Dispersal of early life stage haddock ...

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Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Fisheries and Oceans on 05/01/14 For personal use only.

Dispersal of early life stage haddock (Melanogrammus aeglefinus) as inferred from the spatial distribution and variability in length-at-age of juveniles Nancy L. Shackell, Kenneth T. Frank, Brian Petrie, David Brickman, and Jennifer Shore

Abstract: In southwestern Nova Scotia, haddock (Melanogrammus aeglefinus) spawning is centered on Browns Bank where the variability of a partial gyre influences the distribution of eggs and larvae. An unknown proportion of each year-class is advected northward to the Bay of Fundy. We examined the variability in length at age 2 as an index of retention during early life. We assumed that early life stages that are retained in the Scotian Shelf area grow more slowly, while those that are advected into the Bay of Fundy grow more quickly. An optimization program was used to estimate the proportions of Scotian Shelf and Bay of Fundy sized components in length at age 2 bimodal frequency distributions for year-classes 1968–1993. The median proportion of Scotian Shelf sized fish was 0.89. A physical circulation model showed that the majority of particles released on Browns Bank drifted towards the Bay of Fundy. Results of the physical model and the size-based index differ partly because the former predicts the fate of passive particles, while the latter is an integrated measure of the proportion of fish retained and surviving. Survival is associated with high wind stress (r = –0.5, p = 0.011, n = 25) implying a higher probability of survival of those retained in the Scotian Shelf region. Résumé : Dans le sud-ouest de la Nouvelle-Écosse, le frai de l’aiglefin (Melanogrammus aeglefinus) est surtout concentré sur le banc Browns où la variabilité d’une circulation partielle influe sur la distribution des oeufs et des larves. Une proportion inconnue de chaque classe d’âge est ainsi attirée en direction nord, vers la baie de Fundy. Nous avons examiné la variabilité de la longueur à l’âge 2 à titre d’indice de rétention pendant le début de la vie. Nous avons supposé que les individus des premières étapes du cycle vital retenus dans la zone de la plate-forme Scotian présentaient une croissance plus lente que ceux attirés par advection vers la baie de Fundy. Un programme d’optimisation a été appliqué à l’estimation des proportions des composantes par tailles des individus de la plate-forme Scotian et de la baie de Fundy au sein des distributions de fréquences bimodales des longueurs à l’âge 2 des classes d’âge de 1968 à 1993. La proportion médiane des poissons de la taille correspondant à celle de la plate-forme Scotian était de 0,89. Un modèle de circulation physique a montré que la majorité des particules libérées au banc Browns dérivaient en direction de la baie de Fundy. Les résultats du modèle physique et l’indice fondé sur la taille diffèrent notamment parce que le premier prévoit le devenir de particules passives tandis que le second est une mesure intégrée de la proportion des poissons retenus qui ont survécu. La survie est associée à la force élevée d’entraînement du vent r = –0,5; p = 0,011; n = 25), ce qui suppose une probabilité de survie plus élevée pour les individus retenus dans la région de la plate-forme Scotian. [Traduit par la Rédaction]

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Introduction Haddock (Melanogrammus aeglefinus) spawn in three principal areas in the northwest Atlantic: Western Bank and Received November 25, 1998. Accepted August 25, 1999. J14920 N.L. Shackell1 and K.T. Frank. Department of Fisheries and Oceans, Marine Fish Division, Bedford Institute of Oceanography, Dartmouth, NS B2Y 4A2, Canada. B. Petrie, D. Brickman, and J. Shore. Department of Fisheries and Oceans, Ocean Sciences Division, Bedford Institute of Oceanography, Dartmouth, NS B2Y 4A2, Canada. 1

Author to whom all correspondence should be addressed. e-mail: [email protected]

Can. J. Fish. Aquat. Sci. 56: 2350–2361 (1999)

J:\cjfas\cjfas56\CJFAS-12\F99-172.vp Friday, December 10, 1999 7:14:35 AM

Browns Bank on the Scotian Shelf (SS) and Georges Bank in the Gulf of Maine (Fig. 1). Each of these spawning areas constitutes a discrete management unit for haddock. Peak spawning on Browns Bank occurs in April–May (Hurley and Campana 1989). While there is limited spawning on some of the other offshore banks, there is no spawning in inshore areas. The circulation and dispersion on Browns Bank have been shown to influence the distribution of haddock eggs and larvae. The circulation on Browns Bank is characterized by a year-round clockwise partial gyre, which is weakened typically by wind-forced currents. The range of residence time at 10 m is from 5 to 25 days with a 14-day average (Smith 1989). Initially, O’Boyle et al. (1984) noted that haddock larvae were retained on Browns Bank and proposed that this © 1999 NRC Canada



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was a consequence of the gyre; larvae advected away from the bank, they hypothesized, represented population losses. In 1985, Campana et al. (1989a) observed that the majority of larval haddock appeared to be retained on or near Browns Bank but that a portion of the population was advected inshore. This portion may have been distributed continuously into the eastern Bay of Fundy (BoF)/Digby Neck area, although no direct observations were available to support this claim (Campana et al. 1989a). Campana et al. (1989a) proposed that the variability in the leakiness of the gyre influenced the proportion of larvae retained and subsequently the variability of year-class abundance. We undertook to develop indices that can be examined as proxies for the surviving proportion of a year-class retained in the SS region during the early life history stage. There are no long time series of egg/larval distributions in the study area; however, we do have annual trawl surveys that provide information on juvenile (ages 1 and 2) distributions. Assuming that juveniles do not migrate, we can use the relative abundance of juveniles in the SS area as a potential “geographical” index of the proportion of a year-class retained and surviving in that area. Because juveniles may migrate, we also developed a sizebased retention/survival index. A consequence of the spatial separation of a given year-class is that two distinct growth patterns occur. Juvenile haddock sampled in the BoF in July are, on average, larger at age than haddock collected offshore on the southwestern SS (Hurley et al. 1997). This situation is not unique to haddock, as Atlantic cod (Gadus morhua) show a similar growth pattern between the two geographic areas (Clark and Brown 1996). Differences in growth rates may be established during the larval period because of spatial gradients in planktonic prey or predator abundance known to exist between the two areas (Frank 1988; Suthers and Frank 1990). If growth differences are generated upon settling, the greater rate of growth observed in the BoF may reflect its higher bottom temperature (Marshall 1995) and (or) its richer benthic food supply relative to offshore (Wildish et al. 1989). Our assumption that growth differences seen at the juvenile stage are established during the early life history (either during the larval stage or at the settlement stage) is based on empirical data. Growth differences observed during the larval stage were maintained in the juvenile stage in laboratory studies (Rosenberg and Haugen 1982; Chambers et al. 1988). In juvenile/adult stages, a correlation between earlier and later weights-at-age in northern Atlantic cod has been observed in the field (Krohn and Kerr 1997). The proportion of juveniles in a given year-class of SS size should represent the proportion that had been retained during early life in the SS area and had survived. Conversely, the proportion of juveniles in a given year-class that are of BoF size should represent the proportion that had been dispersed as eggs, larvae, or postlarvae from Browns Bank to the BoF and had survived. In this paper, we investigate whether the spatial distribution of juveniles and (or) the variability in length-at-age of juvenile haddock in southwestern Nova Scotia can be used to infer dispersal patterns during the early life history. We present geographical and size-based retention/survival indices and hypothesize that they reflect the surviving propor-

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tion of a year-class retained on the SS during early life history. We then examine the indices in relation to survival and wind stress to address the suggestion of Campana et al. (1989a) of covariability in cohort survival and gyre leakiness. Finally, we compare the results of the biological indices of retention/survival with the physical retention as suggested by particle tracking using the climatological spring flow fields off southwestern Nova Scotia.

Materials and methods Biological research vessel survey data The SS is divided into Northwest Atlantic Fisheries Organization (NAFO) statistical divisions that form the basic fishery management units. The haddock in southwestern Nova Scotia are managed as a unit stock within NAFO Division 4X (Fig. 1). Since 1970, the Canadian Department of Fisheries and Oceans has conducted annual bottom trawl surveys on the SS. The shelf is divided into strata based on depth, and trawl samples (sets) of groundfish are taken randomly within each stratum. The sampling intensity is proportional to stratum area. There are roughly 90–120 sets per survey in NAFO Division 4X, which begins at stratum 70 and ends in the BoF (for further survey details, see Halliday and Koeller 1981). The strata representing the BoF include strata 85, 90, 91, and 95, while those representing the offshore southwestern SS include strata 70–81 (Fig. 1). These survey strata have been used to assess the status of the NAFO Division 4X haddock. Estimates of population numbers-at-age from the survey are scaled to adjust for areal differences among strata (see Hurley et al. 1997).

Geographical and size-based indices of retention/survival Our main goal was to estimate the proportion of a given yearclass that was retained near its principal spawning ground (Browns Bank, SS) during the early life history. Initially, we examined the relative proportions of age 2 haddock in the SS and BoF areas. If juveniles were sampled accurately and did not migrate, the proportion of juveniles in the SS region represented the surviving proportion that was retained there during the egg/larval/postlarval period, and we refer to that as SSG. Our second approach was to use the spatial size variation of age 2 haddock. The first immature age group fully available to the survey gear occurs at age 2. Ages 0 and 1 haddock are poorly sampled relative to the older ages and are not as representative of the population. Age 2 BoF juveniles are on average larger than age 2 SS juveniles. The size difference between BoF and SS varies among years (Fig. 2). Also, differences at age 2 propagate through to the older age-classes for the majority of year-classes (Hurley et al. 1997). In some years, sizes-at-age are quite distinct between the two areas and in other years are similar. However, there are no years in which mean length at age 2 of the SS haddock exceeds that of BoF haddock. We used the growth differences to estimate the proportion of BoF-sized fish and proportion of SS-sized fish by testing for bimodality in length-at-age frequency distributions for all strata combined. For each haddock year-class from 1968 to 1993 at age 2, we compiled catch-weighted length-at-age frequency distributions to yield total population numbers-at-length-at-age matrices. Selected examples are shown in Fig. 3. The range of sizes is quite broad, about 20 cm in most cases, and the shape of the length at age 2 frequency distributions varies considerably. A unimodal length-at-age frequency distribution represents samples of fish from a similar growth regime. Bimodality represents samples of fish from dissimilar growth regimes. If all surviving larvae were retained in the SS region, we would expect a unimodal © 1999 NRC Canada



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Can. J. Fish. Aquat. Sci. Vol. 56, 1999


Fig. 1. Southwestern SS showing the SS strata (70–81) and BoF strata (85, 90, 91, 95) from bottom trawl surveys of NAFO fishery Division 4X (broken line).

Fig. 2. Time series of mean length at age 2 estimated from research vessel surveys. Solid line, BoF; broken line, SS.

length frequency distribution and a relatively smaller mean lengthat-age. If all surviving larvae were advected away from the bank region, we would expect a unimodal length frequency distribution and a relatively larger mean length-at-age. If the length-at-age frequency distribution for a given year-class was bimodal, and one of the modes corresponded to the average length-at-age of the SS and the other mode corresponded to the average length-at-age of the BoF, we inferred that the bimodality corresponded to a mixture of fish having grown up in either SS or BoF. We created a size-based index of the surviving proportion of haddock retained in the SS region (SSS) using “mixture analysis” (MacDonald and Pitcher 1979) in an optimization program developed by Ichthus Data Systems (59 Arkell St., Hamilton, ON L8S 1N6, Canada). A mixed probability density function g of variable x is the sum of weighted k component densities, consisting of parameters of Gaussian distributions: proportions (π i), means (µ i), and variances (σi ) where i = 1 to k:

g(x) = π1 f1(x) +... + πk fk(x). The goal of the mixture modelling was to determine whether the data were best fit by a bimodal versus unimodal distribution of the 4X area (both BoF and SS). For each year-class, the goal was to see whether a unimodal (g(x) = π 1 f1(x)) or bimodal (g(x) = π 1 f1(x) + π 2 f2(x)) distribution fit the data through the use of the optimization program. A maximum mikelihood method and quasi-Newton algo© 1999 NRC Canada



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Fig. 3. Length-at-age frequency distributions of selected year-classes. The top panels show unimodal distributions, while the middle and bottom panels show varying degrees of bimodality. Year-classes: (a) 1969, (b) 1978, (c), 1974, (d)1975, (e)1977, and (f) 1979.

rithm were used to estimate parameters. In this optimization program, parameters are tested for goodness-of-fit based on a χ2 approximation to the likelihood ratio test (MacDonald and Pitcher 1979). That is, a function is minimized and used as a χ2 statistic to test for goodness-of-fit. The function is scale dependent. Larger values produce larger differences between expected and observed; therefore, the standard errors of the estimates are very small and the χ2 statistic is inflated for very large sample sizes. Simply stated, the program does not work for very large samples. We scaled down the stratified sample sizes for each year-class by dividing through a factor of 1000 in order to be within the range suitable for the optimization program. The parameter estimates themselves did not change substantially between the original and the scaled down samples, but the standard errors of the estimates were larger in the scaled down samples. One of our goals was to examine the relationship of the derived

indices of retention/survival (SSG and SSS) with survival (recruitment), wind stress, and the physical oceanographic prediction of the proportion retained near the spawning area. We developed a survival index by dividing the numbers of age 1 by the spawner biomass (ages 3 and older) that produced that year-class. We used the data as derived from virtual population analysis in Hurley et al. (1997). Wind stress was calculated using the formulation of Smith and Banke (1975) from hourly observations of wind speed and direction made at Sable Island (Fig. 1). Earlier studies indicated that the winds at Sable Island are representative of conditions over the SS (Petrie and Lively 1979; Sandstrom 1980). Scalar average monthly wind stresses were calculated from the hourly values. We used the scalar average of the monthly mean magnitudes during the peak spawning period (April–June) as our primary physical forcing to explore the hypothesis that the important factor was whether fish © 1999 NRC Canada



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Table 1. Summary of SSG of year-classes 1968–1993: geographically based mean lengths at age 2 (SDs in parentheses) estimated separately from the SS and BoF, proportion of year-classes within the SS region, and number of individuals (N) estimated from research vessel surveys. Year-class

SS mean length at age 2 (cm)

BoF mean length at age 2 (cm)

1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

33.9 (2.7) 29.2 (2.4) 26.9 (2.9) 29.9 (2.7) 30.9 (2.5) 31.5 (3.1) 31 (3) 34.7 (3.3) 33 (3) 29.6 (3) 31.7 (3.2) 29.7 (3.1) 24.1 (3) 25.5 (4.1) 24.5 (3.5) 28.7 (5.7) 29.3 (2.8) 29.6 (3.6) 31.9 (2.4) 30.8 (3.2) 30.6 (1.9) 34.5 (3.9) 30.1 (2.5) 31.6 (3.2) 32.9 (3.1) 30.3 (2.7)

34.8 (1.8) 31.8 (2.7) 31.5 (2.8) 32.2 (2.1) 37 (2) 33.4 (3.4) 38.2 (3.7) 37.7 (3) 34.6 (2.9) 34.4 (2.8) 33.2 (4.2) 32 (3.3) 33.2 (3.5) 31.6 (3.7) 35.4 (2.1) 36.8 (2.5) 38 (1.7) 36.8 (3) 35.3 (3.7) 37 (3) 43.9 (3.8) 35 (2.4) 38.2 (3.5) 36.2 (3) 35 (3.1)

during early life were retained in the SS region or not. This provides a crude measure of wind forcing during early life history and does not reflect some potentially important factors such as wind direction, stress variability, and the vertical structure in the winddriven currents. Potential drift patterns of larvae from Browns Bank were determined by tracking passive particles in three-dimensional model flow fields consisting of the climatological spring mean currents and the M2 tidal currents (C.G. Hannah, P.O. Box 1009, Department of Fisheries and Oceans, Dartmouth, NS B2Y 4A2, Canada, unpublished data). The flow fields were obtained from a circulation model (Lynch et al. 1992) initialized and forced by observational data on the tides, seasonal mean wind stress, and seasonal mean density fields (Han et al. 1997) and additional horizontal mixing (eddy diffusivity K = 50 m2·s–1). The model fields agree well with observational current data from moored measurements and drifters in the Browns Bank region. The particle tracking was carried out using the methodology of Werner et al. (1993).

Results Geographical index of retention/survival (SSG) The proportion of age 2 juveniles found in the SS region ranged from 0.14 to 1. The mean and median were 0.72 (SD = 0.21) and 0.74, respectively. In most instances, the distribution of juveniles would suggest that the majority of a year-class was retained in the SS region, with the exception of the 1978, 1979, and 1982 year-classes (Table 1).

SSG

N

0.97 0.98 1 0.84 0.90 0.83 0.64 0.89 0.84 0.52 0.46 0.14 0.64 0.54 0.38 0.74 0.96 0.73 0.50 0.73 0.60 0.64 0.87 0.84 0.62 0.85

5 458 514 13 211 318 272 732 26 797 262 26 950 598 4 032 985 6 677 248 47 201 832 6 201 386 16 254 005 8 275 671 32 529 585 39 440 070 7 572 376 30 985 516 13 172 362 13 425 186 2 168 612 2 943 344 13 828 229 15 038 949 2 027 616 3 527 194 1 500 713 8 254 250 20 495 074

Size-based index of retention/survival (SSS) Combining the data from the entire region (SS and BoF), parameters (proportions, means, and SDs) were initialized and (or) constrained for each year-class, prior to fitting the model. The most useful approach to fitting the model was to have some prior knowledge of parameter values as well as to examine visually the length frequency distributions. To gain a sense of year-class specific growth rate, we estimated mean length-at-age and SD for BoF and Browns Bank/SS separately (Table 1). The spatial distribution of age 2 haddock may not have remained constant since the egg/larval stage, which is one of the reasons that we wished to use a mixture analysis approach. We judged the model fits using the goodness-of-fit criterion and the geographical mean lengths as a guideline to assess the model parameter estimates of mean length-at-age. When a bimodal model was the best fit, changing the starting values and rerunning the program checked the stability of the parameter estimates. Only those years that fit the goodness-of-fit criterion are presented (Table 2). Both bimodal and unimodal fits of year-classes 1971, 1972, 1979, 1981, and 1990 did not meet the goodness-of-fit criterion. Mixtures of BoF- and SS-sized fish were found in several years, although irregular length frequency distributions in some years with very few data precluded an evaluation of the entire time series. That is, the length frequency distributions of the 1970, 1985, 1986, and 1989 year-classes were © 1999 NRC Canada



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Table 2. Summary of mixture analysis of year-classes 1968–1993. Mode 1 Year-class 1968 1969


1973 1974 1975 1976 1977 1978 1980 1982 1983 1984 1987 1988 1991 1992 1993

Mode 2

Mean

SD

32.79 (0.37) 28.28 (0.22) 31.72 (0.19) 30.08 (0.95) 34.64 (0.65) 31.60 (0.84) 27.68 (0.98) 32.15 (0.12) 24.49 (0.51) 23.54 (0.66) 23.93 (0.81) 26.04 (0.64) 30.43 (0.63) 29.27 (0.45) 29.92 (0.31) 32.00 (0.44) 31.40 (0.2)

2.67 (0.28) 2.44 (0.16) 3.77 (0.14) 2.72 (0.62) 3.89 (0.24) 2.67 (0.57) 2.20 (0.55) 3.47 (0.09) 3.78 (0.35) 2.98 (0.4) 2.9 (0.56) 1.52 (0.71) 3.22 (0.43) 1.87 (0.5) 2.24 (0.25) 4.02 (0.33) 3.56 (0.15)

Mean

Mode 1 prop

SD

Mode 2 prop

33.45 (3.17) 31.45 (0.95) 33.7 (0.75) 30.92 (0.71) 37.72 (2.78) 33.45 (1.11) 37.71 (0.8)

1.14 (0.74) 2.06 (1.27) 2.38 (1.1) 2.43 (0.54)

2.94 (1.47) 2.83 (0.53) 3.2 (0.52) 4.2 (0.34) 2 (1.54) 4.53 (0.48) 2.26 (0.62)

p

1.00

1.82

0.762

1.00

2.85

0.723

1.00 35.64 (0.89) 39.2 (1.16) 38.9 (1.8) 33.57 (1.1)

χ2

12.1

0.79 (0.16) 0.89 (0.14) 0.74 (0.15) 0.46 (0.17) 1.00

0.21 (0.16) 0.11 (0.14) 0.26 (0.15) 0.54 (0.17)

0.93 (0.08) 0.62 (0.1) 0.44 (0.08) 0.2 (0.11) 0.93 (0.1) 0.45 (0.15) 0.77 (0.06) 1.00

0.07 (0.08) 0.38 (0.1) 0.56 (0.08) 0.8 (0.11) 0.07 (0.1) 0.55 (0.15) 0.23 (0.06)

1.00

0.4808

0.0596 0.7863

12.41

0.134

1.36

0.8518

2.26

0.5195

9.76

0.2025

0.8849

0.9896

8.53

0.288

9.14

0.2425

2.61

0.7603

1.38

0.9265

3.78

0.7064

3.45

0.3277

10.4 6.89

0.1089 0.5488

Note: Mode 1 and Mode 2 refer to the model estimates that correspond to SS-sized and BoF-sized juveniles, respectively, and “prop” refers to the model estimates of the proportions of the length frequency distributions for each mode. The SEs of the model estimates are given in parentheses. χ2 is the 2 χ approximation minimized in the optimization program, and p is the probability that the model fit the data.

too irregular to classify as either normal or bimodal. These year-classes were also associated with very low abundance, and so it is probable that the year-classes were not sampled well enough to conduct mixture analysis. The proportions of BoF- and SS-sized fish varied somewhat, but larger proportions were generally of SS-sized fish, suggesting that retention was the most common condition and (or) that retention favoured survival (Table 2; Figs. 4 and 5). If SSG and SSS were reflecting the surviving proportion retained near their spawning grounds during early life history, then we would expect them to be correlated. However, the two indices were not significantly correlated (r = 0.161, p = 0.563, n = 17) (Table 3). Is either SSG or SSS related to survival? Both SSG and SSS are based on information about juveniles. Clearly, any retention index constructed from information about juveniles represents the proportion of a year-class

retained and surviving. This raises the question of whether there is differential survival between the SS region and BoF during early life history. The Browns Bank partial gyre is hypothesized to retain eggs and larvae, and both SSG and SSS suggest that retention favours survival. We hypothesized that as wind stress increases, more larvae are advected away from the bank and lost to the population. We explored representations of the wind field including the vector-averaged wind stress, scalar-averaged wind stress, and scalar-averaged wind stress variance (which includes high-frequency components of the wind field) over the peak period of spawning (April–June). We then examined the relationship between survival to age 1 (ln(age 1 population numbers at time t/age 3 + biomass at time t – 1)) and representations of wind stress. The strongest correlation was between survival and wind stress magnitude (r = –0.5, p = 0.011, n = 25), suggesting that survival is lower as higher proportions of larvae are advected away from the spawning area (Table 3; Fig. 6a). It © 1999 NRC Canada



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Fig. 4. Selected examples of model fit from the mixture analysis optimization program showing unimodal model fits (top panels) and varying degrees of bimodality (middle and bottom panels). Parameter estimates of mean length at age 2 are given below the histograms, SD’s are given in parentheses below the means, and parameter estimates of proportions are given within histograms. 69YC refers to the 1969 year-class, etc.

appears that in the complex circulation field in southwestern Nova Scotia, the magnitude of wind stress is more important than its direction. Moreover, it also implies that the longer time over which the monthly stresses act outweighs the stronger (by a factor of 3.4 on average) but shorter period high-frequency components. Given that wind-based retention favours survival, we expected that either the SSG or the SSS would be positively related to survival and negatively related to wind stress. There was no relationship between SSG and survival (r = –0.11, p = 0.613, n = 24) or wind stress (r = –0.1, p = 0.632, n = 26). However, SSS is significantly related to survival (r = 0.57, p = 0.027, n = 15) (Fig. 6b) but not to wind stress (r = –0.43, p = 0.084, n = 17), although the sign of the correlation is in the expected direction (Table 3). The relationship between SSS and survival is heavily influenced by the 1984 year-class. If that datum is omitted from the analysis, the correlation between SSS and survival is not significant. Due to low abundance (which reflects poor survival), we could not use the mixture analysis on the 1970,

1985, and 1986-year-classes. It is notable that these yearclasses were associated with high wind stress. The expected relationship between SSS, survival, and wind stress may be weakened when survival is low, simply because we cannot conduct mixture analysis. SSS has more potential as an index of retention/survival than does SSG. First, there was evidence of bimodality within the SS region, suggesting that juveniles had migrated from the BoF, and second, SSG shows no relationship with wind stress or survival. Third, the magnitude of the growth difference (BoF size – SS size) is related to survival (r = –0.61 p = 0.002, n = 23) (Fig. 6c). Given that survival is related to wind stress, then the relationship between low survival and greater growth differences may reflect an earlier divergence in growth rates and a higher mortality during early life due to increased advection off the bank. We have also observed that bimodality is easier to detect if the growth differences are larger. There was a negative relationship between SSS and growth differences (r = –0.6, p = 0.012, n = 17) (Table 3). Although this might mean that small growth © 1999 NRC Canada



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Fig. 5. Time series of SSS (size-based index of the surviving proportion of a haddock year-class retained in the SS region). The index ranges from 0 proportion of SS-sized juveniles surviving (little or no retention) to 1 (more retention) but no survival of BoF-sized juveniles. Open bars represent years in which length-at-age distributions were too irregular to conduct mixture analysis. Shaded bars represent poor model fits (and therefore, no index of retention/survival).

2357 Table 3. Pearson correlation matrix of SSG, SSS, survival, wind stress, and growth difference between the BoF and SS (BoF mean length at age 2 – SS mean length at age 2).

SSS r p n SSG r p n Survival r p n Wind stress r p n

SSG

Survival

Wind stress

Growth difference

0.16 0.536 17

0.57* 0.027 15

–0.43 0.084 17

–0.6* 0.012 17

–0.11 0.613 24

–0.01 0.632 26

–0.2 0.349 25

.

–0.5* 0.011 25

–0.61** 0.002 23

.

0.21 0.312 25

Note: *Correlation significant at the 0.05 level (two-tailed); **correlation significant at the 0.01 level (two-tailed).

ing distribution (e.g., Waiwood and Buzeta 1989) and biological behaviour (e.g., Suthers and Frank 1989). differences reflect similar environmental regimes in the BoF and SS, the relationship between the difference in growth rates and survival could also suggest that the degree of bimodality may have a biological basis and is not merely an issue of detection due to sample size or sensitivity of the mixture analysis. Does the physical modelling suggest significant larval retention? Particle tracking in the climatological spring flow field indicates that for a release depth of 10 m approximating the vertical position of haddock eggs and larvae, there is a bifurcation of the drift pathways. Some particles remain on Browns Bank but most drift towards the BoF (Fig. 7). This supports the underlying hypotheses of variability in a leaky gyre potentially affecting haddock growth and survival. However, various particle tracking experiments in this flow field indicate greater drift towards the BoF than implied by SSG or SSS. For example, for a release of particles at 10 m spread over the principal haddock spawning zone on Browns Bank (water depths