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COMPLEX TIME: Adaptation, Aging, & Arrow of Time

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Irreversible Processes in Ecological Evolution/Statistical mechanics of microbiomes

From Complex Time

January 29, 2019
3:45 pm - 4:45 pm


Robert Marsland (Boston Univ.)


In a seminal paper in 1972, Robert May studied complex ecosystems using Random Matrix Theory. Nearly fifty years later, the rise of quantitative microbial ecology makes it possible to test and refine this approach. Random matrix models successfully capture a wide range of large-scale patterns observed in real microbial communities, including functional and family-level reproducibility, compositional clustering by environment, enterotypes, dissimilarity-overlap correlations, decreased diversity in harsh environments, compositional nestedness, succession dynamics and modularity. After describing the computational model we have developed to reproduce all these patterns, I will present a set of analytic results that explain why this works in the real world. Adding even a small amount of noise to a sufficiently diverse community induces a phase transition to a “typical” phase, where community-level properties such as diversity and rank-abundance curves are indistinguishable from those of a completely random ecosystem. I will explain how the properties of this phase are governed by “susceptibilities” describing the linear response of the ecosystem to small changes in population sizes or resource concentrations. These susceptibilities can be obtained from Random Matrix Theory, in the spirit of May’s paper, and can also be measured by subjecting a community to controlled perturbations.

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Post-meeting Reflection

Robert Marsland (Boston Univ.) Link to the source page

Questions from my talk:

True or false?

1. Classical ecological models are inadequate for understanding microbial ecosystems.

2. The large-scale, reproducible patterns we see across microbiomes are emergent features of “typical random ecosystems.”

3. Diverse communities will almost always behave like “random ecosystems.” 

Question I want to discuss

Can large-scale ecological changes over time be understood through simple general principles? (Samraat, Jacopo, Priyanga, me: flux balance/metabolic rates, random matrix theory, biochemical and morphological constraints)

Are there ecological summary statistics that change monotonically over time? (Jacopo, and some of my work that I didn't talk about -- see references)

Which properties of individual organisms are essential for predicting large-scale ecological changes?

- Pamela -- why do some vaccines fail to produce large-scale ecological change (i.e., pathogen extinction)?

- Greg -- importance of distribution of susceptibilities to dynamics of epizootic onset.

- Fernanda -- importance of adaptive foraging for understanding why pollinator systems don't collapse -- and why they might under new circumstances.

- Samraat -- taking the mechanics of inter-species interaction seriously, understanding how they affect response of ecosystem to temperature changes.

- Priyanga -- asymmetry of reaction norms for temperature variation.

What do we miss when we focus too much on equilibrium/steady states? (Prevalence of cyclic disturbance/recovery dynamics -- Greg, Samraat)

Reference Material

"The Minimum Environmental Perturbation Principle" (Marsland et al. 2019) is some new work I didn't include in my presentation, but which is possibly more relevant to the irreversibility theme. The main result is that a wide class of niche models exhibit monotonic increase in the environmental perturbation under successive invasions/evolution. I would love any feedback from the ecologists about references to add, things that are unclear, etc.

Marsland and England 2017 and Marsland et al. 2015 contain in-depth explanations of the two kinds of “thermodynamic” irreversibility I wrote up on the board.

Mehta et al. 2018 begins with a discussion of the "bias/variance tradeoff", which is extremely relevant to the use of models with many parameters to make predictions. It also has a section on dimensional reduction and clustering that might be useful to people working with high-dimensional phenotype data. (Note that the wiki didn't allow me to enter the whole author list, which should also include Marin Bukov, Charles Fisher and David Schwab.)

Momeni et al. 2017 shows some of the ways in which Lotka-Volterra can fail to capture the population dynamics of a generalized class of consumer-resource models.

Fisher and Mehta 2014 shows how both niche and neutral regimes can arise in Lotka-Volterra dynamics with immigration, depending on the parameter values.

"Available Energy Fluxes..." (Marsland et al. 2019) contains a full explanation of our microbial consumer resource model in the appendix. The Python implementation can be found at our group github:

I have also included the original Human Microbiome Project and Earth Microbiome Project data papers, which contain the large-scale patterns I was showing in the presentation.

Gutenknust et al. 2007 explains some of the subtleties of Bayesian model fitting in a very accessible way, and strongly influenced the way I think about many-parameter models.

Goldford et al. 2018 contains some of the patterns I was talking about at the beginning of my talk, which are already captured by a preliminary version of the model.

Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
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Lotka-Volterra pairwise modeling fails to capture diverse pairwise microbial interactions Babak Momeni, Li Xie, Wenying Shou eLife 2017 79 0
A high-bias low-variance introduction to machine learning for physicists Alexandre G. R. Day, Ching-Hao Wang, Clint Richardson, Pankaj Mehta 2018 0 9 Download
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The Minimum Environmental Perturbation Principle: A New Perspective on Niche Theory Pankaj Mehta, Robert Marsland III, Wenping Cui 2019 0 1
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