Lianas always outperform tree seedlings regardless of soil nutrients: results from a long-term fertilization experiment

The arcsine square root transformation has long been standard procedure when analyzing proportional data in ecology, with applications in data sets containing binomial and non-binomial response variables. Here, we argue that the arcsine transform should not be used in either circumstance. For binomial data, logistic regression has greater interpretability and higher power than analyses of transformed data. However, it is important to check the data for additional unexplained variation, i.e., overdispersion, and to account for it via the inclusion of random effects in the model if found. For non-binomial data, the arcsine transform is undesirable on the grounds of interpretability, and because it can produce nonsensical predictions. The logit transformation is proposed as an alternative approach to address these issues. Examples are presented in both cases to illustrate these advantages, comparing various methods of analyzing proportions including untransformed, arcsine- and logit-transformed linear models and logistic regression (with or without random effects). Simulations demonstrate that logistic regression usually provides a gain in power over other methods.

We maintained a factorial nitrogen (N), phosphorus (P), and potassium (K) addition experiment for 11 years in a humid lowland forest growing on a relatively fertile soil in Panama to evaluate potential nutrient limitation of tree growth rates, fine-litter production, and fine-root biomass. We replicated the eight factorial treatments four times using 32 plots of 40 x 40 m each. The addition of K was associated with significant decreases in stand-level fine-root biomass and, in a companion study of seedlings, decreases in allocation to roots and increases in height growth rates. The addition of K and N together was associated with significant increases in growth rates of saplings and poles (1-10 cm in diameter at breast height) and a further marginally significant decrease in stand-level fine-root biomass. The addition of P was associated with a marginally significant (P = 0.058) increase in fine-litter production that was consistent across all litter fractions. Our experiment provides evidence that N, P, and K all limit forest plants growing on a relatively fertile soil in the lowland tropics, with the strongest evidence for limitation by K among seedlings, saplings, and poles.