New Paper: Size‐ and stage‐dependence in cause‐specific mortality of migratory brown trout

The paper Size‐ and stage‐dependence in cause‐specific mortality of migratory brown trout by Chloé R. Nater, Yngvild Vindenes, Per Aass, Diana Cole, Øystein Langangen, S. Jannicke Moe, Atle Rustadbakken, Daniel Turek, Leif Asbjørn Vøllestad and Torbjørn Ergon was published in Journal of Animal Ecology.


  1. Evidence‐based management of natural populations under strong human influence frequently requires not only estimates of survival but also knowledge about how much mortality is due to anthropogenic vs. natural causes. This is the case particularly when individuals vary in their vulnerability to different causes of mortality due to traits, life history stages, or locations.
  2. Here, we estimated harvest and background (other cause) mortality of landlocked migratory salmonids over half a century. In doing so, we quantified among‐individual variation in vulnerability to cause‐specific mortality resulting from differences in body size and spawning location relative to a hydropower dam.
  3. We constructed a multistate mark–recapture model to estimate harvest and background mortality hazard rates as functions of a discrete state (spawning location) and an individual time‐varying covariate (body size). We further accounted for among‐year variation in mortality and migratory behaviour and fit the model to a unique 50‐year time series of mark–recapture–recovery data on brown trout (Salmo trutta) in Norway.
  4. Harvest mortality was highest for intermediate‐sized trout, and outweighed background mortality for most of the observed size range. Background mortality decreased with body size for trout spawning above the dam and increased for those spawning below. All vital rates varied substantially over time, but a trend was evident only in estimates of fishers’ reporting rate, which decreased from over 50% to less than 10% throughout the study period.
  5. We highlight the importance of body size for cause‐specific mortality and demonstrate how this can be estimated using a novel hazard rate parameterization for mark–recapture models. Our approach allows estimating effects of individual traits and environment on cause‐specific mortality without confounding, and provides an intuitive way to estimate temporal patterns within and correlation among different mortality sources.

Parameter Redundancy and Identifiability Book Published

Diana Cole’s book Parameter Redundancy and Identifiability has been publish by Chapman and Hall/CRC

Book Synopsis

Statistical and mathematical models are defined by parameters that describe different characteristics of those models. Ideally it would be possible to find parameter estimates for every parameter in that model, but, in some cases, this is not possible. For example, two parameters that only ever appear in the model as a product could not be estimated individually; only the product can be estimated. Such a model is said to be parameter redundant, or the parameters are described as non-identifiable. This book explains why parameter redundancy and non-identifiability is a problem and the different methods that can be used for detection, including in a Bayesian context. Key features of this book:

  • Detailed discussion of the problems caused by parameter redundancy and non-identifiability
  • Explanation of the different general methods for detecting parameter redundancy and non-identifiability, including symbolic algebra and numerical methods
  • Chapter on Bayesian identifiability
  • Throughout illustrative examples are used to clearly demonstrate each problem and method. Maple and R code are available for these examples
  • More in-depth focus on the areas of discrete and continuous state-space models and ecological statistics, including methods that have been specifically developed for each of these areas

This book is designed to make parameter redundancy and non-identifiability accessible and understandable to a wide audience from masters and PhD students to researchers, from mathematicians and statisticians to practitioners using mathematical or statistical models.

Book website:

Code for book available at: