The evolution of living things is often a result of mutually influencing species and family trees, over millions of years. Mathematician Renee Hoekzema is developing new methods to better understand this co-evolution. For her research "Cutting, Pasting and Evolving: From Smooth Forms to the Form of Life" she now receives a Vidi grant from NWO.
How did the enormous diversity of life on earth originate? To reconstruct evolutionary relationships, biologists use family trees that show how species branched out over millions of years. "But evolution does not always follow a single family tree," says VU mathematician Renée Hoekzema. "Organisms constantly influence each other's evolution. Think for example of parasites and their hosts, which often develop together, or of genes that are exchanged between different species."
The mathematics of evolution
"To understand such complex evolutionary processes, new mathematical models are needed. An important development in recent decades has been the idea of studying not only individual family trees, but the full space of all possible family trees. By giving this space a geometric structure, it becomes possible to compare evolutionary family trees, measure distances and perform statistical analyses."
Cut and paste
Hoekzema specializes in topology, a branch of mathematics that studies shapes and spaces. One of the central ideas in her research is that complicated shapes can be understood by cutting them into pieces and gluing them back together in different ways.
In her Vidi project, Hoekzema expands these techniques from smooth shapes to networks and tree structures. Such structures are found everywhere in science, from physics to biology. By studying their underlying mathematical structure, she hopes to make new connections between different areas of mathematics.
Understanding the Evolution of Life
An important application is the development of a new geometric theory for co-evolution: the joint evolution of different species or biological systems. By studying the family trees of parasites and their hosts at the same time, for example, researchers can better understand how their evolutionary histories are intertwined.
The project connects fundamental mathematics with important questions from evolutionary biology. The new theory could eventually contribute to reconstructing evolutionary history, understanding biodiversity and analysing complex biological data.