The influence of sampled biomass on species–area relationships of grassland plants

Understanding scaling relationships in ecology can foster the development of valuable predictive tools and also pave the ground towards the formulation of better mechanistic models. The species–area relationship (SAR) is a classical example of an empirical relationship between species richness (S ) and sampling area (A). This relationship arises from the combined effects of higher detection likelihood due to sampling effects as larger areas are sampled and differential niche effects attributed to the habitat heterogeneity of larger areas (Cam et al., 2002). It has also been argued that SARs could arise from other factors such as dispersal constraints (Rosindell & Cornell, 2007). The SAR is a particularly useful concept in conservation biology as it can provide informative estimates of the recommended size of reserves (e.g.Gitay et al., 1991) but also in extinction ecologywhere it can be used as a basis to calculate species extinctions following habitat loss (Halley et al., 2013). A frequent issue involving the SAR is how it might be affected by net primary productivity. For annual grasslands sampled biomass (SB) may be a good proxy of net primary productivity but for perennial systems, and particularly those that are dominated bywoody plants, the relationship between SB and net primary productivity may be weak. While standing biomass in many cases may be a poor indicator of net primary productivity (for example grasslands may be more productive than forests), for sites sharing comparable seral stages it can still represent a good proxy. For example, intuitively one might expect species richness to increase with SB but there are numerous counter examples such as the tendency for nitrogen enrichment to reduce biodiversity (Stevens et al., 2004) or the low net primary productivity of many rainforest soils following deforestation (Kontowska et al., 2015). While cross-habitat heterogeneity may occasionally compromise SARs (B aldi, 2008) there is compelling evidence that combining data from multiple small-scale quadrats yields robust SARs (Harte et al., 1999). In this paper we address the species accumulation curves of (typically nested) sample areas. Collecting data to fit SAR can be an exceptionally laborious task and it is often the synthesis of existing studies that permits comparison across sites. S olymos & Lele (2012) synthesized existing data to estimate a mean power-law slope (z) of 0.205 and an intercept (c) for 1 km plots of 3.209 (c. 25 plants per km) for vascular plants, globally. However these estimates may vary considerably across different systems. Pastor et al. (1996) fitted Arrhenius-relationship parameters (as power law scaling factors) to nested quadrats in six grassland plots in Minnesota finding that zeta parameters declined with SB whereas c parameters increased. To the best of our knowledge relationships between SAR parameters and SB have not been tested anywhere else. Fraser et al. (2015) established a global network of 30 grassland sites in 19 countries to study SB–diversity relationships. Analysis of their 157 grids each consisting of 64 1 m9 1 m quadrats within an 8 m9 8 m area revealed humped overall SB–diversity relationships at 1, 2, 4, 9, 16, 25 and 64 m scales, but explanatory power of SB diminished with increasing scale. However, the way species–area parameters scale with environmental factors can be counterintuitive; for example when the relationship between richness and productivity within sites is negative but the more productive sites host richer species assemblages (Scheiner et al., 2000). The unique dataset of Fraser et al. (2015) offers great opportunities to better understand SARs. We reanalyzed the dataset to assess the way SAR parameters scale with SB. We expected that at high SB plants compete for a single resource (light) instead of nutrients and water and this would lead to competitive exclusion of rare taxa (Stevens et al., 2004). We thus hypothesized a monotonic negative response of z0 (maximum slope) with SB. We further hypothesized that higher SB would increase c (intercept) as was shown by Pastor et al. (1996). In our analysis we considered both standing plant biomass and litter as constituents of SB. Traditionally SARs were modeled as a Arrhenius equation: a linear relationship between s = log S and u = log A with a slope of z and an intercept of c. However, it is well known that z is not constant but changes with scale. Harte et al. (2009) proposed a framework through which a global curvature constant (g) could be calculated. In this case fitting a SAR once the curvature is assessed requires regression with a modified response variable y(u) for species richness, to find parameters z0 (maximum slope value for 19 1 m quadrats) and c (Supporting Information Methods S1):