Ecological Archives A021-125-A4

Pablo García-Palacios, Matthew A. Bowker, Fernando T. Maestre, Santiago Soliveres, Fernando Valladares, Jorge Papadopoulos, and Adrián Escudero. 2011. Ecosystem development in roadside grasslands: biotic control, plant–soil interactions and dispersal limitations. Ecological Applications 21:2806–2821.

Appendix D. Structural equation modeling: detailed methods.

We modelled the network of relationships between age, dispersal limitations, the biotic communities (plants, BSC and soil microorganisms) and the indicators of ecosystem development (plant similarity, soil fertility and stability) using structural equation modelling (SEM, Grace 2006). This approach is particularly useful when combined with gradient analyses, temporal or spatial, because it can help to improve causal inference from observational data without formal experimental manipulation (Fukami and Wardle 2005). The use of SEM is often motivated by its ability for investigating complex networks of relationships in ecological dynamics (Pugesek et al. 2002), but also because of its application as a means for representing theoretical concepts, using latent and composite variables (Grace et al. 2010).

We used the traditional χ2 goodness-of-fit test, but because of its sensitivity to sample size, the NFI and RMSEA indices were also considered as alternative measures of model fit (Grace 2006). Unlike many statistical tests, low probability values are not desired because these indicate that the covariance matrix implied by the model does not fit the covariance matrix derived directly from the data. A satisfactory fit indicates that the structure of the model is a reasonable explanation of the covariance structure among the variables. Often a satisfactory fit is not initially obtained, and the researcher may wish to make post-hoc alterations in the model based partially upon modification indices. Modification indices are algorithm-derived estimates of model improvement, which could be accomplished with a single alteration. These are applied conservatively, one at a time and only when justified on logical or theoretical grounds, until a satisfactory model is achieved. When a satisfactorily fitting model is developed, path coefficients estimates are obtained, using the maximum likelihood estimation technique (Grace 2006). The path coefficient is directly analogous to a partial correlation coefficient of regression weight, and is interpreted as the size of an effect that one variable exerts upon another. These are also paired with a probability test which tests the hypothesis that these path coefficients are equal to 0.

Our final step was to introduce “conceptual” composite variables (described in the main text). This usage of the composite variable is a graphical and numerical interpretational aid that does not alter the underlying model (Grace 2006). It simply sums together the effects of multiple conceptually related variables upon another, collapsing the effects into a single path coefficient.

LITERATURE CITED

Fukami, T., Wardle, D.A., 2005. Long-term ecological dynamics: reciprocal insights from natural and anthropogenic gradients. Proceedings of the Royal Society of London Series B: Biological Sciences 272, 2105–2115.

Grace, J.B., 2006 Structural equation modeling and natural systems. Cambridge University Press, Cambridge, UK.

Grace, J.B., Anderson, T.M., Olff, H., Scheiner, S.M., 2010. On the specification of structural equation models for ecological systems Ecological Monographs 80, 67–87.

Pugesek, B., Tomer, A., von Eye, A., 2002 Structural equation modeling: applications in ecological and evolutionary biology research. Cambridge University Press, Cambridge, UK.


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