## Abstract

In 1907, the Bergen Institute of Marine Research started regular sampling of scales and lengths from landings of mature Norwegian spring-spawning herring. The actual age of each fish when caught was recorded, and from the early 1920s also the age at which it spawned for the first time. The present analyses concern biological samples secured during the fishing seasons 1940–1964. Herring in this stock do not all reach maturity at the same age. A small proportion of any one year class matures at 3 years. The majority matures from the age of 4–7 years, and a small proportion of some year classes at 8 and even 9 years of age. Subsequent age composition and growth of each maturation cohort were followed throughout mature life after spawning for the first time. The maximum age was found to increase with age at maturation, rising to an asymptote of about 22 years. The von Bertalanffy parameter L _{∞} shows an increasing trend with age at maturation, while K decreases. There is no strict length threshold at maturation and the curve joining the length at which each maturation cohort reaches maturity is less steep than the growth curve itself over the range of maturation ages.

The data suggest that fish in this stock spawn, on average, eight times during a period of their life history in which the mortality rate is independent of age. After these eight spawnings, at an age referred to in this paper as the hinge age, the mortality rate increases sharply. Thus, the adult life is divided into two phases, called here pre-senescent and senescent. The total mortality rates in the pre-senescent phase are relatively stable for all maturation cohorts 3–9, but there is some evidence of a trend towards higher mortality rates during the senescent phase for the youngest maturing fish. This trend is caused mainly by a reduced natural mortality in the fish that mature when older. These findings have interesting demographic implications. Additional mortality due to fishing will change the relative contribution of young and old maturation cohorts in the senescent phase, thus making it appear that natural mortality is dependent on the intensity of fishing. Consequently, for stock assessment, analysis on a cohort basis seems advisable.

## 1 Introduction

Considerable interest in recent years has centred on the quantitative patterns that exist in fundamental life-history parameters of marine populations. Beverton and Holt (1959) identified relationships between growth rates (measured by the parameters K and L _{∞} of the von Bertalanffy growth formula), age (T _{m} ) and length (L _{m} ) at maturation, and longevity T _{max} . T _{max} is also related to the inverse of natural adult maturity M. For a review of such patterns in teleost fish see Beverton (1992) where they were called Growth–Maturity–Longevity (GML) relationships. GML relationships have been demonstrated in other vertebrates ( Charnov and Berrigan, 1991 ; Charnov, 1993 ). Such patterns have been found between major taxa, between species, and also between populations of the same species. Environmental conditions may mediate GML patterns, for example, age at maturation and longevity is higher and size at maturity is lower in colder conditions than it is in more temperate latitudes ( Beverton, 1992 ). This accords with the ideas of evolutionary fitness derived from studies in theoretical ecology ( Roff, 1984 , 1991 ).

GML characteristics may also change in response to fishing, but the study of the dynamics of these phenomena is difficult. Depletion by fishing is often followed by a substantial decrease in the mean age (and sometimes length) at maturity. To determine whether this is associated with an increase in natural mortality and a decrease in longevity is very difficult because the population size and structure in these circumstances are dominated by the increased fishing mortality. Similarly, the extent to which observed maturity trends are purely structural or imply real biological (density-dependent) changes is also difficult to determine. Nevertheless, these questions are discussed later in this paper.

Data collected by the Institute of Marine Research (IMR) at Bergen, Norway, from the population of Norwegian spring-spawning (Atlanto-Scandian) herring ( *Clupea harengus* ) are used in this paper in an investigation of mortality rates and GML patterns. Data were measured from biological samples from the fishing seasons 1940–1964 inclusive. The exploitation of this stock is known as the winter herring season and Figure 1 , taken from Devold (1963) , gives maps of the distribution of these catches between 1946 and 1961. Fishing took place in the area between Stad in the north and southwards towards Haugesund. During the years studied in this paper, the fishing season lasted for approximately two months, starting between mid-February and mid-March when the herring appeared off the Norwegian coast for spawning. Analysis in the present study has been confined to these historical data, although more recent data have been collected at the IMR. The Norwegian spring-spawning herring stock collapsed in the 1960s, possibly in response to increased fishing pressure and possibly as a result of environmental changes ( Toresen and Østvedt, 2000 ). Although the stock has subsequently recovered, fishing has resumed, and fishing mortality has been greater in the 1980s than was the case historically, before the collapse. The introduction of sonar and power blocks in the purse-seine fishery ( Bakken and Dragesund, 1971 ) and of artificial fibres in gill and purse-seine nets has also increased fishing power since the early 1960s. It is therefore safer to leave the study of the later data to a subsequent investigation.

The data derived from these samples (and similar samples from Northeast Arctic cod, *Gadus morhua* ) are probably unique in that it has been possible to subdivide each year class present in the sample according to the age at maturation. Lea (1929) and Runnstrøm (1936) showed that the onset of maturation in the Norwegian spring-spawning herring causes a visible change in the ring structure of the scale. From the late 1920s to 1970 for each herring sampled by the IMR during the winter herring fishing season, not only the age of the fish, but also the age at maturity was recorded. As is the case in other long-lived fish populations, maturation of any one year class occurs not at a single age but over a range of ages. The availability of information on the age at maturation as well as the age of the fish in the sample has enabled each year class to be subdivided according to the year of first maturation. We have called these subdivisions the maturation cohorts. In previous studies, Østvedt (1958 , 1963) published studies of this stock subdivided into maturation cohorts, which he called spawning classes. He showed that the estimation of mortality rates was refined by the use of the data subdivided in this way. However, he commented in the 1958 paper that “… it may be that our presumption of the same mortality rate for all spawning groups of a year class (when all individuals have attained sexual maturity) does not hold true”. This is one of the questions that is discussed in the present paper.

The availability of estimates of mortality rates and growth parameters for each maturation cohort of each year class enables a study to be made of GML patterns in maturation cohorts, thus adding to studies that have previously been made of such patterns in the Norwegian spring-spawning herring population as a whole. It has also been possible to make an assessment of how the total mortality rate (including mortality due to fishing) varies between maturation cohorts and how much of these changes can be attributed to real changes in natural mortality rates with age at first maturation.

A preliminary analysis of the Norwegian spring-spawning herring data divided into maturation cohorts was presented to the ICES Statutory Meeting in 1993 ( Beverton *et al* ., 1993 ). This work has been greatly extended and this more extensive analysis is presented and discussed in this paper. Some of the same data and figures have been referred to by Beverton in a lecture given in May 1994 ( Beverton, 2002 ). A study of maturation cohorts of Northeast Arctic cod was published by Beverton *et al* . (1994) .

## 2 Materials and methods

The source of the biological samples used in this study was the commercial winter herring fisheries along the west coast of Norway described in the Introduction above. The fishing gear from which samples were taken was purse-seine and gillnet, but in this present study, data from these sources are treated in different ways. Three measures of stock abundance were considered for the analysis ( Figure 2 ). Two of these measures were catch per unit effort (cpue) data. For gillnet, these are expressed as the number of fish caught per net, and for the purse-seine they are the number of fish caught per vessel. The third measure is a revised abundance index of spawning-stock biomass (SSB) estimated by Toresen and Østvedt (2000) using virtual population analysis (VPA). Hilborn and Walters (1992, p. 364) discussed the use of VPA in clupeoid fisheries and concluded that such estimates are sometimes unreliable, particularly during periods when stocks are declining heavily, because the shoaling behaviour of these species results in increased catchability as the stock declines. In this study, therefore, we have avoided use of the VPA estimates, although the trends in VPA SSB are very similar to those of gillnet cpue ( Figure 2 ). Of the two cpue indices, gillnet data are a more reliable guide to stock numbers because the gear is fixed, and therefore catchability remains relatively constant, and because over the period considered, the increase in fishing power in the purse-seine fishery was much greater than it was for the gillnets ( Østvedt, 1964 ). In this study, therefore, gill net cpue has been used as a measure of stock abundance.

For the estimation of age composition of the stock, however, gillnet data are subject to bias because of the size selectivity of the gear. Age compositions, and hence maturation cohort compositions, have therefore been constructed entirely from the purse-seine fishery, which is not size selective. Normally, 200 fish were taken from each sample for length measurement and ageing purposes. The gillnet cpue data were normalized to purse-seine cpue by multiplying by the overall average of the ratios of purse-seine to gillnet cpue ( Table 1 indicates the method of calculation). The abundance estimates obtained were then divided up according to the year class and maturation cohort compositions derived from the purse-seine samples. The mean length-at-age composition was also compiled for each maturation cohort in a similar fashion.

Year | Purse-seine cpue a | Gillnet cpue b | Purse-seine cpue/gillnet cpue | Gillnet cpue raised to purse-seine cpue c | SSB d |
---|---|---|---|---|---|

1947 | 3 144 | 647 | 4.86 | 2 956 | 13 888 |

1948 | 4 012 | 852 | 4.71 | 3 894 | 12 975 |

1949 | 3 351 | 679 | 4.94 | 3 103 | 13 091 |

1950 | 3 973 | 670 | 5.93 | 3 063 | 14 267 |

1951 | 3 841 | 507 | 7.58 | 2 317 | 12 817 |

1952 | 3 336 | 465 | 7.17 | 2 125 | 11 897 |

1953 | 2 796 | 480 | 5.83 | 2 193 | 10 781 |

1954 | 4 839 | 642 | 7.07 | 2 934 | 9 640 |

1955 | 4 174 | 535 | 7.80 | 2 444 | 10 454 |

1956 | 4 958 | 498 | 10.04 | 2 276 | 12 017 |

1957 | 2 779 | 537 | 5.17 | 2 454 | 10 376 |

1958 | 972 | 336 | 2.89 | 1 536 | 9 510 |

1959 | 1 162 | 326 | 3.56 | 1 490 | 7 506 |

1960 | 1 152 | 249 | 4.64 | 1 138 | 5 946 |

1961 | 315 | 243 | 2.20 | 654 | 4 339 |

1962 | 702 | 208 | 5.38 | 951 | 3 607 |

1963 | 613 | 123 | 4.98 | 562 | 2 733 |

Grand mean | 4.57 |

Year | Purse-seine cpue a | Gillnet cpue b | Purse-seine cpue/gillnet cpue | Gillnet cpue raised to purse-seine cpue c | SSB d |
---|---|---|---|---|---|

1947 | 3 144 | 647 | 4.86 | 2 956 | 13 888 |

1948 | 4 012 | 852 | 4.71 | 3 894 | 12 975 |

1949 | 3 351 | 679 | 4.94 | 3 103 | 13 091 |

1950 | 3 973 | 670 | 5.93 | 3 063 | 14 267 |

1951 | 3 841 | 507 | 7.58 | 2 317 | 12 817 |

1952 | 3 336 | 465 | 7.17 | 2 125 | 11 897 |

1953 | 2 796 | 480 | 5.83 | 2 193 | 10 781 |

1954 | 4 839 | 642 | 7.07 | 2 934 | 9 640 |

1955 | 4 174 | 535 | 7.80 | 2 444 | 10 454 |

1956 | 4 958 | 498 | 10.04 | 2 276 | 12 017 |

1957 | 2 779 | 537 | 5.17 | 2 454 | 10 376 |

1958 | 972 | 336 | 2.89 | 1 536 | 9 510 |

1959 | 1 162 | 326 | 3.56 | 1 490 | 7 506 |

1960 | 1 152 | 249 | 4.64 | 1 138 | 5 946 |

1961 | 315 | 243 | 2.20 | 654 | 4 339 |

1962 | 702 | 208 | 5.38 | 951 | 3 607 |

1963 | 613 | 123 | 4.98 | 562 | 2 733 |

Grand mean | 4.57 |

Catch in numbers per boat (in thousands).

Catch in numbers per day per net.

Gillnet cpue multiplied by 4.57.

SSB in thousand tonnes ( Toresen and Østvedt, 2000 ).

Ageing of fish needs careful validation ( Hilborn and Walters, 1992, p. 167 ). The method of ageing was based on counting growth rings in the scales ( Lea, 1929 ). Erosion of the scale edge causes difficulty in counting the outermost rings, particularly in older fish. However, throughout the period when samples used in this study were aged, there was a considerable degree of consistency in the ageing of fish. Only two research assistants were responsible for these measurements, the second being trained by and succeeding the first. It is evident from the records that these technicians were aware of the difficulty of accurately ageing fish since a proportion of the samples were recorded as unreadable. On average, this proportion was around 10%, varying between 5% for the younger age groups and 20% for the older groups. Data from these fish have not, however, been discarded from our analysis. For these fish, age–length keys derived from those fish that were reliably aged were used for estimation of age so that the complete sample was used in this study.

### 2.1 Total mortality rate of maturation cohorts

For each maturation cohort in each year class, plots were made of ln(cpue) against age; Figure 3 gives a representative selection of these plots. For many fish populations, including the Northeast Arctic cod where year classes were subdivided into maturation cohorts ( Beverton *et al* ., 1994 ), a linear trend is evident in such plots. For the Norwegian spring-spawning herring, however, the plots are strikingly different; there is a marked increase in mortality for older fish. This is most clearly seen in the very abundant maturation cohorts but, nevertheless, a similar pattern is seen in most plots.

Two mathematical models were investigated to describe this pattern. The three-parameter Gompertz curve, incorporating an age-specific mortality ( Beverton, 1963 ; Witten, 1987 ) was fitted using non-linear regression methods. The second model investigated was one of split regression, with two straight lines having different slopes ( Figure 3 ). It was found that in terms of smallest sum of squares of deviations of the fitted models from the data, the split-regression model gave better fits overall, and it is results from this model that are reported here. This split-regression model divides the adult lifespan into a pre-senescent phase followed by a senescent phase. The mortality rates in the pre-senescent (Z _{ps} ) and in the senescent phase (Z _{s} ), together with an estimate of the hinge age (T _{H} ) marking the change from pre-senescence to senescence, are readily calculated by simple linear regression methodology. Two regressions are fitted to the ln(cpue) data for each of a range of assumed hinge ages straddling the obvious discontinuity in the trajectory. The hinge age giving the smallest residual sum of squares over the two regression lines is selected as the best estimate of the true hinge age.

### 2.2 Longevity of maturation cohorts

The longevity T _{max} of each maturation cohort was estimated from the maximum observed age T _{max(obs)} of fish in the cohort. However, this estimate depends on sample size, it being more likely to record an older fish in a large sample than in a small one. It is therefore necessary to normalize observed T _{max(obs)} values to a standard sample size before comparisons are made between maturation cohorts and year classes.

Beverton (1963) and Hoenig (1983) argued that T _{max(obs)} should be normalized to ln ln(n), where n is the sample size, but this suggestion is based on the double exponential form of the Gompertz curve, and our analyses have suggested that this is not the best model for these data. The simple exponential decay model for the senescent phase implied by the split-regression model for the trajectories of ln(cpue) against age suggests a different normalization. Hoenig (1983) showed that where mortality is independent of age, T _{max(obs)} varies linearly with ln(2n+1), where n represents the number of fish in the sample. In this study, the normalization is applied to fish that are in the senescent phase (hinge age and older). Thus, the constant term for the normalization is the age at the start of the senescent phase, the hinge age (T _{H} ), and the sample size is the number of senescent fish (n _{s} ). The slope (1.17) of the regression of (T _{max(obs)} −T _{H} ) on n _{s} ( Figure 4 ) was statistically different from zero (F=6.71, p=0.011). This regression line enabled observed values T _{max(obs)} to be normalized to 100 fish, the average sample size of the best-sampled maturation cohort (MC-5).

### 2.3 Growth and length at maturity of maturation cohorts

Growth curves for each maturation cohort were fitted to length-at-age data, using non-linear regression methods to fit three-parameter von Bertalanffy growth curves. The absence of immature fish in the samples used in this study led to some difficulty in the estimation of the parameter t _{0} , the theoretical body length at age zero, though the estimation of the growth parameter K and asymptotic length L _{∞} did not cause any difficulty. Estimates of t _{0} were found to vary greatly amongst the maturation cohorts, the standard errors were large, and the estimates obtained were strongly correlated with those of K. This was also seen in the earlier study of Northeast Arctic cod ( Beverton *et al* ., 1994 ). Because this imprecision in the estimation of t _{0} might affect the estimates of all the parameters of the model, a single overall value of t _{0} =−0.83 was first obtained, as described below, and then values of K and L _{∞} were estimated, with t _{0} assumed equal to −0.83. Two sources of information were used to estimate this overall value of t _{0} . The first was the set of values obtained from fitting the three-parameter model, although outliers outside of the range ±5.0 were omitted. The second was data for the richest year classes, the 1934, 1944, and 1947 year classes sampled at ages 7 and 10 years and the 1950 year class sampled at ages 7, 8, 9, and 10 years. Back calculations of length at immature ages from the scales of these samples using a method described by Lea (1910) gave length-at-age data for which three-parameter von Bertalanffy equations were fitted, giving further values to include in the calculation of the overall value for t _{0} .

## 3 Results

For the year classes 1930–1938, the maturation cohorts MC-7 and MC-8 were well represented, but few of the younger maturing fish were seen, MC-3 often being completely absent. In the 1940 year class, all maturation classes MC-3 through to MC-9 were represented, but for all other year classes in the 1940s, MC-8 and MC-9 were both absent. In the rich year class of 1950, MC-8 and MC-9 were particularly abundant. A pattern therefore emerges that in abundant year classes, fish tend to mature later in life, whereas in less abundant year classes they sometimes mature earlier. An explanation for the low proportion of late maturing fish in the post-1940 year classes, with the exception of 1950, might be the expansion of a fishery on young herring from the mid to late 1930s onwards. This variation in the sample sizes available from some of the maturation cohorts means that in some cases, representation of a particular cohort is low, and the estimates of mortality are therefore imprecise. This is taken into account below, when averages of mortality rates are calculated.

The hinge age T _{H} increases with age at maturation ( Figure 5 ). The duration of the pre-senescent phase following maturation is around 8 years, though there is considerable variation between year classes. Thus, for MC-3, T _{H} is on average 11 years whereas for MC-9 it is 17 years. After approximately eight spawning seasons, therefore, mortality rate abruptly increases and the fish enters the senescent phase. Scatter plots of the estimates of total mortality rates (Z _{ps} and Z _{s} ) for the pre-senescent and senescent phases, respectively, are shown in Figure 6a and Figure 6b . Some maturation cohorts with estimates having low precision have been omitted from these figures to improve clarity. The pre-senescent mortalities Z _{ps} do not change noticeably with age at maturation ( Figure 6a ). The weighted average, using the reciprocals of the standard errors of the estimates as weights, is 0.19, and this can be taken as an overall measure of the total pre-senescent mortality rate for this stock over the years studied here. However, the senescent mortality rates Z _{s} decrease with age at maturation after 5 years ( Figure 6b ). This decrease in value is from around 0.82 for MC-5 to 0.26 for MC-9. The pattern is different for early maturing fish, however. The average for MC-3 is 0.28 and for MC-4 it is 0.36, both values being significantly less than for MC-5. This point is discussed further below.

Longevity T _{max} , whether normalized or not, increases with age at maturation ( Figure 7 ). Some of the figures of T _{max} are rather high, normalized values of 25 years being indicated. Since it is most unusual, particularly in modern times, to find herring of such an age, some explanation is necessary. The explanation is simple. These high values are associated with fish maturing at ages 6 and above. These maturation cohorts are now rare, or even non-existent, so it is now not possible for herring to attain such ages. Even in 1960, such fish were very rare.

Turning now to the growth parameters K and L _{∞} of the von Bertalanffy growth model, averages of K increase and those of L _{∞} decrease with age at maturation ( Figure 8 ). The sustained decrease in K with maturation age has the effect of separating the maturation cohort growth curves ( Figure 9 ). After the onset of senescence, these growth curves converge to nearly the same L _{∞} for all maturation cohorts. The length–maturation relationship, that is the line joining the length (L _{m} ) at which each maturation cohort reaches maturity, is indicated by the heavy line in Figure 9 . The length threshold at maturation varies with maturation age, and the relationship is much less steep than the growth curve itself over the range of maturation ages.

## 4 Discussion

It may be argued that the fundamental hypothesis of this paper, that mortality in Norwegian spring-spawning herring abruptly increases after eight spawning seasons, is an artefact caused by errors in scale reading. For older fish, erosion of the scale edges results in the age of fish to be under-estimated. This phenomenon has long been recognized, however, and as was discussed above, considerable care was taken in ageing fish. Moreover, the errors would have had to be very great indeed for this to be an explanation of the small numbers of older fish represented in the samples. MC-4 for the 1942 year class will serve as an example to illustrate this point ( Figure 3 ). If the same mortality rate is actually present throughout the adult life of herring, then those fish aged at 18 years would have had to have been very much older. Extrapolating the line of pre-senescence, these fish would all have had to have been actually around 30 years of age. We have argued earlier that it might be difficult to accept that herring can achieve an age of 25 years. It seems somewhat unlikely that they commonly achieve ages of 30 years and upwards. Moreover, these under-estimates of age would have had to have been made consistently for all fish 8 years older than the age at maturation, but not for pre-senescent fish. Unless there is evidence that increased scale erosion occurs to a larger extent in senescent herring, the erosion of fish scales does not explain the phenomenon of an abrupt change in apparent mortality.

### 4.1 Change of total (Z) and natural (M) mortality rates with age at maturity

Our first consideration in relating observed natural mortality rates with other life-history parameters is to assess the reliability of the estimates of the total mortality rate. Our calculations of total mortality rates are based on cpue of the maturation cohorts within the year classes 1930–1949. For these year classes and all ages of maturation between 3 and 9 years, the total mortality rate (Z _{ps} ) is relatively stable ( Figure 6b ). The mean Z _{ps} of 0.19, calculation of which was described above, agrees very closely with the total mortality rate Z of 0.19 calculated for the mature part of the stock by Østvedt (1964) and Dragesund *et al* . (1980) for the period 1950–1962. Work by Lea (1930) indicated a total mortality for the spawning stock of 0.21 for the period 1913–1926. Assuming a constant natural mortality M of 0.16 (suggested by Dragesund *et al* ., 1980 ) gives a fishing mortality F of 0.03, which is close to the mean fishing mortality of 0.035 indicated for the age groups 5–14 for the period 1926–1939 in the VPA analysis by Toresen and Østvedt (2000) .

The downward trend (from MC-5 onwards) of the senescent total mortality rate Z _{s} against MC-cohort is biologically significant ( Figure 6b ). Since the calculations are derived from purse-seine data, this trend is unlikely to be due to gear selectivity, especially as each maturation cohort for most of its adult life covers nearly the same range of length ( Figure 9 ). An increase in fishing effort during the period would have affected all maturation cohorts similarly.

The values of Z _{s} for MC-3 and MC-4 ( Figure 6b ) are much lower than the corresponding Z _{s} for MC-5. It is unlikely that this phenomenon is caused by gear selectivity or low availability. There is some evidence, however, that fish maturing at ages 3 and 4 start spawning outside the area for the winter herring fisheries, for example, in northern Norway ( Runnstrøm, 1936 ). These fish then gradually recruit to the main spawning area, especially after hinge age. Thus, the low Z _{s} for these early maturing fish might be explained. A gradual recruitment of spawning herring of Icelandic origin could also have the same effect. Icelandic spring-spawning herring migrate from the spawning area southwest of Iceland to the feeding areas north and northeast of Iceland ( Fredriksson, 1944 ). This is the area where the Norwegian spring-spawning herring arrive at about the same time for feeding ( Fredriksson and Aasen, 1950 ). Based on scale readings, Rasmussen (1940 , 1950 ) observed Icelandic spring-spawners spawning on the west coast of Norway. Herring tagged north of Iceland ( Fredriksson and Aasen, 1950 , 1952 ) have been recorded during the winter fishing at the west coast of Norway. These observations strengthen the possibility of outside spawning-recruitment, and thus support the explanation of the low values of Z _{s} calculated for MC-3 and MC-4.

The observed decreasing trend of Z _{s} as maturation age increases from 5 to 9 in the Norwegian spring-spawning stock appears to be due mainly to a lower natural mortality rate M _{s} for later maturing herring during the senescent phase. To narrow this down further, the bold line in Figure 10 shows the central trend based on the year classes 1934–1949. Z _{s} decreases from around 0.82 for MC-5 to 0.26 for MC-9. If we are correct in our surmise that the fishing mortality F of 0.035 was essentially the same for all maturation cohorts, calculated as the mean for ages 11–14 in the VPA extracted from the period 1926–1939 ( Toresen and Østvedt, 2000 ), a line of natural mortality M _{s} decreasing with age at maturation can be constructed that is parallel to the previously fitted line for total mortality Z _{s} at a distance of 0.035 below it, decreasing from M _{s} of 0.79 for MC-5 to 0.23 for MC-9 (dashed line of Figure 10 ).

### 4.2 Longevity and growth

Maximum age (T _{max} ) and natural mortality (M) are dimensionally inverse, but only strict reciprocals if the latter is age-independent ( Beverton, 1963 ; Hoenig, 1983 ; Charnov and Berrigan, 1991 ). This appears not to be the case with the present data, but there may be a different relationship between T _{max} and M. The average values of senescent mortality rates (M _{s} ) from the regression against maturation age ( Figure 10 ) when plotted against mean normalized T _{max} ( Figure 7 ) indicate a linear relationship between the two parameters ( Figure 11 ). An extrapolation of this regression gives estimates of M _{s} of 0.93 for MC-3 and 0.78 for MC-4, very different values from those indicated earlier. An implication of Figure 11 is that the product of M _{s} and the normalized T _{max} varies linearly with age at maturation ( Figure 12 ). Extrapolation to MC-3 and MC-4 together with the mean normalized values of the respective T _{max} ( Figure 7 ) gives M _{s} for MC-3 and MC-4 of 1.16 and 0.98, respectively.

The growth parameter K and natural mortality M vary somewhat between species and populations. However, the ratio M/K is relatively constant, at least within similar groups of species ( Beverton, 1992 ). For the Norwegian spring-spawning herring, however, M _{s} /K is not the same for each maturation cohort ( Figure 13 is derived from Figures 8 and 10 ). The ratio M _{s} /K varies linearly with age at maturation for MC-5 to MC-9. Extrapolation to MC-3 and MC-4 gives predicted values of M _{s} /K of 3.97 and 3.47, respectively. Values for K of 0.34 for MC-3 and 0.31 for MC-4 (from Figure 8 ) imply values of M _{s} of 1.57 and 1.10, respectively.

As stated earlier, the observed Z _{s} 's for MC-3 and MC-4 are low compared with those for MC-5 through to MC-9 ( Figure 10 ). The extrapolations in Figures 11–13 give some guidance on true mortality rates for these maturation cohorts when allowance is made for the parts of the year classes maturing at 3 and 4 years outside the main spawning areas off western Norway and gradually recruiting to the main spawning stock. These extrapolations give a range of possible values of M _{s} for these maturation cohorts ( Figure 14 ). The central estimated M _{s} (covering all maturation cohorts) gives M _{s} equal to 1.10 for MC-3 and 0.90 for MC-4. That M _{s} should be lower for fish that mature later compared with those that mature younger makes physiological sense and is in accordance with general life-history patterns.

### 4.3 Comparison with general GML patterns for other groups

Beverton and Holt (1959) have shown that M in the long-lived clupeids is small in relation to the values for T _{max} and K. Both the ratio M/K and the product M×T _{max} (where T _{max} is normalized for sample size) are lower than for all other groups of fish so far examined, except perhaps for *Sebastes* spp. ( Beverton, 1992 ). This gives some basis for suggesting that the apparent truncation of the lifespan seen in the present herring data ( Figure 2 ), resulting in a smaller T _{max} than would be expected from a projection of the lifespan on the basis of the M for younger ages, is a real phenomenon. Toresen and Østvedt (2000) indicated an M of 0.15 for Norwegian spring-spawning herring. The present study indicates a total mortality Z _{ps} of 0.19 ( Figure 6a ) for herring that spawn eight times or less ( Figure 3 ). By applying a fishing mortality of F=0.035 for ages 5–12 of mature herring (Toresen and Østvedt, 2000) , the corresponding natural mortality M _{ps} is calculated to be 0.15.

Beverton (1992) gives values for M×T _{max} and M/K for long-lived clupeids derived from the literature. The product of M and T _{max} ranged from 2.5 to 3.5, with a central value of 3.0, and none of the values for M _{S} ×T _{max(norm)} in Figure 11 fall within this range. The values for M/K are within the interval from 0.35 to 0.60, with a central value of 0.50. None of the M _{s} /K values in Figure 12 correspond with those sampled by Beverton. However, it should be noted that his data refer to the entire stock of different clupeids, while the present study refers to the senescent lifespan for herring, the period after the hinge age.

It is interesting to place the findings of this study within the context of other species of fish. Some fish are very short-lived. The Cyprinodont *Nothobranchius guentheri* seldom lives longer than 12 months, having adapted to alternate rainy and dry seasons in East Africa. In laboratory experiments, Markofsky and Perlmutter (1973) differentiated between two groups, one short-lived and the other longer-lived. The short-lived fish matured earlier and on average grew to a smaller size than the longer-lived fish. Pacific salmon ( *Oncorhynchus* spp.) also have a severely limited lifespan, spawning only once. Briggs (1953) identified two distinct groups of coho salmon ( *Oncorhynchus kisutch* ), one with a maximum lifespan of 24 months and the other with a maximum lifespan of 36 months. Once again, experiments described by Childs and Law (1972) showed that the shorter-lived fish grew and, of course, matured more rapidly than the longer-lived fish. Thorpe (1989) also showed that smoltification and maturation in salmonids is associated with marked differences in immature growth. The present study suggests that the maturation cohorts comprising a year class of the Norwegian spring-spawning herring have different immature growth rates. There are also differences in size at maturity ( Figure 9 ), although these differences are of a relatively limited range. These characteristics are markedly different from the Northeast Arctic cod where, as described by Beverton *et al* . (1994) , all maturation cohorts have essentially the same immature growth rates. There is also no indication in that stock of a division of adult life into pre-senescent and senescent phases. Mortality rates are constant throughout adult life. We might speculate that *Clupea harengus* , intermediate in evolutionary terms between salmonids and gadoids, has a capacity only for a limited number of years of spawning and has evolved in such a way that the onset of maturity can occur over a range of ages.

Finally, the finding that the mortality rate M _{s} in the senescent phase of the Norwegian spring-spawning herring decreases with the age at maturation ( Figure 13 ) has important demographic implications. Since additional mortality due to fishing will change the relative contribution of young and old maturation cohorts in the total stock, it follows that the overall natural mortality in the senescent phase of an exploited stock is no longer constant, but is dependent on the intensity of fishing. Both for assessment and for the measurement and interpretation of changes in mean age and size at maturation, analysis on a cohort basis seems advisable. This conclusion stands whether the effect is due to fishing or environmental factors and follows especially from a consideration of genetics ( Law and Grey, 1989 ).

The authors wish to express their appreciation to the research assistants responsible for ageing herring from the scales at IMR. Oddvar Dahl worked from 1948 to 1970 and, after being trained by him, succeeded Thoralf Rasmussen who started under E. Lea about 1910.

## References

*Nothobranchius guentheri*(Peters)

*Clupea harengus*, Clupeidae) throughout the 20th century and the influence of climatic fluctuations