Emergent phenomena in community phylogenies: Quantitative punctuated equilibrium and the renormalization group
Macroecological patterns, like species abundance distributions and species-area curves, have often been claimed to display the same or similar behavior across many disparate ecological systems. This apparent universality has led ecologists to wonder whether the great complexity of natural systems can be mapped onto a smaller set of ecological `rules' that then determine the form of these emergent patterns. If this assertion is true, it has implications for our understanding of emergent phenomena across a range of systems, and also very practical implications for modeling and predicting biodiversity patterns. And yet, surprisingly little progress has been made in understanding the theory of how and why complex ecological mechanisms results in simple, emergent patterns. While there are many statistical approaches to predicting macroecological patterns, these rarely model mechanism from the ground up, thus showing which processes we should expect to dominate observed patterns at a given spatial and temporal scale.
We introduce a combination of new empirical and theoretical approaches to shed light on this question. Our empirical approach is based around highly quantitative, coarse-grained backbone structures that we identify across a broad range of community phylogenies. Our central empirical results are that these backbone structures appear at characteristic temporal resolutions, and that they are reminiscent of a kind of punctuated equilibrium. Specifically, we identify bursts of branching appearing throughout these phylogenies, and the size distribution of these bursts scales as a power law. The exponent of this power law then determines the proportion of large bursts of branching vs smaller bursts, and varies across communities. We go on to introduce a theoretical framework to interpret these bursty phylogenies, and the coarse-grained resolution at which these patterns appear, in terms of ecological and evolutionary processes including neutral drift, environmental stochasticity, and simple fitness landscapes. These results lay the groundwork for a methodology to make robust, highly quantitative predictions for complex ecological systems, knowing which processes to keep and which can be safely dropped.