Ecological Archives M085-005-A7

John R. Morrongiello and Ronald E. Thresher. 2015. A statistical framework to explore ontogenetic growth variation among individuals and populations: a marine fish example. Ecological Monographs 85:93115. http://dx.doi.org/10.1890/13-2355.1

Appendix G. Within vs. among individual supplementary results: result descriptions.

Text G1. Within vs. among individual variation results summary

Models 7 and 8 were fitted to each zone's full data set using its optimal intrinsic fixed and random effects structures (Appendix E, Table E1) and compared. Model 8 (i.e., evidence for among-individual differences in temperature reaction norms) was preferred over Model 7 only in EBS (∆AICc=7.09) where there was a strong negative correlation (-0.88) between the random FishID intercept and βW. This implies that faster growing EBS fish had a more negative temperature reaction norm than slow growers. No such effect was evident for fish in the remaining six zones, i.e., within-individual temperature slopes were similar among individuals (∆AICc for each zone: NC 4.64, NSW 6.97, WBS 6.17, CBS 6.10, ETAS 7.84, WTAS 1.72).

The growth of individual fish responded consistently to changes in experienced temperature (βW) in five of seven zones (NC, NSW, WBS, EBS and WTAS; Table 5d), and there was evidence of among-individual differences in growth related to average conditions experienced in three zones (NSW, EBS and ETAS, Table 5d). We note that sampling intensity and biochronology lengths were generally higher for the latter group of zones, which could result in increased power to detect an among-individual effect (Dingemanse and Dochtermann 2013). The βW and βA slopes for each zone can be compared to see whether they differ by replacing the βW term with the original Temperature effect. Temperature combines within and among individual effects while βA now represents the difference between within and among individual effects (see van de Pol and Wright 2009 for detailed discussion). Differences in within- and among-individual temperature slopes were substantial for EBS (slope difference 0.513, t statistic: 17.26) and ETAS (slope difference 0.373, t statistic 7.78).

Text G2: Temporal trends in reaction norms

Temporal patterns in within individual reaction norms can be superficially explored by analyzing the random within-individual slopes generated by Model 8 by Cohort in simple linear regression. A more sophisticated approach, not adopted here, would be to include random βW slopes for each Cohort. The presence of among-cohort variation in reaction norms, especially directional, would suggest that the importance of ecological processes (e.g., temperature related recruitment and thus density dependence) or selective regimes (e.g., temperature-related fitness) vary through time (Hairston et al. 2005, Ozgul et al. 2009). All zones displayed no directional temporal patterning in average individual reaction norms across generations (linear regressions, 6 ≤ n ≤ 38 cohorts; -0.003 ≤ β ≤  0.003, 0.003 ≤ R² ≤  0.197; P ≥ 0.061). Likewise in five of the seven zones (NC, EBS, CBS, ETAS and WTAS), within-cohort reaction norm variation (CV) did not change directionally through time (linear regressions, 6 ≤  n ≤ 38 cohorts; -2.231 ≤  β ≤  0.098, 0.001 ≤ R² ≤  0.391; P ≥ 0.184). In NSW there was evidence for a temporal decline in reaction norm CV (n = 21, β = -0.013, R² = 0.472, P = 0.002), whilst in WBS this relationship was positive (n = 12, β = 0.013, R² = 0.641, P = 0.010).

Literature cited

Dingemanse, N. J., and N. A. Dochtermann. 2013. Quantifying individual variation in behaviour: mixed-effect modelling approaches. Journal of Animal Ecology 82:39–54.

Hairston, N. G., S. P. Ellner, M. A. Geber, T. Yoshida, and J. A. Fox. 2005. Rapid evolution and the convergence of ecological and evolutionary time. Ecology Letters 8:1114–1127.

Ozgul, A., S. Tuljapurkar, T. G. Benton, J. M. Pemberton, T. H. Clutton-Brock, and T. Coulson. 2009. The dynamics of phenotypic change and the shrinking sheep of St. Kilda. Science 325:464-467.

van de Pol, M. V., and J. Wright. 2009. A simple method for distinguishing within- versus between-subject effects using mixed models. Animal Behaviour 77:753–758.


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