A more formal theory of why sex evolved (draft)

A more mathematical or formal look at my theory on the evolution of sex: the advantage of sexual reproduction to the genetic material that codes for it.

Julian O’Dea PhD
Canberra, Australia
(November 2015)

My understanding is that sexual reproduction is often seen as a puzzle because it would seem to impose heavy penalties on both the individual and the population:

• On the individual because half of its genes are not passed on during sexual reproduction and time and resources must be spent on finding a mate.
• On the population because (in some cases) half of the population (males) do not directly produce young.

In my view, both these concerns may focus on the wrong level of selection. If sexual reproduction is viewed in the light of the genetic material itself – both in terms of its being a feature of the material and in terms of its advantages and disadvantages – its evolution could perhaps be explained.

I have written about this idea previously (O’Dea, 2006) and the proposal has been cited (Glansdorff et al. 2009). But in this case I want to try to make the argument (slightly) more rigorous and (slightly) more mathematical.

Suppose G is the percentage of genetic material in the population that is found in sexually reproducing individuals. Let G! be the percentage of such genetic material in the next (new) generation.

The value of G! may be as follows:
G! = G x R x T

Remember G! is the new percentage of genetic material reproducing sexually in the population (the remainder is assumed to be reproducing asexually.)

R is the mean ratio of improved fitness of the organisms containing the relevant [sexually reproducing] genetic material. (I would expect R to be considerably greater than 1 because of improved genomic combinations from sexual reproduction due to novel advantageous mutations being shared and the generation of genomes more closely fitted to any changes in the environment.)

T is the ratio of the fitness factor imposed by sexual reproduction compared with asexual reproduction. (I would expect T to be slightly less than 1 due to the time and resources spent on reproducing sexually instead of asexually.)

It seems to me that it is conceivable that G! will typically be greater than G (for the reasons given in bold above). If so, the percentage of genetic material reproducing sexually (and therefore organisms containing such material) will increase over time in the population.

Most organisms are sexual, with a few noteworthy exceptions (rotifers, for example). The above kind of consideration may well explain why.

References

Glansdorff, N et al. (2009). “The Conflict Between Horizontal Gene Transfer and the Safeguard of Identity: Origin of Meiotic Sexuality”. Journal of Molecular Evolution
69 (5): 470-480

O’Dea, JD (2006). “Did conflict between chromosomes drive the evolution of sex?” Calodema (Sydney: Trevor J. Hawkeswood) 8: 33–34.

O’Dea, JD “Why Sex REALLLY evolved”. Academia.edu (https://www.academia.edu/11776453/Why_sex_REALLY_evolved)

NOTE: I am not much of a mathematician (and the above is more an attempt at logic than real maths). If I have made any errors, or the above could be improved, I would like to be told (politely if possible) in a comment. The above is just an initial draft.

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22 responses to this post.

  1. A genetic mutation is a very hit or miss thingo and even more infrequent. And for every mutation that produces an accidental benefit there are many more likely to produce a deficit.

    Reply

    • Genetic mutations are pretty common. I see two advantages with sex. It can co-opt the good genetic mutations and spread them around and it can cover up the deleterious ones by introducing genes that compensate.

      With sex, it is as if one is playing the game with more cards.

      Reply

  2. Regarding your first link, I found this to be an interesting read: http://www.thedivineconspiracy.org/Z5211B.pdf

    I’m currently doing a (very long) blog post on various parts of Baumeister’s address – backing up certain parts with citations and expanding on others. At this point in the process, I think he really knows what he’s talking about.

    Reply

    • Yes, I saw that some time ago.

      These articles about why sex exists often seem to phrase the “problem” in terms of males.

      What I have attempted to do in this paper:

      https://www.academia.edu/17988383/Explaining_the_evolution_of_sex_using_the_selfish_gene_a_simple_model

      is explain how sex originally evolved. The problem sometimes based on “the twofold cost of sex” (which relates to the puzzle of why males and females exist in some higher organisms) is really a separate problem to the origin of sex. Many organisms do not show much male and female differentiation. So there is no special “cost” of males.

      I can’t say I fully understand the “twofold cost of sex” issue. The differentiation of sexes may have evolved because having female care is an advantage in assuring the survival of the young. So, it is a “feature” not a “bug”.

      I also have a feeling that this is another case of physical scientists and mathematicians (which is what the relevant thinker, John Maynard Smith, was originally) reasoning a priori about animals. I don’t want to accuse such a clever man as Smith of being ignorant, but many organisms don’t present the kind of problem he had in mind, it seems to me, and I think he ignores the point that animals have a history of evolution (once an organism has evolved, say, impregnation and live birth, it is not going to be possible to go back to parthenogenesis. A few lizards do it, and I think some sharks, but I know of no cases in birds or mammals.)

      To take a fairly common and typical type of organism – a fish – I can’t see that male fish somehow contribute less to the next generation. Both male and female fish produce very large numbers of gametes, so I can’t see that there is a bottleneck in reproduction imposed by the existence of separate males and females.

      As to “what is the good of human males?” in a social sense, I think one has a good control for what happens when men can’t or won’t make a contribution to civilisation in the condition of agricultural Sub-Saharan Africa. Feminists of course “celebrate” the huge contribution of women in those parts to daily production, but it is hardly that impressive objectively.

      In fact, if one were in the right mood, one could draw an analogy and point out that males, biologically and socially, seem to provide something very valuable. Animals that don’t have males are mostly undistinguished little creatures like rotifers; and societies with non-functioning males are mostly undistinguished societies like agricultural Africa. I think people intuitively know that men are the leaven of society.

      Reply

  3. Posted by Julian O'Dea on April 1, 2016 at 9:53 am

    http://www.eurekalert.org/pub_releases/2016-04/ku-ltv033116.php

    Lifting the veil on sex: Can males be less expensive?

    Reply

  4. Just a point of notation. Mathematicians use the ! sign to denote factorials (eg 5! = 1 x 2 x 3 x 4 x 5). So I suggest you use G* or similar, not G!.

    Reply

  5. Posted by Julian O'Dea on September 25, 2016 at 11:55 am

    http://www.ncbi.nlm.nih.gov/pubmed/22835046

    “Asexual evolution: Do intragenomic parasites maintain sex?”

    Reply

  6. Posted by Julian O'Dea on October 26, 2016 at 11:22 pm

    http://rspb.royalsocietypublishing.org/content/283/1841/20161280?etoc

    “Sexual conflict and the evolution of asexuality at low population densities”

    Reply

  7. Posted by Julian O'Dea on October 31, 2016 at 8:30 am

    http://cz.oxfordjournals.org/content/early/2016/10/19/cz.zow102.abstract

    “Selfish genetic elements and the gene’s-eye view of evolution.”

    Reply

  8. Posted by Julian O'Dea on November 5, 2016 at 12:57 am

    A record at the Australian National University:

    https://openresearch-repository.anu.edu.au/handle/1885/31410?mode=full

    Reply

  9. Posted by Julian O'Dea on November 24, 2016 at 11:03 pm

    http://stevemoxon.blogspot.com.au/2016/11/new-book-sex-difference-explained-from.html#links

    “In SEX DIFFERENCE EXPLAINED: From DNA to Society – Purging Gene Copy Errors, Steve Moxon argues that all major aspects of male-female human sociality necessarily stem from biological principles; which all arise in solving the core problem faced by all life-forms: the relentless build-up of mistakes in the repeated copying of genes. The ‘genetic filtering’ to deal with this is the function of the male: why males came into being, and why men so fiercely compete with one another to form a hierarchy.”

    Reply

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