Not to be cited without
permission of the authors l
Ne pas citer sans
autorisation des auteurs l
Canadian Atlantic Fisheries
Scientific Advisory Committee
Comite scientifique consultatif des
peches canadiennes dans 1 'Atlantique
CAFSAC Research Document 87/54­
CSCPCA Document de recherche 87/54
Further Work on Nonparametric Prediction of Recruitment of
2J3KL Cod from Stock and Environmental Influences
by
J. C. Rice Science Branch Department of Fisheries and Oceans P.O. Box 5667 St. John's, Newfoundland AlC 5Xl 1 This series documents the scientific
1 Cette serie documente les bases
basis for fisheries management advice
in Atlantic Canada. As such, it
addresses the issues of the day in the
time frames required and the Research
Documents it contains are not intended
as definitive statements on the subjects
addressed but rather as progress reports
on ongoing investigations.
scientifiques des conseils de gestion
des peches sur la cQte atlantique du
Canada. Comme telle, elle couvre les
problemes actuels selon les echeanciers
voulus et les Documents de recherche
qu'elle contient ne doivent pas etre
consideres comme des enonces finals
sur les sujets traites mais plutot
comme des rapports d'etape sur les
etudes en cours.
Research Documents are produced in the
official language in which they are
provided to the Secretariat by the
author.
Les Documents de recherche sont publies
dans la langue officielle utilisee par
les auteurs dans le manuscrit envoye
au secretariat.
6
ABSTRACT
Nonparametric methods for projecting expected recruitments from stock and
environmental influences were used to estimate expected recruitments for the
2J+3JK cod stock. For the recruitments observed between 1962 and 1980, stock
size accounted for 62% of the variance in recruitment. Spring and summer
surface temperatures accounted for 6.5% of the residual variance in
recruitment; winter temperatures and salinities accounted for 7.1% of the
residual variance. Using these results, the 1981 year-class is predicted to be
about 300 million recruits (numbers at age 4), the 1982 year-class is predicted
to be slightly smaller (280 million recruits), the 1983 and 1984 year-classes
between 350 and 400 million recruits, and the 1985 year-class substantially
smaller; perhaps 200 million recruits. Ogives of the probability that
recruitment will be of various sizes are presented for these predictions.
RESUME
Des methodes non parametriques pour la projection des recrutements
prevus a partir du stock et des influences environnementales ont ete
utilisees pour estimer les recrutements prevus pour le stock de morue
2J+3JK. Pour les recrutements observes entre 1962 et 1980 la taille du
stock expliquait 62 % de la variance du recrutement. Les temperatures de
surface au printemps et en ete en expliquaient 6,5 %; les temperatures et
les salinites en hiver en expliquaient 7,1 %. A partir de ces resultats on
prevoit que la classe Wage de 1981 comptera environ 300 millions de
recrues (nombre a 1'age de 4 ans), la classe d'age de 1982 legerement moins
(280 millions de recrues), les classes dge de 1983 et 1984 entre 350 et
400 millions de recrues et la classe d'dge de 1985 un nombre
substantiellement moins eleve soit peut-'etre environ 200 millions. Des
ogives des probabilites des nombres de recrues en rapport avec ces
previsions sont presentees.
3
Introduction
Recruitment of cod in NAFO Divisions 2J+3KL has been shown to be
influenced by both spawning stock biomass and environmental influences,
including water temperatures (Rice and Evans 1986a, b). The true parametric
functions relating these influences to recruitment are unknown, and are
unlikely to be either simple or knowable. In such circumstances nonparametric
probability density estimation methods are likely to be superior to alternative
methods for estimating expected levels of recruitment.
Evans and Rice (in press) have developed a nonparametric method for
estimating the probability density function (pdf) of recruitment expected,
given a historical series of recruitment-independent variable pairs, and the
current value of the independent variable. In this paper the pdf for strengths
of recent year-classes of the northern cod stock are estimated given the
estimated spawning stock biomass, as are the pdf of displacements of the
expected recruitment, given environmental conditions in those years.
Methods
The data: Spawning stock biomasses were taken as the beginning of year 7+
biomass. Values up to 1980 were included in the historic series, and were
taken from the 1986 assessment (Baird and Bishop 1986). Predictions were made
for years from 1981 to 1985, where values for spawning stock biomass were also
taken from Baird and Bishop 1986.
Environmental data were all from Station 27, and consisted of surface
(0-20 m) and deep (100-150 m) temperatures, and surface salinities, for
January, March, June, and October. Data from 1954 to 1986 were ordinated with
both detrended correspondence analysis and principal components analysis
(Gauch 1982). Ordination results will be described at the 1987 NAFO session on
environment, as well as the analyses selecting the appropriate axes to serve as
independent variables for this work (Rice, in prep.).
Analysis methods: Our nonparametric methods are described in detail, and
contrasted with more commonly used parametric methods for predicting
recruitment from stock in Evans and Rice (in press). Of the options described
there, we used the Cauchy step function algorithm. In this algorithm the
recruitment pdf can increase only at historically observed recruitments. The
height of each step is determined by the Cauchy weighting function
1/(1+(X/D) 2 ), where X is the distance between the current value of the
independent variable and the value associated with the historic recruitment,
and D is the width of the influence window. We first determined the pdf for
expected recruitment, from the historic stock-recruit data. We then estimated
the pdf for deviations around the expected recruitment. We used the first two
axes of the principal component analysis of temperatures and salinities as
independent variables. The dependent variable was the deviation of the
observed historic recruitment from the median recruitment of the pdf estimated
using standard jacknife procedures for the stock-recruitment data from each
4
historic year. Because principal component axes are uncorrelated, the pdf's of
recruitment deviations can be constructed separately for each axis.
Predictions for years after 1980 used the series from 1962 to 1980.
Results
For the historic series, we used the median recruitment, given the step
function ogive, as the predicted recruitment for each year. The variance in
recruitment over that period was 5.61X10 8 , and these median predictions from
stock size accounted for 62% of that variation (Table 1). Predictions were
fairly insensitive to the value of D, with a maximum reduction of variance at
1200, about 1/10 the range of the stock axis (Table 2). Largest residuals were
for 1969 (-) and 1963 (+), with strings of large residuals for the 1969-71 and
1976-77 year-classes.
The two principal component axis accounted for similar, small portions of
the residual variance. PC I accounted for 6.5% of the variance; PC II for
7.1%. Both fits were quite sensitive to the value of D, (Table 2) with an
optimum value of 0.40 for PC I (1/8 the range of scores) and 0.41 for PC II
(1/10 of the range) (Table 2).
PC I reflects influences of spring and summer surface temperatures and
salinities. Values on both extremes of this axis were associated with
predictions of large negative residuals, and large positive residuals expected
from median to moderately high values on this axis. PC II reflects influences
of winter temperatures and salinities. Large positive residuals are expected
in years with positive PC II scores, i.e. with warm winter temperature
(Fig. 3).
PC I does moderately well at correctly predicting poor recruitments;
year-classes 1966, 1969, 1970, and 1971 were correctly predicted to be
substantially smaller than expected, given the stock size. PC II is better at
predicting good year-classes, correctly predicting the 1962, 1967, and 1968
year-classes as being strong. Neither axis predicts failures where
exceptionally strong year-classes occurred, or vice versa. False alarms were
also rare (1 of 19 for each axis), but both axes missed several exceptional
year-classes; for example the strong 1963 and 1978, and weak 1964 and 1976
year-classes.
Predictions for 1981-85 year-classes
Based on spawning stock biomasses, the 1981, 1983, and 1984 year-classes
should be about 3X10 8 fish, with the 1982 and 1985 year-classes smaller; about
2X108 fish. Except for 1982 all ogives are fairly steep around the median,
implying recruitment sizes are unlikely to be very different from the median
value, when only the stock influence is considered. For the 1982 prediction,
the ogive is much flatter, and values as high as 3X10 8 are nearly as good as
2X10 8 for the prediction (Fig. 1).
5
When the environmental indicators are considered as well, some predictions
change. PC I predictions suggest that the 1983 and 1984 year-classes may be
stronger than expected, given stock size. Using PC II, all ogives suggest only
small adjustments in stock-based predictions would be necessary (Fig. 2).
However, because the median deviations for the historic series were biased low
for the predictions using both axes, the suggestion from PC II that the 1982
year-class might be slightly stronger than expected may warrant extra
consideration.
The ogives from 1982, 1984, and 1985 for PC II all have gradual slopes
around the median. For the 1984 and 1985 year-classes, the slopes suggest
weaker negative adjustment of the recruitments are possible. For the 1982
year-class, the slope suggests the year-class may be stronger.
In summary, spawning stock biomass suggest the 1981 year-class might be
3.00X10 8 fish with no environmentally based adjustments. The 1982 year-class
might be up to one-third smaller, based on stock size alone, but environmental
factors suggest increasing this value back to the neighborhood 2.7 to 3.0X10 8 .
The 1983 and 1984 year-classes should both be 3X10 8 from stock, with upward
adjustments to 3.5 to 4.0X10 8 for the 1983 and possibly to 3.5X10 8 for 1984.
The 1985 year-class may be substantially weaker, with a value of 2.0X10 8
suggested.
Note that throughout this work, spawning stock biomass has been assumed to
be 7+ beginning of year biomass. Maturity is unlikely to be knife-edge at
age 7, and there is evidence that maturation ogives of 3M cod have changed, as
stock biomass changed (Wells 1986). The observation that recruitment appears
to be on a higher trajectory as the 2J3KL stock rebuilds than it followed as
the stock declined (Fig. 3) suggests that spawning stock biomass may be
underestimated in recent years. Results of the analyses presented here can be
viewed with more confidence when ongoing work on the environmental data base,
and estimation of the actual spawning stock biomasses is completed.
References
Baird, J. W., and C. A. Bishop. 1986. Assessment of the cod stock in NAFO
Divisions 2J+3KL. NAFO SCR Doc. 86/47, Ser. No. N1163, 50 p.
Evans, G. T, and J. C. Rice, in press. Predicting recruitment from stock
without the mediation of a functional relation. J. Du Conseil. 24 p.
Gauch, H. G. 1982. Multivariate Analysis in Community Ecology. Cambridge
University Press.
Rice, J. C., and G. T. Evans. 1986a. Re-examinating target spawning biomass
for the cod stock in NAFO Division 2J+3KL. NAFO SCR Doc. 86/30,
Ser. No. 1144, 5 p.
L•^
Rice, J. C., and G. T. Evans. 1986b. Nonparametric prediction of recruitment
from stock, and the relationship of the residuals to water temperatures
for cod in NAFO Div. 2J+3KL and 3M. NAFO SCR Doc. 86/106, Ser. No. N1233,
13 p.
Wells, R. 1986. Variations in the gonad weight and the percentage occurrence
at length of maturing female cod on teh Flemish Cap. NAFO Ser. Doc.
86/114, Ser. No. 1241, 4 p.
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