SUBROUTINE TEXT(IH) CHARACTER TITLE*80 COMMON /TTCHAR/ TITLE CHARACTER UNDERL*8 DATA UNDERL/'--------'/ IF(IH.EQ.3)WRITE(6,105)TITLE 105 FORMAT('1',A80) 1 WRITE(6,10)IH,(UNDERL,I=1,5) 10 FORMAT('0'/'0THE HYPOTHESIS H',I1,'. (SEE BROWNIE AND ROBSON, 19 *76. BIOMETRICS 32(2):325-336)'/1X,2A8,A2/ *'0ASSUMPTIONS: (1) ANNUAL SURVIVAL AND RECOVERY RATES ARE YEAR-S *PECIFIC.'/' ',A8,A4) IF(IH.EQ.3)GO TO 20 WRITE(6,104) 104 FORMAT(15X,'(2) YOUNG BIRDS HAVE DIFFERENT SURVIVAL AND RECOVERY *RATES FROM THOSE OF ADULTS.') GO TO (2,3),IH 3 WRITE(6,11) 11 FORMAT('0',14X,'(3) IN ANY YEAR, THE REPORTING RATE FOR NEW RELEA *SES IS DIFFERENT FROM THAT FOR SURVIVORS OF PREVIOUSLY' * /20X,'BANDED CO *HORTS, AND HENCE THE CORRESPONDING RECOVERY RATES ARE DIFFERENT.'/ *'0'/' H2 IS AN EXTENSION OF H1 IN THAT THE FIRST YEAR ADULT RECO *VERY RATE IN YEAR I IS DIFFERENT FROM THE RECOVERY RATE IN'/'0YEAR * I OF PREVIOUSLY BANDED ADULTS. (THE SOLICITING OF BANDS FROM HUNT *ERS BY CONSERVATION OFFICERS NEAR BANDING SITES'/'0MAY GIVE RISE T *O THIS SITUATION).') 2 GO TO (4,5),IH 4 WRITE(6,12)(UNDERL,I=1,2) 12 FORMAT('0'/'0PARAMETERS:'/' ',A8,A3/ * ' F(I) = BAND RECOVERY RATE FOR ADULTS * IN YEAR I.') GO TO 6 5 WRITE(6,13)(UNDERL,I=1,2) 13 FORMAT('0'/'0PARAMETERS:'/' ',A8,A3/ * ' F''''''(I)= BAND RECOVERY RATE IN YEAR * I FOR ADULTS BANDED IN YEAR I.'/ ' F(I) = BAND RECOVER *Y RATE IN YEAR I FOR SURVIVORS OF COHORTS BANDED BEFORE YEAR I.') 6 WRITE(6,14) 14 FORMAT(' S(I) = SURVIVAL RATE FOR ADULTS IN YEAR I.'/ *' F''(I) = BAND RECOVERY RATE FOR YOUNG IN YEAR I.'/ *' S''(I) = SURVIVAL RATE FOR YOUNG IN YEAR I.') WRITE(6,15)IH,(UNDERL,I=1,4) 15 FORMAT('0'/'0STRUCTURE OF THE MODEL UNDER H',I1,2X,'(IN TERMS OF E *XPECTED NUMBERS OF BAND RETURNS):'/1X,3A8,A7/'0',29X,'BANDED AS AD *ULTS') GO TO (7,8),IH 7 WRITE(6,16) 16 FORMAT('0',10X,'N(1)F(1)',5X,'N(1)S(1)F(2)',4X,'N(1)S(1)S(2)F(3)' *,3X,'N(1)S(1)S(2)S(3)F(4)'/24X,'N(2)F(2)',8X,'N(2)S(2)F(3)',7X, *'N(2)S(2)S(3)F(4)'/40X,'N(3)F(3)',11X,'N(3)S(3)F(4)') GO TO 9 8 WRITE(6,17) 17 FORMAT('0',10X,'N(1)F''''''(1)',2X,'N(1)S(1)F(2)',4X,'N(1)S(1)S(2) *F(3)',3X,'N(1)S(1)S(2)S(3)F(4)'/24X,'N(2)F''''''(2)',5X,'N(2)S(2)F *(3)',7X,'N(2)S(2)S(3)F(4)'/40X,'N(3)F''''''(3)',8X,'N(3)S(3)F(4)') 9 WRITE(6,18) 18 FORMAT('0',29X,'BANDED AS YOUNG'/'0',10X,'M(1)F''(1)' *,4X,'M(1)S''(1)F(2)',3X,'M(1)S''(1)S(2)F(3)',2X,'M(1)S''(1)S(2)S(3 *)F(4)'/24X,'M(2)F''(2)',7X,'M(2)S''(2)F(3)',6X,'M(2)S''(2)S(3)F(4) *'/40X,'M(3)F''(3)',10X,'M(3)S''(3)F(4)') WRITE(6,19) 19 FORMAT('0') GO TO 200 20 WRITE(6,100) 100 FORMAT(15X,'(2) SURVIVAL AND RECOVERY RATES ARE AGE-DEPENDENT FOR * THE FIRST TWO YEARS OF LIFE. (THIS EMBRACES'/20X,'ASSUMPTION (3) *OF H2 FOR THE TYPE OF DATA BEING ANALYSED.)'/ *'0'/' H3 ASSUMES THE PARAMETERS S AND F ARE AGE-SPECIFIC FOR THR *EE AGE CLASSES (NAMELY, YOUNG, SUBADULT, AND ADULT,) BUT '/'0ONL *Y TWO AGE CLASSES ARE RECOGNIZED DURING BANDING, BECAUSE SUBADULTS * AND ADULTS ARE USUALLY INDISTINGUISHABLE. THUS'/ * '0THE ASSUMPTIONS OF H3 GIVE RISE TO A MODEL FOR WHICH MOST OF * THE PARAMETERS OF INTEREST ARE NOT ESTIMABLE, HENCE NO ESTIMATES' */'0ARE COMPUTED HERE. HOWEVER THE ASSUMPTIONS OF H3 ARE EXAMINED *BELOW BY MEANS OF A GOODNESS OF FIT TEST AND A TEST OF H2'/ *'0AGAINST THE ALTERNATIVE H3') WRITE(6,101)(UNDERL,I=1,5) 101 FORMAT('0'/'0THE HYPOTHESIS H0.'/' ',2A8,A3/'0'/' ASSUMPTIONS: SU *RVIVAL AND RECOVERY RATES ARE YEAR-SPECIFIC BUT AGE-INDEPENDENT.'/ *' ',A8,A3/'0'/' THE AGE-INDEPENDENCE ASSUMPTION OF H0 IS USUALLY I *NAPPROPRIATE FOR BIRDS BANDED AS YOUNG AND ESTIMATION UNDER H0 IS *OMITTED THOUGH'/'0TESTS RELATED TO THIS HYPOTHESIS ARE COMPUTED BE *LOW. IF H0 IS NOT REJECTED, THE DATA SHOULD BE POOLED AND ANALYZED * USING THE'/'0MODELS THAT ASSUME PARAMETERS ARE AGE-INDEPENDENT.') WRITE(6,105)TITLE WRITE(6,102)(UNDERL,I=1,8) 102 FORMAT('0'/'0TESTS TO DESCRIMINATE BETWEEN THE MODELS UNDER H0, H1 *, H2, H3. (SEE BROWNIE AND ROBSON, 1976, BIOMETRICS 32(2):325-336 *)'/1X,7A8,A6, * /'0'/'0H0, H1, H2 AND H3 REPRESENT A *SERIES OF HYPOTHESES WITH PROGRESSIVELY MORE GENERAL ASSUMPTIONS A *BOUT THE POPULATION PARA-'/ '0METERS. * TO DETERMINE WHICH ASSUMPTIONS ARE APPROPRIATE FOR A GIVEN DATA *SET, A SERIES OF TESTS ARE CARRIED OUT, WHERE') WRITE(6,103) 103 FORMAT('0EACH TEST IN THE SERIES COMPARES A GIVEN HYPOTHESIS AGAIN *ST A MORE GENERAL ALTERNATIVE. (THUS THE FIRST TEST IN THE '/ * '0SERIES COMPARES H0 AGAINST THE MORE GENERAL *H1). IN EACH CASE, IF THE TEST RESULTS IN A ''LARGE'' CHI-SQUARE *VALUE,'/'0THEN THE RESTRICTIVE HYPOTHESIS SHOULD BE REJECTED IN FA *VOR OF THE MORE GENERAL ONE, WHILE A ''SMALL'' CHI-SQUARE'/ * '0VALUE SUGGESTS THERE IS NO REASON TO DISCARD THE SIMPLER HY *POTHESIS.') 200 RETURN END SUBROUTINE DEFINE WRITE(6,111) 111 FORMAT('1THIS OUTPUT REPRESENTS A STATISTICAL ANALYSIS OF BANDING *DATA WHEN ANNUAL RECOVERIES ARE RECORDED SEPARATELY FOR BIRDS '/' &BANDED AS ADULTS AND FOR BIRDS BANDED AS YOUNG. DIFFERENT ASSUMPTI &ONS ABOUT ANNUAL SURVIVAL AND RECOVERY RATES GIVE RISE'/' TO A SER &IES OF HYPOTHESES AND A CORRESPONDING SERIES OF STOCHASTIC MODELS. & ESTIMATES OF SURVIVAL AND RECOVERY RATES ARE'/' COMPUTED FOR MOST & MODELS AND THE ASSUMPTIONS OF THE HYPOTHESES ARE EXAMINED BY TEST *S OF GOODNESS OF FIT TO THE MODELS AND'/' BY TESTS TO DISCRIMINATE * BETWEEN ALTERNATIVE MODELS.') WRITE(6,100) 100 FORMAT(/'0DEFINITIONS AND NOTATION' & /' ------------------------'/'0THE MODELS ARE DEFINED IN TERMS OF & TWO BASIC PARAMETERS- S, THE ANNUAL SURVIVAL RATE, AND F, THE ANN &UAL BAND RECOVERY '/' RATE. THAT IS, FOR A BIRD ALIVE AT THE START & OF A YEAR, S IS THE PROBABILITY IT SURVIVES THE YEAR, AND F IS TH &E PROBABILITY'/' IT IS SHOT AND ITS BAND RETURNED TO THE BIRD BAND &ING LABORATORY WITHIN THE YEAR. A ''YEAR'' IS THE PERIOD BETWEEN S &UCCESSIVE') WRITE(6,123) 123 FORMAT * (' BANDINGS, OR BETWEEN ANNIVERSARIES OF THE BANDING TIME. DI &FFERENT ASSUMPTIONS ARE MADE ABOUT THE YEAR-SPECIFICITY AND '/' &AGE-DEPENDENCE OF S AND F UNDER EACH HYPOTHESIS AND THE RESULTING &PARAMETERS ARE DEFINED SEPARATELY FOR EACH HYPOTHESIS.'/' IN GENER &AL, AN INDEX ON S OR F DENOTES YEAR-SPECIFICITY, AND A SUPERSCRIPT & '' DENOTES AGE-DEPENDENCE. FOR EXAMPLE, S(I) ') WRITE(6,112) 112 FORMAT(' IS A SURVIVAL RATE FOR YEAR I, AND S''(I) IS A SURVIVAL R &ATE FOR YOUNG IN YEAR I.'/ &'0OTHER NOTATION WHICH IS COMMON TO ALL MODELS FOLLOWS. &'/'0K THE NUMBER OF YEARS OF BANDING &'/'0L THE NUMBER OF YEARS OF RECOVERY &'/'0N(I) THE NUMBER OF ADULTS BANDED AND RELEASED AT THE STAR &T OF YEAR I, I=1,...,K. '/'0M(I) THE NUMBER OF YOUNG BANDED &AND RELEASED AT THE START OF YEAR I, I=1,...,K. '/'0RROW(I) RO &W TOTAL OF THE RECOVERY MATRIX FOR ADULTS, OR THE TOTAL NUMBER OF &RECOVERIES FROM THE ADULTS '/' RELEASED IN YEAR &I, I=1,...,K. '/'0R(I.) SAME AS RROW(I) &'/'0QROW(I) ROW TOTAL OF THE RECOVERY MATRIX FOR YOUNG, OR THE T &OTAL NUMBER OF RECOVERIES FROM THE YOUNG '/' RE &LEASED IN YEAR I, I=1,...,K. '/'0Q(I.) SAME AS QROW(I)') WRITE(6,113) 113 FORMAT('0R',49X,'ADULTS') WRITE(6,114) 114 FORMAT('+ COL(I) COLUMN TOTAL OF THE RECOVERY MATRIX FOR , & I=1,...,L.') WRITE(6,115) 115 FORMAT('0Q',49X,'YOUNG') WRITE(6,114) WRITE(6,116) 116 FORMAT('0Q(I,I) NUMBER OF RECOVERIES IN YEAR I FROM THE YOUNG R &ELEASED IN YEAR I, I=1,...,K.'/'0W(I) =RCOL(I)+QCOL(I)-Q(I,I) &= TOTAL NUMBER OF ADULTS RECOVERED IN YEAR I, (INCLUDING RECOVERIE &S '/' FROM SURVIVORS OF YOUNG RELEASED BEFORE YEAR I), I &=1,...,K') WRITE(6,117) 117 FORMAT('0T',48X,'ADULTS') WRITE(6,118) 118 FORMAT('+ (I) BLOCK TOTAL OF THE RECOVERY MATRIX FOR , &OR THE TOTAL NUMBER OF RECOVERIES IN YEARS I TO L '/' IN &CLUSIVE, FROM ALL THE RELEASED IN YEARS 1 TO I INCLUSIVE.') WRITE(6,119) 119 FORMAT('+',34X,'ADULTS') 121 FORMAT('+',34X,'YOUNG') WRITE(6,120) 120 FORMAT('0U',48X,'YOUNG') WRITE(6,118) WRITE(6,121) WRITE(6,122) 122 FORMAT('0Z(I) =T(I)+U(I)-RROW(I)-QROW(I)-QROW(I-1)+Q(I-1,I-1) &, A TOTAL INVOLVING BLOCKS FROM '/' BOTH DATA ARRAYS, I= &2,...,K') RETURN END C C SUBROUTINE CHI C C PURPOSE C COMPUTES P(CHISQ) = PROBABILITY THAT THE RANDOM VARIABLE U, C DISTRIBUTED ACCORDING TO THE CHI-SQUARE DISTRIBUTION WITH G C DEGREES OF FREEDOM, IS LESS THAN OR EQUAL TO CHISQ. F(G,CHI C ORDINATE OF THE CHI-SQUARE DENSITY AT CHISQ, IS ALSO COMPUTE C C USAGE C CALL CHI(CHISQ,IDF,SIGCHI,IER) C C DESCRIPTION OF PARAMETERS C CHISQ - INPUT SCALAR FOR WHICH P(CHISQ) IS COMPUTED. C IDF - NUMBER OF DEGREES OF FREEDOM OF THE CHI-SQUARE C DISTRIBUTION. IDF IS AN INTEGER. C SIGCHI - OUTPUT PROBABILITY. C IER - RESULTANT ERROR CODE WHERE C IER= 0 --- NO ERROR C IER=-1 --- AN INPUT PARAMETER IS INVALID. X IS LESS C THAN 0.0, OR IDF IS LESS THAN 0.5 OR GREATER C THAN 2*10**(+5). P AND D ARE SET TO -1.E25. C IER=+1 --- INVALID OUTPUT. P IS LESS THAN ZERO OR C GREATER THAN ONE, OR SERIES FOR T1 (SEE C MATHEMATICAL DESCRIPTION) HAS FAILED TO C CONVERGE. P IS SET TO 1.E25. C C REMARKS C SEE MATHEMATICAL DESCRIPTION. C C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED C NDTR C C METHOD C C THIS FUNCTION WAS LIFTED FROM "NWAY" WRITTEN BY THE STANFORD C COMPUTATION CENTER. THE SCC BORROWED IT FROM JOHN MORRIS OF THE C COMPUTER INSTITUTE FOR SOCIAL SCIENCE RESEARCH AT MICHIGAN STATE C UNIVERSITY. C SUBROUTINE CHI (IDF,CHISQ,SIGCHI,IER) DOUBLE PRECISION CHISQ, SIGCHI INTEGER IDF, IER DOUBLE PRECISION FACT(31), ANSCHI, FF, P, XI, PP, TERM, 1 GAM, TXX, ARGNRM INTEGER I C C FACTORIALS OF 0 THROUGH 30. . DATA FACT /1.00000000000000D00,1.00000000000000D00,2.000000 1 00000000D00,6.00000000000000D00,2.40000000000000D01,1.20000000000 2 000D02,7.20000000000000D02,5.04000000000000D03,4.03200000000000D0 3 4,3.62880000000000D05,3.62880000000000D06,3.99168000000000D07,4.7 4 9001600000000D08,6.22702080000000D09,8.71782912000000D10,1.307674 5 36800000D12,2.09227898880000D13,3.55687428096000D14,6.40237370572 6 800D15,1.21645100408832D17,2.43290200817664D18,5.10909421717094D1 7 9,1.12400072777761D21,2.58520167388850D22,6.20448401733239D23,1.5 8 5112100433310D25,4.03291461126606D26,1.08888694504184D28,3.048883 9 44611714D29,8.84176199373970D30,2.65252859812191D32/ C ANSCHI=1.D0 IF (CHISQ.LE.0.D0 .OR. IDF.LT.1) THEN IER=-1 SIGCHI=-1.D25 ELSE C C GT 60 D.F. OR CHI GT 100 - USE A NORMAL APPROXIMATION IF (IDF.GT.60 .OR. CHISQ.GT.100.D0) THEN ARGNRM=DSQRT(2.0D0*CHISQ)-DSQRT(2.0D0*DBLE(IDF)-1.0D0) CALL NDTR (ARGNRM,SIGCHI) ELSE FF=IDF-2 P=0.5D0*FF XI=0.5D0*CHISQ PP=P+2.0D0 TERM=XI/PP DO 10 I=1,100 ANSCHI=ANSCHI+TERM IF (DABS(TERM).LT.1.0D-6) GO TO 20 PP=PP+1.0 10 TERM=TERM*XI/PP 20 GAM=1.0D0 IF (MOD(IDF,2).EQ.0) THEN GAM=FACT(IDF/2+1) ELSE 30 DO 40 I=1,IDF,2 40 GAM=GAM*DBLE(REAL(I))*0.5D0 GAM=GAM*1.7724588509D0 ENDIF TXX=(P+1.0D0)*DLOG(XI)- XI + DLOG(ANSCHI/GAM) IF (TXX.LE.88.0D0) THEN IF (TXX.GT.-88.D0) THEN ANSCHI=DEXP(TXX) ELSE ANSCHI=0. ENDIF ELSE ANSCHI=1.D0 ENDIF SIGCHI=ANSCHI ENDIF IF (SIGCHI.LT.0.D0 .OR. SIGCHI.GT.1.D0) THEN IER=1 SIGCHI=1.D25 ELSE SIGCHI=1.D0-SIGCHI WRITE(6,900) CHISQ,SIGCHI 900 FORMAT(' PROBABILITY OF A CHI-SQUARE VALUE LARGER THAN', # F8.2,' =',F8.5) ENDIF ENDIF RETURN END C SUBROUTINE NDTR C C PURPOSE C COMPUTES Y = P(X) = PROBABILITY THAT THE RANDOM VARIABLE U, C DISTRIBUTED NORMALLY(0,1), IS LESS THAN OR EQUAL TO X. C F(X), THE ORDINATE OF THE NORMAL DENSITY AT X, IS ALSO C COMPUTED. C C USAGE C CALL NDTR(X,P) C C DESCRIPTION OF PARAMETERS C X--INPUT SCALAR FOR WHICH P(X) IS COMPUTED. C P--OUTPUT PROBABILITY. C C REMARKS C MAXIMUM ERROR IS 0.0000007. C C SUBROUTINES AND SUBPROGRAMS REQUIRED C NONE C C METHOD C BASED ON APPROXIMATIONS IN C. HASTINGS, APPROXIMATIONS FOR C DIGITAL COMPUTERS, PRINCETON UNIV. PRESS, PRINCETON, N.J., C 1955. SEE EQUATION 26.2.17, HANDBOOK OF MATHEMATICAL C FUNCTIONS, ABRAMOWITZ AND STEGUN, DOVER PUBLICATIONS, INC., C NEW YORK. C C ****************************************************************** C SUBROUTINE NDTR (X,P) DOUBLE PRECISION X,P DOUBLE PRECISION AX,T,D C AX=DABS(X) T=1.D0/(1.D0+.2316419D0*AX) D=0.3989423D0*DEXP(-X*X/2.0D0) P=1.0D0-D*T*((((1.330274D0*T-1.821256D0)*T+1.781478D0)*T 1 -0.3565638D0)*T+0.3193815D0) IF (X .LT. 0.D0) THEN P=1.D0-P ENDIF RETURN END