Ecological Archives E090-078-A1

Osamu Kishida, Geoffrey C. Trussell, and Kinya Nishimura. 2009. Top-down effects on antagonistic inducible defense and offense. Ecology 90:1217–1226.

Appendix A. Data correction method used to exclude the possible effect of selective predation on tadpoles having low bulginess induction.

Because selective predation on individuals having reduced levels of inducible defense may have contributed to the observed morphological differences in the tadpole-salamander and the tadpole-salamander-dragonfly treatments, it was necessary to perform a correction on our data. The selective predation hypothesis is modeled by a probability distribution that is a decreasing function of levels of defense. The simplest logically validated probability function without specific information is a triangular distribution. We assumed that the individuals consumed were determined by triangular probability function with order dependent variable (P1). Two alternative hypothetical models with the selective predation and inducible defense are presented (see H1 and H2).

We randomly sampled 16 individuals from the surviving tadpoles in the tadpole-salamander and tadpole-salamander-dragonfly treatments at the end of the experiment. We suppose that we hypothetically sampled more than the actual sample number (16 individuals). The surplus individuals are viewed as having been consumed by salamanders before the actual sampling event. We estimated the number of consumed individuals in this hypothetical sample with the equation ni / (40 – ni) = xi / 16, where 40 is the number of tadpoles at the start of the experiment, ni is the number of individuals actually consumed in aquarium i in the experimental period, 16 is the actual sample number, and xi is the number of consumed individuals in the hypothetical sample. The individuals sampled were sorted in ascending order by absolute body depth and numbered.  We generated xi unique numbers from a triangular probability distribution with its mode at the end of the largest number. We then eliminated the sampled individual that had been assigned the numbers from the data. For example, if 8 of 40 tadpoles had been consumed during the experiment, 4 of 16 tadpoles that had relatively deeper bodies would be removed in this correction method.    

Although our sample correction is an approximation because we cannot know the morphology of the tadpoles that were actually consumed by salamanders, the removal of tadpoles having a larger body depth (the trait targeted by selective salamander predation [Kishida and Nishimura 2004]) corrects for inflated estimates of bulginess caused by selective predation.

   FIG. A1. Example of data correction. Suppose that 8 of 40 tadpoles (20%) had been consumed throughout the experiment, and we sampled 16 tadpoles from surviving 32 tadpoles at the end of the experiment. In this case, 4 tadpoles (25%) from the sample, that have relatively large body depth, are removed for the correction in the manner shown in this figure.



Kishida, O., and K. Nishimura. 2004. Bulgy tadpoles: inducible defense morph. Oecologia 140:414–421.

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