THE LINK BETWEEN SPAWNER ABUNDANCE AND SUBSEQUENT RECRUITMENT

6.2 THE LINK BETWEEN SPAWNER ABUNDANCE AND SUBSEQUENT RECRUITMENT

The spawner–recruit relationship is the basis for estimation of the key parameters needed to under- stand and manage fisheries, e.g. carrying capacity, maximum reproductive rate and the variability in recruitment. The wide scatter and the relatively ‘flat’ relationship often seen between spawners and subsequent recruitment misled the naive into dismissing such data without understanding what can be learned from it. Many fisheries biologists believed that the maximum reproductive rate is so high that recruitment would not decline at low spawner abundance. This belief was due to several factors. First, it had been observed for many fish populations that a reduction in spawner abun- dance was not accompanied by a corresponding reduction in the production of juvenile fish (Gilbert 1997). Furthermore, since many individ- ual fish can produce a million eggs or more, this has been taken as proof that there can be no shortage of juvenile fish (McIntosh 1899). It was only through

a very large meta-analysis of over 300 spawner– recruitment datasets that it has been widely ac- cepted that the production of juvenile fish does in fact decline when spawner abundance is greatly reduced (Myers and Barrowman 1996; Myers 1997).

The maximum reproductive rate for the popula- tion, or equivalently the maximum slope of the spawner–recruit curve, which is realized as the origin is approached where stock size is zero, deter- mines the limits to sustainable fishing and other sources of anthropogenic mortality that a popula- tion can sustain. The quantity, sometimes known

as the compensatory reserve, is the most funda- mental of all population parameters. Population biologists and national and international manage- ment agencies have come to a consensus that the maximum reproductive rate is the appropriate measure of the potential for a population to ‘com- pensate’ for fishing, and is used to construct management targets and limits (Sissenwine and Shepherd 1987; Clark 1991; Mace and Sissenwine 1993; Mace 1994; Myers and Mertz 1998). In this section, I examine examples of how this parameter is estimated. When spawners and recruits are expressed as absolute estimates of abundance, the maximum reproductive rate can be estimated directly from the fitted spawner–recruit relation- ship. This section explains the most common types of stock-recruitment models and provides examples of stock-recruitment data from a variety of fish populations.

The relationship between recruitment (R) and spawner abundance (S), perhaps expressed as num- bers or biomass, both of which are proxies for egg production, would take the form

(6.1) where a is the slope at the origin, and f(S) is usually

a monotonically decreasing function. As such f(S) is the relationship between survival and spawner abundance.

The parameter a in equation 6.1 defines the scope a population has to compensate for any form of increased mortality. For this parameter to be calculated in equation 6.1, it is necessary that the units of spawners and recruitment be the same. For species that die after reproduction (e.g. Pacific salmon, Oncorhynchus spp.) this is simple: one can count the number of female recruits for each female spawner. For species that do not die after reproduction, this is more complex. The process is explained below.

The estimation of a requires an extrapolation because we seldom have abundance estimates at extremely low population sizes. For this estima- tion we require a functional form of the density- dependent mortality, f(S), above:

Ricker (6.2) e ER S S () = - a b

= Sf S () a ,

Recruitment

a tory density-dependent mortality. There was no Beverton–Holt

ER () =

evidence for depensation in most spawner– SK )

recruitment time-series because compensatory

Shepherd

ER () =

g (6.4) mortality appeared to occur throughout the

1 + ( SK )

observed range of spawner abundances (Myers et al. 1995a). The clearest evidence for depensation

where E(R) is the expected recruitment and -b is occurred when population size was reduced to very the density-dependent mortality. The parameter K low levels, e.g. below 100 spawners. Some species has the same dimensions as the spawners, S, and groups, such as the Clupeidae, contained some may be interpreted as the ‘threshold biomass’ for datasets that were consistent with depensation at the model. For values of biomass S greater than the

a moderate abundance of around 20% of unfished threshold K, density-dependent effects dominate. spawner abundance, but it is unclear if this was The Ricker model shows overcompensation, i.e. at due to long-term environmental change or to high spawner abundances recruitment declines. depensation (Myers et al. 1995a; Liermann and The parameter g in the Shepherd model may be Hilborn 1997). We thus conclude that the assump- called the ‘degree of compensation’ of the model, tion that survival, f(S), is a monotonically decreas- since it controls the degree to which the (density- ing function for the observed range of spawner independent) numerator is compensated for by abundances appears to be an adequate approxima- the (density-dependent) denominator (Shepherd tion for most commercial species except at very 1982).

low spawner abundances. However, if populations

The Ricker and Beverton–Holt formulations are reduced to very low abundance, recovery may are standards in fisheries science, but require some

be very slow. For example, the spring-spawning explanation for general ecologists. First, the units herring (Clupea harengus) population in Iceland of R and S may be in biomass as opposed to num- has not recovered since the 1960s, and the cod bers. The reason for this convention is that egg pro- (Gadus morhua) populations in eastern Canada duction in many species is more closely related to have increased at a slower rate than predicted by the biomass of spawners than to the number of the data before the collapse. spawners. The slope,

I now examine several examples of spawner– fishing mortality that can be sustained in a deter- recruit data in which absolute abundances are ministic equilibrium. Note that in these models, estimated. These examples are from a wide variety all density-dependent mortality occurs during the of habitats, include heavily exploited and non- egg, larval or juvenile stage. That is, density- exploited populations, and use a great variety of dependent mortality occurs before the fish ma- techniques in their assessment of the populations. ture. This approximation is consistent with most We begin our examples with a sockeye salmon analysis of data for marine fish (Myers and Cadigan (Oncorhynchus nerka) population because its 1993a).

a, determines the highest

life history is simple to understand: almost all

The estimation of the slope at the origin re- females mature at 4 years, spawn once, and die. We quires an extrapolation to zero spawner abun- next consider brook trout (Salvelinus fontinalis), dance, and thus is an approximation. It is clearly

a slightly more complex example that was necessary to have at least two individuals for suc- experimentally manipulated to investigate cessful reproduction, and in general almost always density-dependent mortality. The last two exam- more for a population to be self-sustaining. Any ples examine more complex life histories. management system will attempt to keep the population size above the point where such depen- sation occurs. Myers et al. (1995a) and Liermann

6.2.1 Sockeye salmon

and Hilborn (1997) examined a large number of For the population of sockeye salmon in the commercially exploited fish stocks for depensa- Adams River, British Columbia, females almost

Chapter 6

always live for 4 years. Spawning females are units, in this case millions of females. If we plot the counted in the river; this is the number of one-to-one line, or the replacement line, then it is a spawners on the x-axis (Fig. 6.1). The number of simple matter to see how much the population females produced from this group of spawning would increase if there was no fishing on the females is simply the number that return to spawn population. It can be seen that in most years the

4 years later in the river, plus the number which number of replacement females produced per were harvested on their way to the spawning site. female was approximately five or six. The average Plotting the number of returning females against replacement rate at low abundance, where densi- the number of females that produced them yields a ty-dependent mortality is not important, is given classic spawner–recruit plot.

by the slope at the origin of the spawner–recruit

Both the spawners and recruits are in the same curve; this quantity is usually termed, by ecolo-

gists, the maximum reproductive rate. Based on the fitted spawner–recruitment curves, at low abundance a female can produce approximately

8 8 nine replacements. This allows the population to persist at very high fishing mortalities; typically

around 80% of the returning fish from the popula-

6 6 tion are harvested. However, this quantity also defines the limits of exploitation: the population

will decline if much more than 80% of the popula- tion is harvested on average, and a lower harvest

4 4 rate would be a much better management strategy. For Pacific salmon, it is relatively easy to calcu-

Resulting spawners

late the maximum reproductive rate because the

Recruits at age 4 (millions) 2 2 assuming no fishing (millions)

fish are usually relatively easy to count, and be- cause complications caused by multiple spawning and complex age structure are avoided.

6.2.2 Experimentally manipulated brook trout populations

Spawners (millions)

Fig. 6.1 Spawner–recruitment data for Adams River sockeye salmon (Oncorhynchus nerka), British

Most good population dynamics data come from Columbia, Canada. On the x-axis is the number of

heavily exploited populations. We now examine spawning females in the river for any one year. Each

seven populations that have experienced very point represents the production of spawners produced

little fishing pressure but which have been for each batch of spawners in a given year. These

experimentally depleted to determine the nature ‘recruits’ are adults that return to spawn 4 years later.

of density-dependent mortality (DeGisi 1994). An The solid and dotted lines are the maximum likelihood

fit for the Ricker and Beverton–Holt models respective- experimental approach has clear advantages in

ly. The straight dashed line is the replacement line. That that the experimenter can manipulate the popula- is, if a point is above this line, the population should

tions at will.

increase if no fishing occurs. If 1000 spawning females The seven brook trout populations are from produced 5000 recruits 4 years later, the population

small lakes in the Sierra Nevada Mountains in would have increased by five times during the 4-year

California. Population sizes were estimated using generation if no fishing had occurred. The solid curved

maximum likelihood depletion methods from line is the maximum likelihood estimate of the mean for

Ricker spawner–recruitment functions under the experimental gill-net surveys. These gave esti-

assumption that the probability distribution for any SSB mates of the number of mature fish present in the is given by a lognormal distribution. The curved dotted

population at the time of spawning and an esti-

Recruitment

group of spawners that survived to age 1. In this example, the unit of spawner abundance is the

number of mature fish present at the time of 500 spawning, and the recruits are the resulting num-

ber of fish that survive to age 1. 400 In interpreting these data, one problem imme-

diately becomes apparent: the units of spawners 300 and recruits are not the same, and thus it is not

possible to use these units to estimate the slope at 200 the origin as in the sockeye salmon example. To 40 Resulting spawners

20 100 to convert the units of recruits into the same units

overcome this problem, the standard procedure is

Recruits at age 1 (numbers)

assuming no fishing (numbers) as spawners. That is, we estimate the number of

0 0 spawners that would be produced from a given

150 200 number of recruits, if no fishing has occurred. We

Spawners (numbers) use the same natural mortality as estimated by the

analysis of these data (DeGisi 1994) and ask how Fig. 6.2 Spawner–recruitment data for brook trout many spawners would be produced from the (Salvelinus fontinalis) in the Hell Diver 3 lake in the observed level of recruitment. In this case, the age Sierra Nevada. On the x-axis is the number of spawning

at maturity is 2 and the natural mortality was adults for any one year. Each point represents the pro- duction of 1-year-old recruits for each level of observed

assumed to be close to 20% a year, although a recruitment on two different scales: on the left-hand side slightly different value was estimated by DeGisi. is the estimated number of trout that survive to age 1, We simplify slightly. Thus 80% of fish that reach and on the right-hand side is the resulting number of age 1 would survive to spawn if 20% died each year. spawners that would be produced if no fishing occurred Once a fish reaches maturity, we need to estimate on the cohort over the lifetime of the cohort. The scale how many times it would spawn on average in on the right-hand side is the scale on the left-hand side multiplied by the average number of times a 1 year old the absence of anthropogenic mortality. For this would be expected to spawn if no fishing occurred (see calculation, we sum the probability that a fish will text for explanation). The straight dashed line is the

be alive in each year after it reaches the age of replacement line. The intersection of the Ricker reproduction. This probability is 0.8 for the first spawner–recruitment curve (solid line) with the replace- year after spawning, 0.8 ¥ 0.8 = 0.64 for the second ment line represents the approximate equilibrium for year, and so on. This is known as a geometric the population. The dotted line is the Beverton curve. series, and its sum is 5 in our case. That is, a fish that survived to 1 year of age would spawn an aver- age of four times. This is calculated from the proba- recruits decreases below the equilibrium level, bility of surviving to spawn once, 0.8, multiplied while below this population size the production of by the average number of times the fish would recruits increases. spawn, five. To plot the spawners and recruits in

When the population was increased to high the same units, we multiply the number of recruits levels, average recruitment decreased in each of from each age-class by the average number of times the seven experimental lakes. This form of densi- they would spawn over their lifetime. This is the ty-dependent mortality, called overcompensation, scale on the right-hand axis of Fig. 6.2.

has rarely been so clearly demonstrated. The maxi- In each of the seven populations, the unex- mum reproductive rate for these populations is ploited population persists around an equilibrium

estimated to be around 19 replacement spawners population size. For example, the Hell Diver 3 per spawner from the Ricker model, a value that is population appears to produce an equilibrium similar in all the seven experimental populations when the number of spawners is between 150 and (Myers et al. 1999).

Chapter 6

stand the nature of the extrapolation to the origin. There are three data points where approximately

15 000 duction of replacement spawners of around 400 for this case, which results in a slope of around 8. The

50 spawners were observed, and we calculate a pro-

extrapolation to the origin increases a pattern that is typical for a curve with overcompensation. If

10 000 there are observations at low spawner abundances,

such as in Fig. 6.1, this is much less of a problem. Also note that the Beverton–Holt model does a

Resulting spawners very poor job of fitting these data, and results in an

Recruits at age 3 (millions)

effectively infinite slope at the origin. 0 0 assuming no fishing (thousand tonnes)

6.2.3 1500 Iceland cod

Spawners (thousand tonnes) The next example is the cod population from Iceland, based on data collected between 1928 and Fig. 6.3 Spawner–recruitment data for cod from 1995 (Fig. 6.3). The history of this population has Iceland. On the x-axis is the biomass of spawning adults been reconstructed from detailed catch-at-age for any one year. Each point represents the production of recruits for each level of observed spawner biomass on records over this time period and represents one two different scales: on the left-hand side is the recruits of the best-documented fish populations in the in millions of 3-year-old cod, and on the right-hand side world (Schopka 1994). This population has re- is the resulting spawning biomass if no fishing occurred cently shown only a small decline in recruitment on the cohort. To convert the scale on the left-hand axis even though spawning biomass has been reduced to the one on the right-hand axis, multiply the number of to less than one-tenth of what it was 50 years ago.

3-year-old fish by the average spawning lifetime biomass

More importantly, from the relatively low produced by one 3-year-old if no fishing occurred (see

text for explanation). The straight dashed line is the population level of 200 000 tonnes of mature fish, replacement line. The intersection of the spawner–

the stock can produce about 200 million 3-year-old recruitment curves with the replacement line represents recruits. Again, we can convert the production of the approximate equilibrium for the population if no these 200 million recruits to the same units as the fishing occurred. spawners. To do this, we ask how much spawning

biomass would be produced for each recruit, and then calculate the spawning stock biomass per re- dance can be estimated, and it is also generally the

cruit with no fishing, SPR F =0 , where the subscript F first age at which it is feasible to harvest. This cal- indicates dependence on fishing mortality, which culation results in the estimate that one 3-year-old is zero for this definition (Mace 1994). This is cod is expected to produce around 24 kg of spawn- calculated as

ing biomass, if no fishing occurs. That is, the 200 million recruits would be expected to produce

SPR F = 0 = Â wlp aaa ,

around 4.8 million tonnes of spawning biomass

aa = rec

over their lifetime. The maximum reproductive rate can be calculated from the Ricker curve in Fig.

where l a is the natural survival from the age of

6.3: at low population sizes, a spawner should pro- recruitment to age a, p a is the proportion of duce more than 20 replacements over its lifetime. fish mature at age a, w a is the weight at age a, and This population has sustained a relatively high

a rec is the age of recruitment, which is 3 years old rate of exploitation, which has typically seen over for Iceland cod. For explicitness, we must state 50% of the fish removed in any one year. Note that that a rec represents the first age at which abun- the slope at the origin for the Ricker model is much a rec is the age of recruitment, which is 3 years old rate of exploitation, which has typically seen over for Iceland cod. For explicitness, we must state 50% of the fish removed in any one year. Note that that a rec represents the first age at which abun- the slope at the origin for the Ricker model is much

The cod population in Iceland and the brook trout population from lakes in the Sierra Nevada Mountains differ in almost every possible way; however, their maximum reproductive rate is approximately the same in both cases.

6.2.4 Striped bass on the east coast of North America

Recently, a detailed assessment of striped bass (Morone saxatilis) on the east coast of North America has been completed (National Marine Fisheries Service 1998). The NMFS assessment can be used to estimate spawner recruitment for the years 1982–95. The biomass of spawners in- creased by a factor greater than five during this period, primarily due to reduced fishing mortality. The reduction in fishing mortality allowed many more fish to reach maturity, which also produced a subsequent increase in recruitment (Fig. 6.4).

The maximum reproductive rate is given by the slope at the origin of the spawner–recruitment plot. In this case, both the Beverton–Holt and Ricker models give similar estimates of the slope at the origin of the curve. The recruitment was

converted to spawning biomass in the same way as for cod described in the last section. These data show that, at low levels, the replacement level is almost 20 spawners per spawner in the absence of anthropogenic mortality, similar to that for the Iceland cod.

The high levels of compensatory reserve esti- mated from the spawner–recruit data are also seen from research surveys of the Hudson River popula- tion of striped bass. Pace et al. (1993) showed that the young-of-the-year (YOY) index of striped bass in the Hudson River was unrelated to the number of larvae. This implies either density-dependent mortality between the early larval stage and the establishment of the YOY index, or inadequate sampling of the YOY when their abundances are high (see Persson, Chapter 15, this volume). Since the analysis of Pace et al. (1993), spawning stock has continued to increase in the Hudson River. Resulting YOY indices have also remained relatively constant despite this increase in stock size (National Marine Fisheries Service 1998).