Performance of finite mixture distribution models to estimate nursery habitat contributions to fish stocks

Background. Otolith microchemistry applications of finite mixture distribution models (FMDM) describe mixed stocks using three sets of parameters: proportional contributions (pi), baseline parameters (θi) and number of contributing nursery origins (c#). Under ideal scenarios, c# is known and all potential sources are sampled to produce source-based ^θi estimates. Hence, ^pi is the only parameter vector estimated by FMDM from the mixed-data. If some/all nursery areas are unknown or not sampled, some or all θi and c# need to be also estimated from the mixed-data. Our goal here was to assess bias and variability in ^pi, ^θi and ^c# when estimated by FMDM, under a range of data availability scenarios. Methods. We used a comprehensive Sparus aurata dataset, tat contained otolith elemental ratios from 301 young of the year, sampled at four nursery origins, in three highly contrasting years. Using bootstrap resampling (n=1000) we produced artificial source- and mixed-samples. Source-samples simulated different scenarios where KU=0-4 nursery sources were excluded. We evaluated bias (BI) and variability (VI) in ^pi by fitting FMDM to mixed-samples with true pi=0.1-0.4. Bias and variability in ^θi and ^c# were, instead, assessed on balanced mixed stock-samples (pi=0.25). Estimations of ^c# were obtained by fitting and comparing multiple FMDMs with c#=1-9. Results. Accurate and precise ^pi estimates (BI<0.03, VI<0.07) were produced by FMDM when samples from all origins were available (KU=0). BI and VI in ^pi tended to increase rapidly as KU increased, yielding unreliable results for KU>1. BI and VI in ^θi were highly heterogeneous among cohorts and less sensitive to KU. Relatively accurate ^θi estimates (BI<0.3) were produced for cohorts 2008 and 2010, but highly biased ones for cohort 2011 (VI>0.53), at all scenarios. Variability in ^θi was relatively low (VI<0.3) and insensitive to KU, across all cohorts. While ^c# tended to underestimate c# (BI=0.05 to -2.06), its variability was relatively high (VI=0.24-1.14) across scenarios and cohorts. Both bias and variability in ^c# were highly sensitive to KU. Discussion. FMDM estimated accurate and unbiased ^pi and ^θi parameters when all origins were known and sampled. FMDM performance decreased rapidly and all three set of estimated parameters became unreliable when ≥2 origins were missing from nursery-samples. Large differences in BI and VI among cohorts emphasized the need for extensive sampling of nursery origins. Being FMDM one default method for mixed stock analysis, we strongly recommend exploring alternative FMDM implementations and extreme caution when using results from FMDM, under incomplete sampling scenarios.