Ecological Archives E095-075-A12

Chun-Wei Chang, Takeshi Miki, Fuh-Kwo Shiah, Shuh-ji Kao, Jiunn-Tzong Wu, Akash R. Sastri, Chih-hao Hsieh. 2014. Linking secondary structure of individual size distribution with nonlinear size–trophic level relationship in food webs. Ecology 95:897–909. http://dx.doi.org/10.1890/13-0742.1

Appendix L. The deviations of generalized MTE predictions caused by heterogenerity of K-means group.

To estimate a reliable size-TL relationship, we statistically grouped the size fractionated stable isotope data by K-means clustering. However, such grouping may introduce some bias to the predictions of general MTE model, becuase statistically grouped sampling dates within a K-means group may not be really homogeneous. The prediction or observation calculated from such heterogeneous K-means groups contains higher variations and thus restricts the predictability of the general MTE model. Indeed, the standardized deviation of model prediction (as defined in Appendix K) exhibits a significant positive correlation with the within-group heterogenerity of K-means groups. Here, the within-group heterogenerity is measured as the average Manhattan distance among size fractionated stable siotope data for each group. However, the correlation is weak, suggesting that the deviation caused by statistical grouping is not as important as that caused by nonequilibrium tate (compared with Appendix K).

FigL1

Fig. L1. The standardized deviation of model predictions exhibits a significant positive correlation with the within-group heterogenerity of K-means groups.


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