Analysis of phylogenetic tree patterns could reveal connections between evolution, ecology

In biology, phylogenetic trees represent the evolutionary history and diversification of species, the “family tree” of life. Phylogenetic trees not only describe the evolution of a group of organisms, but can also be built from organisms within a particular environment or ecosystem, such as the human microbiome. In this way, they can describe how this ecosystem evolved and what its functional capabilities might be.

Now, researchers have presented a new analysis of the patterns generated by phylogenetic trees, suggesting that they reflect previously hypothetical connections between evolution and ecology. The study was led by Swanlund’s professor of physics, Nigel Goldenfeld, who also heads the Biocomplexity Group at the Carl R. Woese Institute for Genomic Biology at the University of Illinois at Urbana-Champaign. The other team members were graduate student Chi Xue and former undergraduate student Zhiru Li, now at Stanford University. Their findings were published in a recent article in the journal. Proceedings of the National Academy of Sciences, titled “Invariant Scale Topology and Bursting Branches of Evolutionary Trees Emerge from Niche Construction”

The most familiar phylogenetic tree of all life on Earth uses genes from the essential cellular ribosomal machinery to represent species. By comparing the differences between the molecular sequences of the same genes in different organisms, researchers can deduce which organisms descended from others. This idea led to the mapping of the evolutionary history of life on Earth and the discovery of the third domain of life by Carl R. Woese and his collaborators in 1977.

Real phylogenetic trees are complex branching structures, reflecting the speciation pattern as new mutants of a species emerge. Branching structures are complex, but it is possible to characterize them in terms of how balanced they are and other statistical characteristics that reflect the tree topology. The simplest characterization is to look at each branch node in the tree: is it divided into two branches of exactly the same length or are the branches unequal in length? The former is said to be balanced while the latter is unbalanced.

Despite the complexity of the trees, there is a consistent mathematical pattern to the topological structure throughout evolutionary time, one that is self-similar or fractal in nature. Using a minimal representation of evolution, the researchers showed how this fractal structure reflects the indelible imprint of the interaction between ecological and evolutionary processes. Nature’s minimal models are not meant to be too realistic, but are built to capture the most important ingredients of a process in a way that facilitates simulation and mathematical analysis.

Goldenfeld’s work frequently uses minimal models to explain generic aspects of complex biological and physical phenomena that are insensitive to precise details. Other aspects of complex phenomena cannot be well described in this way, but it is known that physical patterns, such as self-similarity in space, can be described using minimal modeling approaches.

“Therefore, it seemed reasonable to try this approach to describe self-similarity over time as well,” Goldenfeld said.

“We set out to study the topological property of the phylogenetic tree and ended with an ‘additional fruit of explanation’ for the tree’s special character,” Xue said.

The study revolved around a concept in evolutionary ecology known as niche construction, first proposed about 40 years ago. In building niches, organisms modify their environment, creating new ecological niches in the ecosystem and changing the environment. In turn, these new niches affect the general evolutionary trajectory of organisms that share the environment. The end result is that evolution and the environment are closely linked. The idea that evolution is not occurring in a purely static environment is controversial, despite being intuitively appealing. Their findings add to the existing body of work by identifying the long-term effects of building niches in a way that can be detected by modern genomics and phylogenetic tree building.

In the work presented here, the researchers simulated organisms and associated a niche value that described their interaction with their environment. Those organisms with a high niche value contained a large number of ways to adapt to their environment and ultimately led to their survival, while those with small niche values ​​were less resistant.

“In our model, we relate the niche positively to the probability of speciation, in the sense that an organism with a large niche can probably successfully diversify,” said Xue. “During the evolution of the phylogenetic tree, when two child nodes emerge from their parents, they obtain their niches partially from inheritance and partially from construction.”

The researchers demonstrated that species that run out of niche space can no longer branch or spice. Mathematically, this was represented as a so-called absorbing limit condition at the node representing this species.

“Its sibling node is likely to still diversify as long as that niche remains positive, but the two sibling nodes are no longer symmetric and the tree becomes unbalanced,” Xue explained. “We demonstrated that the absorption limit is crucial to generate the fractal structure of the tree and that the construction of the niche guarantees that some nodes will reach the limit.”

The researchers used a simplified niche construction model and were able to recapitulate the fractal scale in the tree topology. His calculations used methods adopted from a completely different field of science: the physics of phase transitions. An example of phase transition is when a material like iron becomes magnetic as its temperature drops. Magnetism gradually emerges once the temperature falls below a critical value.

Goldenfeld explained how this unusual analogy works: “Very close to this critical temperature, a magnet is also fractal or self-similar: it is structured in nested regions of both magnetic and non-magnetic domains. This nesting or self-similar structure in space is reminiscent of the nesting or self-similar structure of forked tree branches in time. ” Using computer simulations and the mathematics of phase transitions, the research team was able to demonstrate how the fractal scale emerges from the tree topology.

“Our model has a small number of components and assumes a simple mathematical form and yet generates the power law scale with the correct exponent seen in the actual biological data,” explained Xue. “It is just amazing to see how much a minimal model can do.”

“We were able to reproduce not only the behavior of the power law but also a non-trivial exponent that is very close to reality,” said Liu. “In other words, simulated trees are not only scale invariant but also realistic in a way.”

In addition to describing the fractal topology of phylogenetic trees, the model also took into account the evolutionary clade patterns previously documented in microbial communities by Illinois plant biology professor James O’Dwyer, an ecologist trained in theoretical physics like Goldenfeld.

“It was especially gratifying to be able to get an idea of ​​James’ earlier discovery, using a conceptual toolkit that comes from statistical physics,” said Goldenfeld. “This work exemplifies how powerful and unexpected results can emerge from cross-disciplinary research, careful data analysis, and minimal modeling.”

The presence of the niche construction creates a significant imprint on the evolutionary trajectory that cannot be eliminated, even over long time scales. The idea that niche building, which is based on a much shorter time scale, emerges as a long-term memory in phylogenetic trees may surprise some people. In fact, Liu adds that this “scale interference” is also a hallmark of phase transitions, where the space between atoms in a magnetic crystal on the Angstroms scale can influence material properties on the centimeters scale. .

“When I first learned about the idea of ​​scale interference in Nigel’s physics class on phase transitions three years ago, I was not expecting any of the following: joining his group, applying this idea, and solving a biological problem,” he said. Liu. “Now I’m glad I didn’t fall asleep during that conference.”