Biphasic growth modelling in elasmobranchs based on asymmetric and heavy-tailed errors

J.E. Contreras-Reyes*, R. Wiff, J. Soto, C.R. Donovan, M. Araya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Growth in fishes is usually modelled by a function encapsulating a common growth mechanism across ages. However, several theoretical works suggest growth may comprise two distinct mechanistic phases arising from changes in reproductive investment, diet, or habitat. These models are termed two-state or biphasic, where acceleration in growth typically changes around some transition age. Such biphasic models have already been successfully applied in elasmobranch species, where such transitions are detectable from length-at-age data alone, but where estimation has assumed normally distributed errors, which is inappropriate for such slow-growing and long-lived fishes. Using recent advances in growth parameter estimation, we implement a biphasic growth model with asymmetric and heavy-tailed errors. We use data from six datasets, encompassing four species of elasmobranchs, to compare the performance of the von Bertalanffy and biphasic models under normal, skew-normal, and Student-t error distributions. Conditional expectation maximization estimation proves both effective and efficient in this context. Most datasets analysed here supported asymmetric and heavy-tailed errors and biphasic growth, producing parameter estimates different from previous studies.
Original languageEnglish
Pages (from-to)615–628
Number of pages14
JournalEnvironmental Biology of Fishes
Issue number5
Early online date29 May 2021
Publication statusPublished - 29 May 2021


  • ECME algorithm
  • Elasmobranchs
  • Sharks
  • Skates
  • Skew-t distribution
  • Two-stage growth
  • von Bertalanffy model


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