## Implementation of MPs to Control Size Limits

This section includes parameters describing the management agency’s ability to implement an MP that institutes an size limit. For example, an MP may specify a certain size limit, but the managing agency may be unable to limit all take of undersized fish.

SizeLimFrac and SizeLimSD allow the user to specify the actual size of fish retained as a fraction of the desired size limit in the form of a distribution that allows variability between simulations and years.

### SizeLimFrac

Mean fraction of recommended size limit that is actually retained. For each historical simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is the mean size limit fraction obtained across all years of that simulation, and a yearly size limit fraction is drawn from a log-normal distribution with the simulation mean and a coefficient of variation specified by the value of SizeLimSD drawn for that simulation. If the value drawn is greater than 1 the size of fish retained is greater than that recommended by the size limit, and if it is less than 1 the amount of size of fish retained is less than that recommended by the size limit. Positive real numbers.

### SizeLimSD

Log-normal coefficient of variation in the fraction of recommended size limit that is actually retained. For each historical simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is used, along with the SizeLimFrac drawn for that simulation, to create a log-normal distribution that yearly values speciying the actual fraction of the size limit retained are drawn from. Positive real numbers.

### Custom Parameters

See Custom Imp Parameters for information on specifying simulation- and year-specific implementation error values.

### Interactive App

Choose upper and lower bounds for SizeLimFrac and SizeLimSD, as well as the desired minimum size limit. Based on these ranges, the parameter values for 5 simulations will show in the table. Click on any line of the table to view how those parameter values affect the implemented size limit in a hypothetical situation where the desired size limit is specified in the ‘Size Limit’ box.

• Figure 1 shows the effects of size limit implementation error over 50 projection years in a single simulation. The red line shows the size limit recommended by a hypothetical MP, while the blue line shows the actual minimum size of fish retained in each year. The location of the blue line relative to the red line is influenced by whether SizeLimFrac is greater or less than 1, and the variability of the blue line over time is influenced by the value of SizeLimSD, with larger values resulting in greater variation between years.

• Figure 2 shows an example size frequency of the catch under the recommended (pink) and implemented (blue) size limits (note that sizes where the colors overlap show up as a darker blue color). Size structures are a product of the biological parameters, fishing mortality history, and selectivity of the gear, so this size structure is for illustration purposes only and may look different from real-world data.