Developmental Biology - The Physics of Evolution|
Evolution Trees Reflect Relationships Between Species
Fractal changes as small as an angstrom affect cells within and between species...
In biology, phylogenetic "trees of life" show evolutionary history and diversification between species. Phylogenetic trees not only describe the evolution of a group of organisms, but can also be constructed from an organism within a particular environment or ecosystem — such as us humans in our own microbiome.
Phylogenetic trees give us a way to decifer how an ecosystem has evolved — and what its capabilities might be - or become.
Now, a new analysis of a phylogenetic pattern has been generated by a phylogenetic tree. It reflects hypothesized connections between evolution and ecology from a study led by Nigel Goldenfeld PhD, who leads the Biocomplexity Group at the Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign.
Other members of this team were graduate student Chi Xue and former undergraduate student Zhiru Li, now at Stanford University. Their findings were published in the journal the Proceedings of the National Academy of Science or PNAS, titled "Scale-invariant topology and bursty branching of evolutionary trees emerge from niche construction."
The most familiar phylogenetic tree of all life on Earth uses genes from cell ribosomes to represent species. By comparing differences between molecular sequences of the same genes on different organisms, researchers can deduce which organisms descend from each other.
This idea led to mapping the evolutionary history of life on Earth and the discovery of a third domain of life by Carl R. Woese and collaborators in 1977. Real phylogenetic trees are complex branching structures, reflecting patterns of speciation as new mutants emerge from a species. Although branching structures are complex, they are characterized by how balanced they are - along with other statistical features reflecting tree topology.
The simplest characterization is in each branching node on the tree. Does it split into two branches of exactly the same length or are the branches unequal in length? The former is balanced, the latter unbalanced.
Despite the complexity of trees, there is a consistent mathematical pattern in topological structure across 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 interplay between ecological and evolutionary processes.
Minimal models of nature do not aim to be overly realistic, but are constructed to capture the most important ingredients of the process in a way that makes simulation and mathematical analysis easy.
Goldenfeld's work frequently uses minimal models to explain generic aspects of complex biological and physical phenomena insensitive to precise detail. Not all aspects of complex phenomena can be described in this way, but physical patterns such as self-similarity in space are often described with minimal modeling.
"It seemed reasonable to try this approach to describe self-similarity in time too" explains Goldenfeld. "We set off to study the topological property of the phylogenetic tree and ended up with an extra 'fruit of explanation" for the tree's special character,'" Xue adds.
The study revolved around a concept in evolutionary ecology known as niche construction, first proposed about 40 years ago. In niche construction, organisms modify their environment, thus creating new ecological niches in the ecosystem and changing the environment. In turn, these new niches affect the overall evolutionary trajectory of organisms that share an environment. The end result is that evolution and the environment are coupled closely together. The idea that evolution is not occurring on a purely static environmental background is controversial, despite being intuitively appealing. These findings add to the existing body of work by identifying long term effects of niche construction in a way that can be detected by modern genomics and phylogenetic tree construction.
In the work, researchers simulated organisms and associated a niche value to them that described their interaction with their environment.
Those organisms with a large niche value contained a large number of ways to adapt to their environment, ultimately leading to their survival. Those with small niche values were less resilient.
"In our model, we relate the niche positively to the speciation probability, in the sense that an organism with a large niche can likely diversify successfully," Xue said. "During the phylogenetic tree evolution, when two daughter nodes emerge from their parent, they get their niches partially from inheriting and partially from construction."
Researchers showed that species which run out of niche space can no longer branch or speciate. Mathematically, this was represented as a so-called absorbing boundary condition on the node representing this species.
"Its sister node likely still diversifies as long as that niche is still positive, but as the two sister nodes are no longer symmetric, the tree becomes unbalanced," explained Xue. "We demonstrated that the absorbing boundary is crucial to generate the fractal structure of the tree and that the niche construction guarantees that some nodes will reach the boundary."
The researchers used a simplified model of niche construction and were able to recapitulate the fractal scaling in the tree topology. Their calculations used methods adopted from a completely different field of science: the physics of phase transitions.
An example of a phase transition is when a material such as iron becomes magnetic as its temperature lowers. Magnetism emerges gradually as its temperature falls below a critical value.
Goldenfeld explained how this unusual analogy works: "Very close to this critical temperature, a magnet also is fractal or self-similar: it is structured into nested regions of magnetic and non-magnetic domains. This nesting or self-similar structure in space is reminiscent of the nesting or self-similar structure of bifurcating tree branches in time."
Using computer simulations and the mathematics of phase transitions, the team was able to demonstrate how fractal scaling of tree topology emerged.
"Our model has a small number of components and assumes simple mathematical form and yet, it generates power-law scaling with the right exponent that is observed in actual biological data," Xue explains.
"We were able to reproduce not only the power-law behavior but also a non-trivial exponent that's very close to reality," Liu adds. "In other words, the simulated trees are not only scale-invariant but also realistic in a way."
In describing the fractal topology of phylogenetic trees, this model also accounts for patterns in evolutionary clades previously seen to occur in microbial communities by James O'Dwyer PhD, Illinois Professor of Plant Biology, an ecologist trained in theoretical physics like Goldenfeld.
"It was especially gratifying to be able to gain some insight into James' earlier discovery, using a conceptual toolkit that came from statistical physics," Goldenfeld commented. "This work exemplifies the way in which powerful and unexpected results can arise from trans-disciplinary research, painstaking data analysis and minimal modeling."
Niche construction creates a significant footprint in the trajectory of evolution that cannot be eliminated, even across time.
The idea that niche construction - based on a much shorter time scale - emerges as long-term memory in phylogenetic trees, may surprise some people. Liu explains that "scale-interference" is a hallmark of phase transitions, where spacing between atoms in a magnetic crystal on the scale of angstroms can influence the material properties on the scale of centimeters.
"When I learned about the idea of scale-interference in Nigel's physics class on phase transitions three years ago, I wasn't expecting any of the following: joining his group, applying this idea and solving a biological problem," said Liu. "Now I'm glad that I didn't doze off during that lecture."
Phylogenetic trees describe both the evolutionary process and community diversity. Recent work, especially on bacterial sequences, has established that, despite their apparent complexity, they exhibit two unexplained broad structural features which are consistent across evolutionary time. The first is that phylogenetic trees exhibit scale-invariant topology. The second is that the backbones of phylogenetic trees exhibit bursts of diversification on all timescales. Here, we present a coarse-grained model of niche construction coupled to simple models of speciation that recapitulates both the scale-invariant topology and the bursty pattern of diversification in time. These results show, in principle, how dynamical scaling laws of phylogenetic trees on long timescales may emerge from generic aspects of the interplay between ecological and evolutionary processes.
Phylogenetic trees describe both the evolutionary process and community diversity. Recent work has established that they exhibit scale-invariant topology, which quantifies the fact that their branching lies in between the two extreme cases of balanced binary trees and maximally unbalanced ones. In addition, the backbones of phylogenetic trees exhibit bursts of diversification on all timescales. Here, we present a simple, coarse-grained statistical model of niche construction coupled to speciation. Finite-size scaling analysis of the dynamics shows that the resultant phylogenetic tree topology is scale-invariant due to a singularity arising from large niche construction fluctuations that follow extinction events. The same model recapitulates the bursty pattern of diversification in time. These results show how dynamical scaling laws of phylogenetic trees on long timescales can reflect the indelible imprint of the interplay between ecological and evolutionary processes.
Chi Xue, Zhiru Liu and Nigel Goldenfeld.
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A simulated phylogenetic tree. Time runs from top to bottom. Nodes represent species. Lines represent DNA mutations associated with the gene being studied. Bifurcations signify speciation events. This tree is complex in structure, but also is fractal in topology
. CREDIT Nigel Goldenfeld