  Ecology studies biodiversity in its variety and complexity. It describes how
species distribute and perform in response to environmental changes. Ecological
processes and structures are highly complex and adaptive. In order to quantify
emerging ecological patterns and investigate their hidden mechanisms, we need
to rely on the simplicity of mathematical language. This becomes especially
apparent when dealing with scaling patterns in ecology. Indeed, nearly all of
ecological patterns are scale dependent. Such scale dependence hampers our
predictive power and creates problems in our inference. This challenge calls
for a clear and fundamental understanding of how and why ecological patterns
change across scales. As Simon Levin stated in his MacArthur Award lecture, the
problem of relating phenomena across scales is the central problem in ecology
and other natural sciences. It has become clear that there is currently a drive
in ecology and complexity science to develop new quantitative approaches that
are suitable for analysing and forecasting patterns of ecological systems. Here
I provide a road map for future works on synthesizing the scaling patterns in
ecology, aiming (i) to collect and sort a diverse array of ecological patterns,
(ii) to present the dominant parametric forms of how these patterns change
across spatial and temporal scales, (iii) to detect the processes and
mechanisms using mathematical models, and finally (iv) to probe the physical
meaning of these scaling patterns. This road map is divided into three parts
and covers three main concepts of scale in ecology: heterogeneity, hierarchy
and size. Using scale as a thread, this road map and its following works weave
the kaleidoscope of ecological scaling patterns into a cohesive whole.
