Theoretical Ecology

Using networks, matrices, and eigenvalues to investigate ecological structure and stability

I am a fourth year Ph.D. student in the department of Ecology & Evolution at the University of Chicago. Working in Stefano Allesina's lab, I have been exposed to the powerful perspective of seeing the complexity of nature as a network of connected pieces. I have been particularly captivated by the interaction between the dynamics of ecological systems (i.e. the stability and feasibility of equilibria and the role of transient dynamics) and the structures (both local and global) found in network representations of those systems.

Though I have worked primarily with food-webs, many of my projects exploit the extreme generality of mathematical models, and have applied network- and matrix-based methods to a host of systems. I am driven by the development of computational and statistical methods to enhance our ability to detect patterns in ecological data.


More than 40 years ago, Robert May introduced random matrices to ecology in a famous demonstration of the relationship between complexity and stability which was counter to the prevailing view of the time (May 1972). Following a long hiatus, random matrices have recently re-emerged as the impetus behind several important advances in our understanding of complex ecological systems, spearheaded by Si Tang and Stefano Allesina (Allesina & Tang 2012; Tang & Allesina 2014; Tang, Pawar, & Allesina 2014). I am particularly interested in applying random matrix techniques to bipartite networks (i.e. networks for which the nodes can be divided into groups such that all links are between nodes of disparate groups).


Random matrices à la May look for patterns in matrix ensembles which randomize matrix elements. Advances since then have explored alternative modes of randomization (Tang, Pawar, & Allesina 2014), yet these still tend to focus on node degree and interaction strength correlation. An alternative form of randomization would be to preserve small network structures such as motifs or global network structures such as nestedness and modularity. I am interested in applying this technique to evaluate the importance and utility of small structures which are found at unexpected densities in empirical networks.

Science of Science

In addition to my central focus on ecology, I have also been interested in studying the process of doing science, especially aspects related to publication and evaluating performance. For instance, one project I have worked on looked at the influence of multinational affiliation lists on the success of publications. We confirmed a historical result that more countries improves both the quality of journal a paper is published into and the number of citations (compared to peer publications) it receives once published. Furthermore, we showed that the benefit differs according to which countries are in the affiliations -- some collaborations show much greater improvements than others and some actually decrease the expected number of citations!

1 The effect of intra- and interspecific competition on coexistence in multispecies communities
G. Barabás, M.J. Michalska-Smith, S. Allesina; 2016
2 Stability and feedback levels in food web models
M.J. Smith, E. Sander, G. Barabás, S. Allesina; 2015
3 Selecting food web models using normalized maximum likelihood
P.P.A. Staniczenko, M.J. Smith, S. Allesina; 2014
4 The Scientific Impact of Nations: Journal Placement and Citation Performance
M.J. Smith, C. Weinberger, E.M. Bruna, S. Allesina; 2014
5 Whirling disease dynamics: An analysis of intervention strategies
K.G. Turner, M.J. Smith, B.J. Ridenhour; 2014
6 Superelliptical laws for complex networks
S. Allesina, E. Sander, M.J. Smith, S. Tang; 2013
  • ESA2016 & HTML presentations

    August 19, 2016

    Welcome to the site!

    Last week, I attended the 101st Annual Meeting of the Ecological Society of America in Ft. Lauderdale, FL. While there I was able to meet up with several colleagues I hadn’t seen in a long time and see many interesting talks. I also gave a talk of my own, where I presented some recently submitted work on distinguishing ecological categorizations or roles (e.g. parasites vs predators) using a purely statistical consideration of the network structure. For this, we utilized (and enhanced) the group model which was introduced to Ecology by my advisor (Stefano Allesina) and committee member (Mercedes Pascual) back in 2009.

    Read More