Scaling laws and relevance to BEF

Resource managers are generally concerned with the 'big picture'—sustainability in the long-term, suitability/efficacy of protected areas, and ecosystem-based management. To ecologists, the 'big picture' means the net effects of drivers occurring over long periods of time and at large spatial scales, over which it is impossible to conduct manipulative experiments. Thus, if BEF studies are to be used for management purposes, the development of scaling laws to link small-scale experimental results to ecosystem-scale processes is essential. Although this is a daunting task due to the complicated and idiosyncratic relationships between organisms and their environments, there are aspects of organisms and ecosystems that are self-similar across a wide range of spatial and temporal scales that offer promise of scaling relationships (Brown et al. 2002; Schneider 2001a; Schneider 2001b).

Scale transition models (Melbourne and Chesson 2005) are one approach designed to understand the overall dynamics of networks of local communities. The argument is that spatial variation between local communities interacts with nonlinearities within local communities to determine the dynamics of the overall network. Rather than avoiding or imposing artificial controls on variation, generality is sought by building on and measuring variation (see also Hewitt et al. 2007b). To their credit, Melbourne and colleagues have applied the theory using concrete examples with biological data (Melbourne et al. 2005; Melbourne and Chesson 2006). Crucial to the process of developing scale transition models is the identification of 'key quantities', which represent spatial mechanisms that contribute to change with spatial scale. Identification of key quantities is likely to be a product of careful and repeated observations of natural systems in multiple places (Hewitt et al. 2007b; Urban, 2005).

The approach of Melbourne and colleagues is a step forward in understanding functional scaling when functioning is determined largely by single 'key' species. When this is not the case, the approach of Suding et al. (2008) can be adapted. Suding et al. (2008) discuss a framework that integrates two main components: how a community responds to change, and how the changed community affects ecosystem processes. The species in a community that are responding to environmental change may, or may not, be important in a functional sense. So it is important to consider traits that determine responses to change (response traits), traits that determine levels of functioning (effects traits), and correlations between the two. Understanding the impacts of particular anthropogenic activities on community responses may be informed by sampling and experimentation across well-defined environmental gradients. It can also be done theoretically when computer models are informed by observational data. A marine example is provided by Solan et al. (2004), who discussed how changes in bioturbation rate and sediment mixed depth were heavily dependent on the presence of a single key species, as opposed to species richness per se, due to correlations between extinction risk and functional traits. Model results differed dramatically when the extinction of benthic species was random, as opposed to when extinction was modelled under more realistic scenarios. A full accounting of the traits of all the species in natural communities will be dependent upon excellent natural history information and numerous real-world observations.

Much of the work conducted by marine ecologists aimed at determining effects traits—i.e. the relative importance of different species to functioning—has been done in enclosed model experimental ecosystems—'mesocosms', 'microcosms'. Obviously, enclosed micro/mesocosms are reduced in both spatial and temporal scale and remain a limited representation of natural systems. However, they can be useful tools for comprehending BEF relationships (Petersen et al. 2009; Benton et al. 2007). Mesocosm results may reflect null models or define hypotheses that can be tested against nature to indicate the effects of scale and natural variability. There are ways to scale up mesocosm results so long as the enclosed model ecosystem captures critical elements of the systems of interest (Schneider 1994; Schneider 2001a; Rastetter et al. 1992).

BEF researchers have a considerable amount of influence over the extent of scale distortion in meso- cosm experiments, which allows them to strike a balance between experimental control, realism, and scale (Petersen and Hastings 2001). We emphasize the importance of realism and minimizing scale distortions, even if it means sacrificing some experimental control. For example, several studies have suggested that large mobile animals such as spatan- goid urchins are functionally important species in marine soft-sediment systems. These species have movement rates that can exceed 100 cm d-1, and high densities of urchins can rework the entire upper 3-5 cm of sediment once every three days (Lohrer et al. 2005). Limiting their movements, by placing them in undersized containers, negates much of their functional importance. Although the inclusion of single individuals in small containers may be equivalent to realistic densities observed in the field—in terms of numbers per m2 —sediment characteristics in the field are often the product of integrated movements of numerous urchin individuals over long periods of time. Thus the type of information needed to design realistic laboratory experiments comes from familiarity with the natural conditions in which the organisms live, and the degree to which their behaviours change across naturally heterogeneous landscapes.

Cardinale et al. (2004) suggest that small-scale experiments can provide qualitatively robust insights into the regional consequences of species loss for communities structured by local processes, so long as the experiments are conducted across a range of heterogeneity that is relevant to species coexistence. Unfortunately, heterogeneity is not well incorporated into most small enclosure experiments; experimental control is generally the dominant feature of enclosure designs. This suggests a need for multiple iterations of experiments under different sets of conditions to create the necessary range of heterogeneity that would increase applicability at ecosystem scales. On the bright side, incorporating heterogeneity and realism can actually be easier than controlling for it. For example, instead of sieving and homogenizing sediments to create identical replicates—to which animals are added and from which functional variables such as fluxes are later measured—animals can be added to intact cores of sediment collected from the field (Giblin et al. 1997; Sundback et al. 2000; Eyre and Ferguson

2002). With cores collected from defined areas along measured gradients, the range of extrapolation becomes more transparent and easier to justify. For example, Levin et al. (2009) sampled at 50 m intervals along an oxygen gradient between 700—1100 m depth off the coast of Pakistan. This unusually high spatial resolution sampling revealed dramatic, threshold changes in bioturbation and community structure that could not be simply related to oxygen concentration. Finally, benthic chambers (Hughes et al. 2000; Webb and Eyre 2004; Janssen et al. 2005) and field flumes (Asmus et al. 1998; Cornelisen and Thomas 2006) can be positioned in experimentally manipulated field plots or across larger-scale environmental gradients. Although control of all potentially important variables is difficult or impossible in most field experiments, researchers with a detailed understanding of the system should be able to identify and measure such variables. There are numerous statistical techniques that can be applied to datasets with continuous co-variables, and these are likely to be more powerful than categorical analyses in heterogeneous landscapes (McCullagh and Nelder 1989; Hastie and Tibshirani 1990; Cressie et al. 2009).

Meta-analyses of multiple BEF experiments have shown a reasonable amount of consistency, with a generally positive but saturating effect of richness on functioning (Balvanera et al. 2006 ; Cardinale et al. 2006 ; Worm et al. 2006 ). However, Loreau ( 2008 ) cautions that the relationships emerging from small- scale experiments may still not match up with broad-scale patterns. For example, Danovaro et al. (2008) demonstrate a non-saturating, exponential increase in functions with increasing species richness in deep sea sediments. Deep sea sediments are one of the most widespread, globally important, yet unexplored habitat types on Earth. Danovaro et al. (2008) present convincing evidence, despite conducting an observational study, that environmental factors are unlikely to explain fully the observed exponential relationships between biodiversity and ecosystem properties in the deep sea. Positive species interactions are known to lead to accelerating relationships (Gross and Cardinale 2005). This could be important in the deep sea, where we have very limited knowledge of species interactions or even species identities and levels of diversity (Levin and Dayton 2009).

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