PhD thesis

"A theory is something nobody believes, except the person who made it. An experiment is something everybody believes, except the person who made it."  -- Albert Einstein

My PhD thesis research combines theory in critical transitions with experimental microbial systems to investigate the spatiotemporal dynamics before population collapse. In particular, I have demonstrated that a set of warning indicators based on "critical slowing down" can be used to assess the fragility of populationsMy work was awarded the Outstanding Doctoral Thesis in Biological Physics by American Physical Society in 2014. 

Thesis (PDF)




Foreseeing tipping points in complex systems

Theory: nonlinear dynamics

   Fold bifurcation
Population collapse and catastrophic thresholds in many complex systems may correspond to a tipping point in the system (Scheffer et al 2001), i.e. a fold bifurcation in the language of nonlinear dynamical systems theory (Strogatz 1994).

Theory predicts that in the approach of tipping points a system would recover more slowly from perturbations, a phenomenon known as critical slowing down. Thus, we may be able to forecast an upcoming catastrophe by measuring how a system responds to perturbations. This gives hope to developing a toolbox of generic early warning signals before tipping points (Scheffer et al 2009). 

Experiment: laboratory microbial systems

Budding yeast
Saccharomyces cerevisiae, also known as the budding yeast or baker's yeast, is the most useful and well studied species of yeast. In the past few decades, yeast has established itself as a model organism in various areas of biology, including cellular and molecular biology (Botstein et al 1988), genetics (Botstein et al 2011) and ecology and evolution (Replansky et al 2008).

We use yeast to realize the "Allee effect" in population dynamics: an observation that the per capita growth rate of many animal populations is maximal at intermediate densities (Courchamp et al 1999). Yeast hydrolyze sucrose outside the cell and benefit from the hydrolysis products of other cells in the population (Gore et al 2009). The cooperative breakdown of sucrose by yeast is analogous to the cooperative behaviors in natural populations that lead to the Allee effect.   

Research projects

Changes in pattern of fluctuations reflect loss of resilience

Stability landscape
(Scheffer et al 2012)

In the laboratory yeast system, we can deteriorate the environment in a controlled setting by increasing the level of daily dilution. Because of the Allee effect, yeast populations would collapse beyond a threshold of dilution. We find that closer to the tipping point there is a significant increase in the size and timescale of fluctuations of population density, in accordance with theory and simulations. Our experiment suggests that critical slowing down may provide advance warning of  tipping points in a variety of dynamical systems.

Generic indicators for loss of resilience before a tipping point leading to population collapse.
Science (2012) [PDF]

Dynamics of a producer-freeloader ecosystem on the brink of collapse. Nature Communications (2014) [PDF]

 Spatiotemporal dynamics before collapse of connected populations


In reality, populations live in different patches and are connected by dispersal. Spatially resolved data provide us more information but also add complexity into the analysis. How does spatial coupling such as population dispersal influence the pattern of fluctuations? How do we incorporate spatial information into the current toolbox of warning indicators, which are mostly based on time-series data? We use spatially extended yeast populations (i.e. metapopulation) as well as coupled map lattice models to address the above questions.

Slower recovery in space before collapse of connected populations. Nature 496, 355-358 (2013) [PDF]

Early warning signals in multiple deteriorating environments

ollapse of Atlantic cod

Critical slowing down is a generic property of dynamical systems in the vicinity of bifurcations. Warning indicators based on critical slowing down are independent of the underlying dynamics of a system, thus providing a complementary approach to parametric modeling.

We test
the generality of warning indicators experimentally by tuning different environmental drivers of the yeast system. Combining experimental data and modeling, we evaluate the performance of warning indicators before population collapse in multiple deteriorating environments..

Relation between stability and resilience determines the performance of early warning signals under different environmental drivers. PNAS 112(32): 201418415 (2015) [PDF]

Why am I doing this

Physics: understanding criticality

Biology: from microcosms to nature

 Interdisciplinary research: connections

Map of Science
(Bollen et al 2008)
To me, discovering hidden connections between different scientific fields is a wonderful intellectual experience. As an undergrad, I worked on phenomenological high energy physics at an electron-positron linear collider (Dai et al 2008). I was amazed to recognize the close relationship between high energy physics and astrophysics, which investigate objects differing by forty orders of magnitudes in size (from quarks to quasars, as illustrated by the famous film "Powers of Ten"). The connections between the two areas of physics cover a wide range of topics, including cosmic rays, the candidates of dark matter and the origin of universe. So, when I moved on to explore the world of living systems, I was thrilled to find (and build!) links between the two extreme scales in biology: microbiology and ecology.