What "Random Mutation" Means in Science

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What I find encouraging is that an atheist like myself and a believer like @swamidass can find strong agreement when it comes to concepts like random mutations. Given the number of times this topic has come up in various threads I thought it might be useful to discuss what science means by random mutations, and most importantly what science can’t say about random mutations.

What science can say about mutations is that they there is no experimental evidence for dependence between variables, which is what science describes as random. What science CAN’T determine is if God is involved somehow in the production of mutations. Random does not mean unguided by God, at least not in science. The concept of random mutations is much more limited than what some non-scientists may think, and this is the type of misunderstanding that I hope I can help clear up.

In subsequent posts I will describe the experiments and statistical models that scientists have used to define random mutations. I don’t know how successful my attempts will be, but hopefully I can convince a few skeptics that random mutations aren’t the great atheist monster that they think they are.

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I was recently trying to determine what a “single mutation” could be. This is what I came up with:

Given an initial sequence:
CATGCATGCATG

There are three alternative for a single location change:
CATGCACGCATG
CATGCAAGCATG
CATGCAGGCATG
in addition to the original
CATGCATGCATG

There are also insertions, deletions, and reversals, in which a single event might cause change in a sequence, not just a single location::
CATGCA+CATG+GCATG
CATGCATGCATG
CATGCA<ACGT<TG
There are a huge number of variations here, depending on the length of the insert/delete/reverse.

And also duplication
CATGCACGCATGCATGCACGCATG

Did I miss anything?

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The main inspiration for this thread came from an article I ran across in a Google search. The primer boils down a >30 page paper beautifully, and it also explains the basics of what a Poisson distribution is.

I have been a huge fan of this experiment for decades because it is one of those classic experiments that combines simplicity with deep insight. The question that Salvador Luria Max Delbruck faced was how phage resistance operated in E. coli (phage are viruses that kill bacteria). As the paper above describes, the two main hypotheses were acquired immunity and immunity by mutation. This question was being asked in an era before the discovery of DNA, so it wasn’t as simple as sequencing a gene. This didn’t stop Luria and Delbruck from solving the problem, however.

The inspiration for the experiments and model is part of the legend of this experiment. Luria was at a faculty mixer, and part of the entertainment was slot machines. Luria suddenly realized that beneficial mutations could be modeled like slot machine jackpots. The winners could be found by challenging the bacteria with phage, so they had the basics of an experimental design. They could use a Poisson distribution to model the population, so they also had a statistical model. With these two things in hand, an experimental design and a statistical model, Luria and his colleague Delbruck set forth on testing the two hypotheses.

In this post, I will focus on the experimental design which is often called the fluctuation test. The experiments starts by streaking bacteria on a plate and selecting a single colony of E. coli. Each colony was founded by a single bacterium, so all descendants should be genetically identical except for any mutations that occur along the way.

That single colony is used to start some liquid culture which is grown overnight in order to have enough bacteria to work with. The next day, a small volume of that liquid culture is used to start multiple parallel cultures. Once those have multiplied for a while they are spread on agar plates that contain phage.

What do the two hypotheses, acquired immunity and immunty by mutation, predict when it comes to these plates? Like any good experiment, the two hypotheses make very different predictions. The acquired immunity hypothesis predicts that you should see about the same number of bacteria on each plate from each parallel culture since all bacteria should have the same innate mechanism of immunity if that is how it works. The immunity by mutation hypothesis predicts that you can see wildly different numbers of colonies on the plates since the mutation can happen in an early generation and produce many resistant bacteria, happen in a later generation and produce relatively few bacteria, or not occur at all and produce no resistant colonies.

So what did they see?

image
image.png380×572 5.71 KB

In the first two columns you will see that some of the cultures had no resistant bacteria, some had a handful, and a few had many. This is what we would expect to see in the case of immunity by mutation.

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A mutation is considered a singular event that changes the DNA sequence. The rule of parsimony is usually used, so a change to one letter is assumed to be a single mutation instead of multiple mutations at the same base. A block of letters that are different are considered to be a single insertion or deletion instead of multiple indels (the portmanteau of insertion and deletion) right next to each other.

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For the “Large culture” columns, I assume each of these was started with multiple founders as a control? A variance/mean ratio of about 1.0 is expected from the Poisson distribution.

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@T_aquaticus

Would your narrative include the idea that things can appear random to science and scientists… does not necessitate that these events are considered random by God?

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As mentioned earlier, there are two basic concepts: the experiment and the statistical model. The statistical model in this case is a Poisson distribution where you would expect x events over a certain amount of time given a specific rate. A good example is radioactive decay where you can calculate the expected number of decay events over a certain time period with a known decay rate.

A Poisson distribution is used in two ways, the first of which is to determine if we are sampling from the same population or different populations. Remember, we have several parallel cultures, so one of the questions we have to ask is if the variation between cultures is due simply to sampling error. What we know from a Poisson distribution is that the mean should equal the variance. That is, the average number of events should be about the same as the bounce in the numbers. To test this hypothesis you can plate several aliquots of one culture and then compare it to aliquots from different cultures.

In the table in the second post there are 2 sets of columns. The set on the left is for separate cultures ( the parallel cultures). The set on the right is for multiple platings from a single culture. For the set on the right, the mean is close to the variance. This indicates that we are sampling the same population. However, the variance wildly differs from the mean for the set on the left for the separate cultures which means they are different populations. This means that the populations came came upon their mutations independently.

Next, we can calculate the mutation rate by using a Poisson distribution. The paper cited in the second post describes it much better than I can, so I will quote it here:

The one thing to note is that similar rates were found for multiple cultures. The rate of mutation follows a Poisson distribution, and it is consistent between cultures.

The next post will summarize what I have posted thus far.

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So what do these giant walls of text boil down to?

First, mutations conferring phage resistance occur in the absence of phage. Second, the way in which these mutations emerge is consistent with a statistical model of randomness. So what can scientists say about this, and how does it relate the discussions here at Peaceful science.

What scientists can say is that the evidence is consistent with a process where selection doesn’t influence which mutations occur and that mutations are consistent with a statistical model of randomness. What a scientist can’t say is that mutations are random in an absolute sense. The best any scientist can do is say that the observations are consistent with a hypothesis. Period. Could God be influencing mutations, radioactive decay, slot machines, lottery drawings, or other seemingly random processes? Science can’t say. Scientists can only note that these processes continue to match our models. It is on this point that both @swamidass and I find agreement. We agree on what the science says, but have different beliefs with respect to the ontological truths that underpin it.

I will also make note of sloppy scientific communication. Scientists will often jump from “consistent with” to “are”. This is just shorthand. In common parlance, we often say that someone was proven guilty in court, but what we really mean is that someone was proven guilty beyond a reasonable doubt. This is the same type of sloppy language that scientists can use from time to time. Adding all of the hedges and tentative language to every pronouncement in the sciences gets a bit cumbersome, so they tend to get trimmed down, for better or worse.

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I am hoping that the last post helped answer most of these question, but just in case, I would fully agree that events can appear to be random and still be guided by God. I don’t pretend to know what God would consider random, if God exists, but I can talk about the human side of the equation. “Appears to be” is not the same as “is”, and that is an important point to stress from time to time.

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This is entirely accurate.

I agree. The more we clarify this the better. Secular and believe scientists, such as you and I, can do much good by working together to improve communication among our colleagues, and knowledge among the public. The case is stronger when we work together on this.

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You missed quite a lot my friend. The patterns of observed mutation are far more complex than just this. It is an active area of research.

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Do you ever encounter Overdispersion?

If you don’t know the term, the answer is likely “no”.

When sampling rates in human populations, we often encounter an unknown mixture of populations with different rates, resulting in a variance greater than the mean (Overdispersion). This can inflate p-values if we do not adjust for it (deviance or Pearson scaling). That opposite is possible (Underdispersion), but rare, or at least hard to detect.

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Cool! :smile:

But unfortunately, that blows my little side project about GA’s exploring fitness landscapes out of the water. Back to the drawing board! :no_entry_sign:

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According to Aquinas:

The effect of divine providence is not only that things should happen somehow, but that they should happen either by necessity or by contingency. Therefore, whatsoever divine providence ordains to happen infallibly and of necessity, happens infallibly and of necessity; and that happens from contingency, which the divine providence conceives to happen from contingency.

This is mirrored in the 2004 document Communion and Stewardship: Human Beings Created in the Image of God issued by the Catholic International Theological Commission.

So according to Catholic doctrine, events that we perceive as random certainly do not necessarily appear so to God.

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The Law of Large Numbers works in mysterious ways. :slight_smile:

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@clavdivs,

You posted this: “According to Aquinas: The effect of divine providence is not only that things should happen somehow, but that they should happen either by necessity or by contingency. Therefore:”

[a] "whatsoever divine providence ordains to happen infallibly

and of necessity, happens infallibly and of necessity; and"

[b] [what] "… happens from contingency, which the divine

providence conceives to happen from contingency."

Fortunately for me, you summarized your thought with: “So according to Catholic doctrine, events that we perceive as random certainly do not necessarily appear so to God.” And I agree with you 100%!

But as a favor to me, and maybe a few other readers, are you able to explain how the Aquinas quote means the same thing? I found myself completely unable to reach any useful conclusion from that quote.

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Hi George

There’s a slight typo in your rendering of the quote that might make a difference:

Translated into everyday English:

“… if God wants something to happen contingently, it will.”

So, God can make something happen necessarily, even though it appears contingent to us.

Does that help?

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For more on this see Communion and Stewardship: Human Persons Created in the Image of God, para. 69:

In the Catholic perspective, neo-Darwinians who adduce random genetic variation and natural selection as evidence that the process of evolution is absolutely unguided are straying beyond what can be demonstrated by science. Divine causality can be active in a process that is both contingent and guided. Any evolutionary mechanism that is contingent can only be contingent because God made it so.

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@Clavdivs

Gosh… this can be half-way impenetrable narrative: “In the Catholic perspective, neo-Darwinians who adduce random genetic variation and natural selection as evidence that the process of evolution is absolutely unguided are straying beyond what can be demonstrated by science.” < This sentence is perfectly clear to me.

“Divine causality can be active in a process that is both contingent and guided. Any evolutionary mechanism that is contingent can only be contingent because God made it so.”

When translating Latin into English… there must be a better way …

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I think this is an excellent post because it relies on a scientific modeling, a bit of math, and a description of how the model was tested to explaiin the meaning of a scientific conclusion. So we have an answer to the question which reflects the way science answers it.

Too many internet discussions of random mutations degenerate into parsing English meanings and arguing the metaphysics of randomness and probability.

In science, the meaning of ‘random mutation’ is provided by the mathematical model and the explanation of why it applies. See the “Unpacking the Work” section of the linked paper for more detail on this.

I agree with this, but I would add that science uses Inference to the Best Explanation, not deduction. So I think the what is omitted in saying “mutations are random” is that the best explanation of this experiment (and others) is that mutations are random in the sense defined through the scientific model.

In science, “best” often involves simplest in the sense of postulating the fewest entities. So just as Laplace was alleged to have said “I have no need of that hypothesis [of God]”, so science has no need of God for the best (scientific) explain of mutations and of biological evolution in general.

By no means is that science meant to be part of a deductive argument showing that God does not exist. Nor is it an argument that God is inconsistent with the science. Such arguments belong in philosophy, not science.

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