The Froese Length-Based Sustainability Indicator

Using length-frequency of the catch (the numbers of fish in each size class), three simple and easily understood indicators are estimated to assess the status and trends of the fishery using this method. The percentage of mature fish, optimal sized fish and "mega-spawners" (large fish that contribute disproportionately to egg production) are calculated using life history parameters, maximum length (L∞), and length-frequencies from catch data.

Inputs:

• Common Life History Parameters
• Length-frequency of the catch
• Theoretical maximum length (L_∞)
• Theoretical length at age zero (t₀)
• Length at maturity (L_m)
• Expert knowledge of any biases in the data that would make the length composition of the catch less representative of a random sample (e.g., variable catchability of different sexes or length classes by the gear; catch coming from nursery grounds; etc.)

Outputs:  

Three metrics of fisheries sustainability:

• Percentage of mature fish in catch, with 100% as target;
• Percentage of individuals in the catch with optimum length (L_OPT), with 100% as target; and
• Percentage of "mega-spawners" in the catch. If catch can be assumed to reflect the age structure of the population (i.e., if no selectivity mechanisms are in place) than 30-40% of mega-spawners in the catch would likely represent a healthy population, with 20% being a lower limit. If, however, the catch cannot be assumed to reflect the age structure of the population, then 0% would be the target for mega-spawners in the catch. 

Input Sensitivities, Assumptions and Caveats:

• Assumes individual fish length measurements are accurate and format of measurements (i.e., total length, standard length, or fork length) are consistent
• Assumes life history parameters (e.g., maximum length, length at maturity and size frequency) are accurate
• Assumes length composition of the sample is representative of total catch (i.e., not overly selective of some size classes for any reason)
• Assumes length composition of the catch is representative of the population OR selectivity of catch is accounted for by selecting a portion of the length composition data that is relatively unaffected
• L_M = length at sexual maturity
• Length-based proxy for MSY is L_MSY = 0.75*L_C + 0.25*L_INF (where L_C is the length at first capture) 
• Length of optimal yield is L_OPT = 2/3 of L_INF
• L_MEGA = L_OPT + 10%

Reference points:

• Proxy reference points for proportions of catch in different length categories for precautionary management, monitoring, and assessment.  Also useful for creating harvest control methods (e.g., size or slots limits to manage both recruitment and growth overfishing) to help with rebuilding a target fishery.

Recommendations:

Can be combined with methods that estimate F or a reference value for F, effort can be adjusted through harvest control methods (e.g. catch size limits, seasons, or spatial closures) based on how far apart these values are from sized based recommendations.