Stochastic vs Natural Selection

[StringJunky]

In the evolution of the changing prevalence of the colour of peppered moths in the industrial revolution – light versus dark - was the sooted surfaces of their habitats a stochastic effect or classed as natural selection? To my mind the sooted surfaces is stochastic and the predation on the poorly camouflaged whites was natural selection. Is this correct?

[Ophiolite]

I open with a disclaimer: my statistical skills are rudimentary.

 

However, consider the wikipedia article: "In probability theory, a purely stochastic system is one whose state is non-deterministic (i.e., "random") so that the subsequent state of the system is determined probabilistically. Any system or process that must be analyzed using probability theory is stochastic at least in part."

 

Since the industrial revolution poured out vast volumes of soot I see nothing stochastic about the occurrence of surfaces darkened by soot. Unless you wish to say events with a 100% probability of occurrence are stochastic.

 

I await a convincing correction on this point.

[StringJunky]

I was seeing the sooting as a random effect. which happened to cause a change in the choice of the predators. The predators caused the actual change in the allele frequency not the sooty environment the predator and prey exist in. I'm not arguing, just putting up a scenario that I have a rudimentary familiarity with as a focus for learning the difference.

Edited November 21, 2014 by StringJunky

[CharonY]

What is described in the OP has to be seen and discussed as multiple steps otherwise a discussion will be very confusing. First is the appearance or existing of allelic variances. There are dark moths and light moths even before the industrial revolution. However, before we talk about frequencies we have to distinguish their emergence due to mutation (which is random) from stochastic effects on the gene pool. While mutations are random, it is not what is meant with random or stochastic events when we talk about allele changes in populations.

The observed frequencies or frequency changes (i.e. increased prevalence of dark moths since the industrial revolution, at least before changes in air quality) are instead the result of ongoing selection. I.e. the amount of soot resulted in dark moths to be more successful than light ones. Hence the observed frequency is not the result of (random) mutations, but clearly of selection.

 

An example of genetic drift as a stochastic even would be more like this. Assume that there only a handful of moths alive, say with a 50:50 ratio. All but one randomly die (i.e. the color of the moth has no bearing on whether it lives or dies). Now all progeny come from this moth . Ignoring the obvious biological issue with this thought experiment the entire population will now be either light or dark, but not because the environmental pressures (i.e. soot) resulted in the frequency change but to an event that is mechanistically not related the traits conferred by the phenotype.

 

To summarize: the increase of dark moths (which are actually now decreasing with reduced particles in the air) is clearly deterministic and non-random. Selective pressures (predation in this case) favored the black phenotype.

[StringJunky]

What is described in the OP has to be seen and discussed as multiple steps otherwise a discussion will be very confusing. First is the appearance or existing of allelic variances. There are dark moths and light moths even before the industrial revolution. However, before we talk about frequencies we have to distinguish their emergence due to mutation (which is random) from stochastic effects on the gene pool. While mutations are random, it is not what is meant with random or stochastic events when we talk about allele changes in populations.

The observed frequencies or frequency changes (i.e. increased prevalence of dark moths since the industrial revolution, at least before changes in air quality) are instead the result of ongoing selection. I.e. the amount of soot resulted in dark moths to be more successful than light ones. Hence the observed frequency is not the result of (random) mutations, but clearly of selection.

 

An example of genetic drift as a stochastic even would be more like this. Assume that there only a handful of moths alive, say with a 50:50 ratio. All but one randomly die (i.e. the color of the moth has no bearing on whether it lives or dies). Now all progeny come from this moth . Ignoring the obvious biological issue with this thought experiment the entire population will now be either light or dark, but not because the environmental pressures (i.e. soot) resulted in the frequency change but to an event that is mechanistically not related the traits conferred by the phenotype.

 

To summarize: the increase of dark moths (which are actually now decreasing with reduced particles in the air) is clearly deterministic and non-random. Selective pressures (predation in this case) favored the black phenotype.

Thanks Is there a distinction between the soot and the predatory element in the selection process or are they both classed the same?

 

A stochastic event causes population change regardless of genetic makeup?

Edited November 21, 2014 by StringJunky

[MonDie]

CharonY, could it boil down to whether variable survival is more due to internal variables or external variables? For example, if all individuals experience the same external influences, then variable survival can only be due to internal differences.

[Arete]

If an event has an equal probability of eliminating all genotypes in a population, it will not cause the population to deviate from Hardy-Weinberg equilibrium - barring certain demographic changes which violate selection tests such as population subdivision. Therefore such an event will not show up in a test for selection, and is not generally considered a selective pressure. If all genotypes have an equal chance of being eliminated, none are being selected for.

 

Stochastic events can and do change the allelic frequency of a population and thus drive evolution. However, the result is stochastic via the random elimination of certain alleles, relative to their frequency in the population. This is generally why rare alleles have to have high fitness coefficients to persist in a population. If an allele has no effect on fitness, stochastic events are likely to eliminate it from the population.

 

Conversely, if an alelle has a net negative/positive consequence on fitness, and thus is selected for/against, the probability of it being eliminated from a population changes accordingly. Thus, selection will either favor the prevalence or elimination of the allele above and beyond simple chance. This is what is tested for when population geneticists look for the signature of selection in genes and genomes.

[StringJunky]

If an event has an equal probability of eliminating all genotypes in a population, it will not cause the population to deviate from Hardy-Weinberg equilibrium - barring certain demographic changes which violate selection tests such as population subdivision. Therefore such an event will not show up in a test for selection, and is not generally considered a selective pressure. If all genotypes have an equal chance of being eliminated, none are being selected for.

 

Stochastic events can and do change the allelic frequency of a population and thus drive evolution. However, the result is stochastic via the random elimination of certain alleles, relative to their frequency in the population. This is generally why rare alleles have to have high fitness coefficients to persist in a population. If an allele has no effect on fitness, stochastic events are likely to eliminate it from the population.

 

Conversely, if an alelle has a net negative/positive consequence on fitness, and thus is selected for/against, the probability of it being eliminated from a population changes accordingly. Thus, selection will either favor the prevalence or elimination of the allele above and beyond simple chance. This is what is tested for when population geneticists look for the signature of selection in genes and genomes.

So, soot is a selective pressure because it advantages dark moths and therefore not stochastic.

[Arete]

So, soot is a selective pressure because it advantages dark moths and therefore not stochastic.

 

Yes, that is correct. If a force favors the survival or reproduction of one phenotype/genotype over another, it is selective.

[MonDie]

If an event has an equal probability of eliminating all genotypes in a population, it will not cause the population to deviate from Hardy-Weinberg equilibrium - barring certain demographic changes which violate selection tests such as population subdivision. Therefore such an event will not show up in a test for selection, and is not generally considered a selective pressure. If all genotypes have an equal chance of being eliminated, none are being selected for.

 

[snip]

 

You were one step ahead. It's there in the spoiler anyway.

 

 

Coffee → ameteur speculation

 

"If an event has an equal probability of eliminating all genotypes in a population, it will not cause the population to deviate from Hardy-Weinberg equilibrium"

 

Aha! That is the effect. Imagine selection effects denoted by correlation coefficients describing the correlation between survival and that allele. Hypothetically, if an erratic environment is being inconsistent, introducing too much statistical noise, the effect will be a weakening of all selection effects. Suddenly everybody has a (roughly) equal shot at survival. In a large population, this will only stabilize the current allele frequencies. Yet, speculatingly, this should also make genetic drift a greater possibility.

 

Edited November 21, 2014 by MonDie

[StringJunky]

 

Yes, that is correct. If a force favors the survival or reproduction of one phenotype/genotype over another, it is selective.

Understood. Cheers.

[chadn737]

It should be noted that strength of selection and effective population size matter. In the case of the moths, I don't think its a problem and its clearly a case of natural selection.

 

Every trait has a selective advantage/disadvantage and is subject to stochastic effects. In this, what matters is the population size and strength of selection. If something has only a weak advantage or disadvantage, then in a small population, random processes can still dominate even over that weak advantage/disadvantage, rendering them irrelevant. However, as a population gets larger, these weak effects can increasingly be distinguished from stochastic processes, and so become subject to natural selection.

[MonDie]

This thread needs more equations.

[StringJunky]

This thread needs more equations.

What do you mean?

[MonDie]

What do you mean?

 

Stochastic events have been assigned various features in the previous posts: They don't disrupt H-W equillibrium (Arete) except by causing genetic drift if they severely reduce the population (CharonY); they carry the risk of alleles blinking out of existence (Arete); they can overpower selection effects in small populations (chadn737) by introducing noise into the system (my guess).

Some good equations could tie all this together (and answer my question of whether stochastic events actually favor H-W equillibrium).

Edited November 22, 2014 by MonDie

[StringJunky]

If they want to do that they are welcome. I'm happy with the answers now I've received so if you want to take it further I don't mind.

[MonDie]

Thanks, StringJunky.

 

Edit: It didn't append.

Edited November 22, 2014 by MonDie

[MonDie]

[...] If something has only a weak advantage or disadvantage, then in a small population, random processes can still dominate even over that weak advantage/disadvantage, rendering them irrelevant. However, as a population gets larger, these weak effects can increasingly be distinguished from stochastic processes, and so become subject to natural selection.

 

Couldn't this also be said of a randomly occurring but still selective event? It seems that stochastic events will kill an individual regardless, but they don't kill everyone because they don't happen for everyone (the external variable). Yet this random event would still introduce just as much noise is it were selective, assuming it was at least selecting for something different.