Electronic Supplementary Material: Oecologia Appendix S2

Statistical analysis of structural compensatory growth: how can we reduce the rate of false detection?

Alfredo G. Nicieza and David Álvarez

Table B1. Comparison of ANOVA and ANCOVA results (P-values) for differences between control and ‘post-manipulation’ specific growth rates (Gw) and absolute mass increments (w), over two consecutive time intervals (Period I: days 151– 170; Period II: days 171 – 190). The results of a repeated measures MANOVA for the entire post-treatment period (periods I and II) are reported for the treatment × time interaction. Size-corrected absolute growth (adj-S) was analyzed by ANCOVA with the size at the start of a given interval as a covariate. All the analyses were carried out on simulated trajectories based on an ontogenetic growth model which assumes asymptotic growth (see text for details). P-values are shown for trajectories with different levels of stochastic variation. Post-manipulation trajectories were set at the control trajectories for the same initial mass (i.e., there is a perfect matching between control and treatment growth rates), so that the only valid outcome is a nonsignificant F-ratio. These results indicate that even small deviations from linear growth can make the comparison of synchronic growth rates highly questionable, especially when specific growth rates are used.

Random error: / 0.10 g / 0.25 g / 0.45 g / 0.65 g

Period I

Gw / < 0.0001 / < 0.0001 / < 0.0001 / 0.027
Gw-adj / 0.001 / 0.074 / 0.113 / 0.106
adj-w / 0.001 / 0.073 / 0.103 / 0.071
w1 / < 0.0001 / 0.005 / 0.001 / 0.058
Period II
Gw / < 0.0001 / < 0.0001 / 0.009 / 0.089
Gw-adj / 0.096 / 0.066 / 0.090 / 0.348
adj-w / 0.059 / 0.052 / 0.066 / 0.371
w1 / < 0.0001 / 0.004 / 0.044 / 0.242
Repeated Measures MANOVA for three measurement occasions: W1,W2, W3(Periods I+II)
W1, W2, W3 / < 0.00012,3 / 0.0012,3 / 0.0012,3 / 0.1032,3

1Note: ANOVA of w and ANOVA of W for two repeated measures (Period I: W1,W2; Period II: W2,W3) produce identical results.

2P-value associated with the Wilks’ lambda for the treatment by time interaction.

3 Box’s M test for homogeneity of dispersion matrices: all Ps > 0.30.

Fig. B1. Simulated trajectories of size-dependent growth. The solid line is the ‘base’ trajectory derived from the West et al. (2001) model and represents a control. The dotted lines are treatment trajectories (zero growth over days 130 – 150). The central line for the treatment trajectory was produced by assuming zero growth during the first interval, and then replicating the control trajectory for the first and second intervals. Individual lines were generated by addition of a random variation in growth increments of ± 0.25g (see the text). For clarity, only ten individual lines are shown. The arrow indicates the transition between the manipulation and the compensatory phase.