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Evolutionary Tradeoffs: The Geometry of Fitness with Dr. Uri Alon

Science Talk Briefing – October 21, 2015 – Dr. Uri Alon

Dr. Uri Alon, guest lecturer at MSK 10/21/15.

Dr. Uri Alon, guest lecturer at MSK 10/21/15.

Dr. Uri Alon is a professor and systems biologist at the Weizmann Institute of Science in Israel.  Author of “Introduction to Systems Biology”, Overton Prize Winner, and guitar enthusiast, Dr. Alon’s work seeks to describe nature using networks, theory, and computation.  Visit his website for more information.

President’s Research Seminar Series at Memorial Sloan Kettering – Research in Brief

Dr. Uri Alon, a theoretical physicist by training selected by the Gerstner Graduate School first year class, gave a very engaging seminar to the academic gathering at Memorial Sloan Kettering, evoking familiar evolutionary concepts of phenotype and fitness in examples like Darwin’s Finches and ant colonies.  Throughout the talk Dr Alon was pleasantly familiar, promising a guitar concert after the questions and often acknowledging his own faults and ignorance in what amounted to a very informal-feeling invited talk.
The crux of the research Dr. Alon presented is the concept of an “archetype” – essentially the paradigm of fitness for a certain trait.  Fitness, here, is defined as the ability to complete a task.  Examples included finch beaks ideal for cracking seeds, ant body size sufficient to defend a hill, and rodents with teeth suited for particular diets.
As such, individuals can scale from the highest rating of fitness (the archetype) to much lower.  By taking two measurements of the phenotype, the archetype would occupy one point on a two dimensional plane (e.g. where the dimensions are the ratios of different teeth in the mouth, one archetype favoring carnivorous diets, and one favoring herbivorous diets, as in the figure below).
In this figure from Dr. Alon's work we see the space between two archetypes, the fitness maxima for specific traits, is a line along which the majority of variation falls. There is an evolutionary penalty, it seems, for leaving this line. The example here is dimensions of rodent teeth for trait 1 (chewing meat) vs trait 2 (chewing leaves).

In this figure from Dr. Alon’s work we see the space between two archetypes, the fitness maxima for specific traits, is a line along which the majority of variation falls. There is an evolutionary penalty, it seems, for leaving this line. The example here is dimensions of rodent teeth for trait 1 (chewing meat) vs trait 2 (chewing leaves).

The problem grows in complexity as more traits are required – the ideal beak length for open seeds may be different than for feeding young.  In this case there may be a second archetype with maximum “feeding” fitness, but sub-optimal “seed-opening” fitness.  Again, choosing appropriate measurements as axes, the two archetypes will occupy two distinct points in a 2D representation. Here Dr Alon points out the interesting fact that evolution will keep most variation along a line between both archetypes.
In other words, there can be a trade-off of one fitness for another, but evolution will not favor a dimension that doesn’t contribute to either (as shown in the middle panel, above).  This can be expanded with further dimensions, where three archetypes will generate a 2 dimensional triangle, and four archetypes can form geometric shapes.
The figure here from Dr. Alon's work demonstrates how the variation space of different traits can be contained with the dimensions of the archetypes.

The figure here from Dr. Alon’s work demonstrates how the variation space of different traits can be contained with the dimensions of the archetypes.

Moving this argument into the genetics of cancer, we can make the expression of important genes the X- and Y- axes (and more dimensions are of course possible).  Data show that all variation will occur between the archetypes (e.g. dividing cell fitness, migrating cell fitness, etc) but not outside of the space they define.  Clusters of patient data can be fit into geometric shapes, the grey in the above figure, and further modeled for predictive processes.
Dr Alon explained how evolution-based mathematics has enhanced forensics, archaeology, and other fields of science. This mathematical framework could also be useful for identifying cancer types, accurately describing cancer cell behavior, and possibly directing treatment.  His most recent work can be found here:

Also, as mentioned above, Dr Alon is a very enjoyable speaker. This did not go unnoticed as Dr Alon has given a Ted talk, not about network theory, but about the parallels of improvisation in theater and research science.  It’s a fairly uplifting talk, you can check out here, especially if you’re currently a graduate student.
Bust out of the cloud!
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