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Smithwick EAH, Baldwin DC, Naithani KJ.2016. Quantifying spatial patterns of grass response to nutrient additions using empirical and neutral semivariogram models. PeerJ Preprints4:e2078v1https://doi.org/10.7287/peerj.preprints.2078v1
Disturbances influence vegetation patterns at multiple scales, but studies that isolate the effect of scale are rare, meaning that scale and process are often confounded. To explore this, we imposed a large (~3.75 ha) experiment in a South African coastal grassland ecosystem to determine the spatial scale of grass response to nutrient additions. In two of six 60 x 60 m grassland plots, we imposed nutrient additions using a scaled sampling design in which fertilizer was added in replicated sub-plots of varying sizes (1 x 1 m, 2 x 2 m, and 4 x 4 m). The remaining plots either received no additions, or were fertilized evenly across the entire plot area. We calculated empirical semi-variograms for all plots one year following nutrient additions to determine whether the scale of grass response (biomass and nutrient concentrations) corresponded to the scale of the sub-plot additions and compared these results to reference plots (unfertilized or unscaled). In addition, we calculated semi-variograms from a series of simulated landscapes generated using random or structured patterns (neutral models) and compared the semivariogram parameters between simulated and empirical landscapes. Results from the empirical semivariograms showed that there was greater spatial structure in plots that received additions at sub-plot scales, with range values that were closest to the 2 x 2 m grain. These results were in agreement with simulated semivariograms using neutral models, supporting the notion that our empirical results were not confounded by random effects. Overall, our results highlight that neutral models can be combined with empirical semivariograms to identify multi-scalar ecological patterns and this hybrid approach should be used more widely in ecological studies.
Empirical and simulated spatial model parameters of biomass
Spatial model parameters [range (3* φ), sill (σ2), nugget (τ2), and noise to signal ratio (τ2/(τ2 + σ2)] of empirical and simulated biomass across treatments. Sill and nugget values are scaled (0-1) to facilitate comparisons across treatments.
Empirical spatial model parameters of vegetation and soil nutrients
Parameters of the empirical spatial model of vegetation phosphorus and nitrogen (%), soil phosphorus (P) and nitrogen (N), and soil (C) using maximum likelihood analysis across experimental plots in Mkambathi Nature Reserve, one year following nutrient fertilization. nd=not defined.