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Evolutionary processes and patterns of biodiversity: what did we learn?
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The question of modeling evolutionary processes is fundamental to understanding how biodiversity and genetic diversity develop and in particular the dynamics of cancer through time. In a mini-series of lectures spanning three weeks, Amaury Lambert provided a host of probabilistic models which describe the evolution of genes and species over time. By using current genetic data, and historical records, these models can be calibrated to help explain the dynamics of evolution.
Lambert started his lecture series by introducing important models in population genetics that describe the evolution of genes through their mutation forward in time, as well as their coalescence backwards in time. One such example of such a probabilistic model is the Kingman coalescent. Consider a sample of n individuals (e.g. genes at one locus) at the present time. As one moves backwards in time, pairs of lineages merge at some rate, thus forming a sequence of partitions of the numbers 1 through n. Eventually, all of the lineages have merged into a single cluster. This process can be represented by a tree. On top of such a tree, one can superimpose random, neutral mutations which affect all descendants on that branch of the tree. Figure 1 shows an instance of this model. Time flows in the downward direction and mutations affect all descendants below them. The mutations are denoted by circles and the colored ones are the ones which ultimately define what is seen at present time--i.e., the colors at the bottom of the tree (infinite-allele model).
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In genetics, one generally is concerned with coevolution of genes at many loci and the diversity of mutations which are present within a population (see the multiple sequence alignment in Figure 2). Lambert introduced models such as the ancestral recombination graph and the sequential Markovian coalescent which aim to describe the complex dependencies between gene trees are different loci.
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After having probed genetic evolution, Lambert moved to the level of species and presented models for speciation, reproductive isolation and phylogeny. The aim here is to make inference on the dynamical evolution of species over time. At the largest scale, this leads to a tree of life, such as illustrated in Figure 3.
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The models here seek to understand how adaptation to the environment and/or the accumulation of genetic differences drive speciation and shape the tree of life. By statistical methods (e.g. maximum likelihood estimation), one can then use present day data on species (abundances, whole genomes) to infer these processes.
Modeling the coevolution of species and their genes was the final subject developed in Lambert's lecture. Here he presented a notion of coalescent within a coalescent. In other words, species can be modeled through a tree (or backwards in time a coalescent) and within that structure, genes evolve and mutate with their own tree (or coalescent). Remarkably, such nested coalescents models arise not just in models of macro-evolution, but also in describing the complex energy landscape of high dimensional disordered statistical physics model dynamics. Lambert also showed how the existence of gene flow between species blurs that simple picture and proposed innovative models of coalescence and fragmentation accounting for this phenomenon.
Throughout his lectures, Lambert skillfully interspersed deep and cutting edge mathematical concepts with their exciting real-world biological applications.
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Meet Our Associate Members
In this monthly newsletter, we will regularly feature
the many talented members of our Institute.
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Darcy Peterka is a Senior Scientist, and the Director of Team Science and Cellular Imaging at the Zuckerman Institute at Columbia University. His research combines advances in physics, chemistry, mathematics, and statistics to develop novel optical methods to observe and modulate neuronal activity to answer a variety of questions. Darcy is also an associate member of the Herbert and Florence Irving Institute for Cancer Dynamics where he is spearheading the building of a serial two-photon tomography microscope system for imaging tumors in 3D.
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Brent R. Stockwell is a Professor in the Departments of Biological Science and Chemistry at Columbia University. His research involves the discovery of small molecules that can be used to understand and treat cancer and neurodegeneration, with a focus on mechanisms governing cell death. These interdisciplinary investigations led to new methods of small molecule drug discovery, and the discovery of a new form of cell death known as ferroptosis. Brent is also an associate member of the Herbert and Florence Irving Institute for Cancer Dynamics, where he collaborates with Elham Azizi and Jellert Gaublomme on probabilistic modeling of intercellular interactions that drive ferroptosis susceptibility of therapy-resistant cancer cells.
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Openings
2020/2021 DSI/IICD postdoctoral fellow research program
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DSI and IICD are pleased to announce the opening of the DSI/IICD postdoctoral fellow research program 2020/2021.
The Data Science Institute (DSI) postdoctoral fellows are the next generation of leaders in data science. DSI and IICD are seeking fellows who will support our shared mission of improving the understanding of cancer biology, origins, treatment, and prevention through data-driven methods and processes. We are particularly interested in candidates who will further advance core research in statistical and probabilistic modeling. For more information go here and click here to apply for IICD/DSI postdoctoral fellowship. Please indicate your interest in the DSI/IICD program within your cover letter.
The Azizi lab is recruiting!
The Azizi lab, a Computational Cancer Biology Lab in IICD and BME has open positions for motivated and talented postdoctoral fellows with a background in machine learning and/or computational biology. They also have a senior research assistant position for single cell experimental work. For details please click here.
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Congratulation to both Stockwell and Azizi
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The Stockwell lab received a UG3 NIH award to join the HuBMAP consortium, the goal of which is to map the entire human body at single cell resolution. Their effort is a collaboration with Nick Winograd and Hua Tian at Penn State. Their project focuses specifically on single cell lipid and metabolite mapping of the human liver.
The Azizi lab received an Intra/Inter-Programmatic Pilot Program from the Herbert Irving Comprehensive Cancer Center, in partnership with Ran Reshef, Director of the Translational Research, Blood and Marrow Transplantation at Columbia University Irving Medical Center
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