The relative role of density-dependent and density-independent survival in the life cycle of Atlantic salmon Salmo salar

Authors


Abstract

1. Density-dependent factors appeared important for the survival of juvenile Atlantic salmon in the River Imsa whilst density-independent factors were more important for the older fish at sea. In fresh water, density dependence was indicated by a stock−recruitment relationship with increasing loss-rates from eggs to smolts and from eggs to adults as egg density increased. 73% of the loss-rates were explained by variation in egg density. At sea, density independence was indicated by the lack of a significant relationship between loss-rates and smolt densities.

2. The relationship between smolt density and initial egg density was best described by an asymptotic ‘Cushing’ type relationship with a plateau at densities higher than approximately 60 000 eggs for the total river areas of 10 000 m2. The number of smolts developed from the eggs spawned varied between 350 and 2400.

3. The relationship between smolt biomass in wet mass (kg 10 000 m−2) or energy (kJ 10 000 m−2) and the amount of salmon eggs in the River Imsa increased asymptotically. Annual smolt biomass ranged from 13 to 88 kg 10 000 m−2, or 66 000 and 431 000 kJ 10 000 m−2. Variation in egg density accounted for approximately 45% of the variation in smolt biomass (mass or energy).

4. Total wet mass and energy of adults (kg 10 000 m−2 and kJ 10 000 m−2) produced in relation to the amount of eggs at the start of the year-class, were not significantly correlated, due to a high variation among years. The biomass of adults ranged from 73 kg 10 000 m−2 to 655 kg 10 000 m−2 and in energy from 370 000 kJ 10 000 m−2 to 3 270 000 kJ 10 000 m−2.

5. Total adult biomass (adults caught at sea and in rivers) and the returning adults to the River Imsa in mass or energy were correlated with the size of the smolt cohort from which they originated. Yearly total adult biomass ranged between 240 and 3711 kg 10 000 m−2, when the number of smolts ranged from 397 to 2751, respectively. The biomass of adults returning to the River Imsa was between 59 and 614 kg, produced from between 672 and 1621 smolts.

Introduction

The abundance of animal populations varies with time as do the rates of survival and reproductive success of individuals. Density-dependent factors provide a mechanism for population regulation by affecting birth rates, mortality rates and emigration rates (e.g. Elliott 1994). The chief density-dependent factor is often intraspecific competition for resources, which is most effective at high population densities. Other such factors are predation and parasites. At low densities, however, density-independent mortality caused by the abiotic environment is expected to be important for population abundance (Sinclair 1989).

Therefore, Haldane (1956) hypothesized that density-dependent factors are mainly working in benign environments whereas density-independent factors predominate under hostile conditions. This has, for instance, been supported by studies of upland and lowland populations of the spittle bug Neophilaenus lineatus, sparrow hawk Accipiter nisus in stable and declining forests and brown trout Salmo trutta in two highly different but neighbouring streams in England (Whittaker 1971; Newton & Marquiss 1986; Elliott 1989).

Fisheries theory assumes that early juvenile mortality is density-dependent while adult mortality is density-independent (Charnov 1986), and the same notion has been developed for coral reef fish and applied to theories of their community structure (Warner & Chesson 1985). In birds, which have lower reproductive rates than fishes, late juvenile prebreeding density-dependent regulation appears more common, whereas large mammals, with their low reproductive rates, are at least partly regulated through changes in fertility (Sinclair 1989).

Several mathematical models describing density-dependent population regulation have been applied with varying degrees of success in aquatic (Rothschild 1986; Shepherd & Cushing 1990; Fogarty, Sissenwine & Cohen 1991; Elliott 1994) as well as non-aquatic literature (Bellows 1981; May 1981). In salmonids, models describing the numerical relationship between recruits and adults have been tested, e.g. for brown trout Salmo trutta (Elliott 1994), Pacific salmon Oncorhynchus spp.; (e.g. Ricker 1954, 1975, 1989; Rounsefell 1958; Shepard & Withler 1958; Cushing & Harris 1973; Peterman 1980, 1981; Hilborn & Walters 1992) and Atlantic salmon Salmo salar L. (e.g. Elson & Tuomi 1975; Buck & Hay 1984; Chadwick 1985; Gardiner & Shackley 1991; Kennedy & Crozier 1993, 1995; Crozier & Kennedy 1995). In the case of brown trout the relationship between different age-groups of recruits and adults has also been tested (Elliott 1994).

Complex life cycles are common among animals with ontogenetic niche shifts and associated metamorphosis (Werner & Gilliam 1984). The holometabolous insects are well-known examples, but this also applies to vertebrates like fishes and amphibians (Jonsson & Jonsson 1993; Moran 1994). For example, Atlantic salmon live in fresh water as territorial parr for 1–8 years before transforming to smolts and migrating to the ocean (Metcalfe & Thorpe 1990). In the ocean, the salmon are free ranging in surface waters for 1–4 years before attaining maturity and returning to fresh water for spawning (Jonsson, Hansen & Jonsson 1991b). There may be very different mechanisms influencing the population size of a species exploiting such different environments due to different carrying capacities and defensibility of the resources of the habitats. In the case of the Atlantic salmon, we hypothesize that density is regulated in fresh water but not in the ocean. The reason is that rivers are very restricted in area and food availability can be defended by the territorial parr, whereas the ocean is vast in size and the abundant pelagic food resources cannot be defended by juveniles and adults (cf. Murray 1982).

In organisms with indeterminate and flexible growth like fishes, size, growth rate, biomass and production are influenced by abundance. At high population densities, food become restricted and the individual growth rate decreases with consequences for production and biomass (Fryer & Iles 1972; Craig 1987). This growth flexibility provides a plastic phenotypic response to changing environments, not necessarily influencing the genetics of the population. Biomass and production can be given in units of wet or dry mass (Chapman 1978; Mann & Penczak 1986), but the unit of energy gives a more objective measure that is easily comparable across cohorts within and among species and locations and which can be also related to the bioenergetics of the individuals (Craig 1980).

Here, we test the roles of density-dependent and density-independent relationships in the life cycle of Atlantic salmon in fresh water and at sea. The relationships are given in terms of number of individuals, wet mass and energy content.

Materials and methods

Study area

The River Imsa, located near the city of Stavanger, south-western Norway (58°50′N, 6°E), is 1 km long and approximately 10 m wide (total area equals approximately 10 000 m2), and drains Lake Liavatn into the Høgsfjord (32 £ salt). The annual mean water flow in the river is 5·1 m3 s−1, with the highest discharge during autumn and winter (mean value: 10 m3 s−1) and the lowest during summer (mean value: 2 m3 s−1; Jonsson, Jonsson & Ruud-Hansen 1989). The water temperature ranges from about 2 °C in winter to c. 20 °C in summer (Jonsson et al. 1989). Atlantic salmon and brown trout are the dominant species in the river, but Arctic charr Salvelinus alpinus, whitefish Coregonus lavaretus, three-spined stickleback Gasterosteus aculeatus and European eels Anguilla anguilla are also present, as well as rainbow trout Oncorhynchus mykiss, escaped from fish farms.

Fish traps are situated about 100 m above the river mouth and separately catch all ascending (box trap) and descending (Wolf trap; Wolf 1951) fish larger than c. 10 cm. Throughout the study period 1975–94, the traps were monitored twice a day. Natural tip lengths (cm; Ricker 1979), weights (g) and sexes of all fish were recorded and scale samples of the spawners were taken for age determination, before they were released downstream or upstream of the traps. There is no salmon fishing in the River Imsa.

Smolts

All wild Atlantic salmon smolts descending the River Imsa were counted during the period 1975–93. In the period 1975–79 one-third of the smolts descending the river were individually tagged with numbered Carlin tags (Carlin 1955), one-third were adipose fin-clipped and one-third were unmarked. This was to provide estimates of the mortality caused by handling, anaesthesia and tagging. Total return rates of adult Atlantic salmon to the River Imsa of unmarked, fin-clipped and Carlin-tagged smolts were 7·7% of the unmarked, 4·1% of the fin-clipped and 3·1% of the Carlin-tagged fish (Hansen 1988). The mortality of the Carlin-tagged fish relative to the unmarked fish (tagging mortality) was estimated to be (7·7 − 3·1)/7·7 = 59·7%. In the present study this figure has been used when adjusting for the tagging mortality. Furthermore, in 1980, the smolts were retained in the traps and not allowed to migrate to sea, but from 1981 and onwards all the Atlantic salmon smolts descending the river were individually tagged with Carlin tags.

From 1983 and onwards every tenth smolt descending into the trap was sampled for age determination by use of scales and otoliths (cf. Jonsson 1976). The smolt age distribution was used to calculate the actual numbers of smolts originating from different brood years and for previous years we assumed that the distribution was the average of that observed from the age determination.

Adults

All adult Atlantic salmon ascending the River Imsa were recorded from 1976 to 1994; in the trap at the river mouth, the fish were divided into two groups: One group was taken into the hatchery for stripping whereas the other group was released upstream of the trap for natural reproduction. This latter group was used for estimating the within river stock–recruitment relationship. In the period 1982–90, sea-ranched salmon of the River Imsa stock, that were hatchery-reared until smolting and then released at the river mouth, were also allowed to spawn in the river. From 1991 to 1993 no adults were released upstream of the trap for spawning in the river.

Adult Atlantic salmon from the River Imsa ascend rivers other than the home river. The mean observed straying-rate of wild River Imsa salmon is 9·5% (Jonsson, Jonsson & Hansen 1991a). This figure is based on recaptures of adults that were Carlin-tagged as smolts. The tagged adults were recaptured by anglers and fishermen both at sea and in rivers other than the River Imsa. For these fish, length, total mass and place of recapture and scale samples were registered. However, not all tags were reported, and crude estimates have suggested that about 50% of the tags were unreported (Hansen & Jonsson 1989). When estimating the overall survival from smolts to adults, we used this figure for correction when estimating the marine stock–recruitment relationship.

Relationships between fecundity (F) and total body mass (M) of the River Imsa Atlantic salmon are (Jonsson, Jonsson & Fleming 1996):

image

From these regressions, we calculated the number of eggs spawned, assuming that there was no mortality after the fish passed the trap, and that the females spawned all their eggs. Experimental tests indicated that this is a reasonable assumption (Fleming, Lamberg & Jonsson 1997).

Stock–recruitment estimate

The relationship between the number of recruits (R) to the population and the parental stock of fish (B) is in fisheries literature called the stock–recruitment curve (Wootton 1990). If number of offspring increases linearly with parental abundance, the relationship is density-independent. This means that there is a constant proportionate survival (p): R = pB. If the recruitment rate changes with density, the relationship is density-dependent. To estimate the stock–recruitment relationship we used the equation described by Shepherd (1982):

image

where K is the threshold biomass. The model parameters were estimated by non-linear least squares. We used this equation because it is rather versatile. Depending on the value of β the equation can display curves similar to (although mathematically different from) those of Ricker (1954), Beverton & Holt (1957) and Cushing (1973). For β > 1, the curves are dome shaped. The dome, however, has a more pronounced peak than that of the Ricker model (Elliott 1985). For β = 1, the curve is identical to that of Beverton and Holt. For β < 1, it mimics the Cushing equation, except that it has a finite slope at the origin. The null hypothesis tested is that there is no dependence of R on B; values of R vary randomly around a constant, estimated by the arithmetic mean value of R. The alternative hypothesis tested is that R is proportional to B, i.e. R = pB (Elliott 1985).

‘Key-factor analysis’ was used to compare the loss-rates between life stages (Varley, Gradwell & Hassell 1973). In this analysis, the population density was expressed on a logarithmic scale so that the total loss-rate was the sum of loss-rates between successive stages in the life cycle. We measured the loss-rate between the egg and smolt stages, ksmolt = loge (number of eggs in each year-class) – loge (number of smolts produced from an egg year-class), and between the smolt and adult stages, kadult = loge (number of smolts from an egg year-class) – loge (number of adults from the same egg year-class). Total loss-rate (K) is the sum of the loss-rates between the egg and smolt (ksmolt) and smolt and adult (kadult) stages. To test for density dependence, mortalities in different life stages (k values) were plotted against the initial density of the stage (or its logarithm) and tested for a significant relationship (Dempster 1975).

Energy measurements

We measured the energy contents (kJ) of 21 smolts caught in the trap in the River Imsa in May 1995 and of 15 male and 16 female adult salmon caught when ascending the river for spawning in November 1989 and 1995. The fish were sealed in polyethylene bags and frozen shortly after capture. While still partly frozen, the fish were dissected. The energy content of the fish was estimated by adding the energy in protein, lipid and carbohydrate in the tissue (Craig, Kenley & Talling 1978). Total protein content was determined by the analysis of Kjeldahl (Anonymous 1981), the lipid content according to Anonymous (1987), the carbohydrate according to Anonymous (1987) and the glucose according to Anonymous (1978) and Mason (1983) (details in Jonsson, Jonsson & Hansen 1997).

Results

Life history

The River Imsa supports a small population of anadromous Atlantic salmon spawning between Lake Liavatn and the river mouth. The juveniles (parr) use the river as a nursery, and smolt mainly as 2-year-olds. Based on samples of every tenth smolt during 1983–93, the mean age distribution of 1-, 2-, and Ð3-year-old smolts was 14, 78 and 8%, respectively. Smolts older than 3 years were rare, and only one 4-year-old smolt was caught during the sampling period (in 1983). In eight of the 11 years of sampling, more than 80% of the smolts were 2 years old. Furthermore, the proportion of 3-year-old smolts was high in 1983 (33%) whereas the proportion of 1-year-old smolts was high in 1990 and 1991 (32%). The mean body mass of 1-, 2- and 3-year-old smolts was 24, 38 and 52 g, respectively, with mean energy contents of 111, 187 and 262 kJ, respectively.

The River Imsa salmon mature sexually mainly as one-sea-winter fish. During 1976–94, 82% of the adults ascending the river were one-sea-winter fish and 18% were multi-sea-winter. The mean weight of one-sea-winter salmon was approximately 2 kg and that of multi-sea-winter salmon was 5·5 kg. The respective energy contents were approximately 8800 kJ and 32 000 kJ. The sex ratio (M/F) of the adults in the river during 1976–94 was 1·17. The majority of one-sea-winter salmon were males (60%), while the majority of two-sea-winter fish were females (76%).

Stock recruitment

The relationship between the number of smolts (S) and the number of eggs spawned (E) in the River Imsa was asymptotic (Fig. 1a). The increase in abundance of smolts was highest at low egg densities and started to level off at densities above c. 60 000 eggs per 10 000 m2 river area. However, the curve did not reach a maximum within the egg densities investigated (maximum 600 000 eggs per 10 000 m2). The number of smolts in each cohort varied between 337 and 2357 with the highest value in the 1978 cohort. When this year-class was omitted, the coefficient of determination increased from 0·49 to 0·75: S = (0·09E)/[1 + (E/7320)0·77], r2 = 0·75, d_f. = 11, P < 0·01. Furthermore, the relationship between the number of returning adults to the River Imsa and the initial number of eggs at the start of each year-class is described by an asymptotic curve (Fig. 1b). However, the relationship between the eggs produced by these adults and the number of eggs at the start of each year-class was not significant (r2 = 0·22, P > 0·05), because of the large variability among year-classes (Fig. 1c).

Figure 1.

Relationship, with ±standard error of the parameters in parentheses, between (a) number of eggs in the river (E) and number of smolts produced (S) (S = 0·11 (±0·28)E/{1 + [E/9129·3 (±35 131)]0·88 (± 0·24)}, d_f. = 12, r2 = 0·49, P < 0·01), (b) number of eggs in the river (E) and number of adults produced (A) (A = 0·62 (±71·7) E/{1 + [E/166·38 (±20 036)]0·98 (± 0·33)}, d_f. = 10, r2 = 0·30, P = 0·05), (c) number of eggs from the parent stock and number of eggs produced by the offspring year class, (d) number of smolts leaving the river (S) and estimated number of adults (A1) caught at sea and in freshwater (A1 = 0·30 (±0·03)S, d_f. = 16, r2 = 0·73, P < 0·01), (e) number of smolts leaving the river (S) and estimated number of returning adults (A2) to the River Imsa (A2 = 0·078 (±0·008)S, d_f. = 17, r2 = 0·38, P < 0·01). The numbers on parts (a), (b) and (c) refer to the year the eggs were spawned and on (d) and (e) to the year of smolt descent.

The number of adults surviving in the ocean increased linearly with the number of descending smolts from which these adults were produced; this applies both to the total number of adults caught in rivers and at sea (r2 = 0·73, d_f. = 16, P < 0·01; Fig. 1d) and to the number of adults returning to the River Imsa only (r2 = 0·38, d_f. = 17, P < 0·01; Fig. 1e). Furthermore, there was a significant relationship between numbers of multi-sea-winter salmon and one-sea-winter salmon caught in rivers and at sea from the same smolt cohorts (Fig. 2). In the earliest years of the study, from 1976 to 1981, the numbers of one- and multi-sea-winter fish were higher than in the later years, indicating a much larger population size at the beginning of the sampling period.

Figure 2.

Relationship between number of one- (G) and multi-sea-winter (M) salmon caught at sea and in freshwater, produced from the same smolt-year-class (M = 0·52G − 27·59, d_f. = 15, r2 = 0·71, P < 0·01). The figure given at each point is the year of the smolt migration to sea.

In the River Imsa, the loss-rates from eggs to smolts and from eggs to adults appeared to be density dependent, as the loss-rates increased with increasing egg density (Fig. 3a,b). Furthermore, 73% of the variation in loss-rates was explained by the variation in egg density. At sea, however, the loss-rate was density independent as there was no significant difference in loss-rate with changing density (Fig. 3c: r2 = 0·15, P > 0·05 and Fig. 3d: r2 = 0·12, P > 0·05). A graphic illustration of the key factors from eggs to smolts and from smolts to adults as well as the total K, shows that the pattern in total loss-rates resembled that from eggs to smolts more than that of smolts to adults (Fig. 4). This indicates that freshwater survival was the main factor influencing the abundance of returning adults.

Figure 3.

Relationship between (a) number of eggs (Se) and loss-rate of the smolts (ln Se/ln Rs), where Rs is number of smolts; ln (Se/Rs) = 0·67 ln Se− 3·22, d_f. = 13, r2 = 0·73, P < 0·001, (b) number of eggs (Se) and the loss-rate of the parent stock [ln Se/ln Ra (adults)]; ln (Se/Ra) = 0·92 ln Se− 3·62, d_f. = 11, r2 = 0·73, P < 0·001, (c) number of smolts and loss-rate of Atlantic salmon until fished in the ocean and (d) number of smolts and loss-rate of the Atlantic salmon until ascending the River Imsa as adults (fishing including).

Figure 4.

(a) Total loss-rate, (b) loss-rate in freshwater and (c) loss-rate at sea in each egg year class of Atlantic salmon.

Biomass and energy

The relationships between smolt biomass (Pmass, kg 10 000 m−2) and number of eggs spawned (E) in the River Imsa is asymptotic (Fig. 5a). The relationship between energy of smolts (Penergy, kJ 10 000 m−2) and number of eggs can be given by a similar model: Penergy = 12·94 (±17·20) E/{1 + [E/22 351 (±41 638)]1·01 (±0·26)}, d_f. = 12, r2 = 0·45, P < 0·01). The ±standard error of the parameters is given in parentheses. The increase in mass was highest at low egg densities and started to level off at densities of c. 60 000 eggs per 10 000 m2 river area. The yearly biomass of smolts in the River Imsa ranged in mass from 13 kg per 10 000 m2 (in 1983) to 88 kg per 10 000 m2 (in 1978), in energy equivalent to between 66 000 kJ per 10 000 m2 and 431 000 kJ per 10 000 m2. The number of eggs produced in 1978 gave higher biomass estimates than all other egg year-classes studied. When the 1978 figure was omitted from the regression, the coefficient of determination increased and the correlations were: Pmass = (0·00192 E)/[1 + (E/24 533)0·91], r2 = 0·71, d_f. = 11, P < 0·01 and Penergy = (9·38 E)/[1 + (E/25 153)0·92], r2 = 0·69, d_f. = 11, P < 0·05. The variation in egg density accounted for almost 70% of the variation in smolt production in mass and energy, when the 1978 egg year-class was omitted, or c. 25% higher than when the 1978 egg-year class was included.

Figure 5.

Relationship, with ± standard error of the parameters in parentheses, between number of eggs (E) in the river and (a) wet mass of smolts produced (Pmass, kg 10 000 m−2) (Pmass = 0·003 (±0·004) E/{1 + [E/21 385 (±43 977)]1·00 (± 0·25)}, d_f. = 12, r2 = 0·46 P < 0·01), (b) mass of the adults produced, (c) mass of the eggs produced, (d) relationship between number of smolts (S) and estimated total wet mass of adults (A1 mass) (A1 mass = 3·30 (±46·39) S/{1 + [S/9960 (±419 620)]−0·59 (±3·14)}, d_f. = 14, r2 = 0·69, P < 0·01), and (e) between number of smolts (S) and estimated wet mass of returned adults (A2 mass) to the River Imsa (A2 mass = 0·16 (±0·02) S, d_f. = 17, r2 = 0·43, P < 0·01). The numbers on parts (a), (b) and (c) refer to the year the eggs were spawned, and on (d) and (e) to the year of smolt descent.

The relationship between wet mass (kg per 10 000 m2; Fig. 5b) and energy of adults (kJ per 10 000 m2) and the amount of eggs at the start of the year-class was not significantly correlated due to high variability among years. A dome-shaped model gave the best fit with a coefficient of determination as low as 0·23 for both wet mass and energy, but none of the relationships were significant (P > 0·05). The biomass of adults ranged from 73 kg per 10 000 m2 (in 1983) to 655 kg per 10 000 m2 (in 1985) and in energy from 370 000 kJ per 10 000 m2 to 3270 000 kJ per 10 000 m2. Furthermore, the relationship between the number of eggs of the parental population and the eggs of the offspring was not significantly correlated (Fig. 5c). The same holds true if the eggs were measured in energy (kJ). In both cases a non-significant dome-shaped curve gave the best fit (r2 = 0·22, P > 0·05). The egg production in mass ranged between 6·7 kg in 1983 and 49 kg in 1985. The corresponding values in energy were 50 647 kJ and 373 885 kJ.

The total adult biomass (adults caught at sea, in the River Imsa and in other rivers) and the returning adults to the River Imsa were significantly correlated with the size of the smolt cohort from which they originated (Fig. 5d,e). When the biomass was measured in energy (kJ) the relationship between total adult mass (A1 energy) and number smolt (S) was: A1 energy = 63·96 (±154·36)S1·56 (±0·31), d_f. = 15, r2 = 0·70, P < 0·01. The energy of the adults returning to the River Imsa (A2 energy) in relation to number of smolts was: A2 energy = 819·61 (±92·59)S, d_f. = 17, r2 = 0·46, P < 0·01. Standard errors are given in parentheses. The yearly total biomass ranged from 240 kg per 10 000 m2 in 1993 to 3711 kg per 10 000 m2 in 1981, when the number of smolts ranged from 397 to 2751. In energy the total production ranged from 1133 961 kJ in 1993 to 19 711492 kJ in 1981. The corresponding values for the adult biomass 10 000 m−2 in the River Imsa were 59 kg in 1982 and 614 kg in 1988, with smolt numbers between 672 and 1621. The relationship between adult biomass and smolt density seemed to be density-independent.

Discussion

Density-dependent survival appears to determine the number and biomass of Atlantic salmon smolts leaving the River Imsa. Thus, there seems to be a carrying capacity limiting the population size in fresh water. In the North Atlantic Ocean, on the other hand, density-independent factors were important. In this habitat, the population size of salmon is small compared with many other pelagic fish species. Therefore, freshwater survival influenced the number of adult Atlantic salmon returning to the river. This can be seen both from the shape of the stock–recruitment curve and the fact that the loss rate in fresh water, but not at sea, increased with egg density. The stock–recruitment curve of juveniles in fresh water, which was close to that described by Cushing (1973), increased rapidly at low egg densities and started to level off at egg densities of approximately 60 000 eggs 10 000 m−2, or 6 eggs m−2. This shape of the recruitment curve is similar to those found for Atlantic salmon by Buck & Hay (1984) in Scotland, Chadwick (1985) in Newfoundland & Kennedy & Crozier 1993, Crozier & Kennedy (1995) from Ireland. The recruitment curve of North Sea herring is also similar (Rothschild 1986). In brown trout (Elliott 1994) and several Pacific salmon (Ricker 1954, 1975, 1989), the alternative density-dependent ‘Ricker-curve’ describes the population survival better. Gardiner & Shackley (1991) also fitted a dome-shaped stock–recruitment relationship for juvenile Atlantic salmon in a Scottish stream, and a similar relationship was found by Gee, Milner & Hemsworth (1978) for Atlantic salmon in the River Wye. The reason why the stock–recruitment relationship in these cases differed from the present relationship and those fitted by Buck & Hay (1984), Chadwick (1985) and Kennedy & Crozier (1993, 1995) is unknown, but may indicate that the factors regulating population size vary among systems.

The asymptotic stock–recruitment relationship is the appropriate curve if there is a maximum abundance of the population imposed by food availability or space, or if a predator can adjust its predatory activity immediately to changes in its prey abundance (Ricker 1975). The dome-shaped stock–recruitment relationship is the proper model when the cause of the density dependence is cannibalism of the young by adults, or an increase in the time it takes for the young to grow through a vulnerable size range, or when there is a time-lag in the response of a predator or parasite to the abundance of the fish being attacked. In the River Imsa, the smolt abundance is probably imposed by food availability and space limitations.

The exact optimal egg deposition in the River Imsa could not be determined from the Shepherd (1982) model used (although it did not increase much between 6 and 60 eggs m−2 river area); it appears to be higher than that in other Atlantic salmon streams investigated. In tributaries to the Miramichi River and the Pollett River in Canada, Elson (1975) estimated that an egg deposition of 2·4 eggs m−2 gave optimal smolt production in suitable rearing habitats. Chadwick (1985), on the other hand, maintained that this value was too low, in spite of its wide use in eastern Canada. In the small Girnock Burn, Scotland, Buck & Hay 1984) counted the number of upstream migrating spawners and downstream descending smolts. Their estimate of optimal egg density was 3·4 eggs m−2. As in the present case, both Chadwick (1985) and Buck & Hay (1984) gave asymptotic stock–recruitment relationships. Optimal egg deposition of anadromous brown trout in the Black Browse Beck in the Lake District, England, on the other hand, is one order of magnitude higher than that of Atlantic salmon in the River Imsa. The reason for this difference is unknown.

In general, causes of density-dependent mortality in fish populations are generally unknown, except that this is an interaction between food supplies and predators affecting early larval stages. High densities lead to competition and lack of food, which causes slow growth and mortality, either directly or indirectly through increased vulnerability to predators (Sinclair 1989). Cushing (1981) found that the degree of regulation acting on a population was directly related to the fecundity of marine fishes. Species with high fecundity experienced strong regulation and species with low fecundity showed weak regulation. Salmonids, with their large eggs, should consequently show weak regulation. Nevertheless, Elliott's (1994) study of young brown trout in the Black Browse Beck is one of the best examples of population regulation in vertebrate species.

In the ocean, density-independent factors seemed important for the survival of the fish, in accordance with our hypothesis presented in the introduction. The number of adults increased recti-linearly with annual smolt number: the higher the average smolt output, the higher the average number of returning spawners. This indicates that the population density is far below the carrying capacity for Atlantic salmon in the North Atlantic. This agrees with the observation that individual growth rate and asymptotic size are much higher at sea than in fresh water. When the population size approaches the carrying capacity of the habitat, individual growth rate and asymptotic fish size should be small due to the plastic growth performance of fishes (Wootton 1990).

A low salmon abundance, relative to the carrying capacity for the species, might be judged as if the ocean is a hostile habitat for salmon (Haldane 1956). The high marine mortality rate gives support to this assumption. However, low recruitment of smolts relative to the carrying capacity of the system would lead to the same results, and the natural smolt output today is certainly much lower than it used to be in historical times. We feel that a combination of the two is limiting the abundance of adults returning to rivers for spawning, and that the abundance of adults would increase given a higher recruitment rate. In the present study, the high tag mortality (60%) and the killing of 10% of the smolts for age determination are important mortality factors. These mortalities were, however, controlled for in the present estimates. General reasons restricting the recruitment of smolts to the North Atlantic are river regulation and dam building that constrain salmon migration into rivers, pollution and acidification of rivers and fish diseases like gyrodactylosis reducing the survival of salmon and young fish in particular (Johnsen & Jensen 1986; Hesthagen & Hansen 1991). A factor working in the opposite direction is the constant output of farmed salmon into the ocean (Hansen, Jacobsen & Lund 1993; Hansen, Reddin & Lund 1997). At present between 25 and 40% of the Atlantic salmon in the oceanic feeding areas in the north Norwegian Sea are of farmed origin. Whether or not the escape of farmed salmon in the long run will increase salmon abundance in the ocean is, however, highly questionable (Hindar, Ryman & Utter 1991; Jonsson 1997).

Density-independent factors are widely believed to be important contributors to variations in population abundance of marine fishes and Peterman (1981), for example, gave evidence for density-independent marine survival in the Oregon coho salmon Oncorhynchus kisutch, and ocean climate may be the prime determinant of the annual changes in mortality (cf. Frank & Leggett 1994). The productivity of sockeye salmon Oncorhynchus nerka in Bristol Bay appears to be strongly related to fluctuations in climate (Adkinson et al. 1996), and the major change in climate over the Pacific Ocean in the winter of 1976–77 seemed to result in a change in productivity of the Fraser River sockeye salmon (Hare & Francis 1995; Beamish, Neville & Cass 1997). For Atlantic salmon, surface water temperature in the North Atlantic Ocean appears to be a promising candidate for the explanation of year class variation in abundance of adult Atlantic salmon in Europe (Friedland, Hansen & Dunkley 1998).

In contrast to large mammals, adult density dependence in population regulation occurs seldom in fishes (Cushing 1988, 1996; Sinclair 1989; Shepherd & Cushing 1990; Bradford 1992; Elliott 1994), and there was no evidence for it in the present investigation. If such a situation occurs, there should be resource limitation for adults but not for younger individuals (Shuter 1990). This may occur in densely populated stocks because the food requirements differ between adults and juveniles (larger particle sizes and amounts), due to their larger body size as found for Arctic charr by Forseth, Ugedal & Jonsson (1994). Hamrin & Persson (1986) proposed that this asymmetric competition was the prime mechanism behind fluctuations in year class abundance of vendace Coregonus albula in Scandinavian lakes (but see Sandlund et al. 1991 for an alternative explanation). In resident brown trout, Elliott & Hurley (1998) found that the number of spawning females produced in each year class was strongly density-dependent on the initial number of females that laid eggs at the start of the year class, and is probably the first clear evidence for fish population regulation in the adult, rather than the juvenile stage. Obviously, there is no similar situation in Atlantic salmon feeding in the North Atlantic Ocean.

One might have expected positive density dependence of salmon at sea. Sea survival might increase with number of recruits due to improved navigational accuracy (Quinn & Fresh 1984) or increased survival due to a possible functional response of the potential predators (Wood & Hand 1985). There is, however, no support for such effects within the present variation in population sizes tested. On the other hand, there was a slight positive increase in total biomass of adults in years with high rather than low smolt numbers indicating a positive effect of smolt abundance on fish size in the ocean. A similar effect was not found for the fish returning to the River Imsa (Fig. 5).

The fit of a stock–recruitment model to the data provides strong evidence for density-dependent regulation at some stage in the life cycle, but does not indicate at which stage or stages, and it provides no explanation of the mechanism by which density-dependent survival occurs. Here population regulation occurred in fresh water but not in the ocean.

Acknowledgements

We are indebted to the staff of the Norwegian Institute for Nature Research, Research Station at Ims for emptying the fish traps every day all year round in all kinds of weather, to Torbjørn Forseth for helping with the statistical treatment of the data and to J. Malcolm Elliott and Neil Metcalfe for excellent criticism of an earlier draft of the manuscript.

Received 18 September 1997;revision received 22 December 1997

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