Abstract:Scaling means transferring information between or across spatial and temporal scales or organizational levels. Transferring from finer scale to broader scale is called as upscaling, and transferring from broader scale to finer scale is called as downscaling. In both basic ecology and its applications, scaling is the essence of predicting and understanding a phenomenon, and is at the core of ecological theories and applications. However, scaling is often very complex because scaling has to overcome constraints and critical thresholds between different systems, non-linear interactions among different components always occur within the same scale and among different scales, and especially spatial heterogeneity always exists. Therefore, scaling across heterogeneous ecosystems remains an unresolved puzzle, greatly challenging current ecologists devoting to studying environmental problems under global change. As a whole, four general scaling approaches can be distinguished: spatial analysis, similarity-based scaling, local dynamic model-based scaling, and random model approaches. Spatial analysis approach is based on spatial pattern analyzing, such as fractal and wavelet analysis method. Similarity-based scaling approach is an important approach and has been widely used in physics, earth science, hydrology, meteorology, and biology. The similarity-based biological allometry reveals the relationships between biological characteristics and body sizes, while spatial allometry reveals the relationships between landscape characteristics (such as species richness, natural river network, landform features, ecological variables, and landscape metrics) and spatial scales. The simple power law in allometric relations might be the integration of extremely complex underlying processes and mechanisms, possibly related to ubiquitous fractal structure of biological body and landscape, but the validation of this hypothesis will has to be conducted in developing scaling theory. However, allometric relations may only exist within a limited range of scales, beyond which some new processes will occur and the allometric relations at these scales cannot be extrapolated to other scales. Three key problems have to be addressed in local dynamic model-based approach: building a dynamic model at local scale, accurately defining and quantifying spatial heterogeneity of model parameters and input variables at local scale, aggregating or integrating heterogeneous information of output variables at local scale to object scale. The differences in both quantifying heterogeneity and aggregating information decide the merits and lacks of each method within this approach. Firstly, if scaling is conducted between adjacent scales, and the interactions among different spatial units can be ignored, lumping, extrapolation by effective parameters, direct extrapolation, extrapolation by expected value, and explicit integration methods can be used. Secondly, if scaling is conducted between adjacent scales, and the interactions between different spatial units cannot be ignored, lumping, extrapolation by effective parameters, and direct extrapolation methods still can be used, but extrapolation by expected value and explicit integration methods cannot be used any longer. Especially, spatially interactive modeling is another important approach to realize upscaling by developing multiple-scaled models to directly model the interactions among different spatial units. Thirdly, if scaling is conducted among multiple scales for a hierarchical landscape, scaling ladder approach (i.e. hierarchical patch dynamics strategy) can be used. Random model approach is based on the other upscaling approaches or methods. According to whether scaling is conducted in a single landscape or over multiple landscapes, different approaches may be adopted. Understanding, quantifying and reducing the uncertainty in scaling results have become more and more important, but the related studies still extremely lack. All the above methods, approaches and analysis will contribute to the conceptual framework of scaling science.