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Quantifying individual variation in reaction norms: how study design affects the accuracy, precision and power of random regression models
Article first published online: 11 NOV 2011
© 2011 The Author. Methods in Ecology and Evolution © 2011 British Ecological Society
Methods in Ecology and Evolution
Volume 3, Issue 2, pages 268–280, April 2012
How to Cite
van de Pol, M. (2012), Quantifying individual variation in reaction norms: how study design affects the accuracy, precision and power of random regression models. Methods in Ecology and Evolution, 3: 268–280. doi: 10.1111/j.2041-210X.2011.00160.x
- Issue published online: 4 APR 2012
- Article first published online: 11 NOV 2011
- Received 21 June 2011; accepted 21 September 2011 Handling Editor: Nigel Yoccoz
- annual traits;
- I × E;
- mixed model;
- phenotypic plasticity;
- random slopes;
- viability selection
1. Quantifying individual heterogeneity in plasticity is becoming common in studies of evolutionary ecology, climate change ecology and animal personality. Individual variation in reaction norms is typically quantified using random effects in a mixed modelling framework. However, little is known about what sampling effort and design provide sufficient accuracy, precision and power.
2. I developed ‘odprism’, an easy-to-use software package for the statistical language R, which can be used to investigate the accuracy, precision and power of random regression models for various types of data structures. Moreover, I conducted simulations to derive rules-of-thumb for four design decisions that biologists often face.
3. First, I investigated the trade-off between sampling many individuals a few times versus sampling few individuals often. Generally, at least 40 individuals should be sampled with a total sample size of at least 1000 to obtain accurate and precise estimates of individual variation in elevation and slopes of linear reaction norms and their correlation. Contrasting a previous recommendation, it is worthwhile to bias the ratio of number of individuals over replicates towards sampling more individuals.
4. Second, I considered how the range of environmental conditions over which individuals are sampled affects the optimal sampling strategy. I show that when all individuals experience the same conditions during a sampling event, sampling each individual only twice should be strictly avoided.
5. Third, I examined the case where the number of replicates per individual is constrained by their lifespan, as is common when sampling annual traits in the wild. I show that for a given sampling effort, it is much easier to detect individual variation in reaction norms for long-lived than for short-lived species.
6. Fourth, I investigated the performance of random regression models when studying traits under selection. Reassuringly, directional viability selection barely caused any bias in estimates of variance components.
7. Random regression models are inherently data hungry, and reviewing the literature shows that particularly behavioural studies have low sampling effort. Therefore, the software and rules-of-thumbs I identified for designing reaction-norm studies should help researchers make more informed choices, which likely improve the reliability and interpretation of plasticity studies.