Mathbio proposal: Separating the Effects of Genetic Drift and Natural Selection
using a Modification of Tajima's D statistic
Mentors: Tony Weisstein and Pam Ryan
Project Description:
Several statistical measures have been devised to infer past evolutionary forces from current patterns of
genetic diversity in sequence data. Tajima's D detects increases or decreases in overall genetic diversity,
but cannot assess the relative contribution of genetic drift and natural selection to the variation
observed. We previously wrote a computer simulation which starts with a population of 500 identical
DNA sequences and allows the population to randomly mutate and recombine for 20,000 generations.
We then select a sample of 20 organisms (from the last generation) of our population and classify the
mutations in the sample as synonymous or nonsynonymous. Finally, we calculate Tajima's D separately
on each set. In principle, Tajima’s D applied to nonsynoymous mutations (Dnon) should measure the
effect of both drift and selection on the population, while Tajima’s D applied only to synonymous
mutations (Dsyn) should measure the effects of drift within a population. Subtracting these quantities,
we can measure the effects of selection (Dnon – Dsyn). In theory, this refinement to Tajima’s D will allow
us to determine not only whether diversity is increasing or decreasing, but also whether the increase or
decrease is due to a bottleneck or purifying selection (in the case of decreasing diversity) or subdivision
or diversifying selection (in the case of increasing diversity). Our results to date have been encouraging;
however, this method has limited power to distinguish among different scenarios of selection and drift.
We propose to extend our analysis in two key ways:
1) Attempt to improve our resolution of different evolutionary models by using techniques such as
Bayesian analysis, neutral networks, and support vector machines;
2) Assess the accuracy with which our method classifies mutations as synonymous vs.
nonsynonymous mutations, using our computer simulation’s built-in tracker function.
Skills needed:
Both students will need to
- be willing to get out of their “comfort zone” and learn material outside of their disciplines.
- have the ability to do independent research and make hypotheses based on data.
- be willing to work on an interdisciplinary team and consider other points of view.
The ideal Biology student will have
- at least STAT 190 or the equivalent
- a background in molecular genetics and population genetics
- knowledge of (or at least comfortable with) quantitative approaches
The ideal Mathematics student will have
- a strong interest in biology; equivalent of BIOL 107 background
- some programming experience (C++ preferred)
- linear algebra or higher
- a strong interest in and background in statistics; especially in classification techniques
References:
Rand DM and Kann LM (1996). Excess amino acid polymorphism in mitochondrial DNA: Contrasts
among genes from Drosophila, mice, and humans. Mol. Biol. Evol. 13: 735-748.
Williamson SH et al. (2005). Simultaneous inference of selection and population growth from patterns
of variation in the human genome. Proc. Nat. Acad. Sci. USA 102: 7882-7887.
Nei M and Gojobori T (1986). Simple methods for estimating the numbers of synonymous and
nonsynonymous nucleotide substitutions. Mol. Biol. Evol. 3: 418-426.
Tajima, F. (1989). Statistical Method for Testing the Neutral Mutation Hypothesis by DNA Polymorphism.
Genetics, v. 123, 585-595.
Weisstein et al. (2009) Separating the Effects of Genetic Drift and Natural Selection Using a Modification
of Tajima's D Statistic, Techical Report.