Hybrids and Genetic Trees

From Mathsreach

Jump to: navigation, search
Barbara Holland is enthusiastic about the mathematical possibilities of phylogenetics, the building of evolutionary relationships between different species, with the flood of new genetic information.

The Solexa 2 DNA analyser produces terrifying amounts of data! It really excites me figuring out how to use that data across genomes, and then understanding what may end up being much more complex patterns of evolution than we previously thought.”

Phylogenetics is a blend of mathematics, biology and computation. Holland uses stochastic models, graph theory, optimisation and combinatorics in her work at Massey University in Palmerston North and with the Allan Wilson Centre for Molecular Ecology and Evolution.

“It’s a tricky business trying to puzzle out what happened 100 to 500 million years ago just using modern DNA sequences. It’s slender evidence for such vast timescales.” She describes testing mathematical models as “like a fat man in a women’s lingerie store; there might an outfit that fits best but that
doesn’t mean it fits well”.

One questionable assumption used by phylogenetic models is that evolution is the same over all parts of the tree. “It’s ridiculous,” says Holland; “lineages have their own properties”. She gives the example of parasites, which use their hosts’ functions. This makes many of their genes redundant, reduces selection pressures, and enables them to survive more genetic mutations than other organisms.

Holland and PhD student Liat Shavit changed an existing phylogenetic simulation package so that the same DNA site could accept mutations on only some parts of the evolutionary tree, instead of over the whole tree. A large simulation, faking evolution over and over, found that “it was reasonably difficult to make phylogenetic methods break - it took major deviations before the methods produced inaccurate trees”.

Holland is also fascinated by hybridisation, which is common where species respond rapidly to new environments. Hybrids inherit genetic material from two parent species, making them hard to detect when studying single genes. “Every extra hybridisation doubles the number of evolutionary trees; it’s
a very challenging problem,” says Holland.

However, DNA technology now enables the study of many genes simultaneously. Another problem with current mathematical models is their assumption that any conflict in trees is due to hybridisation.

In reality, conflict between possible trees can be caused by estimation errors, missing data, and the random nature of inheritance in populations. Holland has used consensus networks and graph theory to represent these conflicts visually. “Trees are collections of vertices and edges. External vertices correspond to modern species with labels. Internal vertices represent common ancestors. A four-species tree will have two internal vertices and five edges connecting everything. Removing any edge breaks the tree into two parts with two different labels.”

“The most common method is majority rule; it’s quite restrictive and you end up throwing out a lot of information. Using consensus networks relaxes this rule, showing any edge that appears in more than, say, 33% of the trees. It shows more flexibly where sets of trees agree and disagree.” The 33% rule
leads to pictures of two-dimensional boxes; a threshold of 25% can be drawn as cubes.

As a mathematician, Holland can make statements like “in animals, our concept of species may make sense, but in plants, it doesn’t. However, asking biologists what is a species is like throwing in a hand grenade; they disagree strenuously.” Along with Lara Shepherd she’s exploring trees for the
New Zealand five-finger genus, where she thinks hybridisation has been important, and developing statistical methods and software to show how important hybridisation has been in shaping New Zealand plant and animal life.