The origins of emergent phenomena: Renormalization, coarse-graining, and the fingerprints of ecological and evolutionary processes

The question of species coexistence – who, how many, and why – goes back to Darwin, von Humboldt and the origins of evolution and ecology. As these fields have developed as quantitative disciplines this question has been generalized to include a range of quantitative patterns of biodiversity—known as macroecological patterns. Examples of these patterns include quantitative measures of the balance of rare and abundant species in a given community, and the turnover in species composition across space. What is surprising about these phenomena is that they have been observed to display similar forms across many disparate ecological systems, from microbial communities to tropical forests, leading ecologists to wonder whether the great complexity of natural systems can be mapped onto a smaller set of ecological ‘rules’ for these emergent patterns. If this assertion is true, it has implications for our understanding of emergent phenomena across a range of complex systems, and also very practical implications for modeling and predicting biodiversity patterns—predictions derived from understanding how these systems work will be critical to conserving biodiversity and ecosystem health.

My research centers around this question of what rules really govern ecological dynamics and my goal is to address this using a biological version of the renormalization group. The renormalization group is a set of ideas drawn from physics to understand coarse-grained phenomena, and it teaches us two critical lessons. First, that at coarse-grained scales, the behavior of many different models ‘flows’ to the same universality class; second, that the special models defining these universality classes have fewer degrees of freedom than might be expected. For example, liquid-gas and ferromagnetic phase transitions seem very different, and yet both are governed by the same universality class, with essentially just one parameter to tune near that transition.

My recent work has focused on the evolutionary history of a group of organisms, known as phylogenetic diversity, and it sets the scene for an ecological renormalization group. We have found that empirical phylogenetic trees have relatively simple, universal backbone structures at coarse-grained scales. This is very much reminiscent of a renormalization group flow, and I plan to build on this work to develop an understanding of how ecological and evolutionary processes coarse-grain onto models of lower complexity. In summary:

1. We will gain an underpinning for ecologists’ intuition that large-scale phenomena are emergent, governed by simpler coarse-grained models that nevertheless drive empirical phenomena.

2. We will lay the groundwork for a methodology to make predictions for complex ecological systems, knowing which processes are critical in developing predictive models that scale up from small-scale processes to large-scale predictions.

3. We will develop insight into emergent patterns in non-biological complex systems, including the dynamics of social and financial systems. In these systems, heterogeneity, interactions and adaptation are ubiquitous, and aggregated outputs are often analogous to macroecological patterns.