Original Research ARTICLE
Bayesian, likelihood-free modelling of phenotypic plasticity and variability in individuals and populations
- 1Agriculture, School of Natural and Environmental Sciences, Newcastle University, United Kingdom
There is a paradigm shift from the traditional focus on the ‘average’ individual towards a definition and analysis of trait variation within individual life-history and among individuals in populations. This is a result of the increasing availability of individual phenotypic-data. The shift allows the use of genetic and environmental-driven variation to assess robustness-to-challenge, gain greater understanding of organismal biological processes, or deliver individual-targeted treatments or genetic selection. These consequences apply, in particular, to variation in ontogenetic growth. We propose an approach to parameterise mathematical models of individual traits (e.g. reaction norms, growth curves) that addresses two challenges: 1) Estimation of individual traits while making minimal assumptions about data distribution and correlation, addressed via Approximate Bayesian Computation (a form of non-parametric inference). We are motivated by the fact that available information on biological-data distribution is often less precise than assumed by conventional likelihood functions. 2) Scaling-up to population phenotype-distributions while facilitating unbiased use of individual data; this is addressed via a probabilistic framework where population distributions build on separately-inferred individual-distributions and individual-trait interpretability is preserved. The approach is tested against Bayesian likelihood-based inference, by fitting weight and energy-intake growth-models to animal data and normal and skewed-distributed simulated-data. (i) Individual inferences were accurate and robust to changes in data distribution and sample size; in particular, median-based predictions were more robust than maximum-likelihood-based curves. These results suggest the approach gives reliable inferences using few observations and monitoring resources. (ii) At population level, each individual contributed via a specific data distribution, and population phenotype-estimates were not disproportionally-influenced by outlier individuals. Indices measuring population phenotype-variation can be derived for study comparisons. The approach offers an alternative for estimating trait variability in biological systems that may be reliable for various applications, e.g. in genetics, health and individualised nutrition, whilst using fewer assumptions and fewer empirical observations. In livestock breeding, the potentially greater accuracy of trait estimation (without specification of multi-trait variance-covariance parameters) could lead to improved selection and to more decisive estimates of trait heritability.
Keywords: non-parametric, Bayesian inference, individual variation, phenotypic plasticity, reaction norms, Ontogenetic growth, Energy Intake, Systems Biology
Received: 15 Jun 2018;
Accepted: 11 Jul 2019.
Copyright: © 2019 Filipe and Kyriazakis. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Dr. Joao A. Filipe, Newcastle University, Agriculture, School of Natural and Environmental Sciences, Newcastle upon Tyne, United Kingdom, Joao.Filipe@newcastle.ac.uk