We are trying to understand how collective patterns of self-organization emerge from the joint actions of heterogeneous individuals. The phenomena studied include evolutionary adaptation, random genetic drift, epidemic spreading, collective motion, synchronization and jamming. Although these phenomena occur in many complex systems, our experimental efforts are focused primarily on microbial systems that we can study in our wet lab. Our key theoretical challenge is to identify essential dynamical building blocks and to predict how these conspire to generate the complex dynamical patterns observed at the population level.
for an detailed overview of our research. Some recent highlights are described below.
Acceleration of evolutionary spread by long-range dispersal
The spreading of evolutionary novelties across
populations is the central element of adaptation. Unless population
are well-mixed (like bacteria in a shaken test tube), the spreading
dynamics not only depends on fitness differences but also on the
dispersal behavior of the species. Spreading at a constant speed is
generally predicted when dispersal is sufficiently short-ranged,
specifically when the dispersal kernel falls-off exponentially or
faster. However, the case of long-range dispersal is unresolved: While
it is clear that even rare long-range jumps can lead to a drastic
speedup — as air-traffic–mediated epidemics show — it has been
difficult to quantify the ensuing stochastic dynamical process. Yet,
such knowledge is indispensable for a predictive understanding of many
spreading processes in natural populations.
Together with Daniel Fisher, we have developed a simple iterative
scaling approximation supported by simulations that accurately
predicts evolutionary spread which is determined by a tradeoff between
frequency and potential effectiveness of long-distance jumps. In
contrast to the exponential laws predicted by deterministic
’mean-field’ approximations, we show that the asymptotic spatial
growth is either according to a power-law or a stretched exponential,
depending on the tails of the dispersal kernel. More importantly, we
provide a full time-dependent description of the convergence to the
asymptotic behavior which can be anomalously slow and is relevant even
for long times. Our results might be used in the future to improve the
inference of the evolutionary spread based on genealogical trees,
which is however a largely open problem.
O. H., Daniel S. Fisher, PNAS (2014)
Evolution at expanding frontiers
A principal tenet of modern evolutionary biology is that Darwinian selection and random number fluctuations, called genetic drift, compete in driving evolutionary change.
It is widely accepted that genetic drift can have significant effects on small populations that may even lead to speciation.
In large populations, however, random sampling effects are generally considered weak compared with selection (law of large numbers).
A major departure from this paradigmatic behavior occurs when large populations undergo range expansions.
The descendents of individuals first settling in a new territory are most likely to dominate the gene pool as the expansion progresses.
Random sampling effects among these pioneers results in genetic drift that can have profound consequences on the diversity of the expanding population.
In this project, we used simple microbial systems to study the nature of these number fluctuations (genetic drift) in range expansions of large populations.
The colony on the right was grown from a 50:50 mixture of CFP (red) and YFP (green) labeled E. coli bacteria (see here
for experimental details).
Even though both strains were otherwise genetically identical, the growing colony exhibited a striking segregation of the two neutral markers (CFP and YFP) over time.
The dynamics of segregation is restricted to the edges of the colony, while, except for a gradual thickening, the interior distribution of CFP and YFP is essentially frozen.
The genetic segregation on the population level is the consequence of number fluctuations on a much smaller scale, within a thin region of reproducing pioneers at the expanding frontier.
The statistical properties of the observed pattern can be described in the frame work of non-equilibrium statistical physics.
The domain walls radiating out from the center of the image follow a super-diffusive random walk, and annihilate when they meet.
This leads to a model of annihilating super-diffusive random walks (with "inflation") (see
theory for further details).
The neutral genetic patterns found in our experiments could be a general signature of continuous range expansions in populations exhibiting moderate rates of turnover and migration.
Have a look at
for the broader implications of our work.
An illustration of the mechanism by which domains coarsen in expanding populations.
(a) Four monochromatic domains are bounded by a moving frontier (black line).
(b) As the colony grows further in the upward vertical direction, the domain boundaries follow wandering paths.
By chance, the two domain boundaries on the left-hand side meet.
As a consequence, the enclosed domain (red left-hand domain in (b)) loses contact to the population front and is, henceforth, trapped in the bulk of the colony.
We model these dynamics by replacing the tips of the domain boundaries by random walkers that “live” on the growing one dimensional edge of the colony.
Even though these random walkers annihilate when they meet, they have a non-zero survival probability on the growing circumference of a circular colony (inflation).
||Spontaneous mutations and selection
E. coli colonies grown from a binary mixture of differently labeled strains show a pronounced segregation into the component strains.
The meandering of the boundaries between the red and green regions can be described by a super-diffusive random walk.
The yeast species S. Cerevisiae exhibits much weaker levels of genetic drift compared to the bacterium E. coli, which is manifest in the much larger number of sectors.
During a range expansion, Cells compete for colonizing virgin territory.
Mutations that change the expansion velocity have a strong impact on this neck-and-neck race.
We currently investigate frequency and effect of these mutations (With N. Karahan, A. Murray, D. R. Nelson).
Microbial population dynamics
This movie shows the collision of two growing populations of differently labeled E.coli
The developing interface is shaped by the peculiar dynamics of the proliferating "nematic liquid" of rod-like bacteria.