title: Probabilistic models for continuous ontogenetic transition processes.
abstract: BACKGROUND
  Probabilistic reaction norms (PRNs) are an extension of the concept of reaction norms, developed to account for stochasticity in ontogenetic transitions. However, logistic regression based PRNs are restricted to discrete time intervals, whereas previously proposed models for continuous transitions are demanding in terms of modelling effort and data needed.
  
  
  RESULTS
  Here we introduce two alternative approaches for the probabilistic modelling of continuous ontogenetic transitions. The models are simplified in their description of forces underlying transitions, thus being empirical rather than mechanistic by their nature, but therefore applicable to situations where data and prior knowledge of transitions are limited. The models provide continuous time description of the transition pattern, insights into how it is affected by covariates, at the same time allowing for fine scale transition probability predictions. Performance of the models is demonstrated using empirical data on metamorphosis in common frogs (Rana temporaria) reared in a common garden experiment.
  
  
  CONCLUSIONS
  As being user-friendly and methodologically easily accessible, the models introduced in this study aid the concept of probabilistic reaction norms becoming as general and applicable tool in the studies of life-history variation as the deterministic reaction norms are today.
authors.affiliation: Ecological Genetics Research Unit, Department of Biological and Environmental Sciences, University of Helsinki, Helsinki, Finland. anna.kuparinen@helsinki.fi
authors.forename: Anna
authors.initials: A
authors.lastname: Kuparinen
authors.forename: Robert B
authors.initials: RB
authors.lastname: O'Hara
authors.forename: Juha
authors.initials: J
authors.lastname: Merilä
mesh_terms: D000818:Animals; D008675:Metamorphosis, Biological / Q000235:genetics; D015233:Models, Statistical; D011896:Rana temporaria; D016019:Survival Analysis