AFRF: Fisheries Assessment Primer

FISHERIES ASSESSMENT PRIMER:

Age, growth, and death:

Any reliable information about the fishing process or the biology of the stock contributes to the stock assessment. Among the basic biological information that fishery biologists find most useful are the age structure of the stock and the relation between fish length and age. Once this is known then important characteristics of the stock such as growth rate and death rate (mortality) can be determined. This information is used to create a picture of the stock which describes the current status of the stock.

Aging fish:
You cannot tell the age of a fish by looking at it. There are too many differences between species and within a species. Fish are normally aged by examining bony parts such as otoliths ("ear bones") that contain a record of growth like rings on a tree. Once it is established that each ring truly represents a year, then the age of a fish can be determined.

The usual procedure is to obtain fish from fishermen or from a fishery-independent sampling program, age them, and then compare the length and weight to the age of the fish. figure 1 - length at age This results in a length-at-age key in which the age of a fish can be estimated from its length. (See Figure 1 in which each x represents the length of an individual fish.) Also, by looking at the change in length and weight from a one-year-old fish to a two-year-old fish etc., the growth rate can be estimated. The more fish that are aged, the better the picture of the stock.

However, in the case of long-lived fish, growth usually slows in the older fish and past a certain point, the age cannot be readily assumed by the length of the fish. For example, it would be hard to tell the age of 20-inch fish in Figure 1 because a 20-inch fish could be between 4 and 8 years old. In these cases it is better to age as many fish as possible by the bony parts than to rely on the length, especially in the larger, older fish.

When enough fish have been aged, either directly or indirectly, a picture (catch curve) of the age structure of the stock may be drawn (Figure 2). Note that in this imaginary stock there are more two- year-old fish than one-year-old fish. figure 2 - age structure This does not make sense. We expect that the younger fish will be the more numerous and there will be fewer fish at each subsequent age due to fishing and natural causes. There are several possible reasons why fishermen are not catching one-year-olds in proportion to their abundance. The one-year-olds may not be abundant in the same areas as the older fish, or they may not be caught by the fishing gear, or they may be caught but thrown back. When fishery biologists see a graph like this, they say that the one-year-fish are "not fully recruited" to the fishery while the two-year-olds are considered to be "fully recruited." The first year a fish is readily harvested in a fishery it is referred to as a recruit.

A fishery assessment using the abundance of each age group is based on the portion of the stock that is fully recruited to the fishery. It would be desirable to know more about the unrecruited stock between the time of egg fertilization and the age of recruitment, but for many species there is little that management can do that would affect this part of the population.

For other species, management could affect water quality, the amount of suitable habitat, or even the death rate (bycatch, power plant entrainment, etc.) To promote greater survival of young fish before they research harvestable size (are recruited to the fishery).

More information from age structure:
The age structure of a stock is a sort of historic picture of the stock. It reveals something about the current status of the stock as well as the past history of the stock. Figure 3 is the age structure of a fish stock in 1986.

figure 2 - age structure What can be learned from just looking at this graph?

The fish are harvested starting at one year of age.
The species is very long-lived fish -- up to 36 years old.
The number of fish at each successive age (two to three, three to four, etc.) does not follow a smooth downward trend as previously shown in Figure 2.
Ages three to 11 appear to be particularly few in number. Eleven-year-old fish were hatched in 1975 (1986 - 11 = 1975). Three-year-olds were hatched in 1983.
Even though one and two-year-old fish appear relatively abundant, if we look at the age structure of 12-year-old fish out to 23-year-old fish (hatched between 1974 and 1963) we can see that they have not declined in numbers at the same rate as ages three to 11 appear to have declined. In fact, the number of fish that should have been alive from ages one to 11 can be estimated (see Figure 4) by drawing a line from around age 12 back to age one.
This backward project suggests that not only are there not as many three to 11-year-olds as might be expected, but the number of one and two-year-olds may be less than what existed in the 1960s to the 1970s.

figure 4 - age structure

Fishery biologists take this kind of pictoral information and quantify it (put numbers on it) in order to further describe the stock and test ideas about the health of the stock.

Summary of age structure:
The age distribution of a stock provides a graphic picture of the stock as it exists today and, in the case of long-lived fish, can reveal something about the past history. The picture by itself does not reveal how much fish can be caught but provides information which leads to the answer.

Mortality and spawning potential ratio (SPR):
Earlier we said the goal of fishery management was to determine how many (numbers) or how much (pounds) fish can be safely harvested from a stock. In simpler terms we want to know how many fish in a stock can die and still allow the stock to maintain itself. Fishery biologists refer to the rate at which fish die as mortality or the mortality rate. If 1000 fish are alive at the beginning of the year and 200 fish die leaving 800 at the end of a year, then the annual mortality rate is 20 percent (200 divided by 1000) and the survival rate is 80 percent (800 divided by 1000). Each year some fish die whether they are harvested or not. The rate at which fish die from natural causes is called natural mortality and the rate at which fish die from fishing is called fishing mortality.

While it is easy to understand these rates as annual percentages, fishery biologists must convert them to something called instantaneous rates to use them in mathematical formulas. As a result, in a fishery management plan you might see statements such as, "The instantaneous fishing mortality rate is 0.67 (F = 0.67" or that, "The instantaneous natural mortality rate is 0.1 (M = 0.1)." Sometimes the word instantaneous is omitted, but F and M are conventional symbols for instantaneous annual rates. Natural mortality (M) and fishing mortality (F) can be added together to get total mortality (Z). Unless regularly dealt with, these numbers do not mean much relative to our more intuitive understanding of annual percentages. Table 1 gives some examples of annual percentages and the corresponding instantaneous rates (F, M or Z).

table 1 Determining mortality from age structure:
The age structure diagrams (Figures 2 and 3) are a picture of the stock at the time the information was gathered. It is often assumed that if conditions remain the same, then as the younger fish grow older they will decline through time at about the same rate as the older year classes appear to have declined. For example, in Figure 2, there are 6.5 million two-year-olds and 2.5 million six-year-olds. It would seem likely that the current crop of two-year-olds will also be reduced to 2.5 million by the time they are six years old. In this case the annual mortality can be estimated by subtracting 2.5 million from 6.5 million to get 4.0 million and then dividing by 6.5 million to get 0.62 or 62 percent mortality. However, this mortality took place over five years, so the average annual rate is 0.62 divided by 5 which equals 0.12 or 12 percent. This corresponds to a total instantaneous mortality (Z) of 0.13.

Remember that in a fish population, the total mortality includes the fishing mortality and natural mortality. The above example for estimating total mortality from the age structure does not reveal how much of the total mortality is due to fishing mortality and how much is due to natural mortality.

Several methods are used to determine each mortality rate. For example, fishing mortality can be estimated from a tagging study. After a lot of fish from a stock are tagged, the percentage of tagged fish that are caught and reported is an estimate of the fishing mortality. Natural mortality is then calculated by subtracting fishing mortality from total mortality. Sometimes there is no available estimate of fishing mortality for a stock. However, fishery biologists may have a good idea of what the natural mortality might be from studying other similar stocks. In this case, natural mortalities (or a range of possible natural mortalities) can be subtracted from total mortality to get fishing mortality (or a range of possible fishing mortalities).

Spawning potential ratio:
Most recent fishery management plans attempt to define a rate of fishing mortality which, when added to the natural mortality, will lead to the rebuilding of a stock or the maintenance of a stock at some agreed upon level. The level being used in many management plans is based on the spawning potential ratio (SPR). The spawning potential ratio incorporates the principle that enough fish have to survive to spawn and replenish the stock at a sustainable level.

Spawning potential ratio is the number of eggs that could be produced by an average recruit over its lifetime when the stock is fished divided by the number of eggs that could be produced by an average recruit over its lifetime when the stock is unfished. In other words, SPR compares the spawning ability of a stock in the fished condition to the stock's spawning ability in the unfished condition.

As an example, imagine that 10 fish survive the first couple of years of life and are now large enough to get caught (recruited) in the fishery. Four are caught before they spawn (no eggs produced), three others are caught after they spawn once (some eggs produced), and the last three live to spawn three times (many eggs produced) before dying of old age. During their lifetime, the 10 fish produced 1 million eggs and the average recruit produced 100,000 eggs (1 million divided by 10).

In the unfished population, 10 fish survive as before. Three die from natural causes after spawning (some eggs produced) and the other seven spawn three times (very many eggs produced) before dying of old age. During their lifetime, these 10 fish produced 5 million eggs and the average recruit produced 500,000 eggs (5 million divided by 10).

The spawning potential ratio is then the 100,000 eggs produced by the average fished recruit divided by the 500,000 eggs produced by the average unfished recruit and is equal to 0.20 or 20 percent.

SPR can also be calculated using the biomass (weight) of the entire adult stock, the biomass of mature females in the stock, or the biomass of the eggs they produce. These measures are called spawing stock biomass (SSB) and when they are put on a per-recruit basis they are called spawning stock biomass per recruit (SSBR).

In the above example, the weight of fish that contributes to spawning could be substituted for eggs produced to get the SSBR for the fish stock. SSBR (fished) divided by SSBR (unfished) gives the SPR.

The concept of spawning stock biomass is illustrated in Figure 5. The graph shows the weight (biomass) of a stock at each age in the unfished condition compared to the weight of the stock when SPR = 20%. The adult fish in this stock spawn at age four so only the weight of fish four years and older sontribute to the spawning stock biomass.

figure 5 - spawning stockstructure

In a perfect world, fishery biologists would know what the appropriate SPR should be for every harvested stock based on the biology of that stock. Generally, not enough is known about managed stocks to be so precise. However, studies show that some stocks (depending on the species of fish) can maintain themselves if the spawning stock biomass per recruit can be kept at 20 to 35% (or more) of what it was in the unfished stock. Lower values of SPR may lead to severe stock declines.

Summary of mortality and SPR:
Fish die from either natural mortality or fishing mortality. Fishing and natural mortality added together equal total mortality. Total mortality can be estimated from age structure graphs. If either fishing or natural mortality can be estimated, then the remaining unknown mortality can be determined by subtraction from total mortality. Once fishing mortality and natural mortality are known, they can be used to examine the effects of fishing on the stock.

One way of looking at the effect of fishing mortality is to compare the spawning biomass of the fished stock to what it would be without fishing. The ratio of the fished spawning biomass to the unfished spawning biomass is called the spawning potential ratio (SPR). If the SPR is below the level considered necessary to sustain the stock, then fishing mortality needs to be reduced.