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data, assuming that a relationship exists between fishing effort and the percent-
age of crabs harvested (Table 6).

TABLE 6. Number of Boats Per Season Landing Dungeness Crabs at Ports
Between Cape Mendocino and Oregon Border.

Mean number of months

1966-67 198

1967-68 213

1968-69 244 3.3

1969-70 264 3.4

1970-71 257 2.7

1971-72 189 2.8

Mortality Rates

In the calculation of weekly instantaneous mortality rates during the fishing
season, the following equation was used. (Calculations by Eugene Witeck).
In Y = a + b X
Where:

In Y = natural log of weekly mean catch in pounds per trap (Table 7).

a — intercept of line on Y axis.
— b= monthly instantaneous total mortality rate (Z)
X = week number of fishing season.

TABLE 7. Weekly Mean Catch (Lb and Kg) Per Trap of Northern California Dungeness
Crabs Used to Calculate Weekly Instantaneous Mortality Rates.

1966-67 1967-68 1968-69 1969-70 1970-71 1971-72

Week number Lb/ Kg/ Lb/ Kg/ Lb/ Kg/ Lb/ Kg/ Lb/ Kg/ Lb/ Kg/

of season trap trap trap trap trap trap trap trap trap trap trap trap

1 19.6 8.9 19.0 8.6 16.8 7.6 22.4 10.2 20.3 9.2 15.9 7.2

2 11.6 5.3 20.9 9.5 19.2 8.7 20.3 9.2 14.9 6.8 3.8 1.7

3 16.6 7.5 18.8 8.5 - 15.2 6.9 14.1 6.4 6.4 2.9

4 12.8 5.8 - - 25.7 11.7 17.9 8.1 8.0 3.6

5 9.4 4.3 17.4 7.9 15.8 7.2 12.1 5.5 11.6 5.3 5.4 2.4

6 14.9 6.8 14.9 6.8 10.9 4.9 10.2 4.6 7.0 3.2

7 11.5 5.2 19.0 8.6 8.7 3.9 9.6 4.4 - -

8 - 11.2 5.1 16.4 7.4 7.6 3.4 - -

9 9.3 4.2 7.5 3.4 8.8 4.0 10.0 4.5 - - 2.6 1.2

10 13.1 5.9 7.7 3.5 7.5 3.4 10.9 4.9 - - 0.9 0.4

11 18.4 8.4 10.3 4.7 10.3 4.7 5.7 2.6

12 17.9 8.1 8.3 3.8 14.1 6.4 4.8 2.2 10.0 4.5

13 11.4 5.2 7.3 3.3 5.3 2.4 10.3 4.7

14 12.7 5.8 8.7 3.9 - - 3.3 1.5

15 5.3 2.4 3.2 1.4 2.3 1.0

16 6.2 2.8 3.1 1.4 6.0 2.7

17 6.2 2.8 10.0 4.5

DUNCENESS CRAB CPUE

197

18 2.0 0.9 10.8 4.9

19 - - 4.5 2.0

20 -

21 5.1 2.3

22 5.5 2.5

23 7.0 3.2 10.0 4.5

25 4.8 2.2

26 8.6 3.9

27 4.2 1.9

Instantaneous rates of fishing mortality (F) and natural mortality (M) were
calculated from the following (Notation from Ricker 1975).
u= L/N
Where:

u = annual expectation of death from fishery (rate of exploitation from

Table 5).
L = season landings in pounds (Table 4).
N = population in pounds at start of season (Table 5).
and:

A = 1 - e - z
Z/A = F/u
Thus: F = uZ/A
Since: Z = F + M
Then: M = Z - F

Where: Z = instantaneous total mortality rate.
A = total annual expectation of death.
F = instantaneous fishing mortality rate.
M = instantaneous natural mortality rate.
These calculations were based on the assumption that the calculated population
estimate at the beginning of each season was truly representative. The data
yielded significant correlation coefficient estimates for only three seasons, 1967-
68, 1968-69, and 1969-70, at the 5% level or less.

The weekly instantaneous total mortality rates (Z) varied considerably from
season to season (Table 8). The highest rate occurred during the 1971-72 season
(-0.18300) and the lowest rate during the 1966-67 season (-0.00490).

These rates correspond to seasonal survival rates (S) of less than 0.01% and
86%, respectively.

TABLE 8. Mortality Rates and 95% Confidence Intervals for Northern California Dunge-
ness Crabs * (Cape Mendocino to Oregon) During Fishing Season.

— /' Lower Upper Fishing

(weekly confidence confidence season Seasonal rates **

Season rate) limit limit (weeks) -Zt A u Ft Mt

1966-67 -0.00490 -0.00943 +0.00037 30 -0.15 0.14 0.63 0.68

1967-68 -0.07710 -0.07794 -0.07626 32 -2.47 0.92 0.72 1.93 0.54

1968-69 -0.04900 -0.04990 -0.04810 32 -1.57 0.79 0.86 1.71

1969-70 -0.11550 -0.11745 -0.11355 32 -3.70 0.98 0.81 2.94 0.76

1970-71 -0.05740 -0.06663 -0.04817 26 -1.49 0.77 0.87 1.68

1971-72 -0.18300 -0.20602 -0.15998 37 -6.77 0.99 0.73 4.99 1.78

* 159 mm carapace width and larger.
** Notation from Ricker 1975.

The amount of interview data (40 interviews) used to calculate rates for the

198 CALIFORNIA FISH AND GAME

1971-72 season was small when compared to other seasons (i.e. 149 during
1970-71 ); this, plus the fact that most of the interviews were conducted in the
Eureka area thus biasing the data, might explain in part the high mortality rate
for that season (Table 8).

The calculated seasonal instantaneous fishing mortality rates (F) ranged from
0.68 during the 1966-67 season to 4.99 during the 1971-72 season.

The highest calculated instantaneous natural mortality rate (1.78) occurred
during the 1971-72 season; the lowest rate (0.54) occurred during the 1967-68
season. If these rates are representative, we might expect the range of survival
during a 6-month closed season to be 17 to 58%, disregarding seasons where
natural mortality rates could not be calculated because of the low calculated
total mortality rate and corresponding high fishing mortality rate. Jow (1965)
calculated a bi-monthly survival of 27% from tagged crabs released in Pelican
Bay.

The preceding calculated population estimate and mortality rates yield valua-
ble insights into the condition of crab stocks off northern California and therefore
should be helpful in estimating change in yield due to changes in legal sizes.
However, the estimates are no better than the data used to calculate them.
Unfortunately, the catch-per-trap interviews contain two basic weaknesses: they
were neither consistent nor random. These two factors probably account for
most of the variation and inconsistencies. A third factor involved is the increase
in mean pounds per trap that occurred during most seasons in March, April, or
May. At present, it is unclear whether this increase is due to the small number
of interviews, a sudden influx of crabs from some other area, or a new molt.
There is some evidence that some sublegal crabs undergo ecdysis during the
later winter as shown by an increase in the number of soft crabs during this
period.

The Leslie population estimate relies on three assumptions:

1 ) the population vulnerability must not change during the experiment,

2) the entire population must be available for capture,

3) there should not be an excess of recruitment and immigration, over emi-
gration and natural mortality.

The crab population estimates were for legal-sized males only, thus, the first
assumption was met. The second assumption presents little problem during the
first 2 or 3 months of the season; but the increase in the catch per trap in and
during early spring might indicate that either a new segment of the population
has moved into the area, or a molt of sublegal males has increased the number
of legal males. From our tagging studies we speculate that there is very little
movement of crabs into or out of the area.

We do not have sufficient natural mortality data to determine whether it is
excessive or not. The natural mortality rates in Table 8 are based, in part, on the
catch-per-unit-of-effort data. Therefore, they are subject to the same weaknesses
as the population estimates.

One method of obtaining truly representative catch-per-trap data would be
a mandatory log book system. Such a system would provide data for the entire
fishery throughout the season. At present, it is costly, primarily in terms of
man-days, to obtain sufficient interviews to be meaningful during the latter part
of the season when only a few boats are operating out of each port. However,

DUNCENESS CRAB CPUE 199

a log book system might prove more expensive than the interview system
because of the large number of boats in the fishery and the number of man-days
that would be required to process the logs. Utilization of port samplers hired only
for the season to conduct interviews could be less expensive and they might
obtain more accurate data. A log book might prove to be a valuable aid to the
fishermen, particularly new, inexperienced fishermen, in following trends in crab
behavior from year to year.

ACKNOWLEDGMENTS
This work could not have been completed without the assistance of many
Department employees. Melvin Willis, Steven Taylor, Robert Hardy, Nancy
Nelson, John Spann, and Paul Dinnel spent many hours on the docks interview-
ing fishermen. Eugene Witeck calculated population estimates and mortality
rates. Timothy Farley reviewed the calculations and offered many suggestions
for the data analysis. Therese Hoban and Jane Dykzeul designed the figures.
Ronald Warner and Richard Heimann provided the data included in Table 3.

REFERENCES

Cotshall, Daniel W., and Robert Hardy. 1969. Final report of port sampling. January 1966-November 1968. Pac.
Mar. Fish Comm., 21st Ann. Rept.: 28-35.

Jow, Tom. 1965. California-Oregon cooperative crab tagging study. Pac. Mar. Fish. Comm., 17th Ann. Rept.: 51-52.

Ricker, W.E. 1975. Computation and interpretation of biological statistics of fish populations. Can., Fish. Res. Bd.,
Bull., (191):1-382.

200 CALIFORNIA FISH AND CAME

Calif. Fish and Came 64 ( 3 ) : 200-209 1 978

SEX RATIOS OF THE NORTHERN ANCHOVY, ENGRAULIS

MORDAX,
OFF SOUTHERN CALIFORNIA 1

RICHARD A. KLINGBEIL

Marine Resources Region

California Department of Fish and Game

Long Beach, California 90802

Sex ratios for the northern anchovy, Engraulis mordax, were calculated from sam-
ples taken from the southern California commercial reduction fishery and California
Department of Fish and Game Sea Survey cruises for the period 1966-1975.

Sex ratios calculated on a seasonal, monthly, and daily basis for the commercial
fishery seldom approached the expected 1:1 ratio. Only a few ratios slightly favored
males, whereas females were frequently dominant. Although sex ratios for sea survey
cruises were most always close to the expected 1:1 ratio, there were a large number
of samples that showed extreme dominance of either females or males for those
cruises occurring during the period February to June. Sex ratios calculated by area
of capture for this same time period suggested a spatial segregation of the sexes.

INTRODUCTION

Sex ratio data for the northern anchovy has been recorded routinely since the
California Department of Fish and Game began continuous sampling of the
southern California commercial reduction fishery in 1966. The female to male
sex ratio calculated from samples taken during the 1968-69 season was 1.42:1.
For the next six seasons the ratio varied between 1.14:1 and 2.02:1 (Table 1 ).

TABLE 1. Calculated Sex Ratios (F:M) of Anchovies Taken at San Pedro,
1968-69 Through 1974-75 Reduction Seasons.*

Calculated from
Actual Estimated numbers
Season numbers sampled sampled *

1968-69 1.45 : 1 1.42 : 1

1969-70 1.14 : 1 1.14:1

1970-71 1 .60 : 1 1 .60 : 1

1971-72 1.52 : 1 1.52 : 1

1972-73 1 .99 : 1 1 .98 : 1

1973-74 2.02 : 1 2.02 : 1

1974-75 1.57:1

* Using correction factors.

Whether or not these data reflect the actual sex composition of the anchovy
population off southern California is of importance to fisheries management.
Anchovy biomass estimates, calculated by the National Marine Fisheries Service
from California Cooperative Oceanic Fisheries Investigations (CalCOFI ) egg and
larval surveys, assume a 1 : 1 sex ratio (Smith 1972). If, however, the sex ratio
is not 1:1, then biomass estimates should be adjusted.

The mechanisms of meiosis and fertilization tend to dispel the concept of a
pelagic fish population consistently exhibiting a sex ratio other than 1:1. Accept-
ing this premise raises the question of why anchovy fishery sex ratios vary so
much and seldom approach the 1 : 1 ratio expected.

' Accepted for publication March 1978.

NORTHERN ANCHOVY SEX RATIO 201

METHODS

Data for this paper were taken from two principal sources, the southern
California reduction fishery and California Department of Fish and Game Sea
Survey Project cruises. Mais (19746) summarized the scope of these survey
cruises. Estimated sex ratios of the commercial catch from 1968-69 to 1972-73
seasons were published in age and length composition reports (Collins 1971;
Spratt 19726, 1973a, 19736; Sunada 1975). Computer compilations and individ-
ual sample sheets were obtained for these seasons and for the 1973-74 and
1974-75 seasons from Department of Fish and Game files. Sex ratio data from
Sea Survey cruises were taken from individual sample sheets for the years 1966
to 1975. Station data for these cruises were available from CalCOFI Data Reports
16-24 (Mais 1969a, 19696, 1971a, 19716, 1971c, 1972, 1973, 1974a, 1975).

Sex ratios calculated for an entire commercial season were based on an
estimate of total numbers of females and males landed. These ratios involved
a correction for any differences in average weight of the sexes. In most cases,
the correction factors were small and the sex ratios obtained from the actual
numbers of females and males sampled were in close agreement with corrected
ratios (Table 1 ). Sex ratios reported by month or area of capture for the com-
mercial season and all sex ratios reported from sea survey data were calculated
directly from numbers sampled. All sex ratios reported here represent the female
to male (F : M) ratio.

In some cases, samples contained a varying number of fish whose sex were
reported as unknown, usually because of immaturity of the sex organs. These
fish were ignored in calculating the sex ratio.

The numbers of fish used to calculate the sex ratios represented an extremely
small portion of the total population and the standard deviations were high when
using these figures to estimate the sex ratio of the entire central anchovy popula-
tion (Spratt 1972a; Vrooman and Paloma 1975).

In general, sex ratios were compared as they related to both time and space.
Date and location of capture were available on most sample sheets. For Sea
Survey data, actual coordinates of stations were available. For the commercial
fishery, location of capture was reported by the captain of the fishing vessel on
logs collected by the Department of Fish and Game.

RESULTS

Sex ratios calculated from sampling the fishery daily varied considerably.
Monthly sex ratios (Figure 1 ) calculated for 1968-69 through 1974-75 seasons
twice were as high as 3 : 1 and frequently were higher than 2:1. No month
showed a preponderance of males in the samples and only three times did the
monthly sex ratio favor males. The combined numbers for all seasons resulted
in a sex ratio of 1.60 : 1. In contrast, sex ratios from Sea Survey cruises (Figure
1 ) conducted during the same period varied to a lesser degree and combined
numbers for all cruises resulted in a sex ratio of 1.09 : 1. Consistent seasonal or
cyclic trends were not apparent from either set of data.

The monthly sex ratios for the fishery also were collated by Fish and Game
block number (Pinkas 1951 ) or area of capture to determine if the location of
capture by the fishing fleet reflected any geographical differences ( Figures 2 and
3). The San Pedro Channel was the most frequent and consistently fished area.
Landings often occurred from areas northwest, east, and southeast of the chan-

202 CALIFORNIA FISH AND CAME

3:1'

\ 1968-69

1969-70

2:1
i:i<

JS.

s

\

_® _^f

®

ONDJ FMAMJ J

X

ASONDJFMAM

UJ

—J

<

UJ

<

3:1 •
2:1

1970-71
• J8L

1971-72
® *x— •«^ # ^.x'

LU
1

S

ONDJ FMAMJ J

®

ASONDJ FMAM

o

<

X

UJ
CO

3:1 •
2:1

1972-73

v v.

• ® •

® •

*\ 1973-74

I. V

s

ONDJ FMAMJ J

ASONDJ FMAM

3:1 -

1974-75

2:1

C

ammercial fishery- x < 20 samples
• > 20 samples

i:i<

x •"""" v ••""* Sea survey cruises-®

— A I*. -

s

ONDJ F M A M

FIGURE 1. Sex ratios (F:M) of anchovies by month computed from samples taken from the
commercial fishery (1968-69 through 1974-75 seasons) and from California Depart-
ment of Fish and Came Sea Survey cruises.

nel. In a majority of months there was one area where the sex ratio was high
the Santa Barbara Channel only occasionally, but the sex ratio was often high
in samples from these landings (6.40: 1, 4.23: 1, 1.92: 1, 1.28: 1, 3.03: 1). In
April 1973, landings arrived from a fairly large area ranging from just northwest
of Palos Verdes Peninsula to east of San Clemente Island. The sex ratios for this
month exhibited a declining trend from north to south.

Data from Sea Survey cruises were better suited than commercial fishery data
for studying the possibility of spatial differences in the sex ratio. Samples, ob-
tained by mid-water trawl at night ( Mais 1 974b) , were taken over a much larger
area than those from the commercial fishery. The reported location of capture
for these samples was also more reliable. The duration of cruises in the Southern
California Bight normally was less than 1 month, reducing the problem of move-
ment of portions of the population. The sample size was standardized by number
(25 fish ) and, as a rule, all fish were sexed ( samples from the commercial fishery
seldom contained more than 17 fish) (Figure 4). The principal disadvantage of
these data was the relatively small number of samples from each cruise, which
necessitated grouping the data. Since 1966, most cruises took place during five

NORTHERN ANCHOVY SEX RATIO
1970-71 SEASO N ^^^^^^^^ 1971-72 SEASON

flfl^ \ "^^~ *™n Pedro

*o«° ^^^> ^ ^ ^ c ° h onnel

f* SEP -1.56

203

Bn.9/

■■Xzo/

PF 1.4

v-5<

C^P

^^Uft

J^oX

1 ^

I ^

^+>

« ^^

OCT - 1.84

-x»

1 ** ^^

OCT -1.89

^

V

1 V

^

* ^^

NOV - 1.48

-s»

1,^

NOV

•^

wn*\

IK^A

^^tv

VjKp

s\

v

r ^

\

^

■* ^^^

DEC -1.46

■^

1 m ^^

DEC

X^

wx

V

^

\ J

^

*> ^^^

JAN - 1.52

^,

1 * ^^

JAN - 1.39

^

V

\

-*>

^^v-i -

i.iP^.A

• ^^

FEB

-^

1 * ^^

FEB -1.20

«%»

hT

^^^^^ n Pedro
^y,onnel

-*

-» ^^*

MAR

>^

i g ^*

MAR

^

p^

\s

^c^P^^

«• ^^

APR

«V»

1 * ^^

APR -1.74

^

m <^>

V

—*

[ V

^

m ^^

MAY - 2.39

-w

I ^ ^^

MAY

•»*»

FIGURE 2. Sex ratios (F:M) of anchovies computed by month and block number (area of cap-
ture) from samples obtained from the San Pedro reduction fishery in the 1970-71 and
1971-72 seasons.

204

CALIFORNIA FISH AND CAME
197 2-73 SEASON 1973-74 SEASON

Son *«*'<>
£ho nnel

San Clemente

SEP-

- 3.03 ^^ 1

18.

OCT- 2.65

NOV- 1.75

NOV -2.44

1 * ^^

DEC -2.27

"N*

1 • ^^

DEC -2.15 <n^

JAN

*l

1 • ^^

JAN -1.75 «*^ ]

^

\

FEB

FEB -1.14

Pedro

^

MAR

APR -2.11

MAY -1.78

APR-1.51

MAY

FIGURE 3. Sex ratios (F:M) of anchovies computed by month and block number (area of cap-
ture) from samples obtained from San Pedro reduction fishery in the 1972-73 and
1973-74 seasons.

NORTHERN ANCHOVY SEX RATIO

205

periods of the year, "February", "April", "May-June", "October", and "No-
vember." An examination of sex ratio data for these periods produced some
interesting results (Figure 5).

7:1

6:i

* 1972-73 Season

• 1973-74 Season

.. 5:v

<

LU

I

o

I—

<

X

uu
CO

4:i<

*

3:i

2:1

1:1

* *

*• *

10

— 1—
12

14

16

18

20

22

MEAN SAMPLE SIZE

FIGURE 4.

Comparison of daily sex ratios (F:M) for two commercial seasons with the mean
number of fish occurring in samples.

For the "February", "April" and "May-June" cruises, there were areas which
showed significant differences between sex ratios. The delimiting of these areas
for which separate sex ratios were calculated was more or less arbitrary, espe-
somewhat easier for the earlier cruise periods by the occurrence of a large
number of samples that were predominantly either female or male (i.e., 24 : 1,
2 : 23, : 25). One area, southeast of San Clemente Island, showed a consistent
dominance of males, a phenomenon which was not noticed in commercial
fishery samples. Just to the north, there is a smaller area which was predominant-

206

CALIFORNIA FISH AND CAME

FEBRUARY CRUISES

73AI - Fobrrror, II - 27
73A3 - Fnbr»or r 25- Moth 13
7IAI - Fabrtrar, 3- 19
70*1 - Fnbroor, 2- 13
MAI - «^it 19 Fnbruory 3

APRIL CRUISES

74A3 - Aprrl 25-Mo, 7
73A3 - Apr.l 29-Mo r 13
72*3- April 12-37
7IA3 - April 12-30
6.A4 - April 22-Mpt 7
67A3 - April 3-19

MAY-JUNE CRUISES

70A4 - Mor 27 - Junp U
o9Ao - M«r 12 - Jvnp K
MAP - Juno 17 - j.i, |
67A4 - Ma r 18 - Am* 3

OCTOBER CRUISES

73A« - OcNtbw 6
70A7 - Ocrpppr 7
MAI

So as - Ocipbpi

Soprnr ntm . 19 - Ouobn 11

NOVEMBER CRUISES

74A9 - No.pmppr 12 - 26

72A9 - Mp^mbpr 3-20

7IA9 - Novpmbar 15 • 24

69AII - Np.pn.bAr 19 - Oocpmbor

66A9 - Notombor II - 24
67AB - HgnnpA I - II

Son Clnrnrmln

Se. rolio I II I

FIGURE 5. Sex ratios (F:M) of anchovies computed from samples taken by midwater trawl on
California Department of Fish and Game Sea Survey cruises. Stars represent samples
with a majority of males. Circles represent samples with a majority of females. Hatched
areas indicate strong male or female dominance in samples. Cruise designations (i.e.
75A1, 69A6) refer to the chronology of the cruise (first and sixth) on the research
vessel ALASKA (A) during a calendar year (1975 and 1969).

ly female for the first three cruise periods. In the Channel Islands-Port Hueneme
area the sex ratio consistenty favored females. During "April" and "May-June"
cruises, males were dominant in the vicinity of Santa Monica Bay. During the
"October-November" cruises, there was a breakdown of this pattern with few
areas showing large differences in sex ratios.

The observed female distribution in samples of 25 fish for "October-Novem-
ber" and "February-April" were radically different (Figure 6). For the "Febru-
ary-April" period, 34% of the samples fell beyond the 2% probability zone of
the expected binomial distribution, while 13% fell beyond this zone in "October
-November". Of the two distributions, the "October-November" data fitted the
expected distribution more closely. The expected distribution assumed a 1 : 1
sex ratio with no sampling bias and was smoothed for comparison.

The dominance of females in commercial fishery samples could be explained
by assuming that differential mortality or growth rates affected females and
males. If males did not live as long, more females would be expected in landings
as the older year classes were harvested. Conversely, the sex ratio would be
expected to drop when recruitment of younger fish occurred. One might expect
the same trend, if females grew faster or larger than males (Collins 1969) and
the anchovy tended to school by size.

To test the assumptions of a differential mortality or growth rate, a correlation
was attempted using the number of fish in a sample as a quick and easy indicator
of the mean length of fish in the sample. Samples were taken by weight and, in
this respect, were approximately equal, but there was an increase in the number
of fish in the samples when smaller fish were being landed and when recruitment
occurred. For either assumption, there should be a trend apparent in the sex ratio
as the size of the sample varies. The correlation of mean sample size to sex ratio

NORTHERN ANCHOVY SEX RATIO

207

FEB-APR

EXPECTED

OCT-NOV

XPECTED

0-1 2-3 4-5 6-7 8-9

25 0-1'2-3'4-5 6-7'8-9

NUMBER OF FEMALES

25

FIGURE 6. The expected and observed distribution of the number of females in samples of 25 fish
for two different periods of sampling. Samples were collected on Sea Survey cruises
over 8-year period. The expected binomial distribution assumes a 1:1 sex ratio with no
sampling bias and is smoothed for comparison. The distributions are grouped by
increments of two.

for two seasons on a daily basis (Figure 4) indicated no such trend. However,
these data showed that the sex ratio for any day of sampling was often higher
than 2 : 1 and seldom favored males.

DISCUSSION

If I were to assign a sex ratio as a population parameter based on the sampling
of the commercial fishery, it would be higher than the 1 : 1 (female: male)
expected. Through a seven season period, the sex ratio seldom approached the

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