The sustainable yield of a living marine resource is not determined solely by resource size, but is also dependent on the combination of sizes and sexes caught. For example, the MSY (maximum sustainable yield) of a predominantly male fishery (e.g. west coast rock lobster) or predominantly female fishery, will be smaller than if the correct balance between sexes is maintained in the catch. Similarly, if one were to target only very large hake older than 8 years, then the MSY will be different to what would be possible if a wide range of age classes are targeted.
In other words, MSY is the maximum net production in the resource, for a particular mix of size or age classes, and a particular sex ratio in the catch. Theoretically, it is possible to work out what combination of sex and size/age classes will give the largest possible MSY. In fisheries science literature, the term ultimate sustainable yield (USY) has been used to describe this largest MSY value. In practise, the mathematically optimal strategy often requires impractical or unfeasible fishing strategies such as for example harvesting 30% of three year hake, and 100% of all 10 year olds.
The MSY associated with this strategy might only be slightly larger than the MSY for a much more practical strategy, the cost may be phenomenally larger, and for this reason there is not very much interest in advocating a harvesting strategy which leads to USY. Nevertheless, it is important to realise that different MSY levels can be achieved via different sex and size combinations.
Changes in the different sizes in the catch can be brought about by changing the fishing selectivity properties of the fishing gear by, for example, increasing or decreasing mesh size, imposing minimum and/or maximum legal sizes, or by targeting fishing effort in areas with known size classes. Fishing selectivity is measured as the number of fish caught per size or age group, expressed as a proportion of the total number of fish in that size or age group occurring in the population. The effect of changes in fishing method on fishing selectivity is illustrated by the difference in fishing selectivity between trawl gear (spectrum of size classes caught) and long line gear (mostly large sizes of hake caught) in the South African hake fishery.
Yield-per-recruit and selectivity by age and size
The description of sustainable yield presented previously was based on a simple concept of a renewable resource as a lump of matter (i.e. biomass) which has certain very basic properties (the need to regulate itself at a fixed level under unexploited conditions). This concept is a very useful one when one is interested in the productive potential of a resource with a view to determining the total allowable catch.
In reality however, fish populations are dynamic living entities. Fish are born, they grow, and they die. Sexual reproduction occurs. In this view of marine resources, it is of considerable value to try to determine how best to harvest a fish cohort over its lifetime. In particular, it is important to determine the age at which one should harvest fish so as to maximise the yield of the resource to the fishery.
To do this, one has to understand two important but competing effects that take place in all natural populations.
These are that with age, fish (i) die and (ii) grow. The first effect, also known as natural mortality, tends to reduce the biomass of a cohort of fish with the same birth date, while the other, referred to as somatic growth rate, tends to increase cohort biomass. The best age to harvest a cohort is when its biomass is at a maximum level. Fig. 1 shows a schematic of how the number of fish in a cohort decline as they age, and how individual fish might increase in size as they age.
By definition cohort biomass is the product of the two graphs, i.e. number of fish multiplied by body weight, and this product normally shows a maximum cohort biomass at some intermediate age. To maximise the yield of a cohort, one would therefore have to harvest all fish at the age corresponding to the maximum cohort biomass. This is normally quite impractical, and at any rate, it ignores an important biological process, natural reproduction. In the section below, the complications raised by reproductive processes are incorporated into our ongoing expose of quantitative fisheries science concepts.
The relationship between spawning biomass and recruitment
Spawning biomass is defined as the total mass of sexually mature and active fish in a population. There is a level of recruitment that has to be maintained from one year to the next in order to maintain spawning biomass at a given level. This level of recruitment would offset losses to natural mortality and keep spawning biomass at a static level. The relationship between this level of recruitment and the resultant spawning biomass is the straight line in Fig. 2, and is referred to as the replacement line. From the replacement line it is clear that the amount of recruitment required to maintain various fixed spawning biomass levels is proportional to the desired spawning biomass level, as one would expect.
The replacement level of recruitment is not necessarily the same as the amount of recruitment that a given quantity of spawning biomass is able to produce through normal reproductive processes. The curved line in Fig. 2 depicts the amount of recruitment generated reproductively by a given spawning biomass. Clearly, increasing or decreasing the spawning biomass does not result in a proportionate change in the amount of recruitment it is able to produce (in contrast to the proportional relationship that exists between spawning biomass and the amount of ongoing recruitment needed to maintain that spawning biomass level by offsetting losses to natural mortality).
The existence of curvature in the relationship between recruitment from reproductive processes and spawning biomass means that there is a single non-zero point where the replacement line and the curve meet. To the left of this point, the actual recruitment that is generated reproductively by the spawning biomass exceeds the amount of ongoing recruitment required to maintain the spawning biomass. As a result, in the unexploited situation, when the spawning biomass is to the left of the intersection point, it will tend to grow in size.
Conversely, to the right of the intersection point, the actual recruitment that is generated by the spawning biomass is less than the amount of recruitment required to maintain the spawning biomass, and spawning biomass will tend to decline over time. At the point of intersection, the recruitment generated through reproductive processes in the spawning population is equal to the amount of recruitment required to balance natural mortality and maintain the spawning biomass, and the population is said to be in a state of equilibrium, i.e. it neither grows nor declines in size over time.
The fact that the resource tends to grow when it is to the left of the equilibrium point is the basis for the existence of sustainable yield, i.e. the quantity of fish that can be harvested indefinitely without depleting resource biomass. The idea is that fishing keeps the resource below the unexploited equilibrium point by harvesting the extra growth that the population generates while trying to grow back to its unexploited state.
The fact that the species has survived over millions of years indicates that, at least as a long term average, some point of unexploited equilibrium exists. Synonymous with this, for the unexploited equilibrium point to exist, the recruitment generated reproductively by spawning biomass has to average out as a curve which intersects with the replacement line, as shown in Fig. 2. The reasons for the curvature are complex and probably involve many different factors, some acting individually, others interacting with each other in complex ways.
There is evidence from many different fisheries around the world that recruitment does exhibit the kind of curvature referred to here. For example, in many fisheries recruitment is not sensitive to spawning biomass when spawning biomass remains above a critical level of about 20% to 40% of the pristine spawning biomass level.
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