c 

PLANNING DOUBLE-TAGGING EXPERIMENTS 

Jerry A. Wetherall and Marian Y. Y. Yong 

NOAA-TM-NMFS-SWFC-13 

June 1981 

U.S. DEPARTMENT OF COMMERCE 

National Oceanic and Atmospheric Administration 

National Marine Fisheries Service 

Southwest Fisheries Center 
NOAA Technical Memorandum NMFS 

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F 

v - 5 

2 

- 

PLANNING DOUBLE-TAGGING EXPERIMENTS 

Jerry A. Wetherall and Marian Y. Y. Yong 

Southwest Fisheries Center Honolulu Laboratory 

National Marine Fisheries Service, NOAA 

Honolulu, Hawaii 968 12 

NOAA-TM-NMFS-SWFC- 13 

June 1981 

U.S. DEPARTMENT OF COMMERCE 

Malcolm Baldrige, Secretary 

National Oceanic and Atmospheric Administration 

Dr. John V. Byrne, Administrator 

National Marine Fisheries Service 

William H. Stevenson, Acting Assistant Administrator for Fisheries 

.. 
INTRODUCTION 

Although a considerable amount of research has been undertaken on the 

treatment of recovery statistics from double-tagging studies (e .g., Chapman 

et al. 1965; Bayliff and Mobrand 1972: Kirkwood 1981; Wetherall MS'), 

little attention has been paid to questions which arise in the planning 

stages of such experiments 

results may fall short of expectations, and the investment of scarce 

resources in expensive tagging operations may be for naught. 

Yet without careful planning experimental 

Our aim in this paper is to develop some guidelines for planning 

experiments in which a single cohort of double-tagged fish is released 

prior to a total recapture period which may be partitioned into a sequence 

of time intervals. Specifically we wish to establish procedures for 

determining how many fish should be double-tagged , how long the experiment 

should run, and how the recovery data should be grouped. The answers 

depend on the objectives of the experiment, on the level of precision 

desired and on specified or assumed conditions under which the experiment 

Will be conducted. We first develop the statistical framework for making 

planning decisions and then present a series of tables which assist the 

experimenter in deciding how many fish to double-tag to achieve either of 

two different experimental objectives. 

'Wetherall , J. A. 1981. Analysis of double-tagging experiments. 

Southwest Fisheries Center Honolulu Laboratory, National Marine Fisheries 

Service, NOAA, Honolulu, HI 96812. [Manuscript submitted to Fish. Bull., 

U.S., May 1981.1 
2 

While it is often recommended that fish be double-tagged simply to 

increase expected recovery rates (e.g., Hynd 1969; Bayliff 1973), the chief 

aim of most double-tagging experiments is to estimate rates of tag-shedding * 

which are used in turn to correct estimates of mortality and other population 

parameters derived from ordinary single-tagging studies. Less well known is 

that double-tagging experiments may be conducted to estimate mortality rates 

directly, in such a way that no corrections for tag shedding are necessary 

(Wetherall, see footnote 1). Hereafter we distinguish these two purposes as 

Objective I and Objective 11, respectively. 

STATISTICAL MODELS AND ASSUMPTIONS 

In the case of both Objective I and Objective I1 we will assume the 

experimental cohort is double-tagged with tags which have identical and 

constant shedding probabilities that the shedding of individual tags 

occurs independently, that the burden imposed by two tags is the same as it 

is with one, and that all tagged fish recaptured are recovered and 

reported. We assume further that instantaneous probabilities of natural 

mortality and recapture are the same for fish with only a single tag 

remaining as for those fish with both tags still intact. In the case of 

Objective 11, we make the additional assumption that the mortality rates 

are constant over the course of the experiment. 

Let rsi and rdi denote the number of recaptures of fish bearing one Or 

two tags, respectively, during the recapture period centered at time Ti, 

i = 1, 2, ..., n. When Objective I is being pursued, we assume recapture 

statistics are analyzed using the linear regression model of Bayliff and 

Mobrand ( 1 972 ) : 
where 

and (14) and L are the Type I and Type I1 shedding rates, respectively. 

Since our estimate of P will invariably be more precise than our estimate 

of L, we focus our concern on the latter parameter. Specifically, our 

objective will be to achieve a prescribed coefficient of variation in L, 

A 

viz., 

kt x = {Xij) denote the nx2 data matrix such that xil = 1 for all i and 

Xi2 = Ti, and let V = Ivij) be the nxn covariance matrix of the residuals. 

Then the asymptotic covariance matrix of our regression parameter estimates 

is the 2x2 array 

u = (XT v-1 XI’’ = IUij) 

where T denotes transpose. 

Note that V may be factored into two components, viz., 

V = G(i) 

where the scalar quantity N is the number of double-tagged fish released and 

the elements of G are functions of L, p , the mortality rates and the Ti. 

Hence 
4 

To achieve the desired C;, we can manipulate a number of experimental 

A 

factors which affect the variance of L, viz., 

Most obvious of these is the llsample size," N. Also important are the 

number of time periods into which recaptures are grouped md the total 

length of the experiment. These determine the number of data points, n, 

and, along with prevailing mortality rates and shedding rates, the overall 

recapture probabilities. However, for any specified combination of the 

other factors the cohort size N producing the desired coefficient of 

A 

variation in L, say Ci = 6, may be computed as 

22 W 

N6=-. 

L26 

A 2 

If L is normally distributed with mean L and variance 01 then ensuring that 

C2 = 6 is equivalent to ensuring that L will be within 2006 percent of L 

with about 95% confidence. 

A 

It remains now to specify the elements of G. These depend on the 

assumed error distribution for the regression model. In the BayliffMobrand model Wetherall (see footnote 1) assumes that rsi and rdi are 

binomial random variables conditional on the total number of recaptures 

in the ith period. In this event the ith diagonal element of C is 

approximately 
5 

where K = probability that a tag is still attached at time Ti i 

and 

-LTi 

= pe 

pi = probability that a member of the original tagged cohort is 

recaptured during the ith period 

FAi e -(F+M)Ti. . 

Here Ai is the length of the ith time interval centered at Ti, F is the 

instantaneous fishing mortality rate (assumed constant) and M is the 

instantaneous natural mortality rate. 

mutually independent, so that giij = 0 for i # j. 

We further assume that the yi are 

When the double-tagging experiment is conducted with Objective I1 in 

mind the model given by Wetherall (see footnote 1) is appropriate: 

and Z = F + M = qf + M. 

Here q is the catchability coefficient and f is the constant fishing effort 

applied during each unit time interval. 

N which achieves a specified C? = Cr;'z/z = 6. 

In this case we seek the value of 

BY direct analogy this is 

W' 22 -- Nfs - z2 62 

where wi2 is the second diagonal element of (X G'-l XI-' and G' is the 

error covariance matrix for the observations yi. 

distributional assumptions on rdi and rsi, but with the added condition 

that r. 

Under the same 

= rdi + rsi is Poisson, we have i 
6 

1 

and as before we assume gij = 0 for i # j. 

As in single-tagging experiments , the bigger the recapture sample the 

higher the precision in the parameter estimates. The number of tagged fish 

recaptured is the product of the number released, N, and the recapture rate 6, 

n 

where 

The experimenter controls the number released, of course, and may also 

influence the recapture rate by curtailing or extending the total recapture 

period. ’Ihere is a trade off here which the experimenter must evaluate: an 

estimate of L with specified precision may be obtained sooner (shortened 

recapture period) by making a bigger initial investment (releasing more 

double-tagged fish) . Conversely, if the tagging budget severely restricts 

the size of the initial release, the experimenter may have to wait out a 

longer recapture period to achieve the desired results. The effects of 

these two factors on the coefficient of variation in L are illustrated in 

Figure 1. Here we observe that to double the precision the sample size 

must be quadrupled, as expected. Similarly, for a given number of fish 

released, a 4-yr recapture period will almost double the precision in L 

over a 2-yr recapture period. 

h 

h 

Another factor which affects the precision of 2 is the number of data 

points, i.e., the number of grouping intervals into which the total 

recapture period is divided. Figure 2 shows the coefficient of variation 

in L which is attained with different groupings assuming a particular 

combination of mortality and shedding rates, an initial release of 5,000 

h 
n 

7 

Y 

DURATION OF EXPERIMENT (YRS) 

Figure I.--Effects oE duration of experiment arid Gumber of double-tagged 

fish released on the coefficient of variation of L, C.V.(L). 

L = 0.3, p = 0.9, F = 0.4, M = 0.4, A = 0.5 yr.] 

[Assumes 

OOL-+---L 2 3 4 5 6 I 7 I 8 I 9 I _I IO 

NUMBER OF GROUPING INTERVALS PER YEAR 

Figure 2.--Effects of grouping interval and duration of experiment on the 

coefficient of variation of 2, C.V.(E). 

M = 0.4, N = 5,000.1 

[Assumes L = 0.10, p = 0.9, F = 0.4, 
8 

fish and total recapture periods of 1, 2, or 4 yr. At least for this set 

of conditions there apparently is little to be gained from grouping 

recapture data into intervals shorter than one quarter of a year. A finer 

partitioning would provide a slight increase in precision , but this would 

not be advisable unless a reasonably large number of recaptures could be 

expected in each interval. Choice of the grouping interval will thus be 

influenced strongly by the intensity and seasonality of fishing. For 

example , where recapture effort is concentrated in a relatively brief 

annual fishing season the data will be clustered in intervals centered at 

T, = 'I yr, T2 = 2 yr, and so on. 

DETERMINING SAMPLE SIZE 

We turn now to the Appendix Tables and the problem of determining how 

many double-tagged fish to release in a single cohort to achieve a 

specified precision in 2 (Appendix A) or ^z (Appendix B). 

tables one must specify 

To enter the 

(1) guesses of the parameters L and P; 

(2) estimates of the instantaneous fishing mortality rate, F, and 

natural mortality rate, M; these are assumed constant over the 

duration of the experiment; 

(3) the minimum width of recapture intervals (grouping intervals) : the 

table computations assume intervals have equal width. 

It is assumed that these are immutable features of the experimental 

setting. Three key factors then remain, each determined by the 

ex per imen ter : 
9 

x 

(1 1 The desired precision in 2 or hz, measured by the appropriate 

coefficient of variation ; 

(2) the duration of the experiment; 

(3) the number of double-tagged fish released. 

Usually the precision and duration will be explicitly stated in the 

experimental objectives, and the sample size will then be chosen to achieve 

the desired results. However , sample size and duration may be traded off , 

as indicated above , and either budgetary or time constraints may force an 

adjustment of goals with respect to the precision in L or 2. h A 

Appendix A contains the sample size tables for the situation where 

Objective I is of interest. 

combination of L and p. We give results for three values of L (0.10, 0.30, 

0.70) and four of p (1.0, 0.90, 0.70, 0.50). Each page has four tables, 

corresponding to grouping intervals of 0.10, 0.25, 0.50, and 1.0 yr. 

Within each table results are given for 25 combinations of F and M, with F 

ranging from 0.10 to 1.20 and M from 0.10 to 0.80. Finally, each cell 

contains, from top to bottom, the number of double-tagged fish (thousands) 

which must be released in a single cohort to achieve a 25% coefficient of 

variation in 2 when the total recapture period is 1, 2, or 4 yr. 

bch page corresponds to a different 

As noted above, if 2 is normally distributed, expecting a coefficient 

of variation of 25% is equivalent to expecting an estimate of L within 50% 

of the true value of L with about 95% confidence. If more or less 

precision is desired, the sample sizes given in Appendix A may be easily 

adjusted , using the formula 
1.0 

 NE^ = 0.0625 

where tabled sample size corresponding to a coefficient of 

variation of 0.25 

N0.25 = 

6 = desired coefficient of variation (e.g., 10% or 0.10) 

N6 = desired sample size. 

Although the tabled sample sizes were computed assuming constant F and 

M and equal grouping intervals, they should provide useful guidelines even 

for cases with unequal intervals and for the common situations where 

fishing is periodic. Should one wish to onmpute the expected number of 

recaptures for a given set of experimental conditions, the result may be 

obtained as the product of the sample size from Appendix A and the 

appropriate expected recapture rate from Appendix C. Note that the 

recapture rates are independent of the grouping interval. 

To illustrate the use of Appendices A and C, suppose that our research 

plan calls for estimating L with a coefficient of variation of 10% (if we 

are willing to assume normality of ^L, this is equivalent to specifying a 95% 

chance of estimating L within 20% of its true value). We aren't sure of the 

natural mortality rate, but guess it is about 0.4, based on experience with 

another population of the same species. We also guess that F = 0.2 and that 

the recapture data could be grouped in 340 intervals. To integrate with 

other analyses, we will need our shedding rate estimates in about 2 yr. 

Finally, other studies suggest to us that Type I shedding is probably about 

lo%, and that Type I1 shedding occurs at the rate of about 25% per year: 

thus, we guess that p = 1.0 - 0.1 = 0.9 and L = -In( 1 .O - 0.25) = 0.30. 
11 

With this information we enter Appendix A, page 17, and find that a 

release of about 1,120 double-tagged fish will give a 25% coefficient of 

variation under the specified conditions. Using the formula above, with 

6 = 0.10 and 

According to Appendix C, we would expect to recapture about 7,000 x 0.21 

= 1,470 tagged fish over the course of the experiment. At this juncture, we 

would determine whether our budget would permit us to tag 7,000 fish; if 

not, precision would have to be reduced, the experiment extended or some 

other adjustment made. 

= 1,120, we compute our final result, No. = 7,000 fish. 

In practice, it is a good idea to explore a range of values of the 

various parameters and to check the effects on sample size. For example, in 

the hypothetical case above if L was guessed to be 0.10 instead of 0.30 we 

would compute a sample size requirement of 22,560 fish instead of 7,000; if 

L was 0.70 instead of 0.30 we would require only 5,000 fish. 

higher the Type I1 shedding rate, the easier it is to detect and estimate it 

prec i sel y . 

Clearly, the 

In the case of Bjective 11, sample sizes may be computed using tables 

in Appendix B in the same manner as above. Note , however , that results are 

given for the additional situations when L = 0. Thus they include the combination of parameters associated with no shedding, i.e., p = 1-0 and L = 0. 

This particular set of tables may be used in planning either double-tagging 

or ordinary single-tagging experiments designed to estimate 2. 

For many sets of circunstances Appendices A and B will show that 
12 

h h 

Objective I or Objective I1 the answer would depend on how L or 2 is 

ultimately used and on the robustness of the associated decision procedures. 

However, a coefficient of variation of 25% is probably the minimum level of 

precision acceptable. Many published estimates of L or Z are far less 

precise, with coefficients of variation exceeding 100%. 

LITERATURE CITED 

BAYLIFF, W. H. 

1973. Materials and methods for tagging purse seine- and baitboatcaught tunas. [In Engl. and Span.] Inter-Am. Trop. Tuna Comm., Bull. 

15: 465-503. 

BAYLIFF, W. H., and L. M. MOBRAND. 

1972. Estimates of rates of shedding of dart tags from yellowfin tuna. 

[In Engl. and Span.] Inter-Am. Trop. Tuna Comm., Bull. 15:441-462. 

CHAPMAN, D. G., B. D. FINK, and E. B. BMNETT. 

1965. A method for estimating the rate of shedding of tags from 

yellowfin tuna. [In Engl. and Span.] Inter-Am. Pop. Tuna Comm., 

Bull. 10: 333-352. 

HYND, J. S. 

1969. New evidence on southern bluefin stocks and migrations. Aust 

Fish. 28(5 1 : 26-30. 

KIRKWOOD, G. P. 

1981. Generalized models for the estimation of rates of tag shedding by 

southern bluefin tuna (Thunnus maccoyii). J. Cons. ht. Ekplor. Mer 

39: 256-260. 
13 

APPENDIX A 

Sample sizes (thousands of fish) in double-tagging experiments of 1-yr 

(upper figures), 2-yr (middle figures), or 4-yr duration (lower figures) 

required for estimating L with a coefficlent of variation of 25%. Dashes 

denote infeasible cases. 

p =1.06 

L =o. IO 

INTERVAL- 0.10 VU 

_-__ - 

o .no 

__ 

o.ab 

0.35 

O.?? 

~ 

L .02 

Q.39 

0.26 

- 

t.?' 

0.48 

0.15 

I .7a 

0.59 

O.4b 

___ 

I .43 

0. r: 

0.54 

___- 

0.10 0.20 0.40 0.20 0.40 ?"20 

3.88 

1.10 

0-41 

- 

4.1 I 

1-24 

0.50 

2.05 

0. b2 

0.25 

(.IS 

0.39 

0.19 

2.71 

0.73 

0.ZR 

- 

2.80 

0.82 

0.35 

0.00 

0.35 

0.27 

.. . 

3.85 

r,,79 

0.31 

i I 5.12 

2.17 

0.69 

O.Ji 

2.az 

0.80 

o .*a 

1.22 

0.43 

0.23 

. .. 

1.36 

0.53 

0.32 

4.60 

1.54 

0.15 

___ 

5.15 

1.92 

1.09 

3.23 

1.02 

0 .SI 

I .BI 

0.63 

0.31 

2.73 

1.07 

0.05 

1.52 

0.64 

0.45 

3-67 

I.LV 

0.74 

2-01 

0.7~ 

0.52 

1.07 

0.57 

3.50 

s. rr 

2.31 

1.53 

3.05 

1 .31 

O.9Q 

:.ro 

0.80 

O.hO 

?.%a 

0.96 

0.70 

--- 

I.20 

0.49 

0.62 

0.20 

4.43 

0.92 

0.12 

2" ?io 1 .S9 1.36 

0.58 

0.25 

0.10 

0.52 

+ 

4.7P 

1-04 

0.40 

. 

s.31 

1.30 

0.60 

8.86 

1.85 

0. b5 111 I :0.00 

2.32 

-- 

HE 11.29 

12.16 

U.03 

6.00 

I sb3 

0.88 

I6.78 

2.04 

I .Zd 
14 

Appendix A.--Continued. 

p = 1.00 

L50.30 

lN~CRvLC= 0.10 vu INlERVAL- 0.25 VR 

0.20 

0.15 

0.35 

1.57 

0.66 0.41 

0.47 0.31 

O.9V 

0.91 O.4V 

0.63 J.41 

- 

0.40 0.90 1.20 

0.50 

0.20 

0.13 

0.42 

0.1e 

0.14 

0.35 

0.18 

0. IS 

0. 19 0.14 

0.12 0.13 

0.33 0.27 

0.17 0.lb 

0.13 

__ 

0.36 1 I 0.30 

0"::: 

0.33 

0.24 0.22 

0.21 0.21 

0.52 

0.22 

0.15 

0.44 

0.20 

J. Ib 

- ___ 

0.49 

0.25 

0.20 

0-37 

0.20 

0.11 

.__.- 

0.41 

0.2r 

0.21 

0.59 

0.27 

0.20 

0.97 

0.59 

0.65 

0.33 

0.27 

0.55 

0.30 

0.26 

0.46 

0.2u 

0.26 

0.13 

0.40 

0.34 

0.62 

0.36 

0.32 

0.51 

0.33 

0.11 

INTEUVIL= 0.50 VII INrERVIL- 1.00 VU 

0.10 0.20 0.40 0.90 1 1.20 0.10 0.20 0.40 0.a0 

-.__ 

-- 

0.47 

0.27 

__ 

-- 

0.53 

0.32 

3. 69 

0.90 

0.40 

1-96 

0.50 

0.2* 

1.11 

0 -32 

0.18 

2.0e 

0.56 

0.30 

1.18 

0.J5 

0.21 

-__ 

1-91 

0.44 

0.29 

-___ 

l.Sl 

0.54 

0.40 

3.92 

1.J1 

0. *9 

4.u 

1-26 

0. 71 

5.01 

l.S8 

1.00 

0.20 

2.3b 

0.71 

0.42 

--_ 

2-61 

0.09 

0.59 

-- 

0.7s 

0.57 

-- 

0196 

0.77 

-- 

I .23 

1.03 

-- 

I .2n 

0.62 

-- 

1-64 

0.90 

____ 

-- 

2.11 

1-29 

-- 

0.69 

0..s . 

-- 

0.97 

0.63 

-- 

1.12 

0.96 

9.40 

0.69 

5.67 

I .97 

1.39 

3.02 

1-09 

0.u0 

-_ 

1.71 

0.67 

0.53 

0.93 
O"Z0 

- - -. ._ - 

0.75 

0.57 

1.83 

0.10 

0.20 

0.40 

-_ 

0.b0 

0.80 

15 

Appendix A. --Continued. 

p = 1.00 

L =o.m 

INrtRYACr- 0.10 VR INlEUVhLz 0.25 VR :i 0.20 

I 

- 0.21 __. :;i 

0.13 

0.12 

0. IO 0.20 0.40 0.80 

1-14 

0;56 

0.43 

0.00 

0.31 

0.2e 

0.34 

0.10 

0.1s 

0. 29 

0.1b 

0.15 

--- 

0.30 

3.18 

0.16 

1.21 

0.6. 

0.4Y 

O.bb 

0.34 

0.23 

0.35 

0.70 

0.17 

1.34 

0. re 

0. b2 

0.71 

0..0 

0.35 

0.37 

5.24 

0.22 

3.34 

0.21 

0.20 

I 3.40 

I 

t - - --- 

1.50 

0.98 

0. ?a 

_. . 

1-06 

1.25 

U. 'I5 

0.19 

0.48 

0.63 

0.4b 

0.28 

0-2b 

0.38 

0.25 

0.24 

0.88 

0.57 

0.52 

O.kP 

0.33 

0.31 

0.42 

0.24 

0.2- 

INrERVILI 1.00 VR 

0.40 0.40 

____ 

-- 

O.b4 

0.42 

-- 

0.72 

0.49 

-- 

0.93 

O.bM 

___ 

__ 

1.19 

0 -92 

-- 

1.53 

1.24 

0.10 0.20 

-~ 

1 .47 

0.51 

0.63 0.37 

I .51 

1.07 0.57 

0.73 0.42 

.- . . 

3-21 1-71 

1-26 0.70 

O.VR 0.54 

- - 

1-64 1-94 

1.55 O.Rb 

1.28 d.72 

~ ~ 

4.13 2.20 

1.89 1.05 

1-63 0.92 

-_ ___ 

0.80 1.20 

- 

0.51 0.44 

0.24 0.23 

0. 20 0.21 

___ - 

0.S5 0.67 

0.26 0.2s 

0.23 0.24 

0.62 0.53 

0.32 0.31 

0.29 0.29 

___ 

0.7s 0.b0 

o.ia 0.37 

0.Jb 0.35 

o.no O.bJ 

0e.b 0.44 

0-43 0.42 

d.eo 

0.31 

0.24 

0.85 

0. J5 

o.Za 

- -- 

0.97 

0-43 

0 -36 

1.10 

0.52 

0.46 

-. 

I.Zb 

0.63 

0.58 
16 

t.49 

2.33 

32.67 

e.02 

3.4.5 

3C.36 

9.91 

5.01 

:.el 

I .42 

----___ 

17.23 

4.46 

2.09 

19.18 

E. TC 

2.99 

Appendix A.--Continued. 

I .a4 

5.50 

2.75 

1-45 

1.04 

- 

S.CS 

2.F8 

1.42 

__ 

r.10 

-. 

-- 

C.Cl 

1.43 

-- 

7.6. 

I.?€ 

-- 

9-65 

P. 75 

-- 

17.?3 

a.21 

-- 

15.56 

t.34 

INTEPVLLI 1.OC Ve 

C.2C C.4C o.ec 

-- -- -- 3.~2 2.41 1.95 

0.69 C.65 0179 

-- -- -- 4.29 2-71 t.zn 

1.11 c.eC 0.97 

-- -- -- 5.43 z.45 2.00 

1.7C 1.25 1.42 

-- -- -- 6.90 as30 3.59 

2.55 1.93 2-01 

-- -- -- e.7~ 5.61 4.59 

3.@6 2.83 2.19 

p = 0.90 

L = 0.10 

INlePVILi 0.10 VU 

z1 

0.13 

____ 

1.20 

1.49 

1.21 

0.w 

0.80 

_. 

4-24 

1.21 

0.62 

I .20 

3.76 

1.25 

0.81 

1 

3.96 I 

1-30 

C.95 

4.42 

I.6S 

1.26 

4.92 

2.05 

1.C. 

i 

0.10 

23.55 

a.63 

1.24 

2b.eo 

5.14 

1.53 

1.41 

1.3. 

0.74 

3-60 

1.34 

0.92 

77-53 

6-33 

2.31 

4.97 

1.t4 

1.?2 

4.09 

l.t3 

1.22 

.c.ct 

7.84 

3.42 

5.52 

2.@I 

1.39 

4.54 

1.98 

1.59 

0.8') 

o.eo 

-?.Fa 

9.C6 

4.94 

6.13 

2.45 

1.84 

5.14 

2.38 

2.Cl 

17-89 9.94 

5.36 T.?" 

2.9. i.0F 

I~TEEVLL- r.50 VP 

0.m 0.40 

17.04 C.51 

2. e2 1.75 

O.RO a.nc 

1e.00 ir.cf 

3.14 1.55 

0.S8 0.7. 

2r.12 11.25 

3.CI 2.a3 

I ..e I .05 

- 

22.51 12.61 

&.e6 3.02 

2.19 1.58 

25.22 14.15 

6-01 3.75 

?.le 2.22 

-_ 

z r.10 

-- 

0.80 1.2c 

5.96 5.00 

1.35 1.39 

O.f6 0.80 

6.30 5.30 

1.51 1.55 

0.79 1.02 

7.e7 s.55 

1.88 1.91 

1.11 1-38 

T.94 6.70 

2.32 2.35 

1.e4 1.83 

e.53 7.55 

2-87 2.80 

2.07 2.37 

1.20 
@.I* 

5. E3 

1.46 

0.b2 

--- 

S. 04 

1.b3 

0.76 

6.51 

2.01 

I .CV 

7.27 

2.ae 

1.53 

0.20 

2.92 

0.81 

0.38 

3.F@ 

t.OP 

0..0 

3.44 

1.12 

O.C¶ 

- 

3.84 

1.10 

0.90 

0.40 I 0.80 

1.63 1.01 

0.w 0. 3n 

0.27 O.Pd 

1.72 1.07 

t.5t 

0.32 0.30 

n.42 

1.97 1-19 

r.ts 0.51 

c5.5 0.40 

2-14 1.33 

C.C. 0.62 

0.61 0.51 

1.20 

0.04 

0.30 

0.30 

O.EV 

0.41 

0.3b 

0.99 

0.30 

C.43 

1.11 

0.b0 

0.5a 

2.8C 

0.~7 

0.44 

3.12 

1 a07 

0.63 

3.47 

1.31 

0.87 

3-06 

1 .fO 

1.16 

1.56 0.96 0.79 

O.*Z 0.40 0.39 

0.3: 0.20 0.32 

1.74 1.07 , 0.68 

0.t. 0.40 0.47 

0.43 0.30 0.41 

__I 

I .93 1.19 0.98 

e.co 0.58 0.55 

0.58 8 0.49 0.50 

2.15 1-12 I .09 

c.57 0.70 O.tS 

6.76 0.61 0.81 

1.49 

0.75 

0.65 

1-13 

0.71 

0.t5 

O.CO 

1.44 

0.44 

0.29 

1.13 

0.5h 

0.24 

1.13 

0.bI 

0.48 

I.P. 

0.75 

0.60 

1.20 

1.22 

0.4s 

0.35 

1.30 

0,SO 

0.40 

1.47 

0.61 

0.s2 

1.b6 

0.75 

0.60 

2.20 

0.92 

0.78 

1.88 

0.91 

O.OP 

17 

Appendix A.--Continued. 

p =Om 

L = 0.30 

INTEPVIL* 0.25 VR INTERVAL* 0.1F VI( 

0 .70 0.40 

0.3r 0.26 

0.36 0.35 

0.2s OI2V 

1-39 

1-01 

c.rc 

0. no 

- 1 

INTEUVLC. 1.00 TU 

I 

n.10 

1- o.eo 1.20 

-- -- 0.74 0.82 

0.41 0.65 

-- -- 0.84 C.92 

0.49 0.64 

-- -,. 1.08 1.1v 

0.70. 0.88 

0.20 C.40 

1.06 2.ZE 

0.52 O.S9 

0.81 0.3-2 

4.30 2..2 

1.C3 C.64 

a.b9 c.35 

4.ea 2.72 

1-29 C.80 

0.71 C.5C 

0.40 

-- 

C.90 

0.30 

0.10 1 1::: 1.42 

2-13 1.b0 

I.CI 0.62 

-.I 

-- 

I .03 

0.b7 

0.20 

-,. 

1.31 

Ceb8 

0.40 

(0.26 

0.60 P.87 

11-56 

0.80 3.5b 

2-35 

0.60 

PsZb 

9.95 3.37 

3.29 1-97 

0.eo 
18 

c.40 

0.80 

C.10 

6.29 

C.84 

6.40 

C.25 

C.94 

0.4C 

c.42 

1.01 

0.sc 

c.52 

1.17 

C.69 

c.t3 

__-+ 

- 

0.w 

0.50 

0.26 

0.23 

0.s1 

0.29 

0.2t 

0.59 

0.34 

0.32 

?.t5 

0.41 

0.3@ 

0.7. 

0.48 

Q.46 

0.10 

2.70 

I.C0 

0.76 

?e86 

1.20 

0.88 

3.19 

1.46 

l.IE 

3.57 

1.77 

I .*e 

3.98 

2.12 

1.e6 

-- 

0 .PO 

1 .A3 

0.60 

0.44 

1.51 

0.66 

0.51 

1.65 

O.CO 

0.t5 

__ 

I .se 

0.97 

0.C3 

2.IE 

1.It 

1.03 

?e04 

1.60 

I .3t 

1.61 

0.e7 

0.7.5 

C.2C 

-- 

I .34 

C. 78 

-- 

I .sz 

C.94 

-- 

I.9t 

1.32 

-- 

2.52 

8.82 

-- 

3.23 

2.4e 

C.40 

-- 

C.86 

C.56 

-- 

C.9C 

r.66 

-- 

I.ZC 

(-91 

-- 

1-61 

1.2. 

-- 

2.07 

1.67 

Appendix A. --Con t I nued . 

p = 0.90 

L = 0.70 

I*IEfiVbL= 0.10 TP IhlERvbL. 0.25 VP 

0.40 1.20 

c.41 

0.2s 

0123 

R.6@ 

C.33 

0.27 

___. 

C.72 

C. zt 

0.30 

0.5: 

0.41 

1.29 

O.Cl 

c.44 

C.P7 

0.28 

0.44 8136 

0.24 

0.25 E.44 

0.36 0.32 

0.34 

0.80 

r.44 

0.?9 

C..F 

C.32 

0.30 

0.54 

0.37 

0.36 

0.60 

0.43 

0.42 

1.3 

I .or 

0.80 

C.52 

0.47 

t.to 

IE.90 

C.61 

c.F.7 

-_ 

3.37 

!.GI 

I .t9 

1.70 

I .GI 

0.93 

P. ec 

INTEPVIL= 0.50 Yfi 7- 

0.10 ~ ___ 0.52 

2.34 

C.40 o.ea 1.20 

-1- 

1.2. 

0.46 

0.35 

C.*O 

0.35 

0.29 

0.68 

E.34 

0.31 

1.32 

0.51 

C.4G 

a. es 

0.38 

0.33 

0.72 

C.38 

0.3s 1.57 -I-- 0.20 

1.50 

C.63 

c.52 

t.t5 

2.99 

2.26 1.2s 

t.3? 3.39 

2.77 I rs3 

2-55 1.33 

0. PO 

0.47 

0.42 

1-09 

0.56 

0.52 

0.e2 

0.45 

0.42 

0.93 

0.54 

0.s2 

c.4n 3.46 

C.60 4.44 

3.10 

I.CS 

r.77 

c.ec 

m. til 

0.80 

---+--- 1.52 

c.93 

C.83 

1.23 

0.60 

0.64 

1.05 

0.f. 

0.62 

1 I 
- 

.as37 

7.SO 

2.43 

45.45 

9.31 

3.63 

5F.20 

11.55 

5.31 

61.E4 

14-32 

7.62 

___ 

21-64 

1.17 

2.66 

30.92 

7.16 

3.01 

34.a 

6.68 

5.34 

30.84 

10.98 

?-32 

zc9.zc 

a1.47 

17.CC 

110.51 

23.10 

10.62 

19 

Appendix A. --Continued. 

p = 0.70 

L L.O.10 

INTEOVLL. 0.10 VR 

__.I. 

0-QO 

20.51 

4.L4 

2. 12 

-11 

1.20 

15.06 

4.79 

2.e3 

0.10 0.20 lr20 

16-90 

4.VC 

2.17 

1@.72 

5.30 

3.32 

10.S6 

ha46 

.. 49 

119.89 

2C. b0 

5.11 

tl.C2 

5.18 

2.56 

17.03 

5.43 

1.37 

I33 -00 

25.41 

7.74 

24.G4 

6.63 

3.64 

1% 65 

6.66 

4.5? 

2o.e~ 

7.90 

5.93 

26~7l) 

6.15 

Sa06 

22.10 

0.13 

6.06 

_I__-. 

P*r6l 

9.PV 

?.E6 

I 22.90 

9.97 

7.67 

29.77 

0.99 

t.Fb 

I .tC YF 0.10 c.20 1.20 

a. lr) 

0.20 

0.40 

0.60 

0.00 

21.81 

8.32 

3.01 

-- -- e.78 6.99 

2.16 2. eo 

-- 

7.53 

3.05 

-- 

0.50 

4.40 

-- 

10.05 

6-29 

0. In 

4.21 

1-------+---- ~ .- -. 

23.09 

5.92 

3.56 

-- 

25.09 

7.32 

4.80 

151.09 w.6e 

71.79 12.12 

2.2C 1 3.21 

0.79 

i.te 

4.00 4.53 

29.07 

9.03 

6.56 

32.60 

Il.11 

8-64 

-- 

12.06 

8.8. 

-- 

17.7t 

12.26 

-- 

24.0S 

8.15 

-- 

31.48 

12.26 

-- 20.01 16-28 

-- 9.07 I 9.43 

6.80 
0.80 

3.25 

i.oe 

0.66 

3. 42 

1.20 

n.ao 

- 

3-80 

1.46 

1.Ot 

4.22 

1.78 

1.39 

- 

4.69 

2.14 

1-70 

-- 

1.20 

2.67 

1.07 

0.81 

7.82 

1.18 

0.93 

, 3.13 

, 1.43 

i.ie 

I 

3.47 

1.71 

1.49 

3.85 

2.05 

I.Sb 

C.10 

24.U4 

4.63 

1-63 

- 

26-26 

I r99 

5. IC 

- 

29.39 

t.47 

2.93 

32.93 

7.51 

4.23 

36.55 

S.eq 

s.95 

_- -__ 

0.20 0.4P 

13-13 7.35 

r.*e 1.60 

0.00 0.7- 

13.C9 7.18 

1.21 o.re 

2.e~ 1.15 

15.55 e.72 

3.58 2.22 

1.77 1.26 

17.44 0.79 

4.44 2.75 

2.52 1.75 

19-57 II-OC 

5.5@ 3.40 

3.SO 2.'8 

0.m 

_- 

I .a5 

0.9. 

*- 

2.10 

1-14 

-- 

2.C8 

1.62' 

-_ 

1.41 

2.27 

-- 

4.41 

3-14 

1.20 

-- 

2.PI 

1.20 

-- 

2.29 

1.52 

-- 

2.94 

2.09 

-- 

:.?e 

2-05 

-- 

4.02 

3.04 

4.62 

1.24 

0.14 

-- 

4.e9 

I.3C 

0.m 

-- 

5.10 

1.10 

I.lV 

@.I9 

2.10 

i.te 

6-97 

2.57 

2.07 

3.89 

1.26 

0.02 

4.12 

1 .a0 

1.@6 

4.Cb 

I .I2 

1.31 

5.23 

2.10 

1.77 

5.90 

2.56 

2.24 

Appendix A. --Continued. 

p =0.m 

L =o.m 

1 

0. IO 

t.2c 

0. IO 

1.51 0.96 .% 20.24 10.67 

2.C. 

5.5. 

1.59 

0.83 

C.lt 

1 1.9< 

1.16 

3.05 

1.23 

0.55 

0.20 

22-51 11.81 

0.40 ..PV 3.21 

2.80 i.cc 

25.06 13.22 

O.CO 7.26 4.C3 

4.00 2.37 

2'7.90 14-72 

0. eo 1.53 4.0. 

3.51 3.25 

3.39 

I .*O 

1.23 

3. ?e 

1 .?9 

1.5s 

4.21 

2.15 

1.92 

0.40 

-- k 

*.IO 

@.IO 0.20 C.40 

-- 

3.59 

1.1. 

-- 

1-04 

1.41 

-- 

5.14 

2.13 

-- 

2.28 

C.87 

-- 

2.51 

1-06 

0.m 

0.40 

- 

o.eo 

- 

o.sn 

- 

@.SO 
iriE@baL= 

______._. 

c.2n 

3.91 

1-41 

0.97 

4.m 

(..e 

1.12 

-- 

b.69 

8.w 

I .an 

S.CI 

2.3c 

I .*a 

5.5P 

I. I? 

.?.a 

0.2s va 

- ____ 

C.40 0.00 

- 

2.13 I a 32 

<.et 0.C3 

r.65 0.53 

Z.0' 1.40 

c. qe 0. b9 

O.?. G.69 

2-51 1.Sb 

1.1Y 0. c3 

r .e. 0.7. 

2~?9 1-73 

I.1C C.99 

1.20 0.91 

2.11 1.93 

1.t6 l.l? 

1.b5 1.10 

-__ 

21 

Appendix A.--Continued. 

p = 0.70 

L = 0.70 

-- __ 

1.20 

-- 

1.10 

o.to 

0.s5 

C.20 1 0.00 

1.93 1.19 

0.02 o.eo 

I .2e 

0.98 

0.56 

0.59 

3.48 

I .35 

I .03 

0.tl 

0.51 

1.16 

0.66 

c.tt 

1.1. 

0.?2 

0.68 

1 .E9 

0. re 

0.73 

____ 

1.43 

0.91 

o.eo 

1-96 

0.8. 

0.00 

4.51 2.51 1.55 

2.17 I 1.30 1 C.S2 

1 .el 1-14 0.B5 /--+---- a 

1.b0 

0.97 

C.94 

I .29 

I .07 

1.03 

I I 9.54 

IhlCFVbC. 0.'0 VP INlCWvbL* 1.00 VS 

P Ti-- __ ___ 

h.20 l.2C 0.lC 1 0.20 

3.33 

I.C? 

I .ce 

S.66 

1.01 

I .2C 

__ __ 

6-30 

2-25 

I .OB 

I" ir.05 

13.56 

0. eo .. 55 

3.ee 

I .e3 

c.75 

Cab? 

-- 

I .73 

0.C3 

0.75 

I.9E 

1 .OD 

0.53 

-- 

a. ?C 

2a.C 

_- 

5.32 

2.CC 

I -- -- 

7.19 

I.7. 

2.ZC 

2.ZI 

I .2C 

1.13 2. I6 

3.3. 3.t. 

1 

2-06 3.2~ 

2.50 

1 .a4 

1.36 

-- 

..OC 

3.21 

15-28 

0. Lr C.C? 

5.C.l 
22 

I c 0.i~ 0.20 

264.77 

3e.m 

7.b8 

270.12 

40.22 

9.85 

0.40 

147.18 

12.36 

t.07 

I5S.98 

2a.e~ 

7.47 

0.80 

9I.YO 

17.1? 

6.01 

96.55 

19.12 

0.2. 

107.91 

23.71 

11.52 

I20.16 

29.39 

i6.et 

1.20 

76.C9 

17.60 

9.40 

00.51 

19.59 

11.24 

50.22 

24-21 

I5.S. 

10l.22 

29.95 

2 I. 04 

Appendix A.--Continued. 

p 0.56 

L=O.iQ 

1 

r.io 

I I20 

I_- 

59.32 

16.31 

9.01 

---I--- 

71.53 50.75 

l7.5C 11.70 

7.02 10.56 

62.SO 

lI.39 

10.71 

--- 

69.61 

21.11 

I#.t5 

77.44 

27. I7 

I0.Cl 

- - 

06.27 

33.12 

9s.tq 

----t-- 

---+---- 

-

INIFPVbL= 1.00 VD 

I 17-91 

(129.54 

O.?l 1 72.40 

15.f6 

n.?* 

0.4n 

O.tO 

0.m 
0.10 

0.20 

E7.46 

12.20 

1.09 

ta.52 

$3.55 

5.00 

€7.16 

0.10 

22.09 

4. .e 

1.92 

24.20 

5.10 

2.13 

2r.o~ 

6.33 

3.34 

30.35 

7.05 

4.70 

14.0. 

9.71 

C.It 

0.09 

14.13 

3.53 

1.99 

15.S7 

3.93 

2.35 

11.02 

4-86 

3.23 

19.12 

5.09 

4.34 

21.50 

7.37 

5.73 

23 

Appendix A.--Continued. 

p = 0.50 

L =0.30 

INTERVAL* 0.25 VR 

---.--I

lz?i- I 7.43 

1.37 

11.06 

12.20 

5.36 

79.43 

21.03 

10.12 

ea.37 

I I 

I- - 1hTERVIL.I 0.50 VR INlERVAL- 1.00 VR I y 

E. 10 

- 

0.10 c.2e 

-- _- 11.57 5.87 

4.68 2.90 

.,- -_ 15.73 11-09 

s.ai 3.ee 

__ -_ 24.57 14.07 

c.et 5.41 

-- __ 31.72 87.09 

13.20 0.02 

-- __ 40.40 22.01 

19.42 11.70 

1.20 

12.03 

3.60 

2.50 

C.40 0.00 

-_ _- t.24 5.05 

2.20 2.43 

i.20 

-- 

5.49 

3.32 

12.15 

---I

4.00 

2.90 

0.2’) 

14.33 

4.92 

3.02 

16.13 

6-03 

4.55 

-- 

7.9t 

1.47 

-- 

lC.19 

7.49 

0.*0 

0.60 

0.00 

lC.17 

7.36 

6.32 

14.57 11.93 

0.30 1 0.20 
24 

i1.i.5 

4.C7 

3.51 

C.b7 

2. e2 

2.2e 

..e2 

2156 

2.22 

3.99 

2.40 

2.27 

1.20 

4.30 

1.a6 

1.63 

4.s7 

2.05 

1.83 

5.16 

2.b9 

2.28 

5.03 

3.00 

2.80 

6.59 

3.59 

3.42 

I 

Y F Fa10 c.20 C.bO 0.?0 I.2C 

e.17 

n. 20 

9. b0 

O.6n 

0.09 

26.89 

7.19 

4-21 

211.50 

8.01 

5.07 

32.G3 

0.91 

C.51 

?6.C5 

12.21 

9.21 

bO.tO 

15.~1 

12.0b 

Appendix A.--Continued. 

,o = 0.w 

L=0.70 

1 IhTEUVLL* 0.IP YF 

e.4~ 

2.47 2.12 

2-23 

2-67 

0.80 1.20 

2.70 

I.bC 

1.33 

2.93 

1.61 

lmb7 

, 3.2r 

1.91 

1.70 

3.t0 

2.24 

2.1' 

3.9~ 

2.62 

2.52 

0.IC 0.20 

3.38 

1.5s 

1.28 

-___ 

3-16 

1.70 

1.*4 

25.16 

C.b7 

b.02 

21.20 

).I6 

..7c 

23.71 

e. 77 

6-21 

5.93 

2.15 

i.:e 

t.16 

2.42 

1.81 

t.O 

2.94 

2. zt 

10.54 

1. cc 

2.35 

11.23 

3.96 

2.73 

-_ 

12.11 

a.eb 

3.t3 

1.62 1-36 

1.39 

3.89 z.22 

1.70 1.70 

1.55 

2.58 1: 1 2.03 

i.ea I r.ae 

4.21 

0.4- 

3-96 

2.03 

1.80 

24.36 

o.eo ir.27 

b.?9 

2.42 

2.21 

2C.bZ 

io.te 

F.25 

13.9% 

5.~9 

4.71 

7.77 

7-56 

3.00 

12.1). 

1.t'L 

Ib.26 

6.e~ *.c7 

5.77 3.tc 

0. t1 -$"" 77.06 

"27 

3.04 1 :::: 2-03 2.70 

... . 

29.45 

12.95 

ie.58 

15.5b 

7.12 

e.cc 

C.80 

1 

@.eo 

o.20 I 

----t-- 

lb.25 

2.5. 

15.10 

ba.5 

2.57 

5-07 

I .80 

1.11 

5.19 

2.08 

1-71 ----+-- e. 'le 

2.53 

2.1a 

t.et 

3.00 

2.75 

7. 7. 

3.73 

3. b2 

E.2P 1. b2 

t.Cb 4.37 
25 

APPENDIX B 

Sample sizes (thousands of fish) in double-tagging experiments of 1-yr 

(upper figures), 2-yr (middle figures), or 4-yr duration (lower figures) 

required for estimating 2 with a coefficient of variation of 25%. Dashes 

denote infeasible cases. p = 1.00 

L =0.00 

lNTL-YVAL= 0.10 VU INTERVAL- 0.25 vn 

0.19 0.40 

- 

13.23 2.64 

1-63 0.40 

0.31 0.08 

. 

7.83 I .V3 

0.31 

0.21 

0.06 

-___ 

2.40 0.85 

0.43 0.17 

0.12 0.06 

1.71 Oabb 

0.34 0.15 

0.12 0.06 

___ 

1.20 

____ 

0.1e 

0.04 

0.02 

0.2’) 0.60 0.83 I .20 

. 

1.*9 

0.40 

0.08 

0.80 

. . 

0.47 

0.09 

0.93 

12.53 

1.91 

0.11 

0.50 

0.09 

0.03 

0.20 

0.05 

0.02 

-- ? .b I 

1.13 

0.21 

1 .*? 

0.11 

0.07 

1.14 

0.21 

0.Oh 

__ 

0.81 

0.ll 

0.06 

0..0 

0.OR 

0.03 

0.17 

0.0. 

5.02 

0.18 

0.04 

0.02 

__ 

0.15 

0.04 

0.02 

25.06 

0.23 1 J.62 

, 0.61 

- - -1 y::: 0.IO 

0.33 I 

0.41 

0.08 

0.03 

O.J1 

0. 07 

0.03 

3.65 

O.bI 

0.14 

. 0.lc) 

0.04 

0.02 

- 

3.1 1 

0.04 

0.02 

2-21, 

0.03 

0.11 

.. . __ 

1-61 

0.34 

0.12 

0.2? 

0.07 

0.03 

0.13 

0. o* 

0.42 

I 5.04 

I .00 

0.26 

__ 

I. 10 :-I o.ao a. r5 

i 5.24 .. ._ 

0.21 

0. 06 

3.33 

0.11 

0.OI 

0.03 

0.23 

J. ab 

0.03 

0.19 

0.04 

O.OJ 

INTERVAL- 0.50 YR II INIfRVALn 1.00 VR 

~~- ~ .. ......... :ye- ?0. 70 

0.10 7.83 

0.20 1 -o;;r; 

___ - __ - 

Ih.55 

I .v3 0.43 

0.31 0.08 

~ __ . 

+.no 2.42 

I .PI 5.33 

0.22 0.07 

4.w I. 51 

0.66 0.23 

0.15 O.Ob 

- 

3.02 1.08 

0.46 o.in 

Us13 0.0b 

-- 

2.15 0.83 

0.36 0.15 

0.12 0.0b 

____ 

0.23 I ’:::: 

13.22 

0.40 1 1-71 

0.34 0.02 

0.29 

0.07 

0.04 0.03 

Y __t--- 

I 
26 

-- 

0.40 

2.b5 

0.41 

0.09 

1-91 

0.32 

0.08 

_-_- 

1 .ZI 

0.22 

0.07 

0.86 

0.17 

0.06 

0.6b 

0.15 

0.06 

0.80 

0.50 

0.10 

0.03 

0.43 

0.09 

0.03 

-_ 

0.33 

0.07 

0.03 

0.27 

0.07 

0.03 

0.23 

0.06 

0.04 

4.10 

- 

-_ 

9-96 

1.30 

-- 

4.91 

0.71 

-- 

9-19 

0. J9 

-- 

1-39 

0.31 

-- 

1 .os 

0.28 

lNfERVAL= 1.00 VR 

0.20 0.ao 0.60 

-- -- -- 2.46 0.ss 0.13 

5.36 0.10 O.OJ 

-- -- -- 1.54 0.42 0.12 

0.25 0.08 0.03 

-_ -- -- 0.95 0.30 0.10 

0.17 0.07 0.04. 

-- -- -- 0.59 0.24 0.10 

0.14 0.07 0.04 

-- -- -- 0.48 0.21 0.09 

0.14 0.01 0.04 

Appendix B.--Continued. 

p = 1.00 

L =0.10 

INTERVIL* 0.10 VR 

0.20 0.40 0.80 

- 

12.58 2.51 0.47 

1.84 0.41 0.09 

.Os33 0. ov 0.03 

- .- 

7.44 1.83 0.40 

1 .I5 0.31 0.08 

0.23 0.01 0.03 

1-66 1-11 0.31 

0.63 0.22 0.07 

0.16 0.07 0.03 

1.20 

0.19 

0.03 

0.02 

0.10 

36-85 

7.60 

1-23 

2 6-50 

J. 74 

0.67 

0.20 

13.29 

1.87 

0.34 

1.20 

0.20 

0.05 

0.32 

0. IO 

- 

0.20 

~ 

0.40 

0.17 

0.04 

0.02 

7 Ab 

1-16 

0.23 

0.1u 

0.04 

0.02 

0.14 

5.04 

'0.02 

10.50 

1.t.s 

0.37 

3 .e7 

0.64 

0.16 

2-41 

0.44 ' 

0.13 

1-11 

0.34 

0.13 

0.15 

0.04 

0.02 

0.13 

0.04 

0.j3 

0.12 

0.04 

0.03 

0.13 

0.04 

0.03 

0.11 

0.04 

0.03 

5. YQ 

1.04 

0.26 

4. 02 

0.77 

0.26 

Oil7 

0.22 

0.34 0.15 0.0b 

0.13 0.06 0.04 

lNIERV4Li 0.50 VR 

\i 1 

0.10 

___ 

I .20 

-- 

0.07 

0.02 

0.20 0.40 

3.32 

0.43 

0.09 

___. 

2.43 

0.J3 

0.08 

71.04 

0.10 1 7.97 

16.61 

1.96 

O-Jb 

_- 

9.m 

1.22 

0.23 

4.85 

0.67 

0.16 

3.03 

0.46 

0.13 

0.03 0.02 

0.23 

0.09 0.05 

0.03 0.02 

-- 

0-06 

0.03 

33.23 

13-21 

?.52 

0.60 

0.29 

0.20 

1.52 

0.23 

0 -07 

1 .oe 

0.18 

0.06 

0.84 

0.16 

0.07 

-- 

0.06 

0.03 

-- 

0.06 

0.0J 

-- 

0.0b 

0.04 

0.40 

0.60 

- 

0.60 

----t-- 5. Ob 

0.60 1 0.e2 

0.26 

2.16 

0.31 

0.13' 
0. I1 

0.06 

0.42 

0.10 

0.05 

__ ._ .

0.35 

0.03 

. __ __ 

0.1s 

3.05 

0.0J 

- - . . __ 

-- 

0.12 

0.06 

-- 

0.07 

0.05 

27 

Appendix B.--Continued. 

p = 1.00 

L=O.30 

INlE9VAL= 0.10 VI INTLRV4L- 0.25 VI 

.-_ . -

0.10 0.20 D.b0 0.e0 1.20 

59. IO 

9.13 

2.46 

13.R2 

2.25 

0.67 

2.75 

0.50 

0.18 

0.52 

0.12 

0.06 

____ 

0.4s 

0.10 

0.05 

0.21 

0.06 

0.03 

I .91 

0.38 

0.15 

e.in 

1.40 

0.4b 

2-01 

0.18 

0.15 

0.19 

0.05 

0.03 

0.16 

0.05 

0.03 

0.14 

0.05 

0.04 

I .l* 

0.2b 

0.12 

11.02 

I.YU 

0.71 

6-23 

1.25 

0.53 

_. 

4.18 

0.93 

0.46 

4 -03 

0.17 

0.J3 

2.51 

0.53 

0.24 

I .2b 

0.26 

3.12 

__ 

0.89 

0.21 

0.11 

O.bY 

0.18 

0.10 

- 

0.31 

0.09 

0.05 

____ 

0.28 

0.08 

0.35 

0.8I 

0.20 

0.11 

- ~- -_ 

0.65 

0.17 

0.10 

I .?S 

0..2 

0.22 

3.24 

0.07 

0.05 

_. 

0.13 

0.05 

3.04 

INlLRVAL' 1-00 VP 

- T 

1.20 

0.26 

0.06 

0.04 

0.24 

0.06 

0.OL 

.. - . ... . . + .. .. . . 

0.10 

. . -. . .- - 

0.20 

0.40 

- 

3-10 0.20 

73.38 

U.bJ 

2.m9 

1?.17 

2.35 

3 -6.7 

0.10 

0.20 

0.40 

14.14 

4. 70 

1.15 

10.17 

I .4? 

0.b4 

__ _. - 

5.02 

O.*O 

0.10 

13.t2 

2. UB 

0.IZ 

Q.20 

0.05 

0.04 

7.78 

1.31 

0.54 

5-24 

0.98 

0.*7 

.. . 

3.14 

0.96 

0.25 

o.in 

0.05 

0.04 

-- 

0.15 

0.05 

0.04 

-~ ~ 

0.60 

2.24 

0.44 

0.22 

.- 

0.80 
28 

3. bb 

I .OV 

0.T1 

2+5* 

0.84 

0.62 

1.58 

0.57 

0.45 

1.12 

0.44 

0.31 

_____ 

0.87 

0.31 

0.32 

_.__ 

0.66 

0.25 

0.20 

0.Sb 

0.22 

0.18 

0.43 

a. I8 

0.16 

0.35 

0.16 

0.14 

0. JJ 

0.15 

0.14 

__ 

Appendix B.--Continued. 

p = 1.00 

L 50.70 

1 

0.10 

INTERVAL= 0.10 VR INTERVAL= 0.25 VR 

0.10 0.20 0.40 0.80 I 1.20 0.10 0.20 I .20 

- 

I 7.35 

b .98 

3-21 

10.28 

3.09 

2.09 

-___ 

5-01 

1 .6? 

1 .LJ 

70. Vb 

80.07 

12-53 

16.S9 

4.93 

'3.19 

3-31 

1.08 

O.?? 

_- 

2.42 

0.83 

O.bl 

1.51 

O.5b 

0.44 

0.26 

0.11 

0.10 

0.23 

0.11 

0.10 

_- 

0.20 

0.10 

0.09 

0.25 

o.in 0.09 

JIlY 

0. I8 0.14 

0.lb 0.09 

7b. 14 

23.27 

IZ..O 

34. 70 

9.Y6 

6.43 

13.w 

b.31 

3. JY 

0.10 

0.20 

-- 

0.4J 

13-19 

9.H5 

b-39 

9.82 

3-01 

2.08 

4.64 

1.65 

1.22 

3.02 

I.IJ 

0.89 

0.20 

- 

0.40 

- 

0.60 

- 

0 .eo 

_I 

13.24 

4. Jt 

3.07 

I. 48 

2.67 

2.05 

-----r-- I .0? 

0.43 

0.36 

?a81 

2. ?I 

2.07 

3-16 

1.14 

U.90 

0.18 

O.OY 

0.09 

.____ 

0. I6 

0.OY 

0.OR 

0.60 

5.02 

1.95 

1.59 

2.14 

0.df 

0.72 

0.82 

O.J(i 

0 .XI 

5.27 

1-98 

1.OL 

2.25 

0.88 

0.13 

0.80 

INTEOVAL= 0.50 VI? 

0.20 0.40 I.2U 

0.69 0.29 

0.23 0.12 

0.19 0.10 

20.13 

5.18 

J.2V 

~ 

12.36 

3.23 

2.1') 

~ . .. 

6.13 

I -7b 

1.21 

- 

3.m 

1.21 

0.9b 

1.18 

I.lb 

0.80 

3.06 

0.88 

0.64 

41.66 

6- 5R 

... 

Lb.71 

4.58 

, Y.51 

0.60 1 2-60 

1.92 

o .eo 

O..? 

0.25 

0.11 

0.10 

0.44 J.22 

0.18 0.10 

0.16 0.10 

0.09 

___ 

+--+--+--+ t.18 

0.47 

0.39 

- -_- 

1-01 

U.4U 

0.34 

b.43 

2.11 

1.69 

2.15 

J.94 

O.?? 

O..9G 
0.40 

__-.I_ 

2-81 

0.41 

a.08 

- 

I .9s 

0.32 

0.01 

- __ 

1.22 

U.ZZ 

0.06 

_- 

0.8b 

0.ll 

0.0b 

- 

O.b? 

0.1s 

O.UO 

__ - 

_____._____ 

0. BO 

__ 

0.51 

0.16 

0.01 

0.b3 

0.00 

0.01 

, 0.13 

0.01 

0.03 

- 

0.27 

U.07 

0.03 

.- __ 

0.23 

0.W 

0.03 

-- 

12.b9 

I .03 

0.31 

.. __- __ 1.50 

1-14 

2.53 

0.40 

0.09 

. - - . - 

I .ns 

0.31 

29 

Appendix B.--Continued. 

p = 0.90 

L = 0.00 

INIERVAL- 0.10 VR 

T-- __ 1 __ 

0.10 

___. 

51-31 

7.5s 

1-14 

I__ 

0.20 

----- 

13.40 

1.8b 

0.31 

1.93 

1.10 

0.20 

I__

1.20 

0.20 

0.05 

0.02 

__ 

0.18 

0.04 

0. J.! 

I .20 

-__ 

0.IV 

0.04 

0.02 

0.20 I 0.40 0. 90 

0.49 

0.09 

0.03 

. 

0.41 

0.00 

n.03 

__ 

0.31 

0.0? 

0.0) 

- __ 

O.Zb 

0.Jl 

0.03 

- 

0.22 

0.0lJ 

0.03 

____ 

0.10 

0.11 

0.04 

0.01 

0.20 

0.61 

0.14 

0.04 

0.02 

0.13 

0.04 

0.02 

--- 

U.11 

0.04 

0.03 

____ 

I 

3.90 

0.b3 

0.1. 

10.09 

1-01 

0.34 

0.15 

0.04 

0.02 

0.13 

0.09 

0.02 

U.12 

0.04 

0.03 

0.40 

____ c . . ___ 

0.34 - 

2.43 

0.44 ' 

0.19 

I -13 

0.). 

0.12 

----I------ 

0.60 I :::: 

__ .- 

0.80 

0.64 

0.10 

0.03 

0.54 0.23 

0.09 0.05 

0.03 

2.4s 

0.33 

0.07 1~~ -- - 

4.09 1.53 

0.40 0.67 0.23 

0.15 0.06 

__ 

I .09 

-~ 

-I- 2.19 0.m 

0.90 0.37 0.16 

0.25 0.12 0.06 

0.20 

-.. 

4. dP 

0.67 

-- 

2-18 

0. 37 

0.40 

0.b0 1-38 

0. LV 

0. 01 

0.03 0.03 

0.16 

0.07 

0.04 0.03 

-+ 

I 

0.90 
0.40 

2.12 

0.43 

0.10 

- _- 

1.99 

0.33 

0.00 

.- 

1 -21 

0 -23 

___-___ 0.00 I .20 

- 

0. 51 0.20 

0.10 0.05 

0.01 0.02 

0.44 0.1% 

0.09 0.05 

0.03 0.02 

- 

0.3. 0.16 

0.00 0.0* 

0. 01 0.03 

ij: 1 0.01 O.Z* 0.01 

0.60 0.23 

3-15 0.07 

0. 01 0.04 

- 

. 

0.03 

_- 

0.1101 

0.03 

0.12 

0.04 

0.03 

30 

Appendix B.--Continued. 

p = 0.90 

L=O.IO 

INTEWVILI 0.25 VR 1 

0.10 

0.20 

___ 

3.40 

0.1 0 3.20 0.10 0.20 

53.24 

?.e2 

1.32 

25.82 

3.65 

0. 72 

10-29 

I.?G 

0.39 

12.91 

1.02 

0.36 

__ __ 

?ab4 

I .20 

0.25 

50.33 

1.92 

IsJ3 

13.63 

1 .95 I 013b 

1 0.20 

i b-- 

I OebO 

I--- -- I27.27 

3-90 

0.13 

8.01 

I .2I 

0.25 

3.76 

U.bS 

0.11 

IO.*? 

1.72 

0. *o 

.- __ 

4.15 

1.m 

0.30 

1-13 

0.81 

0.20 

3.91 

0.bb 

0.ll 

. __ 

2.48 

0.10 

0.11 

Is76 

0.36 

0.14 

8.81 

I.J? 

0.30 

2.31 

0.45 

0.1. 

0.i3 

0.01 

0.03 

0.83 I O.2b 

0.10 1 0.07 

0.01 ~ 0.04 

0.60 

3.90 

0.79 

0.21 

-- 

1-66 

0 .3b 

0.13 

_I_ 

0.12 

3.01 

0.01 

INTERVIL- 0.50 Yb4 

3.40 0. b5 0.2b 

0.10 dr 31 2.0s 0.11 0.0s 

1.31 0.02 

0.00 

0.13 

0. Ob 

0.01, 

0.01 

0.10 0.01 

0. 05 0.04 

34rIO I -- [ 0.20 1 1.09 

0.73 

10.10 

I .20 

0.2s 

2.19 0.55 0.?3 

0.35 

0.09 

0.20 1 -- L 0.20 

0.05 

0.03 

0. 10 

0.10 0.03 

1.12 0.35 0.18 

0.60 1-14 0.49 0.19 3.01 0 .05 

0.31 0.15 0. 04 0.03 

5. I9 2.22 0.30 0.16 

0. eo 0.05 0.07 0.05 

0.28 3-01 I 0.0. 0.03 
. 

Y F 

0.10 

0.20 

0.40 

-- 

0. bo 

___I 

0.00 

31 

INILRVALm 0.10 Vu 

0.10 0.20 0.40 

59-46 13.90 2.77 

IU.00 2.48 0.S5 

2.UY . 0.10 0.21 

2 7. UO 0 .e3 1.02 

4.Vb l.S5 0.42 

I.5T 0.54 0.17 

11.00 4 e05 I a20 

2.ZO O.U* 0.29 

0.R.l 0.19 0.11 

n.26 2 .s2 U.09 

l.JO 0.58 0.23 

O.b2 0.m 0.13 

. 

4.20 I .79 0.69 

1.02 0.46 O.1V 

0.53 0.2s J.12 

___I 

Appendix B.--Continued. 

0.14 

0.05 

0.04 

0.13 

0.05 

0.04 

- - 

b.bl 2.67 

0.bO I. 40 0. 99 

0.61 0.20 

-. -. - 

4. 44 I .89 

0.10 1.04 0.41 

0.93 0.25 

I -_---I 

0.19 

-- 

0.40 

0.07 

-- 

0.Ib 

p f 0.90 

LrO.30 

3.00 0.40 

0.52 

0.13 

6-01 

2.Y2 

O.bb 

0.21 

-- 

2.1; 

0.43 

0.17 

- .__ 

I .3.1 

0.30 

0.14 

0.55 

0.13 0.06 

0.07 0.04 

0.45 

0.11 

0.JO 

- _- 

3.34 

0.10 

0.06 

0.04 

0.36 0.1? 

0.10 o.on 

U.Ob 0.04 

0.2a 

0.09 

0.06 

0 

0.13 

0.23 

.v5 

- I-

0.'30 0.15 

0.09 I 0.05 

0.06 0.04 

0.24 

--+ 0.0n 

3.01 

0.13 

0.20 

0.12 

_..__ 

0.2s 0.lJ 

0.00 1 0.05 

0.06 0.04 

.- 

0.80 1.20 0.40 1 0.00 I .2O 

0.2n 

3.07 

0.U4 

0.25 

0.0b 

0.01 

0.22 

0. Ob 

0.04 

0.IY 

0. Ob 

0.04 

0.17 

0. Ob 

0.05 

-__- I__ 

18.19 

Z.63 

0 .no 

IU.10 

1 .b4 

065 

3abb 

0.50 

0.21 

- 

2-bb 

0.45 

0.111 

-- 

0.12 

0.23 

-- 

0. I0 

0.00 

O.bY 

0. I4 

0.01 

___- 

0.59 

0.12 

0.- 

O.4b 

0.11 

0.Ob 

?I. 12 

2.VJ 

Jb >n 

14.54 

0.20 

0.40 

0.W 

-- 

0.09 

0.05 

.- 

-- 

0.09 

0.05 

-- 

0.00 

0 -05 

0.10 

0.20 

0.40 

c 

5.32 

0.90 

0.1b 

I .b7 

0.31 

0.14 

x 

0.38 

0.lJ 

0.06 

-- 

0.09 

O.Ob 

-- 

0.00 

0.01 

-- 

0.19 

0.32 

-- 

0.64 

0.30 

0.b0 

5. ab 

0.00 I 1.10 

0.9s 

0.32 

0.09 

0.Ob 

-- -- 0.20 I 0.13 

0.15 0.00 

0.00 
32 

Appendix B.--Continued. 

p =0.90 

L =o.m 

IN?ERVAL= 0.10 YII II INlERV4L= 0.25 VR 

0.40 

3.93 

5.92 I .30 

3-86 0.93 

__-. 

2. n? 

0.14 

. 

5. r5 I. 79 

1.00 0.44 

2.55 0. PI) 

0.44 

0. ne 9.38 

-_ 

0.40 1.90 I .20 

__ 

3.75 0.n 0.2e 

1.20 0.29 0.13 

0.w 0.24 0.12 

z.ra 0.81 0.25 

0.917 0. 2b 0.13 

0.73 0.22 0.11 

1-71 0.4) 0.21 

0.61 0.21 J.11 

0.53 0-19 0.10 

- . 

1.21 0.3q 0.19 

0.51 3.19 0.11 

0.43 0.17 0.10 

__ 

0.93 0.32 0.1 r 

1.43 0.17 0.10 

0.39 0.lb 0.10 

- . __ .- .- ...... 

0.10 0.20 

__--____ 

80.89 18.r~ 

23.02 5.e5 

14.81 3 .n3 

~ ~- 

37.5b 11-12 

1l.?0 3-63 

7. b7 2.50 

__ 

14. ‘a9 5.*8 

5.13 I .9b 

1. LR 1-46 

~ ~ - 

8.48 3.42 

3.17 I .33 

2.4s 1.Ob 

- ._ .- .. 

5-69 2.42 

2.32 1-03 

1.90 0.9b 

__-__ 

0.80 1.20 

0.75 

0.29 

0.24 

0.29 

0.14 

0.12 

0.b4 

O.2b 

0.22 

o.2r 

0.13 

0.11 

0.20 

0.49 

0.22 

0.19 

0.b0 

0. I9 

0.l? 

0.23 

0.12 

0.11 

0.20 

0.11 

0.10 

0.40 

0.3. 

0.17 

0-lb 

0.19 

0.10 

0.10 

I 

M F 0.10 

-- 0.10 32.bO 

17.61 

1 0.33 

0.b0 4. 87 

3.33 

0.13 0.20 0.40 0. 90 

101.3. 

25.20 

I5m.29 

23.?9 

h-21 

3.91 

..?e 

I .37 

O.9b 

0.31 0.15 

0.25 

0. I9 0. J4 

o.zn 

0.23 

0.20 

0.51 

0.21 0.12 

0.19 

__ 

0.4. 

0.20 0.12 

0.19 0.11 

-----I--- 14.13 

3 .e1 

2.60 

3-51 

1 .os 

0.7I 

19.11 

9.49 

3.35 

7.01 

2.11 

1.54 

2.21 

0.?2 

0.57 

10.90 

3.43 

2.60 

r. Jn 

2.53 

2.04 

.. __ 

3.Ib 

1.13 

0.93 
2-84 I 1-01 

0.51 

0.14 0.07 

I 0*20 

. 0.32 

0.0d 

0.04 

33 

... Appendix B.--Continued. 

p = 0.70 

L = 0.00 

lNTERVU= 0.10 VI 

1.20 

__ - 

0.10 0.20 0.40 i 0.8O J.10 1.20 

-----t 63. b5 

6.11 

1.33 

14.83 

2-14 

0.3h 

n .77 

1.33 

3.25 

0.22 

0.05 

9.02 

61.01 

e. u2 

1-34 

0.56 

0. IO J.OJ 

0.2) 

0.05 

0.02 

-- 

0.21 

0.05 

0.02 

0.18 

0.05 

0.01 

0.10 

t.- -- -- 

0.20 

0.05 

0.32 

0.20 

11-13 

4.34 

0.73 

12.49 

1.42 

0.40 

1l.82 

i.nv 

J.40 

0.17 

0.0s 

3.93 

0.15 

0.05 

0.03 

0.11 

0.05 

0.33 

0.40 

. 

0.60 

0 .no 

6.5@ 

1.19 

0.31 

- 

4.47 

O.UlI 

3.2B 

0.16 

0.05 

0.03 

4. 74 

0. ?O 

0.28 

0.14 

0.04 

O.UJ 

INICRVIL' 0.50 VR lNTERV4Li 1.00 YR 

-~ 

o.no 

0.74 

0. I2 

0.OJ 

1- . 

3.10 

0.10 0.20 0.4" I .2O 

~ . 

3-91 

0.50 

U.10 

I .20 

-__ 

0.30 

0. Ob 

0.02 

83.7V 

9.21 

1-35 

- - 

19.19 

4.56 

0. r4 

19.59 

2.28 

0.1). 

-- 

0.00 

0.01 

0.10 

0.20 

11.60 

1.42 

0.26 

2.8b 

J.19 

0.09 

0.64 

0.11 

0.03 

0.21 

0. Ob 

O.OJ 

-- 

I .7P 

0.2? 

-- 

0.07 

0.01 

0.20 

15. b4 

2.32 

0.40 

5. r2 

0.7R 

0.11 

I. ?9 

0.27 

0.07 

0.49 

0.09 

0.04 

0.23 

0.05 

0.03 

-- 

0.99 

0.15 

0.40 0.b0 

a 

(1.66 

L.27 

U. 31 

3.5n 

0.54 

0.15 

1.27 

0.21 

0.07 

0.40 

0.08 

0.04 

0.20 

0.03 

0.01 

-_ 

I-b? 

d.34 

-- 

0.01 

0.04 

0.60 

5.9b 

O.V5 

0. L9 

2.55 

0.43 

0.14 

0. *P 

0.18 

0.07 

0.35 

0.00 

0.0. 

0.18 

0.05 

0.02 

o.no 
34 

- 

0.80 

-- 

0.m 

0.05 

I .PO 

-- 

0.09 

0.04 

0.40 

0.60 

0.80 

2.92 

0.59 

__ 

-- 

1.66 

0.41 

-- 

1.42 

0.41 

Appendix B.--Continued. 

p = 0.70 

L r0.10 

INTE%VAL* 0.10 VR INTERVAL- 0.25 TR 

16-62 

2.4R 0.55 

0.50 0.1. 

0.10 0.20 0.40 1 0.80 1.20 

15.73 

2.45 

0.50 

9.11 

I .Y2 

0.14 

4.5n 

O.dl 

0.23 

6I.35 

9.94 

1.63 

-- 

31.47 

4.89 

1.00 

-- 

12.54 

2-19 

0.54 

1. JP 

I.3b 

0.42 

3.13 0.59 

0.54 0.lJ 

Oat4 0.05 

2.29 0.51 

0.62 0.11 

0.12 0. 05 

.___-__ 

I -41 O.J9 

0.29 0.10 

0.10 0.05 

- ___ 

1.01 0.32 

0.21 3.09 

0.09 0.05 

-_ __ 

o.rn 0.27 

0.19 J.O1 

0.09 1 0.05 

___ 

0.23 

O.J6 

0.03 

0.21 

0.06 

0.03 

o.tn 

0.04 

0.33 

0.61 0.25 

0.05 Od3 

0.4I 0.19 

0.04 

0.15 

0.55 

0.05 0.04 

71.07 

11-25 

0.40 2.20 

0.5n 

0. to' 

0.20 

__- 

0.40 

--- 

0.b0 

1-55 

0.35 

0.83 

0.23 

' 3.QL 

0.59 0.23 

0.20 O.U9 

- 

2.1s 

0.46 0.90 

0.19 0.09 

2-06 

0.58 

0.19 

-_ 

2.53 

0.45 

0.16 

0. lo 

u.05 

0.04 

T. a0 

0.60 I 1.J8 

0.42 

5. 03 

0.00 I 1.01 

0.3~ 

o.no 

INTtRVALI 0.50 TR INltYVAL- 1.00 VR 

I__- 

0.20 

20.78 

2-60 

0.54 

__- 

0.40 

__ -_ 

4.15 

0.58 

0.14 

0.80 J.20 

0. I9 

0.14 

0.05 

I .PO 

.- 

0.11 

a. O? 

0.03 

-- 

1.2) 

0.53 

12.11 

I .a3 

0.15 

1.04 

0.45 

0.12 

0.08 

0.12 

0.05 

0.29 

3. Ob 

0.01 

-- 

2 -05 

0.37 

_I- 

-- 

1-13 

0.25 

6-00 

0.w 

0.2. 

1.90 

0.31 

0.10 

0.52 

0.13 

0.05 

0.2% 

0. Ob 

0.04 

-- 

0.40 

0.11 

3.80 

0.62 

0.20 

. 

.?.?I 

0.49 

0.19' 

-- 

1-10 

0.25 

0.09 

1.0s 

J.21 

0.10 

0.4) 

0.10 

0.05 

-__ 

0.JI 

0.09 

0.0s 

0.22 

0.06 

0.04 

0.20 

0.06 

0.04 

-- 

0.80 

0.22 

-- 

0.64 

0.21 

-- 

0.32 

0.11 

-- 

0.m 

0.11 I- 0.13 0.w O.O? 0.08 
-- I 

0.40 0.80 

3.08 0.?4 

0.82 0.19 

0.33 0.10 

____- 

2.Bb 3.bJ 

O.CJ 0.17 

0.28 3.10 

1.?7 0.40 

0.43 0.Ib 

0.22 0.09 

I -2h 0.40 

0.34 0.13 

U.20 0.09 

.- 

0.9? 0.34 

0.20 0.12 

0.19 0.09 

1.20 

0.29 

0.09 

0. 06 

0.2b 

0 .OY 

0. Ob 

0.22 

O.Od 

0.06 

0.20 

0.00 

0.0b 

- 

0.18 

0.08 

O.Jh 

- 

0.10 

- 

d3.02 

14.V3 

4-bl 

_- 

30.9s 

I. 36 

2.50 

15.31 

J.26 

1.33 

8.78 

2. 05 

O.Y8 

-, 

5. YO 

I. 53 

0.34 

0.20 

19-42 

J.68 

I .a5 

11.51 

2.30 

0.06 

__ 

5.67 

I -2b 

0.05 

__ 

3 US4 

0.87 

0.45 

2 .52 

U.b9 

3s.') 

- 

_ 

3. b? 

0.80 

0.31 

____ 

0.70 

0.19 

0. IO 

2.b8 

O.bd 

0.27 

I .6? 

0.43 

0.22 

0.59 

0.17 

0. IO 

0.46 

0.14 

3. 00 

-- 

3b.82 

7.27 

2.49 

..-- - 

I4.bV 

3.22 

I. 32 

8.31 

2.02 

3.V? 

s.58 

1.50 

0.03 

__ ~ 

10.90 

2.27 

0.85 

5.37 

I .24 

0.s5 

3-35 

0.8b 

0.44 

2.31) 

0.67 

0.40 

__- 

1.19 

0.34 

0.20 

0.92 

0.29 

0.19 

0.3? 

0.13 

0.09 

0.32 

0.12 

0.01 

___ - 

0.40 

-- 

1.l.l 

0.37 

0.80 

-- 

0. Z? 

0.13 

0.20 

0.40 

0.b0 

0.80 

4e. 39 

I. 74 

2.54 

~ 

19.38 

1-44 

I.Jb 

1l.02 

2.17 

1.01 

- 

I- b4 

1-63 

O.Y? 

. - - 

35 

x Appendix B.--Continued. 

p =O.tO 

L = 0.30 

-I 

0. id 

INTERVIL= 0.10 VU INlEUVLLI 0.25 VI( 1 

0. IO 

__ 

0. LO 

1.20 

0.27 

O.OV 

0. 06 

0.85 

O.JJ 

0.06 

0.20 

, 0.21 

0.J8 

0. $0 

.. - 

0.10 

0.08 

J.Jb 

_- 

0.17 

0.07 

0.36 

0.40 

___ 

0. bo 

___ 

0.80 

INfellVIL- 1.00 Ve 

__ y; 0.20 

103.21 

____ 

I .20 

-- 

0.16 

0.08 

___ 

-- 

0.14 

0.00 

1 

0.10 

0. b0 J.90 1.20 0.10 

24.19 

3.nr 

1.27 

4.05 

O.LI6 

0.34 

0.93 

0.20 

0.11 

0.37 

0.10 

-t- 0.07 

14-35 

-I-- 2. 42 

a.07 

3.55 

0.46 

u .28 

0.00 

0.18 

0.10 

0.34 

0.09 

0.O? 

-- 

v.72 

2.73 

0.23 

---t--- 7.10 

1.33 

0.5r 

2.23 

O.ab 

O.2J 

O.b2 

Oalb 

0. IO 

U.ZY 

0.09 

0.01 

-- 

4. 39 

I.bn 

-- 

0.13 

0.09 

0.40 

4.4b 

0.92 

0.b6 

1-59 

0.31 

0.21 

0.51 

0.14 

0.10 

0.2b 

0.09 

0.O? 

_- 

2-83 

1.13 

0.63 

3.1'4 

0.73 

0.b2 

I .24 

0.31 

0.20 

0.44 

0. I3 

0.10 

0.23 

0.09 

0.07 

-- 

0.20 

0.15 

0.80 0.44 

I 

0.26 
36 

- - - 

0.20 

-- 

37-31 

10.20 

6.56 

-- 

22.03 

b-37 

be30 

10-97 

3.48 

2.55 

-. 

be92 

Z.bO 

1-38 

___ 

0.40 

- .- 

7.6b 

2-26 

1.59 

5..8 

1-74 

1.28 

___ 

3.46 

I .ZO 

0.91 

- - 

2-19 

O.Y4 

0.79 

___ 

Appendix B.--Continued. 

p =o.m 

LxO.70 

INTEUVAL- 0.10 VP 

___ 

0.80 

1-01 

0.46 

0. 30 

- 

0.91 

0.41 

0-35 

__ 

0.20 

____ 

28.11 

9.36 

6.20 

_____ - 

16.05 

5.n~ 

4.0. 

_.. 

8.21 

3.14 

2.37 

. ~ 

5-13 

2.14 

1.72 

.- ___ 

3.64 

1-65 

1.39 

-. - 

I .20 

0.42 

0.21 

O.1V 

0.10 0.20 

1 20. 09 

23.96 

{ 36.21 1 ~ 12.40 

1 0.20 I 18.72 

0.40 

5.bl 

2.05 

I .4v 

5.91 

2.09 

1.51 

I 2b. 51 

0.10 3n.75 

2b.21 

-I-- 

29.b3 

9.53 

6.27 

17.57 

5.92 

bad9 

4.11 

+-I-- 

L.5) 

1.IY 

0.38 

0.25 

0.18 

4-3b 

1 .*0 

1 .ZO 

____ 

2. 72 

1.09 

0.m 

1.93 

U.Rb 

0.71 

1.49 

0.70 

O.bZ 

t. . - e-- .. 

2.46 

1.07 

O.Rb 

. -. __ 

I .e2 

0.82 

0.70 

0.70 

0. 3b 

0.30 

- 

0.57 

0.30 

0.27 

0.32 

o.in 

0117 

8.68 

3.21 

2.40 

0.28 

0.17 

*.IO 

5. 43 

2.19 

1 .75 

-___ 

3.87 

1.69 

1.43 

1 ..O 

0.68 

0.60 

.- ~ 

0.bn 

0.2r 

0.25 

.___. 

0.25 

0.16 

0.15 

- 

INTER(VIL= 0.40 ru . ._ . . .. 

?\; - 

0.10 

0.10 0. 80 1.20 0.40 0.80 1 1.20 

1sr.w 

b1.35 

25.20 

1.45 

0 -52 

0.42 

0. $6 

0.25 

0.22 

-- 

3.33 

2.07 

-__ 

-- 

2 -02 

1.70 

__I 

-- 

I .nn 

I .32 

..___ 

__ 

1.54 

1.15 

I 

O.O1 I 14-31 

20.41 

13.12 

29.84 

9. Ob 

be30 

0 

0.88 O.b2 

0.5). , 0.30 

-- 

0.bb O.b2 

0.53 1 0.37 

I .Zb 

0.b7 

0.39 

0.97 

0.40 

0.3b 

-__ 

o.no 

0.35 

0.31 

0.53 

U.23 

0.21 

__ 

0.4b 

0.22 

0.20 

0.41 

0.21 

0.1Y 

0.20 

0. bO 

17.07 

5. bb 

be31 

0. bo 

11.59 

4.19 

3.39 

0.69 

0.33 

0.30 

0.30 

0.20 

0.IV 

b.97 

I .ne 

1.55' 

1 .Y4 

0.79 

O.b8 

0. 00 

0.53 1 0.39 
__ 

52.Y3 

7.34 

1.23 

I5.bh 

2.29 

0.43 

0.05 

0.17 

0. Ob 

-__ 

0.66 

0.15 

0. Ob 

0.54 

0.13 

0. $6 

O.4b 

0.13 

3.01 

0.30 

0.00 

0.04 

0.30 

0.00 

0.05 

-__--___ 

0.21 

0.m 

0.05 

0.24 

0.08 

0.05 

+- I 

0.62 

0.14 

O.Ob 

J.29 

0.00 

0.04 

21.10 

3.24 

O.B7 

11.93 

2.04 

0.52 

. 

1.71 

t -25 

0.29 

4.Ul 

0.01 

0.24 

8. 00 

1.52 

O..R 

- 

3.41 

0.68 

0.23 

37 

Appendix B.--Continued. 

p =0.50 

L *o.oo 

IJ1.20 

____ 

0.40 

4.99 

0 .0O 

0.17 

1- -. 

0. IO 

_- 

0.20 

0.40 

5.27 

0.81 

0.17 

P 

0.19 0.09 

0.06 0.04 

0.34 

0.17 0.09 

0.0b 0.04 

14.w 

2.2s 

0.42 

3.65 

0.6'2 

0.14 

50. I I 

7.24 

1-21 

0.20 

r.29 

1.23 

0.29 

4.5b 

0.85 

0.24 

2.27 

0.43 

0.12 

19.96 

3. 20 

O-b? 

2.40 

O.4J 

0.12 

1-71 

0. J4 

0.12 

0.40 0.40 

-~ 

0.00 

-__ 

0.80 

11.28 

2.UI 

0.52 

I .6l 

0.34 

0.12 

____ 

1.24 

0.29 

0.12 

0.51 

0.06 

0.43 

0.12 

0.01 0.05 

0.00 

7.Sb 

1.50 

0.47 

3.22 

0.67 

0.23 

1-12 

0.29 

0.12 

0. 80 

- 

INTEUVALI 0.50 VU lNlERvAL- 1.00 VR 

0.10 

. 

0.20 0.10 

9-06 0. J4 

Os4b 

o.in 0.09 

O.Ob 0.04 

0.20 0.40 I .20 

33.1 1 

3.85 

O.b? 

____ 

19-61 

2.40 

*.43 

b.01 

0.85 

0.17 

____ 

4.83 

0.66 

0.15 

-- 

0.23 

0.01 

9.b7 

1-12 

0.29 

3.02 

0.4b 

0.13 

-- 

0.21 

0.07 , 

-- 

0.12 

0.0b 

b.05 

0.91 

0 .2S 

2-15 

0.M 

0.12 

0.bO -- 1.11 I ::47 

0.21 1 0.13 

I 0.08 

I.bl 

0.49 

6-31 

0.12 

0 -24 

I .b7 

0.31 

0.12 

-- 

0. IP 

0.w 

-- 

0.11 :::: I :::: 0.07 0.80 0.13 0.09 

0.07 0.06 
38 

1-05 

0.23 

O.OV 

.-__. 

0.90 

0.21 

0.09 

0.60 

0.18 

0.09 

_.-__ 

0.56 

0.Ib 

0.09 

- 

0.48 

0.15 

0.10 

0.41 

0. I I 

0.Vb 

_____ 

0.38 

0.11 

0.06 

_- 

, 0.32 

0.10 

5.06 

0.28 

0.10 

0.07 

0.25 

O.lU 

0.07 

0.8b 

ll.d7 

2.02 

0.7b 

._ 

0.39 

4 .e2 

O.VI 

0.37 

Appendix B.--Continued. 

p = 0.50 

L=O.IO 

I INTtRVAL- 0.10 YR INTERVAL= 0.2s YR 

____ 

I .20 

. 

0.44 

0.11 

0.0b 

1 

0.10 

_~__ 

0.10 

125.74 

18.54 

1-58 

_ . 

0.80 

-. 

1.11 

0.24 

0.09 

0.40 

I__._ 

0.80 1 I.2O 

5.55 

1.00 

0.2? 

4.05 

0.77 

0.23 

--___ 

2.53 

0.53 

0.1’4 

58.81 

9. I3 

1.96 

17.41 

2 .85 

0.68 

4.29 

0.70 

0.2J 

0.95 

0.21 

0.01 

0.40 

0. I I 

0.06 

0.20 

23.4b 

4-05 

1.07 

0.58 

1-56 

O.*b 

2.b0 

9.5. 

0.19 

0.73 

0.18 

0.09 

a. 34 

0.1U 

0.07 

i -+--. . -+ 1.79 

0.42 

0.18 

13.28 

2.55 

0.02 

5.35 

1.08 

0.38 

1.90 

0.43 

0.18 

0. bo 

0.16 

0.09 

0. JO 

0.10 

0.07 

1-30 

0.3.5 

0.10 

n.*i 

I.YO 

0. I4 

3.83 

0.85 

0.36 

__- 

1.41 

O.J7 

0. in 

0.27 

0.10 

0.07 

0.51 

0.15 

0.10 

0.80 

INTLRVAL= 0.50 YR INTERVAL- 1.00 VR 

0. 40 0.80 1.20 5.20 1.20 

1.41 

0.25 

0.09 

I .20 

0.23 

0.09 

0.93 

0.19 

0.09 

0.17 

?.I8 

0.10 

0.56 

0.12 

0.06 

0.51 

0.12 

0. Ob 

-- 

0.4* 

0.11 

0.07 

0.39 

0.11 

0.91 

7.36 

1.07 

0.27 

5.39 

0.02 

0.23 

~- 

3.38 

0.57 

0.263 

2.41 

0.e5 

0.1v 

-- 

0.17 

0.01 

__ 

-- 

0.16 

0.00 

-- 

O.lb 

0. 08 

-- 

0.1b 

0.10 

1 

0.39 

.e7 

I 

0.19 

0.8b 

0.17 

0.10 

0.35 

0.11 

3.08 

0.80 
INTERVAL. 

_._____ 

0.20 

__ 

37.01 

r.44 

2.6a 

21 .93 

b.61 

I .79 

IO.I2 

2.55 

1-16 

- 

n.77 

I .?? 

0.93 

b.81 

I .39 

0.03 

Om25 VR 

-__ 

0.40 

.__ - 

r.39 

1.65 

0.69 

5-41 

I .2? 

0.58 

3.38 

0.0.9 

0.46 

2.41 

0.89 

0.41 

__ 

I .ab 

0.59 

0.3v 

-___ 

1-41 

0.39 

0.22 

0.56 

0.19 

0.13 

39 

Appendix B.--Continued. 

p = 0.50 

L = 0.30 

INTERVAL* 0.10 VR 

0.80 

___ 

1.20 

0.52 

0.18 

0.13 

0.13 

119.57 

2% 71 

9.52 

6% 98 

14.86 

5. I? 

____ 

27.94 

8. 5u 

2.74 

0.20 

-_ 

34.99 

1.33 

2-18 

20.73 

b.58 

I .77 

1-33 

0.38 

5.11 

0.sr 

1.2s 

0.21 

0.4? 

0.1 

5.13 

7 

, 

I .20 0.51 

0.35 0.18 

0.21 0.13 

0.3093 Fz . - 

0.16 

0.13 

0.65 

0. I9 

1.13 

0.34 

0.20 

74.02 

29.58 

16. 77 

2.04 

IO -22 

2.50 

1.15 

3.19 

0.n7 

0. 46 

0.81 

0.29 

0.19 

0.40 

0.16 

0.13 

15-81 

b. 08 

2.02 

6.38, 

1.73 

0 a92 

0.ll 

O;b8 0.26 

0. I9 

.~ 

0.60 t 0.w 0.24 

0.39 0. IV 

._ 

0.35 

0.15 

0.13 

0.32 

0.15 

0.13 

10.82 

3.03 

l.?2 

4 .s3 

1.36 

0.82 

I I*TERVAL- 0.50 VR 

___ 

I .20 

____ 

0.12 

0.20 

0.14 

INTEUVALE 1.00 VR I -_-__ 

u F 3.14 

-- 0.10 40.88 

10.49 

0.a0 0.110 1.20 

-- -- -- 2. JI 0.5) 0.J0 

0.?Y 0.27 0.10 

- 

-- -- -- 1.80 0.52 0.29 

0.67 0.26 O.lO 

o.no 

__ __ 

1 .80 

0.42 

0.23 

198. 41 

93.05 I a54 

0. 38 

0.22 

0.68 

0.19 

0.14 

-- 

6.43 

5.82 2.02 

-- 

9.24 

37.34 

21.27 

14. 38 

0.80 3.33 

1.32 

I .20 

0.32 

0.21 

0.99 

0.2Y 

0.21 

0.50 

0.18 

0.14 

0.50 

0.18 

0.1. 

0.0s 

0.27 

0.21 

0.48 

0.111 

0.15 

-- 

2. IO 

I -05 

.___ 

Y 

Y 
40 

___ 

4 F 

0.10 

.. .. 

0.10 

-. 

244. b9 

70.~1 

49.18 

~ 

19.8? 

12.96 

4.37 I .OO 

3-13 0.82 

- 

12.37 3.35 0.89 

Appendix B.--Continued. 

p = 0.50 

L = 0.70 

I: 

5.10 

0.20 0.40 o.no 1 .eo 0. IO 

57.30 

19-11 

12.75 

2.18 

0.9b 

0.79 

O.db 

0.44 

0.39 

260.20 

30-?b 

49-89 

__ __ 

lPl.9H 

39.75 

25.92 

__- 

48.n7 

17.50 

12.52 

33. Yb 

12.06 

8.37 

lb.76 

be52 

4.a9 

8 -38 

3.26 

2.44 

-- 

5.23 

2.22 

I .78 

1-86 

0. Hb 

0.72 

. -_ 

I .43 

0.71 

0.63 

0.76 

0.41 

0.38 

___. 

, O.6a 

0.38 

0-35 

10.47 

4.44 

3.5b 

3.72 

1.71 

1-05 

1-17 

0-62 

0.57 

0.58 

0.35 

0.33 

27.76 

IU.tI7 

8. 39 

0. b0 

7.44 

3.43 

2.89 

2.06 

1.42 

I .Z5 

0.99 

0.56 

0-52 

0.52 

0.33 

0.32 

18.bV 

7. v7 

6.53 

0.80 

INTERVAL 0.50 YR 

7-- 0.20 0. b0 0.80 1.20 

70.72 

21 -70 

IJ.7a 

15.90 

4.82 

3-36 

3.10 

1-12 

0.90 

1.25 

5.53 

0.47 

-- 

1.86 

1.33 

-- 

0.97 

0.74 

46-90 

13.57 

9.03 

11.70 

3.72 

2.70 

2-06 

1.01 

0.83 

1.15 

0.51 

0.45 

-- 

0.95 

0.77 

-- -- 20.34 5.78 I i 21.48 34.86 11.71 3.b7 

___.. 

17-64 

I--- +- L-- 

23.40 

7.43 

5.3V 

7.40 

2-37 

2.00 

2.08 

0.85 

0.73 

0.99 

0.47 

0.43 

11.56 -- 1 ::I6 

_- 

1.52 

1.IB. 

P--- t - ---+ 14.79 

5-14 

4.00 

5.32 

2.01 

1.bb 

1-72 

0.7b 

0.b8 

0.88 

0.45 

0.42 

-- I 0.60 I 19.22 

-- 

0.94 

0. 82 I;:-- I *. 88 

IO. 62 

10.65 

4 -03, 

3. 31 

4.16 

1-70 

1-17 

0.81 

0.43 

0.41 

1-49 

0-70 

0.64 

I 
I e20 

0.870 

o.am 

0.910 

U.b44 

0.801 

0.841 

-- 

0.597 

J-IIb 

0.764 

-- 

0.555 

3.b4b 

0.bbJ 

0.518 

0.m) 

0.597 

L - 0.10 0.20 

O.OVO 0.112 

3.163 0.2vn 

0.2bh 5.429 

0.01)6 0.IOb 

O.I+Y 0.213 

0.246 0.389 

0.OIB 0.150 

*.I25 0.231 

O.Lb9 0.297 

0.012 0.137 

J.191 0.198 

0.132 O.23b 

0.Obh 0.126 

3.092 3.172 

5.101 0.194 

0.10 - 

O.4Q 

0.314 

0.501 

0.676 

0.300 

O.r(b2 

0.5'44 

0.275 

0.396 

0.412 

0.252 

0.344 

0.388 

0.232 

0.301 

0.321 

I 

41 

APPENDIX C 

Proportion of fish initially released with two tags which are recaptured 

with at least one tag remaining during experiments of 1-yr (upper figures), 

2-yr (middle figures), or 4-yr duration (lower figures). 

p" 1.00 

1 I i" 

r- 0.2) 

~ 

L = 0.00 

0.20 0.40 o.no I .20 

I 

0.173 0.315 0.521 0.b72 

0.301 0.506 0.742 0.854 

'0.466 0.692 0.865 0.918 

O.HO 

0.526 

3.731 

J.115t 

0 m 504 

O.bO7 

1 

*.775 

O.OHh 

0.150 

0.233 

0.20 

0.465 

O.bO3 

5.655 

0.n19 

0.40 0.126 

0.012 io 1 0.108 

3.134 

3.430 

0.534 

0.lb5 

5.557 

0. b4P 

O-bbb 

0.519 

0.589 

O.hOO 

.__I 

0.366 

3.0'43 

o.ion 

O.JV8 

9.4111 

J.4Vb 

0.80 

L = 0.30 

0.20 0. 40 0.00 

-- 

5.517 

0.70b 

0.1VO 

I .20 

0.308 

0.4?4 

0.600 

0.485 I 0.b23 

0.615 0.136 

Osb'50 0.155 

0.466 0.600 

0.519 O.b9Y 

0.b07 0.714 

3.431 0.559 

0.517 0.634 

0.531. 0.643 

0.400 0.521 

0.160 OnS7Y 

0.476 0.58s 

0.373 0.40d 

0.b23 0.512 

0.429 0.S36 

0.226 

I 0.49b 

0.b60 

0.125 

3.635 

0.71b 

0.810 

0.095 

0. I40 

0.1'45 

0.161 0.795 

0.258 0.439 

0.340 0.534 

0.I.I 0.210 i O.PI9 0.376 

0.2b1 0.b34 

, 

0.20 

0. +sa 

0 -581 

0- 620 

0.5dY 

O.bVb 

0.711 

0.011 

0.40 0.119 

0.150 

---+--- 0.135 0.24s 

a.189 0.330 

0.217 0.3b2 

0.824 0.229 t 0.1b5 0.291 

0.181 0.310 

Y.423 

0.517 

0.540 

0.548 

O.b3O 

Oeb4J 

0.071 

0. I32 

0.120 

0.b0 

0.593 

O.Lb4 

0.478 

0.512 

0.514 

0.582 

0.0bS 

0.099 

I I I I I 

".I..-.... . - 
42 

Appendix C.--Continued. 

p =0.90 

.. ................................. ... ......... 

L = 0.00 

T-- 

0.40 

0+3!rl 

0.50: 

O.t.4', 

c. a+c 

0.h5 i 

~-. .... L 1~. .>'O"S I 0.ISI 

....... 

...... .+. ........ .! - 

... >. .... I 

........... - . . ~ 

....... I i .......... -. ............. ..... r .--- I. - 0.30 

L - 1.70 

It. 3t.9 

0. IF9 

0.41,s 

~~. 

0.941 

0.318 

0.3.9 

0.223 

0.281 

O.ZVY 

c 

U.584 

O..b'i 

J.454 

B.LP.1 

0.275 

O.Z*8 

0.201 

0.24? 

0.256 

a.131 

0.IRZ 

0.208 

__ 

0.121 

0.159 

0.176 

'J.3511 

0.404 

0.410 

O+Ob3 

5.085 

5.095 

L 
0.40 

__ 

0.238 

0.323 

C.3bO . 

0.229 

0.303 

0.110 

I__ 

0.110 

9.405 

0.503 

0.528 

0.3YJ 

0.475 

0.495 

0.20 

___ 

0.140 

0.235 

0.318 

0.139 

0.717 

0.280 

0.128 

0.105 

0.222 

Osll? 

J.161 

0.182 

- 

0.108 

0.141 

0.15J 

0.40 

0.207 

C.400 

0.496 

0.255 

0.311 

0.443 

0.214 

0.321 

0.363 

0.216 

0.281 

0.306 

0.199 

0.249 

0.Zb4 

- 

0.IU 

3.068 

0.100 

0.121 

0.065 

4.093 

0.109 

___. 

0.060 

0.081 

0.090 

0.055 

0.071 

0.076 

0.051 

O.06J 

3.066 

0.20 

_- 

0.130 

0.186 

0.217 

-. 

0.124 

0.173 

Q.197 

0.114 

0.151 

0.165 

0.105 

0.133 

0.142 

0.098 

0.119 

01124 

k: 

J.2O 

0.40 

O.b0 

o.ea 

0.076 

0. I 81 

'.IL8 0.073

3.118 

0. I59 

0.067 

0.100 

0.124 

0.061 

0.086 

0.100 

0.056 

0.015 

0.083 

0.211 

0.267 

0.2M3 

0.195 

0.237 

0.247 

0.1111 

0.213 

O.Pl9 

0.362 

0.426 

0.430. 

0.136 

0.386 

0.391 

0.314 

0.352 

a.356 

- 

43 

Appendix C.--Continued. 

p * 0.70 

1 - 0.00 L - 0.10 ___ 0. IO 0.20 0.40 0.80 I .to 0.10 0.20 1.20 

0.082 

0.150 

0.251 

0. I57 

0.274 

. 0.424 

O.28t 

0.160 

0.629 

___- 

0.274 

0.424 

0.552 

--__ 

0.251 

0.363 

0.*37 

____ 

0.230 

0.315 

0.357 

O.48U 

0.615 

0.787 

0.460 

0.629 

0.719 

0.421 

0.552 

0.602 

0.192 

0.480 

O.5llJ 

0.61 I 

0.778 

0.815 

o.sm 

0.731 

0.?77 

0.945 

0. bS5 

0.681 

0.5Ob 

0.590 

0.bOb 

0.081 

0.143 

0.2ZB 

__- 

0.077 

J.lJl 

0.195 

01070 

O.llO 

0.14b 

0. 15.4 

0.262 

0.389 

_.-I 

0. I47 

0.240 

0. 33b 

0.IJ4 

0.2U4 

0.258 

9.10 

- 

0.20 

- __ 

0.ao 

O.bO 

0.10 

0.20 

-_ 

0.40 

0.079 

0.117 

0.212 

- 

0.072 

0.1>5 

0.151 

0 -0 65 

0.098 

0.122 

0. I50 

0.251 

0.161 

0.137 

0.212 

0.276 

0. IPS 

0. In2 

0.2IB 

0.0bb 

0.094 

0.115 

0. I23 

0.17s 

O.2Ob 

0.498 

0.576 

0.590 

- 

0.4bb 

0.924 

0.531 

0.b0 

J.060 

0.099 

0.OVR 

9.115 

0- 157 

0. 179 

0.212 

0.276 

0.101 

0.363 

0.437 

0.454 

0.0'39 

J.Odl 

0.013 

O.lI1 

0.152 

0.170 

.- 

0.00 

__ 

J.80 

L - 0.30 1 - 0.70 Y 

z 0. IO 

- 

0.20 

- 

0.40 

I- \F I 0.10 0.80 I .20 I .20 

0.515 

3.705 

0.739 

0.551 

0.667 

d.b9J 

___- 

0.514 

0.600 

0.617 

0.449 

U.bO0 

0.b65 

-- 

0.431 

0.563 

0.612 

0.398 

0.498 

0.527 

0.509 

0.979 

0. 500 

0.471 

0.528 

0.514 

0.441 

0.484 

J.488 

0.3b9 

0.444 

O.4b2 

0.343 

U.400 

0.bll 

0.479 

0.545 

, 0.555 

0.448 

0.494 

0.504 

0.60 

- 

0.80 

- 

0.413 

0.441 

I 

0.449 
44 

Appendix C.--Continued. 

p = 0.50 

L - 0.00 1 - 0.10 

. 

0.40 

0.229 

0. JIB 

0.472 

_____ 

0.20 

0.126 

0.212 

0.311 

0.120 

0.1'45 

3.210 

0.109 

0. lb5 

0.208 

0. IO 0.20 

__ 

0.130 

0.226 

.0.3.9 

I .20 

.--I 

0.504 

Dab41 

0.b99 

-.- 

0.484 

0.b04 

0.b41 

O.4.Y 

0.5.0 

0.5b2 

0.417 

0.4I)b 

0.500 

0.189 

0.442 

0.450 

3.065 

0.113 

O.i?L, 

0.124 

0.ZOb 

0.209 

0.11v 

0.49s 

0.553 

0. a59 

o.oa5 

0.1 10 

0.liJ 

0.175 

0.22) 

0.201 

0.295 

0.334 

0.140 

0.456 

0.470 

_-_ 

0.314 

0. J97 

0.401 

0.054 

0.081 

0. ID1 

- -_ 

0.044 

0.070 

0.08 I 

_-- - 

O.05t 

0.011 

O.OY3 

0.100 

0.142 

0.lb7 

0.111b 

0.249 

0.216 

___. - 

0.110 

o..?ie 

0.235 

0.048 

0.0bb 

0.0)b 

0.w2 

0.124 

0.119 

0.292 

0.14) 

a.3so 1. L - 0.30 L - 0.10 

0.20 

I 

I 

i0.00 

.- __ 

0.40 

-. - 

0.lU 

_I ._ 

0.012 

0.1 01 

a.Ib3 

- 

0.099 

0.091 

0.124 

- .. ___._ 

0.20 

0.111 

0.197 

0.249 

0. b0 

I_ 

0.215 

0.118 

c. 190 

0.80 I .PO O.iO 

- 

J.054 

0.019 

0.092 

0.20 0.90 1.20 

0.3bZ 

u.479 

0.529 

0. bb4 

0.565 

0.591 

0.102 

0.145 

0.167 

0.121 

O.JV.3 

0..12 

0.415 

0.47u 

0, 489 

0.19s 

0.252 

0.?79 

0.101 

0.23b 

0.256 

O.11Z 

0.112 

0.219 

.. 

0.103 

0.1411 

0. I 15 

0,094 

0.128 

n. 144 

0.097 

0.Il2 

0.122 

__- 

0.200 

0.295 

0.350 

0.348 

0.450 

0.487 

0.447 

0.53s 

0.95s 

O.OSI 

0.012 

0.084 

0.099 

0.135 

0.152 

-___ 

0.090 

O.IlU 

0.129 

D.JO9 

0.372 

0. 391 

0.054 

0.OdO 

0.098 

0. I09 

0.256 

0. 299 

3. I22 

0.199 

0.421 

O.lb7 

0.209 

0.221 

0.291 

0.135 

0.344, 

0.2b7 

0. Job 

0.109 

0.410 

0.483 

0.495 

o.38n 

0.439 

Oebbb 

0.311 

0.b17 

0.422 

0.351 

0.3~3 

0.106 

0.40 

0.0.9 

O.Ob9 

0.019 

0.II4 

0.225 

0.24b 

~ . __. - 

O-lbl 

0.199 

0.211 

.. 

0.298 

0.351 

0.310 

1.043 

0.055 

0.059 

0.093 

0.104 

0.110 

0.IS4 

0.l8b 

O.IY3 

0. b0 

3.277 

0.322 

0.330 

0.040 

0.OI9 

0.052 

0.017 

0. w3 

0.091 

0.143 

0. I b8 

0.1 ?I 

0.250 

0.219 

0.291 

0.129 

0.354 

0.350 

0.00