Random, stochastic, and improbable - Educate me

I would like a simple explanation of the difference between random processes and stochastic processes (with examples) and clarification about how the two are related but not the same. Also, how do random and stochastic relate to probability?

Anyone game?


Random and stochastic are largely synonymous with the only big difference being usage. Most often, a variable is described as random while a process is described as stochastic. In this case, the singular events are random and the result of one or many random variables interacting with each other over time is a stochastic process. For example, a single hand of blackjack is random while a casino uses a stochastic model to predict profits.


So stochastic has to do with calculating the probability of random events over time?

So, take the biological sex of babies. Whether an X sperm or a Y sperm fertilizes a specific egg is random. It cannot be predicted. But the general process of fertilization is stochastic because you can calculate the probability of a Y sperm fertilizing a specific egg at 50%?

What about lightning striking blue cars? Is that totally a random event and not stochastic in any way because lightning strikes in relation to blue cars are not something that we observe as a process? Could you still calculate the probability?

Looks to me like the word “stochastic” is addressing the parts of definition of the word “random” that refer to a lack of rule, method, or pattern. This isn’t really lacking in the use of the word “random” in probability theory but only in common usage. In probability theory, random variables have a probability distribution which can have all kinds of patterns as well as methods determining which results are more likely than another. In quantum physics, this even produces fixed and even precisely measurable quantities like energy differences – they just have to be measured statistically.

So I suppose the point is that a stochastic processes is not purely random but random within an ordered framework and pattern. Individual outcomes may be undetermined while the group or statistical behavior is highly and precisely determined.

P.S. Perhaps an implication here is that the meaning of “stochastic” includes high population sizes where the statistics can be so precise and would not be used for something like rolling a single 6-sided dies one time.

So in evolution, a specific mutation arising is purely random. But mutations spreading through populations are a stochastic process? Or a non-random process? Or does it depend?

That is the one.

In fact I think you can even say it is in general more accurate to call evolution stochastic rather than random. Though if you followed our discussion of the development of resistances in viruses to drugs in the other thread… you can see I came to a concession with @glipsnort that this was a bit more random than I originally thought.

Generally speaking, ‘stochastic process’ = ‘random process’. Mutation and allele frequency change are both random or stochastic processes. In both cases, all outcomes are not equally likely: some mutations are more likely to occur, and some variants are more likely to spread (typically because of natural selection, although there can be other biases as well). Thus I don’t find thinking of natural selection as a process so much as a particular bias in a stochastic process.

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You can look at events over time (i.e. rates), or a group of events that happen all at once. For example, the probability of someone winning a single lottery is predicted by a stochastic model that contains random variables while the drawing of the lottery balls is a random event. In the end, it is more semantics than anything else.

That’s how I use those terms. I use random to describe individual events and use stochastic to describe the general outcome of a system.

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Thank you for this information. It seems to me that there are usually two ways of doing science. The older way is more descriptive of how natural processes work. The newer one is more based on strictly math, and this is your way. I do not think either way should exclude the other and there are advantages to the old way which I prefer.

You say that evolution is a stochastic process, which is defined as random. I would say that a better definition would be probabilistic. The genetic aspect is definitely random or probabilistic, but the natural selection aspect is not. Also evolution is a two step process that doe4s nor submit to mathematical analysis.

You say “some variants are more likely to spread (typically because of natural selection.” How can some variants be mire likely to spread because of natural selection? Natural selection is not a quality as far as I know. If it is, the only way we know that a variant has natural selection is if it spreads, True or false? The way we know if it has spread is by counting, right or wrong?

I have found my copy of the Blind Watchman and in it Dawkins is very clear that NS is a process based on adaptation. “Variation and selection work together to produce evolution. The Darwinian says that variation is random in that it is not directed toward improvement, and the tendency in evolution toward improvement comes from selection.” TBW p. 308

Recently you verified out that dark skin appears to be an adaption to intense sunlight. If variants spread if they allow biota to survive and spread, then variants, which allow biota to adapt to their environmental niches will spread. Variants that so not help the biota to adapt will disappear.

I am not afraid to agree with Dawkins, actually Darwin on this. I disagree on the character of Natural Selection, Survival of the Fittest, and the Selfish Gene.

Science indicates the Natural Selection is based on ecology. Failure to adapt to a changing environment doomed most of the dinosaurs, while successfully adapting saved the avian dinosaurs who were transformed into birds. Evolutionary change is not random in relationship to the ecology.

I would say those descriptions are synonyms.

Natural selection is probabilistic. A fitter allele has a higher probability of being passed on. Individuals with this allele can still have fewer offspring than other individuals with less fit alleles. I believe @glipsnort said earlier that natural selection is a bias towards having more offspring, and that’s a perfect description. When you are dealing with probabilities you are dealing with randomness and stochastic processes.

It’s pretty hard to adapt to a massive change in environment that occurs over a single day.

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Probabilistic is based typically on a bell curve, which means that some possibilities are much more probable than others. Random means that all possibilities are equally probable.

This is not natural selection. A fitter allele has a higher probabilities of being passed on because by definition biota with this allele have more offspring, thus there is nothing random or probable about this process.

What is “a bias toward having more offspring?”
Bias means “prejudice for or against.”
“Statistical bias results from an unfair sampling of a population, or from an estimation process that does not give accurate results on average.” Wikipedia

I do not see how we can call an evolutionary advantage a bias. How can a bias cause biota to have more offspring?

Natural selection is a process which is determinative. There is nothing random or probabilistic about it. Either the variable is selected in or out. Evolution is not random because it is “stochastic process,” which I am sure that Darwin never heard of. Evolution is a determinative process because it is governed by natural selection which is determinative.

  1. This climate change did not occur in a single day.
  2. The avian dinosaurs did escape extinction as birds.
  3. Even if the climate change took place in a single day, that doe not change anything.
  4. There was nothing random or probabilistic about the extinction of the dinosaurs.
  5. .The changes in the environment at the end of the Cretaceous age put non-avian dinosaurs at a disadvantage and mammals at a relative advantage.
  6. All this confirms the fact of ecological natural selection.

A lot depends on the system considered. I am also aware of mathematical techniques developed for stochastic processes, but I do not know of similar things that are for purely random events (although statistical methodologies may be focused on specific random events).

From my experience with chemical kinetics, I abhor using the term random for any reacting system, although stochastic treatments can be used as predictive tools. All chemical events are the result of clear reaction routes - in very complicated processes, we may lack the understanding needed to fully treat them and we resort to techniques that we know are simplifications. Often these are models that fit data and rely on hypothetical reaction routes, and stochastic treatments may be useful.

Considering biochemical and biological systems, these are often orders of magnitude more complicated and any treatment must recognize this.

Chance and necessity strike again.

That’s not true at all. The roll of dice in craps is random, and yet 7 is the most likely outcome.

It is natural selection. You even admit that natural selection is probabilistic which means there will be times when a more fit individual will have fewer offspring than a less fit individual just by probability alone.

Watch me. An evolutionary advantage confers a bias in the frequency of specific alleles.

That’s how you do it.


" A fitter allele has a higher probabilities of being passed on because by definition biota with this allele have more offspring, . . ."–Relates

So much wrong, so little time.

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@T_aquaticus, @GJDS, @Klax, Thank you for your responses. @glipsnort

What I wrote is exactly true. The roll of the dice in craps is NOT random, because not all of the variables have an equal chance of appearing. And yes the probability distribution for craps is a nice bell curve.

Natural selection is based not on probability, but on results, therefore one cannot say an allele is more fit than another until it has been fully selected in.

No you don’t. Alleles that are better adapted to the environmental niche than others have an evolutionary advantage because they are more likely to live longer than others and they are more likely to be mor4e attractive mates. That s how you really do it.

Is the fitter allele has a better chance of being passed on by definition, then it seems as if the probability of the fitter allele of having more offspring is 1, non-probabilistic.

It is most unfortunate that you failed to discussion the real life example of natural selection in the extinction of the dinosaurs.

Incorrect. That’s not what ‘random’ means in contemporary science – there are many random distributions besides the uniform distribution. (Infinitely many, in fact.)

No, it’s not. You can learn about the difference here: https://math.stackexchange.com/questions/1204396/why-is-the-sum-of-the-rolls-of-two-dices-a-binomial-distribution-what-is-define

Also incorrect. Natural selection is the tendency of traits or genotypes that increase the probability of surviving and reproducing to increase in frequency. In other words, it’s a change to a probability distribution.

‘More likely to live longer …’ is precisely a statement of a bias in a probabilistic process.

Do you not see the word ‘chance’ in what you just wrote? On average, fitter alleles get passed on more often, but that’s only true on average. Any given fitter allele may not be passed on at all. New mutations that give a fitness advantage of 1%, for example, are completely lost ~98% of the time.

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Then what is a roll of the dice if it isn’t random?

I don’t understand why one negates the other. A process based on probabilities will have results. Even if we are looking backwards with selection we are still assigning a higher probability of that allele being passed on.

You say advantage, I say bias. Same thing.

That isn’t what happens. There will be individuals with the fitter allele who will have fewer offspring than individuals without the allele.

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Okay, What does random mean in contemporary science/ Why did the definition change from the common one? It seems with quantum physics that everything is probabilistic or random. Is that true?

The only legitimate reason to doubt science in terms of evolution is if science is saying that evoulution is at its core without order, because it does not. But if science says it is random, then it sure seems to say this. Yes. or No? Is it or not?

Are you saying that the odds for the game of craps are very different from the the ones we lear5ned in school?

I looked at the website. I tried to understand what it was saying. I say the curve nicely worked out and read where they said it was wrong.

I am afraid I am very concerned when it looks lke people are messing with numbers in a way that I so not understand. Not theat I play craps, but next maybe someone might say that 2 + 2 do not make 4 and have the “math” to prove it.

There is an old saying that figures don’t lie, but liars know how to figure. I am not accusing you or any one else of being a liar, but to say I want more information that I received here.

Ok, we are looking at the science from two different perspectives, you from your mathematic statistical view and mine from a naturalistic view. I am sorry, but I do not understand how “a tendency” can so anything. It is a word, an abstraction. It is not a thing or a name of a thing.

If natural selection changes the probability distribution,
How does it change it? what does it do or how doe it change? That is what I want to know. Is that too much to ask?

Alleles that are better adapted to the environmental niche than others have an evolutionary advantage RAS
A great and wise scientific thinker Karl Popper insisted that science be subject to verification. He was subjected to all sort of pressure because he refused to accept survival of the fittest because it like what you state is not verifiable. In a sense he gave into this pressure, because he said that natural selection could be verifiable using ecological selection, but it never has been, so it still has not been verified, so it still is not science by the best definition we have.

Again, who gives these ratings and why? Again my position is clear. Natural selection is based upon how the allele relates to its environment and of course we are not talking about one individual, but many so the probabilistic aspects work out. If the adaption to the environment, enables the allele to better survive and thrive, then it is selected in If not it is selected out.

On the other hand, environments change and species can become less well adapted then optimal and thus may be selected out in favor of another species that is better adapted. As far as I can see this is not accounted for in you view.

It seems to me that if natural selection can be shown to have a positive correlation to environmental adaption or failure to adapt, this should prove the case. I really do not understand why no one seems to want to do this

The roll of one die is random. The probability curve of many is not.

The probability of a variable that has been selected in is 100%.

They are very much not the same thing.

“Let your conversation be always full of grace, seasoned with salt, so that you may know how to answer everyone.” -Colossians 4:6

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