Models and Molecular Clocks of Evolution

The degree of the genetic code's redundancy allows us to classify specific sites within a codon:

• Fourfold degenerate sites: All possible nucleotide changes at this position result in a synonymous substitution.
• Twofold degenerate sites: One of the three possible nucleotide changes is synonymous, while the others are non-synonymous.
• Nondegenerate sites: Any change at this position results in a non-synonymous substitution.

To measure the evolutionary pressure acting on a gene, scientists use the $K_A/K_S$ ratio, where $K_A$ is the rate of non-synonymous substitutions and $K_S$ is the rate of synonymous substitutions.

Exam Tip: The $K_A/K_S$ ratio is a powerful indicator of selection.

• If $K_A/K_S > 1$, the gene is undergoing positive selection (favoring change).
• If $K_A/K_S < 1$, the gene is undergoing negative (purifying) selection (conserving the sequence).

For example, the env gene in HIV shows $K_A/K_S > 1$ because it must constantly change to evade the host immune system, whereas the pol gene shows $K_A/K_S < 1$ because its function in replication is highly sensitive to change.

Protein Substitutions

Amino acid substitutions are significantly more complex than DNA substitutions because there are 20 different amino acids to consider. These residues are often classified by their physicochemical properties, such as:

• Nonpolar/Hydrophobic (e.g., Alanine, Leucine, Valine)
• Polar uncharged (e.g., Serine, Threonine, Asparagine)
• Negatively charged/Acidic (e.g., Aspartic acid, Glutamic acid)
• Positively charged/Basic (e.g., Lysine, Arginine, Histidine).

Evolutionary changes within the same chemical class (e.g., replacing one hydrophobic residue with another) are generally more common and more likely to be tolerated than changes between different classes.

The Neutral Theory of Molecular Evolution

In 1968, Motoo Kimura proposed the Neutral Theory of Molecular Evolution, which revolutionized our understanding of molecular change. The theory posits that the majority of evolutionary changes at the molecular level are caused by neutral or nearly neutral mutations.

Under this framework, evolution is viewed as a stochastic (random) process driven primarily by mutation and random genetic drift rather than natural selection. This provides a "null hypothesis" that allows scientists to create mathematical models of how sequences should change over time if no selection is occurring.

Models of Sequence Evolution and the "Multiple Hits" Problem

When comparing two sequences, we count the number of observed differences. However, this often leads to an underestimate of the true evolutionary distance due to multiple hits.

A "multiple hit" occurs when a single site undergoes more than one substitution over time. For instance, a site might change from A $\rightarrow$ G and then later from G $\rightarrow$ C. An observer would only see the final difference (A $\rightarrow$ C), missing the intermediate step. Other forms include:

• Parallel/Convergent substitution: Different lineages independently evolve the same nucleotide.
• Back substitution: A site changes and then changes back to its original state.

As species diverge and more time passes, the probability of multiple hits increases, causing the relationship between observed substitutions and actual time to curve downwards rather than remain linear.

To correct for this, we use Models of Sequence Evolution. These are mathematical descriptions that attempt to recover the "hidden" substitutions.

• DNA Models: Range from the simple Jukes-Cantor (JC) model to more complex ones like HKY85 and the General Time Reversible (GTR) model.
• Protein Models: Include the Poisson, Dayhoff, and WAG models.

Molecular Clocks

The concept of the molecular clock was proposed by Zuckerkandl and Pauling, who observed that the rates of amino acid replacement were approximately constant across different lineages. If the rate of molecular evolution is constant for a given protein, we can use the number of sequence differences to estimate the time since two species diverged.

Calibrating the Clock

To use a molecular clock, it must first be calibrated using independent data, such as fossil records or biogeographic events.

Worked Example: Estimating Divergence with Insulin

1. Observe: Humans and Elephants differ by 2 amino acid substitutions in the insulin protein.
2. Calibrate: Suppose fossil data tells us the common ancestor of humans and elephants lived 90 million years (Myr) ago.
3. Calculate Rate: $\text{Rate} = \frac{2 \text{ substitutions}}{90 \text{ Myr}} \approx 1 \text{ substitution per } 45 \text{ Myr}$
4. Apply: Humans and Alligators differ by 9 amino acid substitutions. Using our rate: $\text{Divergence Time} = 9 \text{ substitutions} \times 45 \text{ Myr/substitution} = 405 \text{ Myr}$

Strict vs. Relaxed Clocks

While the idea of a universal clock is controversial, biologists use two main approaches:

• Strict Clock Methods: Assume a single, constant rate applies to all lineages in a tree.
• Relaxed Clock Methods: Account for the fact that different lineages may evolve at different rates due to variations in metabolic rates, generation times, or DNA repair mechanisms. Relaxed clocks are generally more accurate and use complex Bayesian or maximum likelihood modeling.