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Macroecological patterns, such as the highly uneven distribution of individuals among species and the monotonic increase of species richness with area, exist across ecological systems despite major differences in the biology of different species and locations. These patterns capture the general structure of ecological communities, and allow relatively accurate predictions to be made with limited information for under-studied systems. This is particularly important given ongoing climate change and loss of biodiversity. Understanding the mechanisms behind these patterns has both scientific and practical merits. I explore two conceptually different approaches that have been proposed as explanations for ecological patterns – the process-based approaches, which directly model key ecological processes such as birth, death, competition, and dispersal; and the constraint-based approaches, which view the patterns as the most likely state when the system is constrained in certain ways (e.g., the system has a fixed number of 100 individuals among five species, but the distribution may vary). While the process-based approaches directly link patterns to processes, the constraint-based approaches do not rely on the operation of specific processes and thus can be more broadly applied. I develop a new constraint-based approach to one of the most well established patterns in ecology, the power-law relationship between the mean and variance of a population. This pattern has been widely observed and adopted as characterization of population stability. I find that the shape of the pattern can be well explained with two numerical constraints on the system, lending support to the idea that some macroecological patterns may not arise from specific processes but be statistical in nature instead. I further examine the performance of the process- and constraint-based approaches for patterns of biodiversity and energy use, which are among the most essential as well as most well-studied aspects of community structure. Candidate models from both categories are able to partially capture the patterns across 60 globally distributed forest communities, however the process-based model is shown to provide a better general characterization of community structure than the constraint-base model in all communities. Thus the constraint-based approaches in their current forms do not fully encapsulate the effect of processes, which also contribute to the shape of the macroecological patterns of biodiversity and body size in addition to the constraints.