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Me and some friends are interested in opinions for the following:

Conjecture

The maximum number of species must be limited by the maximum combinatorial/permutational space that can be occupied by DNA. Thus if there is a maximum physical genome size this is what will determine the maximum number of species that can possibly exist.

Explanation

E.G. say maximum number of DNA base pairs able to fit in a genome was $3$, each base pair can be one of either ${A,G,T,C}$. Then there are $4^3 = 64$ possible combinations of genomes. Extrapolate to genome sizes of $x$ base pairs, then there are $4^x$ combinations.

Questions

Would it be possible to claim that the underlying "blueprint" that codes for living diversity sets the absolute maximum for the total "diversity space"?

**Does it make sense to define the total number of species life can achieve with the simple function:

$S < 4^x$, where X is the maximum genome size measured in DNA base pairs?**

Notable Comments

@Shigeta: for $S<4^x$ the combinations involved quickly dwarf the number of atoms in the universe at ~10^80.

@GriffinEvo: Even at this simplification of: $S<20^{x/3}$ there are $1.024e+13$ possible combinations with just 10 codons, many many more than there is likely species in the world.

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You would have to alter the current library of amino acids- the 64 nucleotide patterns you mention currently only code for 20 amino acids –  GriffinEvo Nov 26 '13 at 7:43
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The edits made are good, but the robotics bit is a little out of place, so if that is better expressed as a biological question I will vote to reopen. Just as a note, given that a codon of three bases codes for 1 of 20 amino acids the better simplification would be 20^(x/3) ... at just 6 bases (2 codons) the number of possibilities is 10 times lower (400 vs 4096). Even at this simplification there is 1.024e+13 possible combinations with just 10 codons, many many more than there is species in the world. –  GriffinEvo Nov 26 '13 at 12:19
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Thank you @GriffinEvo I must argue that non-coding DNA has many functions: genome.gov/10005107 –  hello_there_andy Nov 26 '13 at 12:34
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let us continue this discussion in chat –  GriffinEvo Nov 26 '13 at 15:18
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@GriffinEvo There are 22 proteinogenic amino acids (including selenocysteine and pyrrolysine), not 20. Just playing the pedant here but I did my thesis on predicting selenocystein-containing genes so it's kind of a personal issue for me :). –  terdon Nov 27 '13 at 2:19

4 Answers 4

up vote 6 down vote accepted

Yes, we can say the number of species is limited as you conjecture. However, quick estimation shows that the limitation has no apparent usefulness:

A reasonable estimate of the largest known genome is 150 GB (150,000,000,000 or 1.5e11 nucleobases). The limit would be 4 raised to that power. That limit is so high that it is too large for most calculators to calculate. For instance. Wolframalpha.com fails to calculate 4 raised to 1e11, its maximum being about 4 raised to 1e9. The result of 4 to the 1.0e9 power is about 1.0e602059991 or 10 raised to the 602059991'th power.

That rough result, 1.0e602059991, is so enormous that it is exponentially greater than the number of atoms in the universe (which is less than 1.0e100). Hence, assuming the definition of species requires an organism to use at least one atom for its body, there is no consequence to saying the number of species must be less than this number.

The number of possible combinations of nucleotides is so outrageously large that it does not constrain the number of unique individual organisms or species.

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That's an interesting conjecture about the total amount of genetic variation that is possible. I would modify a few things. First, since the size of genomes varies greatly among organisms (from 0.5 Mb to 15 Mb just for prokaryotes), there should be a fifth character in your set, representing the absence of a nucleotide.

There are also issues of whether various combinations are equivalent. For instance, bacterial genomes are often circular, so if we could convert one genome into another simply by rotating it, we would consider those genomes identical. For example, if the genomes each had 99 As and 1 T, it would not be meaningful to say that they are different just because of the location of the T. I think this would require use of the multinomial coefficient to count the number of identical variants.

Regarding your main thesis, your use of the term "species" has no relation to how that term is used among biologists. Biological species include genetic variation, so each of them would include many of your species. Also, one criteria for identifying species is the clustering of these sequences (and the absence of other, intermediate sequences). This implies both that many possible DNA sequences simply cannot produce a viable organism and competition among similar genotypes is an important aspect of species identity.

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+1 Very good answer. Of course there is the fact that DNA contains more potential information that what a protein can contain. And therefore, the total space possibility of proteins from x base pairs is lower than $x^4$. the OP might be interested in the [quasi-species theory][en.wikipedia.org/wiki/Quasispecies_model] presented in [this book][amazon.com/Evolutionary-Dynamics-Exploring-Equations-Life/dp/… for example. –  Remi.b Nov 26 '13 at 8:27
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The OP might as well be interested to the concept of robustness ([this book][amazon.com/Robustness-Evolvability-Living-Systems-Complexity/dp/… for example) –  Remi.b Nov 26 '13 at 8:28

I'm going to define a species according to the biological species concept, probably the most widely "accepted" species concept where a species is a group of individuals that reproduce, or have the potential to do so. Using a simplified example I will show you that gene*environment interactions affecting phenotype can allow separate species to occur despite being genetically identical.

Imagine a very short section of DNA which affects seminal fluid proteins in a fruit fly. It is just 10 bases long. The first three triplets of bases code for a protein constructed of three amino acids which affects the females behavior upon receipt of the male ejaculate. The final base regulates the expression of the first codon and is sensitive to developmental environmental factors (let us say nutrient richness). When the development of the male fly is in a nutrient rich background the section of DNA produces all three codons in equal amount to construct a protein and that protein stimulates the female to release eggs for fertilization. If we take a genetically identical male reared in a nutrient poor environment then the regulatory base increases the production of the first codon's amino acid. This makes a different protein structure which no longer stimulates the female in to releasing eggs, therefore the males from nutrient poor backgrounds can not reproduce with the females from a nutrient rich background, and these two genetically identical populations are different species.

Thus I would say, no, the theoretical maximum number of species is not capped by the length of the DNA. However, given that just the potential number of bases (current highest estimates recorded are 150,000,000,000) far far far exceeds the number of species in the world, we can say that the number of base combinations is not the limiting factor on the biodiversity we see. That is down to evolution (selective and neutral processes). Phenotypes determine the ability of two individuals to reproduce, phenotypes are the result of more than just genetics:

$phenotype = genotype + environment + genotype*environment$

Further, as @mgkrebbs has already stated, the number of possible species (given by $4^x$ when $x$ is 150,000,000,000) is, not only far more than the number of species that do exist, but also far more than the number of atoms in the universe. Assuming each species requires at least one atom then the number of atoms available will halt increasing numbers of species before the number of possible base combinations does.

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Coupled with @mgkrebbs answer of atoms in the universe, I have been convinced to a great extent how irrelevant 4^x is. Thank you all for giving me the perspective! –  hello_there_andy Nov 27 '13 at 1:13
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the combinatorics involved quickly dwarf the number of atoms in the universe in fact. ~10^80 –  shigeta Nov 27 '13 at 15:28
    
Nobody would consider those flies to be different species. Since there are no females that will mate with the "nutrient poor" (NP) males, those males do not form a separate species -- they just fail to reproduce. Even if the NP males could mate with NP females (to the exclusion of other males), the NP population would not be a separate species because it would still maintain the potential to reproduce with the other members of this species. The isolation of the NP subspopulation from the rest of the species would be transient -- similar to physically separating them. –  adam.r Nov 28 '13 at 4:39
    
Maybe you could imagine some sort of feedback loop that would stabilize the mating preferences -- perhaps having been born on a certain type of fruit, they preferentially mate and lay eggs on that fruit. However, I still doubt they would be considered separate species if all that was needed was to transfer larvae between fruit in order to change the preference (which would probably happen on occasion in the wild) –  adam.r Nov 28 '13 at 4:44
    
@adam.r sorry, it is a gross over-simplification and to keep it simple I made the (unstated) assumptions that NP females would only be responsive to NP males, and that these environments were isolated during development - artificially bringing adults of the two groups together to mate would then lead to the conclusion that they are separate species as NP<->NP and NR<->NR matings would work... bit of a large jump but, like I say, it is an oversimplification. I should have been clearer in the answer but wanted to keep it simple. –  GriffinEvo Nov 28 '13 at 8:40

Well... this is true in the same way that books are constricted by letters. We could have more letters and create more combinations with the same length of DNA. But, like books, there are just so many combinations.

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Nice that you spotted the similarity with books. In fact it is more general than that.. it goes for the whole of language, music, computer programs and perhaps all kinds of technology (think about the periodic table). –  hello_there_andy Mar 6 at 1:30
    
Well... kind of. With all of those things you are true... except for music. I don't mean to be nitpicky; actually, the science behind the repetitive nature of music is quite fascinating. See this link for more info. youtube.com/watch?v=DAcjV60RnRw –  louie mcconnell Mar 6 at 1:33
    
I guess I simplified music to a string of notes and timings. E.g. the possible number of ways you can create a finitely long sheet of music. More generally I guess there are only a finite number of ways of putting various kinds of sound waves together? –  hello_there_andy Mar 6 at 1:36
    
Yes; in the video, it says that in a 5 minute time period (exactly 5 minutes, not a second more), there are about 10^67 different songs. –  louie mcconnell Mar 6 at 1:37

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