We live in a world dominated by rankings. Besides soccer teams, movies and restaurants, rankings of Universities and researchers have become commonplace.
The Scientific Wealth of Nations has been measured in many ways, all centered on a very simple idea: if a country producing a certain proportion of papers (pp) accrues a much larger proportion of citations (pc), then the country is producing high-quality science. Conversely, countries for which pc < pp would produce lower-quality research.
This appealing simplicity, however, conceals one of the most important factors determining the influence of a scientific article, the journal where it was published. Clearly, publishing a paper in Nature would guarantee a much wider audience than that reached by The Bulletin of Koala Research — even for papers of the same quality.
We thus took 1.25M articles in eight disciplines (from 1996 to 2012), and parsed the country of affiliation of all the authors. We then measured how the country(ies) of affiliation influenced the journal placement (i.e., where was the paper published) and the citation performance (i.e., whether the article received more or fewer citations than its “peers”). Differently from other studies, we kept a tally for each possible combination of countries, such that we can see which international collaborations are more effective.
Originally, we thought of measuring the effect of the institution (rather than country) of affiliation—how much is an Oxford affiliation worth? We’re sufficiently proficient in regular expressions to distinguish India from Indiana, but affiliations like The Miami University in Oxford, Ohio made us decide to stick with countries.
In the paper, we start by talking about the 1982 study by Peters and Ceci. This is one of the most intriguing paper I’ve ever seen, and even the lengthy commentary (you can find here) is a pleasure to read.
In hindsight, we should have changed our own affiliations to the wonderful ones used by Peters & Ceci. The Northern Plain Center for Human Potential sounds just right!
After studying the stability of large ecological networks, we wanted to try to describe the transient dynamics following a small perturbation of the equilibrium. We thus studied “reactivity”, which tells us whether perturbations of a stable equilibrium are going to be amplified before decaying.
which we published in frontiers in Ecology and Evolution, a new journal with an interesting peer-review scheme (a topic dear to my heart!). In fact, I am so happy journals are trying new ways of doing peer review I decided to join the editorial board.
I always joke in the lab that anybody who wants to propose a new measure in ecology (or index, etc.) should pay $1,000, $2,000 if the new measure has an acronym. These funds could pay for graduate students to go to some conference.
The only exception to the rule is for studies showing that two seemingly different measures are in fact the same thing. This is the case of our recent study on nestedness, published today in Nature Communications:
The ghost of nestedness in ecological networks
Phillip P. A. Staniczenko, Jason C. Kopp & Stefano Allesina Ecologists are fascinated by the prevalence of nestedness in biogeographic and community data, where it is thought to promote biodiversity in mutualistic systems. Traditionally, nestedness has been treated in a binary sense: species and their interactions are either present or absent, neglecting information on abundances and interaction frequencies. Extending nestedness to quantitative data facilitates the study of species preferences, and we propose a new detection method that follows from a basic property of bipartite networks: large dominant eigenvalues are associated with highly nested configurations. We show that complex ecological networks are binary nested, but quantitative preferences are non-nested, indicating limited consumer overlap of favoured resources. The spectral graph approach provides a formal link to local dynamical stability analysis, where we demonstrate that nested mutualistic structures are minimally stable. We conclude that, within the binary constraint of interaction plausibility, species preferences are partitioned to avoid competition, thereby benefiting system-wide resource allocation.
We uploaded the code needed for the analysis here.
Back in 2001, when I was studying for my PhD entrance exam, I read May’s 1972 paper for the first time, and fell in love with this problem.
May’s result is very simple to explain: take S species and suppose that each species interacts with any other with probability C. Then, the expected number of connections for each species is SC. Now assume that the ecosystem is at a steady state: species do not change in density through time if not perturbed. If two species interact, the effect of species a on species b is taken from a normal distribution with mean 0 and variance σ². Finally, the effect of a species on itself is assumed to be -1 (i.e., there is some sort of self-regulation).
May showed that such networks are almost surely stable (i.e., persist in time despite small perturbations) whenever σ√SC<1, while whenever this threshold is crossed the system is almost surely unstable, and thus should not persist through time. This result sparked a fierce “complexity-stability” debated that lasts to this day. In fact, May’s results are difficult to reconcile with the staggering diversity observed in nature: many species (large S) interact in complex networks (large C) of ecological interactions, despite mathematical considerations would tell us this is not possible.
Si and I tackled this problem in a new article just published by Nature:
Stability criteria for complex ecosystems
Forty years ago, May proved that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations. May analysed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (for example predator–prey, mutualistic or competitive). Here we extend May’s results to these relationships and find remarkable differences between predator–prey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. We provide analytic stability criteria for all cases. We use the criteria to prove that, counterintuitively, the probability of stability for predator–prey networks decreases when a realistic food web structure is imposed or if there is a large preponderance of weak interactions. Similarly, stability is negatively affected by nestedness in bipartite mutualistic networks. These results are found by separating the contribution of network structure and interaction strengths to stability. Stable predator–prey networks can be arbitrarily large and complex, provided that predator–prey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.