title: Performance of maximum likelihood mixture models to estimate nursery habitat contributions to fish stocks: a case study on sea breamSparus aurata.
abstract: BACKGROUND
  Mixture models (MM) can be used to describe mixed stocks considering three sets of parameters: the total number of contributing sources, their chemical baseline signatures and their mixing proportions. When all nursery sources have been previously identified and sampled for juvenile fish to produce baseline nursery-signatures, mixing proportions are the only unknown set of parameters to be estimated from the mixed-stock data. Otherwise, the number of sources, as well as some/all nursery-signatures may need to be also estimated from the mixed-stock data. Our goal was to assess bias and uncertainty in these MM parameters when estimated using unconditional maximum likelihood approaches (ML-MM), under several incomplete sampling and nursery-signature separation scenarios.
  
  
  METHODS
  We used a comprehensive dataset containing otolith elemental signatures of 301 juvenileSparus aurata, sampled in three contrasting years (2008, 2010, 2011), from four distinct nursery habitats. (Mediterranean lagoons) Artificial nursery-source and mixed-stock datasets were produced considering: five different sampling scenarios where 0-4 lagoons were excluded from the nursery-source dataset and six nursery-signature separation scenarios that simulated data separated 0.5, 1.5, 2.5, 3.5, 4.5 and 5.5 standard deviations among nursery-signature centroids. Bias (BI) and uncertainty (SE) were computed to assess reliability for each of the three sets of MM parameters.
  
  
  RESULTS
  Both bias and uncertainty in mixing proportion estimates were low (BI≤ 0.14,SE≤ 0.06) when all nursery-sources were sampled but exhibited large variability among cohorts and increased with the number of non-sampled sources up toBI= 0.24 andSE= 0.11. Bias and variability in baseline signature estimates also increased with the number of non-sampled sources, but tended to be less biased, and more uncertain than mixing proportion ones, across all sampling scenarios (BI< 0.13,SE< 0.29). Increasing separation among nursery signatures improved reliability of mixing proportion estimates, but lead to non-linear responses in baseline signature parameters. Low uncertainty, but a consistent underestimation bias affected the estimated number of nursery sources, across all incomplete sampling scenarios.
  
  
  CONCLUSIONS
  ML-MM produced reliable estimates of mixing proportions and nursery-signatures under an important range of incomplete sampling and nursery-signature separation scenarios. This method failed, however, in estimating the true number of nursery sources, reflecting a pervasive issue affecting mixture models, within and beyond the ML framework. Large differences in bias and uncertainty found among cohorts were linked to differences in separation of chemical signatures among nursery habitats. Simulation approaches, such as those presented here, could be useful to evaluate sensitivity of MM results to separation and variability in nursery-signatures for other species, habitats or cohorts.
authors.affiliation: Centro i∼mar, Universidad de Los Lagos , Puerto Montt, Los Lagos , Chile.
authors.forename: Edwin J
authors.identifier: 0000-0001-5561-3494
authors.initials: EJ
authors.lastname: Niklitschek
authors.affiliation: Center for Marine Biodiversity, Exploitation & Conservation, Centre National de la Recherche Scientifique , Montpellier , France.
authors.forename: Audrey M
authors.initials: AM
authors.lastname: Darnaude
keywords: Fish stocks; Mixed stocks; Mixing models; Mixing proportions; Mixture models; Otolith chemistry; Population structure; Sparus aurata; Stock identification; Stock structure