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Quantitative Analysis Using Structural Equations

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Causal networks clarify productivity-richness interrelations, bivariate plots do not
Bogong subalpine grassland in Australia

Photo: Bogong subalpine grassland in Australia, a participating site in the Nutrient Network Global Cooperative. Photo credit: Eric Land, Nutrient Network.

Lay summary from Functional Ecology:

Species diversity and productivity are among the most fundamental characteristics of ecosystems. While the importance of these ecological properties is universally agreed upon, the mechanisms connecting these two variables have been debated for decades without resolution. In an attempt to achieve a synthetic understanding of the collective effects of proposed mechanisms, some ecologists have turned to the examination of bivariate plots to see if particular patterns are consistently observed in nature.

In a recent study, Adler et al. (2011, Science) reported only weak correlations between richness and productivity in grasslands from around the world and urged future studies to “focus on fresh, mechanistic approaches to understanding the multivariate links between productivity and richness.” While some have applauded this call for a fresh approach, others remain focused on the study of simple scatterplots. Most recently, Pierce (2013, Functional Ecology) has reexamined the original data reported in the Adler et al. (2011) study using boundary regression and claimed that there are strongly predictive, humped boundary relationships between richness and productivity. Pierce goes on to argue that failure to support one particular model, referred to as the Humped-Back Model (HBM), undermines conservation efforts.

In our paper, we illustrate that Pierce’s analyses are invalid and that defensible statistical methods for examining boundary relationships confirm that any relationship between productivity and richness in the Adler data is weak at best. The main focus of our presentation, however, is on explaining why scatterplot patterns cannot help us understand controlling mechanisms.

In our paper we examine the HBM through the lens of causal networks. We begin by translating the HBM into a causal diagram, which shows explicitly how multiple processes are hypothesized to control biomass production and richness. We then evaluate the causal diagram using example data, showing that alternative mechanisms cannot be distinguished through the examination of scatterplots. Going further, we show that more sophisticated multivariate approaches are far more useful for both understanding ecological systems and informing conservation efforts.

Link to article:

Grace, J.B., P.B. Adler, W.S. Harpole, E.T. Borer, and E.W. Seabloom. 2014. Causal networks clarify productivity-richness interrelations, bivariate plots do not. Functional Ecology.

 


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