Sure, here is an example of a scenario where one of the three assumptions of conventional stock assessments is violated:
Management unit: A single fishing zone that encompasses two distinct biological units.
Biological units: A northern unit and a southern unit. The northern unit is characterized by colder water temperatures and a higher abundance of prey fish, while the southern unit is characterized by warmer water temperatures and a lower abundance of prey fish.
Assumption: The assumption of homogeneity. This assumption states that all fish within a management unit are essentially the same, and that they are all subject to the same fishing pressure.
Violation: The assumption of homogeneity is violated in this case because the two biological units are different in terms of their environmental conditions and prey availability. This means that the fish in the two units will respond differently to fishing pressure.
Misleading stock assessments: If a stock assessment is conducted within the management boundaries of this fishing zone, it is likely to be misleading. This is because the assessment will not take into account the differences between the two biological units. As a result, the assessment may underestimate the impact of fishing on the southern unit, and overestimate the impact of fishing on the northern unit.
Discussion: The violation of the assumption of homogeneity can have a significant impact on the accuracy of stock assessments. This is because the assumption is often used to simplify the stock assessment model, which makes it easier to calculate the stock's biomass and productivity. However, the simplification of the model can also lead to the omission of important factors that can affect the stock's dynamics.
In the case of the fishing zone described above, the violation of the assumption of homogeneity could lead to a stock assessment that underestimates the impact of fishing on the southern unit. This is because the assessment will not take into account the fact that the fish in the southern unit are more sensitive to fishing pressure than the fish in the northern unit. As a result, the assessment may recommend a fishing quota that is too high, which could lead to overfishing of the southern unit.
It is important to note that the assumption of homogeneity is not always violated. In some cases, the fish within a management unit may be homogeneous enough that the assumption can be used to simplify the stock assessment model without significantly affecting the accuracy of the assessment. However, it is important to be aware of the potential for the assumption to be violated, and to take steps to mitigate the impact of the violation if it does occur. Hope this helps.