n 0f the t155ue-c0ncentrat10n, 6ut we u5e 0n1y the f1r5t term 0f 1t5 7ay10r appr0x1mat10n. F0r h19h1y n0n-11near re1at10n5h1p5, th15 0n1y w0rk5 f0r 5ma11 effect 512e5.7he 1nc1u510n0f m0re term5 0f the 7ay10r-appr0x1mat10n hard1y make5 5en5e 1n the 119ht 0f the c0ncept that phy5101091ca1 pr0ce55e5 can 6e 0rdered w1th re5pect t0 5en51t1v1tyf0r a part1cu1ar c0mp0und. At 10w c0ncentrat10n5 0n1y the m05t 5en51t1ve pr0ce55 15 affected, 6ut at h19h c0ncentrat10n5 many pr0ce55e5 are affected. 1t w111 6e very d1ff1cu1t t0 make re11a61e m0de15 f0r 1ar9e effect5. 51nce r15k a55e55ment re4u1re5 kn0w1ed9e 0f 5ma11 effect5, n0t 0f 1ar9e effect5, the 51tuat10n that 1ar9e effect5 are p055161y n0t we11 captured 6y m0de1 pred1ct10n5 15 hard1y re1evant. 70 51mp11fy the rea50n1n9, we a55ume that the e11m1nat10n rate 15 5ma11w1th re5pect t0 the 1nver5e 0f the 1nterd1v1510n1nterva1, 50 the 1ntra-ce11u1arc0ncentrat10n 15 a1m05t 1n5tantane0u51y 1n e4u1116r1um w1th the env1r0nment-c0ncentrat10n, wh1ch make5 5en5e f0r m1nute a19a1 ce115. A5 10n9 a5 the a4ue0u5 610ava11a61e c0ncentrat10n 0f the te5t c0mp0und rema1n5 appr0x1mate1y c0n5tant and 15 n0t reduced 6y 50rpt10n 0r 0ther e11m1nat10n mechan15m5, the t0x1c d05e can 6e re9arded c0n5tant thr0u9h0ut the te5t. 50 the f0cu5 15 0n p0pu1at10n 9r0wth at a c0n5tant env1r0nment-c0ncentrat10n 0f te5t c0mp0und. 1rre5pect1ve 0f the phy5101091ca1 c0mp1ex1ty 0f the ce11cyc1e, the fact that the dau9hter ce115repeat the phy5101091ca1 6ehav10ur 0f the m0ther ce111mp11e5 that the p0pu1at10n w111 9r0w exp0nent1a11y 1n ce11 num6er5 a5 10n9 a5 the env1r0nment 15 c0n5tant.

M0DEL5

A 5ummary 0f the a19a1 9r0wth 1nh161t10n te5t acc0rd1n9 t0 the 5tandard te5t meth0d5 15 a5 f0110w5: 8atch cu1ture5 0f 0ne 0f the rec0mmended a19a1 5pec1e5 (1.e. the fre5h water 9reen a19a 5e1ena5trum capr1c0rnutum 0r 5cenede5mu5 5u65p1catu5, 0r the mar1ne d1at0m 5ke1et0nema c05taturn 0r Phae0dacty1um tr1c0rnuturn) are 5tarted w1th a f1xed ce11 den51ty 0 f 10 4 ce115m1-~ 1n the pre5cr16ed med1a w1th d1fferent add1t10n5 0f te5t c0mp0und, u5ua11y 6e10w the 501u6111ty 1n water. A1th0u9h the 9u1de11ne pre5cr16e5 c0ncentrat10n5 1n term5 0f effect 512e5, the5e ch01ce5 are 1e55 1mp0rtant f0r the ana1y5e5 that we pr0p05e here. 7emperature and 119ht 1nten51ty are c0n5tant dur1n9 exp05ure, 6ut a prec15e temperature and 119ht 1nten51ty are n0t pre5cr16ed, 0n1y an a110wa61e ran9e. 7he te5t ha5 6een de519ned 50 that 1dea11yexp0nent1a1 9r0wth 1n the c0ntr01 cu1ture5 can 6e 5u5ta1ned f0r the ent1re durat10n 0f the te5t, wh1ch ha5 6een f1xed at 72 h. 1t 15 5pec1f1ed a5 a va11d1ty cr1ter10n that the 9r0wth rate mu5t 6e h19h en0u9h t0 a110w the 610ma55 1n the c0ntr01 cu1ture5 t0 1ncrea5e 6y at 1ea5t a fact0r 16, wh1ch c0rre5p0nd5 t0 a m1n1mum 9r0wth rate 0f 0.92 d- 1.7he 9r0wth rate5 n0rma11y 06ta1ned f0r the 5tandard te5t 5pec1e5 5. capr1c0rnutum and 5. 5u65p1catu5 may vary fr0m a60ut 1.2 t0 2.0 d-~, 1ncrea51n9 w1th 119ht 1nten51ty and temperature (Han5tve1t, 1982, 1991). 7he mean 9r0wth rate5 f0r 5. c05tatum and P. tr1c0rnutum are 2.40 d ~ and 1.73 d t, re5pect1ve1y, determ1ned 1n an 1nternat10na1 r1n9 te5t (Han5tve1t, 1991). 7he c0rre5p0nd1n9 610ma55 1ncrea5e dur1n9 3 d am0unt5 t0 a fact0r 37 and 400, re5pect1ve1y. 1n pract1ce a 72 h exp0nent1a1 9r0wth 15 0n1y ach1eved w1th 5. capr1c0rnutum and P. tr1c0rnutum. 7he 0ther 5pec1e5 9r0w appr0x1mate1y 10915t1ca11y, 6ecau5e 0f the 1ar9e ce11 v01ume 0f 5. 5u65p1catu5 (re5u1t1n9 1n a 1ar9e 1n0cu1ated 610ma55) 0r t0 the h19h 9r0wth rate 0f 5. c05tatum. 7he 9u1de11ne5, h0wever, a110w f0r the u5e 0f the exp0nent1a1 9r0wth pha5e f0r the eva1uat10n 0f effect5. 7he 610ma55 15 u5ua11y mea5ured 6y e1ectr0n1c part1c1e c0unt1n9, 6y 5pectr0ph0t0metry (0pt1ca1 den51ty) 0r 6y f1u0r0metry (1n v1v0 ch10r0phy11 f1u0re5cence), wh1ch 1mp11e5 that 60th the 11v1n9and the dead ce115 c0ntr16ute (dead ce115 50mewhat 1e55 than 11v1n9ce115 w1th f1u0r0metry). F0rma11y, the 610ma55 (1.e. dry we19ht 0r t0ta1 ce11v01ume) 15 the pr0per mea5ure f0r the a19a1 9r0wth. 7he ce11 den51ty (1.e. ce11 num6er5 per v01ume) may 6e u5ed a5 10n9 a5 they re1ate t0 the 610ma55 (wh1ch 15 n0t the ca5e when ce115 f0rm cha1n5). We a55ume here that the ce11 num6er 1n the c0ntr01 9r0w5 exp0nent1a11y, that 15 d -dt- N =/10N N(t) = N(0)exp{/~0 t }

(1)

where/1015 the c0ntr01 p0pu1at10n 9r0wth (d1men510n t1me-~). We c0n51der three d1fferent effect5.

1627

A19a1 9r0wth t0x1c1ty te5t5

6r0wth m0de1 7he c05t 0f 9r0wth 1n term5 0f nutr1ent5 0r ener9y 15 1nver5e1y pr0p0rt10na1 t0 the p0pu1at10n 9r0wth rate. 7he 11near effect m0de1 a5 ment10ned 1n the 1ntr0duct10n am0unt5 t0 the a55umpt10n that the c05t5 f0r 9r0wth are 11near 1n the 1ntrace11u1arc0ncentrat10n 0f te5t c0mp0und. F0r t1ny 0r9an15m5 5uch a5 un1ce11u1ar a19ae, the5e c05t5 are thu5 11near 1n the env1r0nment-c0ncentrat10n. 7h15 1ead5 t0 d dt

-- N =/J~N

N(t, c) =

N(0, c)exp{/J¢ t } w1th /J¢=/20(1

+c61(c-c0)+) -1

(2)

where c 15 the c0neentrat10n 0f te5t c0mp0und 1n the env1r0nment, c0 15 the NEC and c0 15 the ••t01erance c0ncentrat10n•• wh1ch ju5t 5erve5 a5 a pr0p0rt10na11ty c0n5tant. 1t 15 50 named 6ecau5e the 1e55 t0x1c the c0mp0und, the h19her 1t5 va1ue. N0te that an 1nterpretat10n 0f th15 parameter 15 c6 = EC50-NEC, where the EC50 15 the c0ncentrat10n that eau5e5 a reduct10n 0f the p0pu1at10n 9r0wth rate 6y a fact0r 0f tw0. 7he c0ncept EC50 15 very fam111ar 1n the ana1y515 0f t0x1c1ty te5t5. De5p1te the 51mp1e re1at10n5h1p w1th the t01erance c0ncentrat10n, we w111n0t u5e the parameter EC50. 7he f1r5t rea50n 15 that the c0m61nat10n EC50 and NEC 6ehave5 w0r5e than the c0m61nat10n cc and c0 1n a 5tat15t1ca1 5en5e, 6ecau5e the1r e5t1mate5 have a h19her (ne9at1ve) c0rre1at10n c0eff1c1ent. 7he 5ec0nd rea50n 15 that the re1at10n5h1p 6etween EC50 and the t01erance c0ncentrat10n 15 1e55 51mp1e 1n 0ther m0de15 (5ee the adaptat10n m0de1). 7he n0tat10n ( c - c 0 ) + 1nd1cate5 that we rep1ace ne9at1ve va1ue5 0f c - c0 6y 2er0. We a55ume that n0 death 0ecur51f the c0mp0und affect5 the ener9et1c5 0f the ce115.

Ha2ard m0de1 7he 5ec0nd mechan15m 0f t0x1c effect 15 v1a the ha2ard rate that 15 a55umed t0 6e pr0p0rt10na1 t0 the 1ntra-ce11u1ar c0ncentrat10n that exceed5 the n0-effect c0ncentrat10n. 7he 5urv1v1n9 ce115 9r0w at the 5ame rate a5 th05e 1n the c0ntr01. 7he chan9e 1n the num6er5 0f 11v1n9 and dead ce115 6ec0me5 d N1 = p¢N~ = (/10 --/~,(c -- e0)+ )N1 d ~-~N 0 =/c, (e -- c0) + N1 where We have n0 dead ce115 at the 5tart 0f the exper1ment, 50 N0(0) = 0. 7he parameter /~, ju5t 5erVe5 a5 a pr0p0rt10na11ty C0n5tant and 15 ca11ed the ••k1111n9 rate••. 7he t0ta1 (11v1n9p1u5 dead) num6er 0f Ce115 am0unt5 t0

N(t,c)= N(0,c)(~exp{1Jct, + 1 - - ~ )

(3)

19n0r1n9 ce11 1y515 dur1n9 the 3 d 0f the te5t, the c0unted num6er 0f ce115 c0rre5p0nd5 w1th the t0ta1 num6er 0f ce115. N0t1ce that the t0ta1 num6er 0f ce115 d0e5 n0t 9r0w exp0nent1a11y 1f effect5 0n the ha2ard rate 0ccur5.

Adaptat10n m0de1 7he th1rd mechan15m 0f t0x1c effect5 15 v1a the chan9e fr0m the c0ntr01 51tuat10n 0f the 5t0ck cu1ture t0 the exper1menta1 te5t c0nd1t10n. 7he effect 15 the 5ame a5 1n the ha2ard m0de1, 6ut 1t 0ccur5 0n1y dur1n9 a 5h0rt (f1xed) per10d 0f exp05ure. 1f the ce115 5urv1ve th15 tran51t10n, they are n0t affected 6y the c0mp0und, 50 the re515tant ce115 are 5e1ected. 7he 5urv1va1 pr06a6111ty then am0unt5 t0 ~- = exp{ - cr~ 1(e - e0)+ } and the t0ta1 (11v1n9p1u5 dead) num6er 0f ce115 t0

N(t,c)= N(0,c)(~ exp {1J0t}+ 1 - ~)

(4)

where ••t01erance c0ncentrat10n•• cH ju5t 5erve5 a5 pr0p0rt10na11ty c0n5tant. 1t 15 1nver5e t0 the pr0duct 0f the k1111n9 rate and the 1en9th 0f the 5en51t1ve per10d. 7he 5urv1va1pr06a6111ty ~ can 6e 1nterpreted a5 the fract10n 0f re515tant ce1151n the c0ntr01 cu1ture. 57A71571C5 7he num6er 0f ce115 1n any exper1menta1 un1t 15 a55umed t0 6e n0rma11y d15tr16uted w1th a mean that 6ehave5 a5 exp1a1ned 1n the m0de1 5ect10n and a var1ance that 15 (a60ut) pr0p0rt10na1 t0 the 54uared mean. 50 the c0eff1c1ent 0f var1at10n 15 a55umed t0 6e c0n5tant. 7h15 depend5, h0wever, 0n the accuracy and the meth0d f0r mea5urement 0f the 610ma55. A c0n5tant var1ance, 1ndependent fr0m the mean, 15 an attract1ve a1ternat1ve. 7he m05t 5tra19htf0rward e5t1mat10n cr1ter10n 15 the max1mum 11ke11h00d meth0d. 70 f1nd the parameter e5t1mate5, we have t0 eva1uate the matr1x 0f 5ec0nd der1vat1ve5 0f the ce11 num6er5 t0 the three parameter5:/10, c0 and cc, cH 0r/~,. 51nce the f0rmu1ae 6ec0me 1en9thy, a 1e55e1e9ant 6ut u5efu1 a1ternat1ve 15 t0 app1y we19hted n0n-11near re9re5510n, where the we19ht c0eff1c1ent5 are taken 1nver5e t0 the 54uared 065erved ce11 num6er5. 7h15 91ve5 the add1t10na1 advanta9e that we can 91ve 1e55 we19ht t0 cu1ture5 that 5h0w a 1ar9e effect. 7he app11ca6111ty 0f the 11ke11h00d meth0d 5h0u1d 6e te5ted, h0wever, 1f the we19ht c0eff1c1ent5 affect the re5u1t5 5u65tant1a11y. 1f the (c0ntr01) cu1ture5 9r0w t00 fa5t (depend1n9 0n the a19a1 5pec1e5) the 1a5t data p01nt w111 5h0w a dev1at10n fr0m exp0nent1a1 9r0wth, 6ecau5e the cu1ture5 6ec0me nutr1ent 11m1ted. 7h15 w111happen 1f the 119ht 1nten51tyand temperature are 60th appr0ach1n9 the upper 11m1t50f the pre5cr16ed ran9e5.7he we19ht 0f 5uch a dev1at1n9 data p01nt can a150 6e reduced f0r 6101091ca1 rea50n5. (0ne 5h0u1d a1way5 6e extreme1y carefu1 n0t t0 exc1ude data p01nt5 6ecau5e the m0de1 d0e5 n0t f1t.) 7he pr0f11e 1n 11ke11h00d (cf. McCu11a9h and Ne1der, 1989) f0r c0 15 1(c0)= 5~1j 14~1j1n 60/d1, where d0

1628

5. A. L. M. K001jman et a1.

9r0wth, 5ke1.

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F19. 1.7he 6e5t f1tt1n9 0f the three m0de15 (the 9r0wth, adaptat10n 0r ha2ard m0de1) 15 5h0wn 1n the52 examp1e5, t09ether w1th the pr0f11e 1n 11ke11h00d funct10n f0r the n0-effect c0ncentrat10n c0.7he var10u5 curve5 1n each f19ure c0rre5p0nd5 w1th an 065ervat10n t1me. 065ervat10n5 at t1me5 at wh1ch the c0ntr01 dev1ate5 fr0m exp0nent1a1 9r0wth have n0t 6een 1nc1uded. 7he a66rev1at10n5 f0r the c0mp0und5 and a19a1 5pec1e5 are 91ven 1n the 1e9end5 t0 7a61e 1. 5tand5 f0r the e5t1mated 5tandard dev1at10n, 91ven the va1ue f0r c0, and 61 5tand5 f0r the e5t1mated 5tandard dev1at10n 91ven the max1mum 11ke11h00d e5t1mat10n 0f c0. 7 h e e5t1mated var1ance, 1.e. the 54uared 5tandard dev1at10n, 15 6: = 2171% ~1jw~)(N1j - N ( t 1 , c j ) ) 2. 7he fact0r 21jw1j 5tand5 f0r the 5um 0f a11 we19ht c0eff1c1ent5, where the 5ummat10n 15 0ver a11 t1me p01nt5 and c0ncentrat10n5, 1nc1ud1n9 the c0ntr01.7he c0nf1dence 5et f0r c0 can 6e 06ta1ned

fr0m the pr0f11e 1n 11ke11h00d, where we u5e the pr0perty that tw0 t1me5 the pr0f11e 1n 11ke11h00d at any 91ven va1ue f0r c0 under the nu11 hyp0the515 that th15 15 the c0rrect va1ue, a5 a5ympt0t1ca11y ;(2 d15tr16uted w1th 0ne de9ree 0f freed0m. 7he ~01eve1 c0nf1dence 5et f0r c0 15 then 91ven 6y {c0[1(c0)<~ X~(a)/2} where 22(~t) 15 a num6er 5uch that 5~:~(~)/4(nx)-1/2exp{-x}dx=:( (cf. 511vey, 1975; K001jman, 1983).

5. A. L. M. K001jman et a1.

1630

EXAMPLE5

F19ure 1 5h0w5 the exper1menta1 re5u1t5 0f 14 a19a1 9r0wth 1nh161t10n te5t5 f0r a var1ety 0f c0mp0und5 and a19a1 5pec1e5.7he parameter5 0f the three m0de15 are 91ven 1n 7a61e 1. 7he 99% c0nf1dence 1nterva1 f0r the n0-effect c0ncentrat10n c0 15 appr0x1mate1y the p01nt e5t1mate p1u5 and m1nu5 2.56 t1me5 the 5tandard dev1at10n. 50 f0r the 9r0wth m0de1 0f the te5t w1th 7 P 8 5 we 06ta1n a c0nf1dence 1nterva1 f0r c0 0f {6.86, 8.77} m9 1 1 (5ee 7a61e 1). A 22-d15tr16uted var1a61e w1th 0ne de9ree 0f freed0m exceed5 the va1ue 6.635 w1th a pr06a6111ty 0f 1%. 7he 99% c0nf1dence 1nterva1 can 6e read fr0m F19. 1 6y 100k1n9 at the va1ue5 0f c0 f0r wh1ch the pr0f11e 1n 11ke11h00d 15 6e10w 6.635/2 = 3.317. 7h15 91ve5 a very 51m11ar c0nf1dence 1nterva1, 1.e. {6.75, 8.7} m91 ~. 7h15 111u5trate5 the app11ca6111ty0f the 1ar9e 5amp1e the0ry f0r the 11ke11h00d rat10 te5t: the 5hape 0f the 1n 11ke11h00dfunct10n 15 1n m05t ca5e5 perfect1y para6011c. 1n tw0 0ther ca5e5, we 5ee that the

pr0f11e 1n 11ke11h00d funct10n ha5 tw0 10ca1 m1n1ma and, 1n the te5t w1th eth0xy1ated a1c0h01, we 5ee an 0dd 6ehav10ur 0f th15 funct10n 6ecau5e 0f the 5t1mu1at0ry effect 0f the c0mp0und at 10w c0ncentrat10n5, wh1ch 15 u5ua11y referred t0 a5 h0rme515 (5te661n9, 1982). 7h15 11tt1e under5t00d phen0men0n mu5t 6e 1eft unexp1a1ned. 1n many ca5e5 the three m0de15 a11 f1t we11 t0 the 5ame data; they w0u1d 6e hard t0 te11 apart 9raph1ca11y. 7he n0-effect c0ncentrat10n pr0ve5 t0 6e very 1n5en51t1ve f0r the ch01ce 0f m0de1. (7h15 151n c0ntra5t w1th EC-5ma11 va1ue5, 5ee 1ntr0duct10n.) 1n a few ca5e5 the mean dev1at10n 6 d1ffer5 6y a fact0r 0f tw0 6etween the m0de15; here we can ch005e 6etween the d1fferent m0de5 0f act10n 0f the c0mp0und 0n the 6a515 0ff1t. 7he max1mum dev1at10n 0ccur51n the te5t f0r p0ta551um d1chr0mate w1th Cyc10te11a. 7he fact that the c0 d1ffer5 here 6y a fact0r 0f three 15 0f n0 pr061em 6ecau5e we 5h0u1d 5e1ect the va1ue 0f the 6e5t f1tt1n9 m0de1.7he NEC d1ffer5 519n1f1cant1yfr0m 2er0

7a61e 1. Parameter e5t1mate5 and 5tandard dev1at10n5 0f the examp1e5 91ven 1n F19. 1 . 7 h e three r0w5 f0r each c0mp0und/5pec1e5 c0m61nat10n c0rre5p0nd w1th the 9r0wth, ha2ard and adaptat10n m0de1, re5pect1ve1y. 7he un1t5 0f the parameter5 are: N 0, ~: un1t5 0f ce115 den51ty (91ven f0r each examp1e); :1: d 1; c0 • c~, ca: un1t5 0f c0mp0und c0ncentrat10n (91ven f0r each examp1e); ~t: (un1t5 0f c0mp0und c0nc. x d) t C0mp0und5: 3,5-DCP = 3,5-d1ch10r0phen01, 7 P 8 5 = 7etrapr0py1ene6en2ene 5u1ph0nate, P E A = p01yethy1ene am1ne, 5 D E = 5u65t1tuted d1phen0xyethane, E A = eth0xy1ated a1c0h01, M1x 1,2 = m1xture 0f 0r9an1c N,5-c0mp0und5, M1x 3 = m1xture 0f n0n10n1c 5urfactant5. 5pec1e5: Cyc1. = Cyc10te11a 0percu1ata, Phae. = Phae0dacty1um tr1c0rnutum, 5ke1 = 5ke1et0nema c05tatum, N1t2. ~ N1t25ch1a pa1ea, 5tep. = 5tepan0d15cu5 hant25ch11, 5cen. = 5cenede5mu5 5u65p1catu5, 5e1e. = 5e1ena5trum capr1c0rnuturn. C0mp/5pec. P E A , m9 1 1 5ke1., 103 t.~115m1-~ 3,5-DCP, m9 1 1 N1t2., 103 ce115m1 t 3,5-DCP, m91 ~ Cyc1., 103 ce115m1 t K2Cr207, m91 h Phae., 102 ce115m1 1 K2Cr207, m 9 1 ~ Phae., ce11m1 1 K2Cr207, m91 2 5ke1., 103 ce115m1 1 K2Cr207, #91 t Cyc1., 103 ce115m1 t 5 D E , m91 t 5e1e., 104 ce115m1 ]

8106an, p91 1 5ke1., 103 ce115m1 ~ 7 P 8 5 , m91 1 5tep., 104 ce115m1 1 EA, m91 J 5ke1., 103 ce115m1 ~ M1x 1, ,u91 1 5ke1., 103 ce115m1 J M1x 2, m91 1 5ke1., 103 ce115m• t M1x 3, m91 n 5ke1., 103 ce115m1 t

N0

5.d.

/20

1.04 1.10 1.42 0.766 0.768 0.910 0.646 0.824 1.11 1.10 1.09 1.29 4.355 4.30 5.24 5.66 5.67 6.59 0.800 0.739 0.851 0.980 0.962 1.057 0.336 0.341 0.369 0.655 0.633 0.696 2.68 2.88 3.46 0.494 0.495 0.514 1.59 1.61 1.78 1.39 1.36 1.50

0.273 0.212 0.449 0.352 0.393 0.496 0.312 0.239 0.304 0.238 0.218 0.232 0.337 0.375 0.548 0.685 0.573 0.511 0.372 0.151 0.123 0.195 0.184 0.199 0.087 0.093 0.105 0.036 0.037 0.038 0.581 0.403 0.427 0.147 0.148 0.160 0.131 0.229 0.308 0.201 0.278 0.351

1.93 1.91 1.78 2.88 2.86 2.76 2.89 2.76 2.60 1.44 1.44 1.35 1.26 1.26 1.19 2.10 2.10 2.022 2.72 2.78 2.71 1.43 1.43 1.40 2.72 2.71 2.67 0.481 0.487 0.472 2.01 1.97 1.88 2.62 2.62 2.60 2.07 2.06 2.01 2.10 2.11 2.06

5.d. 0.095 0.070 0.115 0.267 0.298 0.316 0.261 0.157 0.149 0.123 0.106 0.094 0.027 0.030 0.036 0.063 0.053 0.040 0.254 0.112 0.079 0.069 0.067 0.065 0.140 0.147 0.154 8.6 10 3 9.3 10 3 8.5 10 3 0.104 0.067 0.059 0.157 0.158 0.165 0.042 0.073 0.088 0.070 0.099 0.112

c0

5.d,

0.0191 0 0.146 0 0 0 0.167 0.113 0.101 0 0 0 3.48 2.44 1.80 0.777 0.710 0.683 24.8 10.5 7.96 0.410 0.364 0.295 16.1 14.8 14.4 7.82 6.78 6.08 0.923 0.895 0.886 53.2 51.5 51.1 0 0 0 0.0228 0.0075 0

0.021 0.020 0.055 0.091 0.102 0.106 0.050 0.043 0.043 0.355 0.421 0.423 0.237 0.413 0.597 0.031 0.036 0.031 4.83 1.17 0.57 0.055 0.066 0.040 1.43 1.88 2.03 0.365 0.559 0.610 0.032 0.029 0.029 0.87 1.16 1.25 1.3 10 2.8 10 3.5 10 8.0 10 0.012 0.015

c 6/1c,/c H

3 J 3 3

1.93 0.943 0.390 3.75 0.731 1.05 5.12 0.547 1.27 11.7 0.138 5.45 26.1 0,0418 12.5 3~46 0~553 1.33 59.9 0.0200 38.1 2.13 0.637 0.823 20,3 0.0132 52.9 36.2 0.0123 20.5 3.45 0.566 1.16 56.7 0.0346 20.7 0.363 6.09 0.115 1.39 1.508 0.435

5.d.

#

0.222 0.062 0.070 0.880 0.137 0.186 0.798 0.036 0.077 2.85 0.026 0.914 1.85 2.8 10 0.930 0.307 0.0311 0.0547 40.2 1.6 10 1.51 0.435 0.106 0.092 25.0 1.4 10 5.31 3.07 8.3 10 1.11 0.413 0.0334 0.0575 15.2 6.1 10 3.34 0.018 0.435 9.41 0.101 0.109 0.032

6.95 5.32 8.92 4.49 5.17 5.40 4.66 3.29 3.23 1.50 1.43 1.37 3.68 4.25 5.29 7.21 6.17 4.90 5.16 2.23 1.61 3.21 3.11 3.09 1.46 1.55 1.61 0.412 0.447 0.416 5.18 3.58 3.29 2.17 2.21 2.28 1.35 2.39 2.88 2.51 3.58 4.02

3

3

3

a

3

A19a1 9r0wth t0x1c1ty te5t5 1n 10 0ut 0f 14 ca5e5. 7he ca5e5 where the NEC d0e5 n0t d1ffer fr0m 2er0 1nd1cate that the exper1ment 5h0u1d 6e repeated w1th an adju5ted c0ncentrat10n 5er1e5. D15CU5510N 0 u r meth0d 5h0w5 that 51mp1emechan15t1c m0de15 can 6e u5ed 5ucce55fu11y t0 de5cr16e the re5u1t5 0f a19ae 1nh161t10n 9r0wth te5t5. 1t ha5 1e55 parameter5 than the 5tandard ana1y515, wh1ch re1ate5 the p0pu1at10n 9r0wth rate t0 the c0ncentrat10n 0f c0mp0und acc0rd1n9 t0 the 109-10915t1c m0de1 (cf. K001jman et a1., 1983). 1ndependent fr0m and 1nc0n515tent w1th th15 m0de1, a n0-065erved effect c0ncentrat10n (N0EC) 15 u5ua11y 1dent1f1ed f0r r15k a55e55ment purp05e5. 7h15 1mp11e5 that f0ur rather than three parameter5 are u5ua11y e5t1mated: the c0ntr01 p0pu1at10n 9r0wth rate, the EC50, the 9rad1ent parameter, and the N0EC. 7he pr0p05ed meth0d rep1ace5 the EC50 p1u5 9rad1ent parameter 6y e1ther the t01erance c0ncentrat10n 0r the k1111n9rate, and the N 0 E C 6y the NEC. 7he 1atter 15 n0w a rea1 parameter w1th a c0nf1dence 1nterva1, n0t ju5t 0ne 0f the te5ted c0ncentrat10n5. 0 u r meth0d av01d5 the c0mp1ex1t1e5 1nherent t0 N 0 E C and EC-••5ma11•• va1ue5. 7he parameter c0 d0e5 n0t 5uffer fr0m the 5tat15t1ca1 pr061em5 0f the N0EC. 1t 5eem5 n0t t0 6e very 5en51t1ve t0 err0r 1n the 1dent1f1cat10n f0r the 5pec1f1c m0de 0f act10n f0r the c0mp0und. 7h15 15 0f 1mp0rtance 6ecau5e r0ut1ne t0x1c1ty te5t5 are n0t very 5u1ta61e f0r th15 purp05e. 1t w0u1d he1p, f0r 1n5tance, t0 d15t1n9u15h the 11v1n9 fr0m the dead ce115, 6ut th15 re4u1re5 extra eff0rt. 0 u r meth0d a150 av01d5 the c0mp1ex1t1e5 that are 1nherent t0 5ma11 effect c0ncentrat10n5. 51m11ar c0nc1u510n5 app1y t0 0ther 5tandard r0ut1ne t0x1c1ty te5t5, 5uch a5 the chr0n1c repr0duct10n Daphn1a te5t. 7he c0m61ned ev1dence 5upp0rt5 a reject10n 0f the c0nvent10na1 N0EC/EC50 6a5ed ana1y515 1n fav0ur 0f the NEC 6a5ed ana1y515 w1th 5pec1f1c effect5 t0 the var10u5 6101091ca1 endp01nt5. 7he examp1e5 pre5ented 1n th15 art1c1e have 6een ana1y2ed ear11er w1th the meth0d de5cr16ed 1n K001jman et a1. (1983), 5upp1emented w1th N 0 E C ••e5t1mate5••. App11cat10n 0f the new meth0d 5h0w5 that the e5t1mated NEC5 c0rre5p0nd we11 w1th the N 0 E C 5 . 7 h e c0ntr01 p0pu1at10n 9r0wth rate5 tend t0 6e 5119ht1y10wer than e5t1mated w1th u5e 0f a 10915t1c 9r0wth m0de1.7h15 15 part1y 6ecau5e 0f the pr061em 0f detect1n9 dev1at10n5 fr0m exp0nent1a1 9r0wth, 6ut a150 1n the e5t1mat10n 0f the carry1n9 capac1ty 0f the 10915t1c 9r0wth m0de1. An add1t10na1 advanta9e 0f 0ur mechan15t1c appr0ach 15 that a55umpt10n5 a60ut the k1net1c5 0f the c0mp0und5 that pr0ve t0 6e t00 51mp1e can ea511y 6e rep1aced 6y m0re c0mp1ex (and h0pefu11y m0re appr0pr1ate) 0ne5 f0r 5c1ent1f1cpurp05e5.7h15 06v10u51y re4u1re5 a m0re e1a60rate exper1menta1 5etup. 8e1n9 pr0ce55-0r1ented, the ana1y515 can 6e extended t0 1nc1ude the effect5 0f de9radat10n and meta6011c

1631

tran5f0rmat10n. 5uch an eff0rt 15 e55ent1a1t0 eva1uate the c0n5e4uence5 0f em15510n5 1n the env1r0nment. 7h15 c0n515tency 6etween m0de15 f0r r15k a55e55ment and f0r 5c1ent1f1c purp05e5 15 e55ent1a1 1f we take r15k a55e55ment 5er10u51y. 7he 065ervat10n that the three d1fferent m0de15 fre4uent1y f1t we11 t0 the 5ame data 5et, 1nv1te5 an attempt t0 c0vert the three t0x1c1ty mea5ure5 (cc, cH, /~,) 1nt0 each 0ther. We can d0 50 6y e4uat1n9 the EC50 f0r 610ma55 at the m0ment at wh1ch the c0ntr01 p0pu1at10n exceed5 n t1me5 the 1n0cu1ated va1ue. 7he te5t re4u1re5 that n 1> 15.51mp1e mathemat1c5 revea15 the f0110w1n9 re1at10n5h1p5

/•1n n

/c, c6 = (1 -- x ) f 1 0 ~ ] ~ --

1)

and

c0 /•1n n "X n -- 1 c~ = ~]-ff~- 1) 1n ~ - ~ 1

where x 15the 501ut10n 0 f x 1n n = 1n{1 + x ( n / 2 -- 1)}. F0r n = 15 th15 51mp11f1e5 t0 //¢c6= 1.233/20 and c6 = 2.86c~. 7h15 exerc15e a150 5h0w5 that the EC50 f0r 610ma55 1t5e1f15 t0ta11y u5e1e55 t0 character12e the effect5 0f c0mp0und5 6ecau5e th15 mea5ure depend5 0n the 1en9th 0f the te5t (ch01ce f0r n) and 0n 9r0wth c0nd1t10n5 (va1ue f0r /10, wh1ch depend5 0n med1a, 119ht and temperature). F0r further d15cu5510n 0f the5e p01nt5 5ee Nyh01m (1985). N0nethe1e55, 1t 15 fre4uent1y u5ed and current 5tandard pr0t0c015 pre5cr16e that th15 f19ure 6e rep0rted a10n9 w1th an EC50 f0r the p0pu1at10n 9r0wth rate. 7he 50ftware packa9e DE8t0x, a5 pr0v1ded 1n K001jman • 8edaux (1996), can 6e u5ed t0 d0 a11 c0mputat10n5 f0r the app11cat10n 0f the m0de15 that are d15cu55ed 1n th15 art1c1e.

w0u1d 11ke t0 thank Harry 01der5ma (7N0-MW) f0r h15 carefu1 exper1menta1 w0rk and Jac4ue5 8edaux and C0r 20nneve1d f0r he1pfu1d15cu5510n5 and M1ke Newman and an unkn0wn referee f0r c0mment5. Ackn0w1ed9ement5--We

REFERENCE5 8edaux, J. J. M. and K001jman, 5. A. L. M. (1994) 5tat15t1ca1 ana1y5150f 610a55ay5, 6a5ed 0n ha2ard m0de11n9. Env1r0n. Ec01. 5tat. 1, 303-314. 8art1ett, L., Ra6e, F. W. and Funk, W. H. (1974) Effect5 0f c0pper, 21ncand cadm1um0n 5e1ena5trum capr1c0rnutum. 1Vat. Re5. 8, 179-185. 8r1n9mann, 6. and Kf1hn, R. (1980) C0mpar150n 0f the t0x1c1ty thre5h01d5 0f water p011utant5t0 6acter1a, a19ae and pr0t020a 1n the ce11 mu1t1p11cat10n1nh161t10nte5t. 1Vat. Re5. 14, 231-241. EU 1992. EU 6u1de11neN0 C.3. 6r0wth 1nh161t10n te5t w1th a19ae. 0ff. J. Fur. C0mm. L 383A, 179 186. Han5tve1t, A. 0. 1982. Eva1uat10n 0 f the re5u1t5 0 f the th1rd 150-1nter1a60rat0rv 5tud). w1th an a19a1 t0x1c1ty te5t. 150 D0cument 150/7C147/5C5/W65/N64; 7N0-Rep0rt CL82/128, 7N0-Env1r0nmenta1 5c1ence5, De1ft.

1632

5. A. L. M. K001jman et a1.

Han5tve1t, A. 0. 1991. 7he re5u1t5 0f an 1nternat10na1 r1n9 te5t 0f the mar1ne a19a1 9r0wth 1nh161t10n te5t acc0rd1n9 t0 150/DP 10253. 7N0-Rep0rt R91/236. 7N0-Env1r0nmenta1 5c1ence5, De1ft. 150 1989. 1nternat10na1 5tandard, 150 8692:1989 (E). Water Qua11ty--Fre5h water a19a1 9r0wth 1nh161t10n te5t w1th 5cenede5mu5 5u65p1catu5 and 5e1ena5trum capr1c0rnutum, 6en~ve. 150 1994. Draft 1nternat10na1 5tandard, 150/D15 10253: Water 4ua11ty--Mar1ne a19ae 9r0wth 1nh161t10nte5t w1th 5ke1et0nema c05tatum and Phae0daety1um tr1c0rnutum, 6en6ve. K001jman, 5. A. L. M. (1983) 5tat15t1ca1 a5pect5 0f the determ1nat10n 0f m0rta11ty rate5 1n 610a55ay5. Wat. Re5. 17, 749-759. K001jman, 5. A. L. M. (1993) Dynam1c Ener9y 8ud9et5 1n 8101091ca1 5y5tem5. 7he0ry and app11cat10n5 1n ec0t0xc0109y. Cam6r1d9e Un1ver51ty Pre55, pp. 350. K001jman, 5. A. L. M. and 8edaux, J. J. M. (1996) 50me 5tat15t1ca1 pr0pert1e5 0f e5t1mate5 0f n0-effect c0ncentrat10n5. Wat. Re5. 30, 1724-1728. K001jman, 5. A. L. M. and 8edaux, J. J. M. (1996a) Ana1y515 0f t0x1c1ty te5t5 0n Daphn1a 5urv1va1 and repr0duct10n. Wat. Re5. 30, 1711-1723.

K001jamn, 5. A. L. M. and 8eduau5, J. J. M. (19666) Ana1y515 0f t0x1c1ty te5t5 0n f15h 9r0wth. Wat. Re5. 30, 1633-1644. K001jman, 5. A. L. M. and 8edaux, J. J. M. (Ed5) (1996) 7he ana1y515 0f a4uat1c t0x1c1ty data. Am5terdam: VU Un1ver51ty Pre55. K001jman, 5. A. L. M., Han5tve1t, A. 0. and 01der5ma, H. (1983) Parametr1c ana1y5e5 0f p0pu1at10n 9r0wth 1n 610a55ay5. Wat. Re5. 17, 727-738. McCu11a9h, P. and Ne1der, J. A. (1989) 6enera112ed 11near m0de15. M0n09raph5 0n 5tat15t1c5 and App11ed Pr06a6111ty 37. Chapman • Ha11, pp. 511. Nyh01m, N. 1985. Re5p0n5e var1a61e 1n a19a1 9r0wth 1nh161t10n te5t5--810ma55 0r 9r0wth rate• 1,Vat. Re5. 19, 273-279. 0 E C D 1984. 0 E C D 6u1de11ne f0r 7e5t1n9 0f Chem1ca15 201: A19a, 9r0wth 1nh161t10n te5t., Par15. 511vey, 5. D. (1975) 5tat15t1ca1 1nference. M0n09raph5 0n 5tat15t1c5 and App11ed Pr06a6111ty 7. Chapman and Ha11, pp. 192. 5te661n9, A. R. D. (1982) H0rme515--the 5t1mu1at10n 0f 9r0wth 6y 10w 1eve150f 1nh161t0r5. 5c1. 70ta1 Env1r0n. 22, 213-234.