The Three Necessary and Sufficient Conditions of Natural Selection

Natural Selection is the key creative force in evolution. Natural selection, together with specific histories of populations (species) and adaptations, is responsible for the design of organisms. Most people have some idea of what Natural Selection is. However, it is easy to make conceptual errors when thinking about this important force of nature. One way to improve how we think about a concept like this is to carefully exam its formal definition.

In this post, we will do the following:

  • Discuss historical and contextual aspects of the term "Natural Selection" in order to make clear exactly what it might mean (and not mean).
  • Provide what I feel is the best exact set of terms to use for these "three conditions," because the words one uses are very important (there are probably some wrong ways to do it one would like to avoid).
  • Discuss why the terms should be put in a certain order (for pedagogical reasons, mainly) and how they relate and don't related to each other.

When you are done reading this post you should be able to:

  • Make erudite and opaque comments to creationists that will get you points with your web friends.
  • Write really tricky Multiple Choice Exam Questions if you are a teacher.
  • Evolve more efficiently towards your ultimate goal because you will be more in control of the Random Evolutionary Process (only kidding on this third one...)

Here are some definitions of Natural Selection I found on the web for your review:

  • The differential survival and reproduction of organisms with genetic characteristics that enable them to better utilize environmental resources [source]
  • Natural selection is the process in which some organisms live and reproduce and others die before reproducing. Some life forms survive and reproduce because they are better suited to environmental pressures, ensuring that their genes are perpetuated in the gene pool. [source]
  • Process by which the genotypes in a population that are best adapted to the environment increase in frequency relative to less well-adapted genotypes over a number of generations. source
  • The concept developed by Charles Darwin that genes which produce characteristics that are more favorable in a particular environment will be more abundant in the next generation. [source]
  • the differential survival and/or reproduction of individuals within a population based on hereditary characteristics. [source]
  • The process by which new species evolve when influenced by selective pressure (Martin et al, 2000). Natural selection occurs when the natural factors of environmental resistance tend to eliminate those members of a population that are least well adapted to cope and thus, in effect, select those best adapted for survival and reproduction (Nebel et al, 1998). [source]
  • central thesis of the biologist Charles Darwin which suggests that within every population of living organisms there are random variations which have different survival value. Those which aid survival (or enhance reproductive capacity) are 'selected' by being genetically transmitted to succeeding generations. [source]

There are things I don't like about most of these definitions. A definition may focus on environmental conditions and thus ignore many very important other things such as developmental processes and mating. Definitions may focus on the individual's survival, etc., which works, but we may want to speak of traits as well as individuals. Some definitions use active verbs such as "ensuring that their genes are perpetuated in the gene pool." This may not be linguistically wrong but it incorporates teleological concepts, which don't need our help in creeping into our thinking (especially in the formal definition of a natural force!). There is often a direct link to Charles Darwin. This is good because it is true that this is his concept. However, a modern definition of Natural Selection needs to be Neo-Darwinian. So specifically referring in the definition to Darwin without more attention to the historical development is inadequate. Referring to Darwin's concept as a concept about genes is jarringly wrong.


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As a whole these definitions are not terrible, but they are mostly flawed for one reason or another. The definition I want to lay out here will have specific reference to the same process these definitions are about. However, there is also one very large problem with many of these definitions that is a bit more subtle than most but that is, to me, critical, that relates to the object of study. It is probably best to not assume a one-to-one correspondence between the process of Natural Selection that we are going to describe here and the concept of "adaptation." Ultimately, I would like to say that "adaptation" is the noun and "Natural Selection" is the verb in a key evolutionary process. But having said that, a useful and precise definition of Natural Selection may have to leave out processes that are nonetheless related to adaptations, both in terms of understanding the historical aspects of an adaptation and the functional aspects, but that do not fall under the process "Natural Selection" as it is best defined.

An adaptation may reach its particular form through the process of Natural Selection, but there are aspects to that form that have to do with, for instance, abiotic realities. You cannot have adaptations that involve swimming without bodies of water, for example. Our definition does not say "Oh, and there must be air, and water, and trees to climb in."

I actually want to provide TWO different (linguistically) but identical (functional) definitions of natural selection. The first is the coolest one, the simplest one, the one that makes you think. The second is a better pedagogical tool and serves better as the basis for adaptationist analysis of biological systems. The second also links better to certain historical aspects of the development of the concept.

The first definition is conceptually related to the following definition of evolution:

Change in allele frequency over time.

Which is something of an oversimplification, but an allowable one. And in this context we can define Natural Selection as:

Nonrandom elimination of alleles.

I believe that this was suggested by Ernst Mayr.

This is a cool definition because it is short, sweet, and correct. Note the very important asymmetry that this definition implies. There is no non-random generation of novel alleles. Only elimination. This jibes with selection as a creative force, but neutral processes as providing the raw material. Neutral processes lay down the sediments that become the marble, Natural Selection is the sculptor. The adaptation is the sculpture.

The second definition, and the one I really want to get to, involves the so called "three necessary and sufficient conditions" and it goes something like this:

  1. Variation in a trait
  2. Heritability of the trait
  3. Differential fitness conferred by the trait.

Just as important as these elements is the theoretical and logical framework in which they are placed. They are the THREE NECESSARY and SUFFICIENT conditions. Let's parse that out more.

Three ... That there are three is obviously because all important things happen in threes, sevens, or tens, for unknown cosmic reasons. Be that as it may, I want to point out that "three" implies "three different" things. If two of them could have been combined, then we would have only two. But there are three.

What this implies is the following: If there is a trait that varies, then it meets the first criterion. But "No," you say, "what about hair color? If I see a bunch of people with different color hair, and I KNOW they dyed their hair to get that way, this is not trait related to selection. So it does not meet the first criterion."

But you would be wrong. Remember, there are THREE DIFFERENT criteria. The first one is variation. If you see a bunch of dogs and they have different coats because they went to a very creative groomer, or a bunch of students standing around the cafeteria with blue, red, unnaturally black, and vivid yellow hair because they all went to Target and got dye and colored their hair, then in both cases you have met the first criterion because there is variation. By saying "these traits are not inherited" you have skipped ahead and cheated.

The second criterion is usually stated as "heritability" and that is a small problem, because the term "heritability" has a specific meaning in biostats that falls apart for our present use. It is the measured variance in the genotype divided by the measured variance in the phenotype, squared. (Thus indicating something like the proportion of measured phenotypic variance that is accountable by genetic variation.) What is meant in our definition, however, is this: Is the variation in the trait conferred by genes? The dyed hair and the clipped poodle do not meat this criterion.

The third criterion is often stated as "Differential Reproductive Success" and that is simply wrong. The correct term is "Differential fitness" and it has to be differential fitness that is conferred by the trait. Why fitness instead of Reproductive Success (RS)? That is an important matter, and I will not discuss it here. For now, let's just go with it.

OK, back to the theoretical context: Necessary.

Why are these three necessary? By necessary it is meant that ALL of them have to be true or it is not Natural Selection. This is fairly obvious. If you are missing any one of these three then what you are observing may be an interesting phenomenon but it is not Natural Selection. This also speaks to the need to be Neo-Darwinian. Darwin was aware of inheritance, but lacking an understanding of the mechanism, the necessary requirement of "heritability" (remember, shorthand for "the trait is passed on by genes"), any Darwinian definition (and I've avoided using his specific words here) is not good enough.

I had said at the beginning that the ordering of the three conditions is important. This is because they interact with each other in order. Here is how.

First, you need a trait that shows variation. Second you need to show that that trait is heritable, AND that the inheritance pattern relates to that variation. Third you need to show that the variation that is heritable maps on to differential fitness. So there is a strong logic to the order, that is embedded in the functional meaning of Natural Selection and any test criteria that are set up to investigate possible cases of it.

So the ordering works both for the understanding of the concept (pedagogy) and the investigation of the phenomenon.

Sufficient. That is a really important part of the context for this definition. If these three conditions are true, then Natural Selection IS happening. There is no alternative. The force of Natural Selection is activated when these three conditions are met, no matter what.

Does this mean that the selective force will have an effect? It depends. Natural Selection is a force, but there are other forces, including other instances of Natural Selection that may be operative in a particular organism. Gravity is a force but a fly can still walk on the ceiling. The gravity is still acting on the fly, but so is another force (adhesion) that keeps it up there.

This is an important point that bears emphasis. When the Three N&S Conditions of N.S. are working, Natural Selection happens. Period. The absence of an EFFECT is due to countervailing forces (including chance, because within it's operation there are still stochastic effect).

I believe it is incorrect and counterproductive to make "Sexual Selection" distinct from and parallel to "Natural Selection." Darwin was puzzled by apparent inconsistencies, especially along the lines of exaggerated traits mostly in males, and came up with Sexual Selection as a process to explain this. Fine. But I think it is best to think of both Sexual and Artificial Selection as subsets of Natural Selection.

The term "Selection" by itself is often used interchangeably with "Darwinian Selection," but often (usually?) as not really meaning the same thing as Natural Selection. Natural Selection works between generations on reproducing organisms and their genomes. Darwinian Selection, or selection in general can work on other things, like prospective students trying to get into law school, or neurons during culling, etc.

This has been an enhanced repost from a very long time ago. You might imagine that I'm about to write a post on Falsehoods related to Natural Selection, and needed this post nearby. You'd be right!


Other posts of interest:

Also of interest: In Search of Sungudogo: A novel of adventure and mystery, which is also an alternative history of the Skeptics Movement.


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Good post Greg... can you help out the non-bio types by telling us what an allele is and how and why they vary?

An allele is simply a variant of a gene. So, there if in a given organism there is a "gene for tail length" (that would be oversimple, but as an example...) then there might be a "short tail" allele and a "long tail" allele.

"Why" they vary depends on what you mean by "why" ... but the "how" part of the "why" is simply that there is a slightly different getnetic code specifying a slightly different protein, or that there are more than one proteins involved and the "short tail" allele is simply a non-functioning version so you end up with a short tail.

IIRC, eye color is an allele.

Roger... Eye color is not an allele. There are various alleles that code for pigment proteins which are (normally) expressed in the iris. Many of different alleles can produce pigments which look the same. These alleles may (or may not) be expressed in other tissues and have other effects. Also, the function of alleles depends on the environment they are in (including the organism and the rest of the genome).

The last bit is a complication I like to point out with a simple question: What is the fitness of whatever allele on the moon? Answer = 0 for anything I can think of.

To the main point:
"Nonrandom elimination of alleles" almost gets it, but falls down a bit. The process doesn't actually need to eliminate the an allele from a population... just reduce the relative abundance.

I favor a mathematical definition of natural selection based on information theory. Probably not terribly useful pedagogically.

Here is a thought experiment wrinkle for you:
How would you describe natural selection with respect to things which don't reproduce? "Persist" is a useful word.

I also have never understood why sexual selection and natural selection were cosidered separately. I come at it from the idea of simple Darwinian Fitness, a measure of how succussful one is at raising offspring to sexual maturity. We know this varies; I can't think of any organism where all individuals produce the same number of offspring. Variation in fitness is necessary, but not sufficient, There has to be some correlation between genotype and fittness. If so, then natural selection can happen.

Of course, there is Inclusive Fitness, which is a measure of how many copies of your genes you manage to pass on to the next generation. This is more sophisticated, harder to measure, and more directly tied to natural selection.

It strikes me that natural selection is a statistical phenomenon. So, in small populations, it may be overwhelmed by the noise of luck.

By Jim Thomerson (not verified) on 25 Aug 2009 #permalink

Roger: "IIRC, eye color is an allele."
Um, there are multiple alleles for eye colour, but eye colour its self is not an allele. (However it might be possible that albino/not albino is a separate trait, thus leading to coloured/not coloured eyes as the alleles)

Nice post, but for the first definition wouldn't "nonrandom changes in allele frequency" be better? There must be many cases where you don't need to have elimination of alleles for natural selection to occur.

Hilary is right. If carriers of one allele just out-reproduce the hell out of carriers of the other allele -- e.g. entirely occupying a new environment -- natural selection has occurred. The difference between alleles might not even matter; it could just be luck that that allele was carried into that environment first.

By Nathan Myers (not verified) on 25 Aug 2009 #permalink

Actually, Nathan, that's called the Founder Effect, and it is not natural selection, it's closely related to genetic drift when no selective pressure is involved. Now, a differential Founder Effect (populations with allele x stay and allele y are forced into new territory previously) IS selection in a sense, but not the classical sense and I have seen no evidence of this actually occurring.

Hilary and Nathan: You are lucky you are not talking directly to Enrst, because he would just call you ninkompoops and walk away!!!

Jared is right. Look at the definition. One two three. Natural selection is not change in what adaptation is out there or how common it is. That can happen a lot of different ways. The hypothetical scenario you describe is genetic drift.

Great post, Greg. Not only for the science, but for the very readable and simple explication of "necessary and sufficient." Tricky terms, almost as often misunderstood as "natural selection". You've explained them clearly.

One quibble. You say "This jives with selection as a creative force". The word is "jibe" (or 'jybe' or "gibe"); not "jive". says its derivation is uncertain, but I think it comes from the nautical use of the term; when you're running before the wind and want to shift course slightly in the direction of the wind, you have to bring the boom of the mainsail to the other side of the mast, to let the sail fill most efficiently. It can be a violent maneuver (and frequently catches beginners by surprise, leading, in worst-case scenarios, to a snapped mast), but the overall effect of a controlled jybe is to bring the boat's trim into conformity with the wind and fill the sails without having them flap.

Just so you know.

With admiration and regard,


So you seem to be saying that changes in allele frequency are only ever the result of genetic drift? I don't agree - I was specifically thinking of situations where the difference between alleles definitely does matter, not just where individuals with a particular allele happen to reproduce more by chance as in Jared's example. What about frequency-dependent selection in the immune system for example? Where a pathogen evolves resistance to a common allele but remains susceptible to rare alleles, causing those rare alleles to become more common and the common alleles to become rare. There is not necessarily elimination of alleles in this example. Are you saying this is not an example of natural selection?

Hilary, let's call your alleles C and R, C being common and R being rare, when a single allele is selected for, there will be elimination of other alleles. There may be, as the case in the immune system, multiple other parts of the genome with very similar sequences for a very similar function, but these are different alleles. The reason for the frequency of R to increase is due to the higher risk associated with C resulting in untimely death, not the survival of R, but the lack of survival of C. Alleles do not have to be eliminated completely, (as in Sickle Cell with heterozygous individuals having optimal survival) but the selection IS resulting from the death of homozygous R and homozygous C.

In short, selection does not require elimination of an allele from a population, just differential survival (or reproduction) conferred by alleles.

A good example, I think, may come from Plasmodium and it's interaction with Sickle Cell. Heterozygous individuals (because it is co-dominant) have the benefits of Sickle Cell and non-sickle hemoglobin.

[13]So you seem to be saying that changes in allele frequency are only ever the result of genetic drift?

By definition, there are exactly two (natural) causes for change in allele frequency: Non-random (= selection) and random (= drift)

[14] The term "elimination" does not mean "elimination from a population" .. it means elimination on a case by case basis, via selection on individuals.

Sickle cell gene is not dominant. It codes for a B-polypetide which has a "greasy spot" on its surface and is thus less hydrophyllic than the normal B-polypeptide. When an individual is hetrozygous, both sickle and normal B-polypeptides are produced. (One wonders if ratios vary among individuals and among RBC's of a particular individual.) I am confused as to whether this is codominance or incompete dominace.

As I recall, in the "village in Western Nigeria" I had the data for, 8% of homozygous normals died early of malaria, and almost all homozygous sickle individuals died early. As said, heterozygotes were immune to malaria.

The only heterozygote I have known personally was a female student on our cross-country track team. She told me she made every effort to stay fit and avoid going anarobic.

I think one could teach a pretty good comprehensive biology course of study only discussing sickle cell anemia. It covers all the bases from molecular biology to social policy questions.

By Jim Thomerson (not verified) on 26 Aug 2009 #permalink

Sorry, I missed the last paragraph of jared's post. What he said!

By Jim Thomerson (not verified) on 26 Aug 2009 #permalink

"Evolve more efficiently towards your ultimate goal because you will be more in control of the Random Evolutionary Process (only kidding on this third one...)"

Wait, isn't there a falsehood for this?

Actually, Jim, I think you can use ring species, sickle cell, and the four Agkistrodon species to fairly well illustrate evolution, but to teach eukaryotic genetics and mutation, you really need Drosophila and Saccharomyces. Prokaryotic genetics really needs at least Bacillus, Vibrio fischeri, Pseudomonas, Mycoplasma, and, of course, E. coli. Then, of course, you have the genetics of viral species, which are so very distinct from one another, you can't really have a single model for each type.

I think sickle cell is a very useful illustrative tool because it's so well documented. (not really, but more so than other things like lactase persistence) It still doesn't really illustrate enough to cover the breadth of biological systems, though, but it would make a good starting point for many different lectures. Maybe I'll put a some together to see what it can be used as an introduction for.

Jared. If you want a good teaching model, I've got one for you...

..... one word. Globins.

[14] The term "elimination" does not mean "elimination from a population" .. it means elimination on a case by case basis, via selection on individuals.

Ah, there's the discrepancy. I was taking your definition to mean on a population level (as thats how I tend to think about allele frequencies), not elimination of individuals with particular alleles. In that case I fully agree with your definition!

By Hilary Miller (not verified) on 27 Aug 2009 #permalink

One of my colleagues, a biochemist, claimed expertise on sickel cell anemia. She felt that we field biologists were operating on a lower level. Once I got interested in sickle cell, I followed it in the literature and was pleased to call her attention to articles she had not seen. Because my interests were broader than hers, I read literature which she did not see. Anyway, so long as one is not homozygous for sickle, it is pretty neat stuff.

By Jim Thomerson (not verified) on 27 Aug 2009 #permalink

Science educators need a good scientific description of how selection operates in nature. What are the causes and consequences of evolutionary processes?
The following is my proposed scientific description of natural selection.

Charles Darwin (1859:62) used the metaphor âStruggle for Existenceâ to describe the ecological interactions that individual organisms have with (1) the physical conditions of their environment, (2) individuals of other species, and (3) individuals of the same species. These ecological interactions cause the natural (including sexual) selection of hereditary variations, that is, cause the selective survival of genes, the selective exponential multiplication of genes and the selective recombination of genes (via mate choice) that affect adaptations (designs) for survival and reproductive success each generation.
The adaptations we observe today are the product of natural selection operating on genetic variation produced by mutations, sampling error (genetic drift) and selective recombination (via mate choice) each generation over billions of generations.

Science educators need some kind of comprehensive description like this to help students better understand what processes cause adaptive evolution and its relationship to nonadaptive evolutionary processes. Evolution is the result of "chance and necessity" with necessity (selection) superimposed on chance every generation.
This is a proposal. There probably are better ways to summarize the causes and consequences of selection that also include interations with accidents--mutations and sampling error.

By Carl Bajema (not verified) on 28 Aug 2009 #permalink

What you are describing is selective breeding done by nature, not man. The problem is that selective breeding produces new breeds and varities but not new species. I am talking about species that can not interbreed with the parent species due to genetic incapatibility, not species that simply don't for a variety of reasons. I think genetic incapatibility in closely related species must have something to do with changes in the chromosomes. I have been curious about this for a long time but a never had anyone to ask. So, how do these changes occur? How come horses and donkeys cannot produce fertile offspring, but all the very different looking dog breeds, wolves and coyotes can?

With horses and donkeys it is a matter of number and make-up of chromosomes. This is not always the case. I crossed blackstripe topminnows (40 chromosomes) with blackspotted topminnows (48 chromosomes) and got fertile hybrids. There are sixteen known localities where these two species occur together. They produce a few hybrids, but there is no evidence of of nuclear gene introgression beyond the area where they are together.

Isolating mechanisms for species can be divided into premating and postmating. Basically the premating mechanisms keep them from trying and the post mating mechanisms keep them from succeeding. The basic idea here, which is not always true, is that individuals who hybridize have reduced fitness.

Suppose all canids except Great Danes and Chiuahuas became extinct. How many species of canids would be left? One or two?

By Jim Thomerson (not verified) on 28 Aug 2009 #permalink

Jim: one. But it would quickly go extinct depending on certain details.

Marcie: There are a lot of things that can make two populations unable to reproduce that can be genetic other than chromosome differences, but chromosome differences certainly could have more importance than we usually assign.

Artificial insemination is a normal and regular practice
in certain breeds of dog where natural mating is difficult. My question was not about how nature prevents genetically compatible species from interbreeding. I want to know how genetic incompatibility developes. How do changes in chromosomes come about for example?

If we presume no human intervention, I would see Great Danes and Chiuahuas as having strong premating isolation and likely postmating isolation as well. Whether extinction would occur is speculative and irrelivant.

In the topminnows mentioned above, there is the fusion of two small acrocentrics to form one large metacentric. The hybrids have 44 chromosomes. In meiosis two little acrocentrics line up with each metacentric, and meiosis proceeds right along. Interestingly enough, there is a natural population with 44 chromosomes which is not the result of interspecific hybridization. I am pleased that colleagues are carrying on further investigation of these species.

By Jim Thomerson (not verified) on 29 Aug 2009 #permalink

Natural Selection
Beyond Historical Concepts

Natural selection is E (energy) temporarily constrained in an m (mass) format.

Dov Henis
(Comments From The 22nd Century)
03.2010 Updated Life Manifest
Cosmic Evolution Simplified
"Gravity Is The Monotheism Of The Cosmos"

By Dov Henis (not verified) on 08 Apr 2010 #permalink

"Natural selection is E (energy) temporarily constrained in an m (mass) format.

Really, my chair is natural selection?