The pandemic has given us a crash course on evolution. Evolution deniers must be having a hard time explaining away the evolution-suffused news dealing with mutations, growth rates, and the like. But it also provides an opportunity to explain some of the mathematics of the phenomenon.

You would think that if a mutation had a slight advantage over its predecessor, then it would over time grow in size relative to the other but the older one would still be around. But that is not what happens. We see how some new variant, if it has some advantage over its competitors such as greater transmissibility, rapidly becomes dominant in the population, pushing the previously dominant ones into the background.

This graph shows the different peaks due to the different variants at the current time.

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(Previous posts in this series: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7)

We have now acquired most of the background knowledge needed to start directly addressing the question that this series of posts started with, as to whether an electric charge and a neutral particle dropped from the ceiling will hit the ground at the same time. The first stage of that is what is known as the Principle of Equivalence.

Recall the Postulate #1 we started with that said that all objects falling freely in a gravitational field will fall at the same rate and hit the ground at the same time. We were able to explain this by saying that it followed from the fact that gravitational and inertial masses were equal. But we did not explain why they should be equal. The two masses were arrived at, after all, by distinct methods using different operational definitions. But by considering accelerating frames and the Principle of Equivalence, we have a simple explanation for it.

Consider two objects floating freely in space that are at rest with respect to each other and to an observer S, to signify space. No suppose we enclose the two objects in a closed room and accelerate the room ‘upwards’ (i.e., in the direction from the ‘floor’ to the ‘ceiling’) with a value g. We will call this frame E to signify an elevator or Earth. Then in the frame E, both objects will seem to be accelerated ‘downwards’ (i.e., towards the floor of the room) with a value g, just as if they were falling freely on Earth, and will both hit the floor at the same time. They will behave just as if they were falling down near the surface of the Earth and since they hit the floor at the same time, we can infer that their gravitational and inertial masses are equal, rather than tacitly assuming it to be the case as we did before.
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The virus that causes covid-19 is officially called SARS-CoV-2. This website gives the definition of the various elements of this virus.

Viruses like SARS-CoV-2 continuously evolve as changes in the genetic code (genetic mutations) occur during replication of the genome. A lineage is a genetically closely related group of virus variants derived from a common ancestor. A variant has one or more mutations that differentiate it from other  variants of the SARS-CoV-2 viruses. As expected, multiple variants of SARS-CoV-2 have been documented in the United States and globally throughout this pandemic. To inform local outbreak investigations and understand national trends, scientists compare genetic differences between viruses to identify variants and how they are related to each other.

Key Definitions:

• Mutation: A mutation refers to a single change in a virus’s genome (genetic code). Mutations happen frequently, but only sometimes change the characteristics of the virus.
• Lineage: A lineage is a group of closely related viruses with a common ancestor. SARS-CoV-2 has many lineages; all cause COVID-19.
• Variant: A variant is a viral genome (genetic code) that may contain one or more mutations. In some cases, a group of variants with similar genetic changes, such as a lineage or group of lineages, may be designated by public health organizations as a Variant of Concern (VOC) or a Variant of Interest (VOI) due to shared attributes and characteristics that may require public health action.

When the Omicron was labeled as a ‘variant of concern’, that label is one of four that is used to classify the nature of the danger the variant poses, which are in increasing order: Variant Being Monitored (VBM), Variant of Interest (VOI), Variant of Concern (VOC), and Variant of High Consequence (VOHC), the last being the most alarming. Delta and Omicron are the only two in the VOC category, while there are ten in the VBM category, including the Alpha and other variants with Greek letter labels that did not get much publicity.

There are none as yet that fall into the VOI nor (thankfully) the VOHC categories. One shudders to think what a VOHC variant would do.

I wrote earlier about the amazing migration of the monarch butterfly. This tiny creature does the same trek of thousands of miles each year even though their lifetimes are so short that any given butterfly will do it only once.

This website gives more information.

Some monarch butterflies are able to fly for a migration of 2500 miles. Most of them can find their ways to their ancestors’ winter homes when they go there, and then find their ways back to the places they left in spring. This ability made them seem like the strongest, smartest, and toughest of all butterflies. In much of their range they are also the biggest butterflies, with wingspans up to four inches (10cm).

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