The Length-based Integrated Mixed Effects (LIME) method for estimating Spawning Potential Ratio (SPR) works by simulating population dynamics for different age groups (using length as a proxy for age) under varying levels of fishing mortality and recruitment. This allows for the estimation of SPR without depending on the assumption that the population is currently at equilibrium. Additionally, LIME helps analysts tell whether a shift in length composition of the catch (e.g., higher proportions of small fish being caught) is likely due to a shift in fishing mortality, or to a recruitment pulse (e.g., a bigger batch of juveniles joining the population in a given year), which is difficult to determine using other methods (though local knowledge can help). Each annual recruitment is treated as a random event, while mean recruitment and standard deviation are treated as fixed effects.
LIME uses length of individuals in the catch as a proxy for age based on standard relationships between length and age, so it requires at least one year of length-frequency data. Maximum Sustainable Yield (MSY) is estimated by finding the fishing mortality rate that maximizes Yield-per-Recruit. One of the strengths of LIME is that it can accommodate catch trend and fish abundance data to improve the accuracy of the SPR estimates. Moreover, with the addition of catch and abundance data, LIME can be used to estimate spawning stock biomass and catchability.
Simulation testing indicates that LIME produces unbiased estimates of SPR across a range of fishing mortality and recruitment scenarios for a wide variety of species with different life history types (e.g., opportunistic: small, rapidly maturing, short-lived fishes; periodic: highly fecund fishes with longer life spans; and equilibrium: fishes with fewer offspring but with high parental care and juvenile survivorship), although the method may overestimate SPR for short-lived species (less than 20 years). Using a monthly time step in the model when assessing short-lived species can reduce this bias, while an annual time step results in good results for longer-lived species. Simulation also suggests that at least 100 fish from the catch should be sampled for best results and that care should be taken to include samples from the full range of length frequencies.
Methods like LIME that do not assume equilibrium may be especially important in fisheries that are strongly affected by climate change, since this increases the risk of non-equilibrium conditions. For more information on LIME, see Rudd and Thorson (2017) and to run LIME, click on the GitHub link (see below).
Inputs:
- Length-frequency data from the catch (sample size at least 100 fish for species that live less than 20 years, at least 500 for species that live longer than 20 years)
- Life history parameters (fecundity, von Bertalanffy (k), natural mortality (M), age-at-maturity, length at age relationships)
- Weight to length parameters (Wa, Wb)
- Fecundity at age parameters (fa, fb)
Outputs:
- Selectivity of the gear (lengths at which 50% and 90% of the fish are caught)
- Maximum Sustainable Yield
- Fishing mortality
- Fishing mortality rate that maximizes yield per recruit
- Spawning Potential Ratio (the ratio of current reproductive capacity to maximum potential reproductive capacity of an unfished population)
- Spawning stock biomass (if catch and biomass data are added)
Input Sensitivities, Assumptions and Caveats:
- Assumes individual fish length measurements are accurate
- Assumes length data are representative of length distribution in stock
- Assumes Natural mortality rate (M) is known and accurate
- Assumes life history data are accurate, particularly sensitive to growth and maturity parameter
- Assumes length samples represent length composition of the catch without bias
Reference points:
- FMSY
- Target reference point for fast growing species: SPR20; slow growing species: SPR40
Recommendations:
- Adjust fishing mortality with harvest control methods (e.g. catch limits, seasons, or spatial closures) based on harvest control rules triggered by status indicators relative to reference points.
- Run LIME with monthly time step for species that live less than 20 years
- Run LIME with annual time step for species that live longer than 20 years