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Quoting wikipedia:

Greater choice and variety of mates increases a female's chance to produce more viable offspring.

This led me to the question: "How sperm parameters are connected with entity parameters?"

Actually, sperm parameters are usually: motility and morphology. I am speaking about a single sperm, therefore any parameters involving their count or parameters of semen are not included.

On the other hand, what helps a particular entity to survive is determined by many parameters. Some of them are: speed, endurance, strength, agility, stealthiness and savvy. It is hard to find out how strength of being is connected with motility or morphology of sperm it has been conceived. And even less obvious is the connection of stealthiness with such sperm parameters.

But since sperm competition exist, it helps in natural selection, therefore there must be a connection. But how does it really work? How are stronger/faster/stealthier/etc. entities are the product of more motile or better in morphology sperm?

After some thinking about it I think that if there is some correlation between sperm parameters and genome, it can answer the question. E.g. presence of gene that increases fitness of organism makes sperm faster.

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Greater choice and variety of mates increases a female's chance to produce more viable offspring.

The claim is a little hard to address because it is vague. However, one can give a simple example to give you a feeling of why this could be the case.

This example is based on Zaahavi handicap principle. Spermatozoids aren't free to produce. A male that can produce more and stronger spermatozoids can do so because he is a healthy males. As many of the traits that determine health, in a general sense are heritable, healthier males tend to have healthier offspring.

On the other hand, what helps a particular entity to survive is determined by many parameters. Some of them are: speed, endurance, strength, agility, stealthiness and savvy.

You are mainly listing traits that are very specific to human's sport ability. In reality, there are loads of other traits that are much more fundamental such as the efficiency of the potassium pump or of the mechanism to produce ATP.

[..] it helps in natural selection [..]

I don't understand what you mean by this sentence.

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  • $\begingroup$ "I don't understand what you mean by this sentence." This is how biology works. Females who were involved in multiple-male relationships with sperm competition gave birth to more fit offsprings. Otherwise sperm competition would not exist. Also, you are ignoring the principle: why sperm competition is more efficient for females than sexual selection? (And males in many species are more sexually selective when it comes to how female looks). $\endgroup$
    – rus9384
    May 13, 2018 at 15:07
  • $\begingroup$ "healthier males tend to have healthier offspring." Actually this should make female sexual selection superior to sperm competition but somewhy it really isn't. "You are mainly listing traits that are very specific to human's sport ability." Not really, speed is helpful for animal to run away from predator and it is helpful for predator to catch an animal. Same applies to stealthiness, for example. Instead, in humans intelligence massively outweights such parameters (well, strength is needed to make and use tools, but other parameters are not that essential). $\endgroup$
    – rus9384
    May 13, 2018 at 15:36
  • $\begingroup$ @rus9384.Isn't that just biased stats? Ain't it possible that the females gave birth to more fitter offsprings precisely bc they mated with a more fitter guy?I mean they mated with more people. And in monogamous relationships,you only mate with one person, ofc that one person can be either a very fit guy or a unfit guy. Its all on probability. Females who'll mate more people will have more odds of mating with a fitter guy rather than monogamous folks,I think its just a simple trick of stats you say,fitter here means in the evolutionary context.Sorry if I'm wrong,this is just pure speculation. $\endgroup$
    – AScientist
    May 14, 2018 at 4:27
  • $\begingroup$ And that speed comes from more efficient ATP generation.That strength comes from more efficient potassium ion pumps in nerves and muscle cells. $\endgroup$
    – AScientist
    May 14, 2018 at 4:29
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You are over thinking sperm competition, just like two males can compete for access to a female, multiple sperm compete for access to eggs. If male A's sperm are faster than male B's sperm and both are present in the same female, more of her offspring will be from male A. So male A has advantageous genes. Additionally that female is going to have male offspring that may also engage in sperm competitions so having good genes for sperm competitions benefit her genes in the long run.

It benefits her in the same way having more males compete for her helps her: she is getting the best from a wider selection of individuals thus more likely to carry genes that will benefit her male offspring. Every mating is a roll of dice, those who can play the game more often have a better chance of getting a jackpot. If male A has Gene X and male B has Gene Y the female gets offspring with gene X and some with Gene Y. Since most genes are contextual it increases her chances of getting a better gene into her offspring.

Let's think of an example:

Female A mates once with the best male of 5.

Female B mates 3 times with the best male from three separate competitions of 10 males each.

Female B has an advantage because she not only has taken the best from a wider range of options, Thus by pure chance is more likely to get the best available genes, but also because she had three separate chances vs just one.

Now of course there are thousands of other factors at play like offspring cost this is just for understanding why competition helps both males and females in some cases.

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  • $\begingroup$ "that female is going to have male offspring that may also engage in sperm competitions" The problem with such reasoning is following: sperm competition is the consequence of sperm competition itself while it can't be true. Females started to be involved in multiple mate sex not because of faster sperm being more competetive. If there are some genes (as I proposed) which both increase fitness of offspring and sperm, than I would like to see any research supporting this. $\endgroup$
    – rus9384
    May 13, 2018 at 21:46
  • $\begingroup$ The gene does not have to make healthier offspring just healthier sperm, There are genes that reproduce themselves at the expense of the organism,(R2D2 in rats), genes do not have ot benefit the organism they just need to spread themselves. . to tweak a famous biology saying, sometimes a man is a just a sperm's way of making another sperm. There is nothing special about males or sperm they are both products of genes. $\endgroup$
    – John
    May 13, 2018 at 21:57
  • $\begingroup$ But how does it justify the sperm competition itself? E.g. if everyone stops sperm competition nothing differs according to your point (which is wrong, females with lesser fitness will give birth to the same amount of children, as opposed to polygamic species). $\endgroup$
    – rus9384
    May 13, 2018 at 22:07
  • $\begingroup$ If peacocks stopped there displays and females stopped preferring displays both would be far better off, the costs are huge, but any adaptation to do so is quickly selected out of the population because it has to deal with all the other females who are looking for the display. sexual selection can be hugely detrimental to an organism as long as it favors the genes. All it takes ot start sperm competition is females who mate with more than one male which is not uncommon in the slightest, in many cases it is not even the females choice. $\endgroup$
    – John
    May 13, 2018 at 22:16
  • $\begingroup$ The reason why peacock females preferred displays is a coincidence of natural selection: it was easier for females to notice those peacocks who had more colorful tails. Therefore, their male offsprings became more colorful through natural selection at first and female offspring became to care about male tails through natural selection. But then they start to choose males who are too noticable. This is what I call sexual selection overkill. $\endgroup$
    – rus9384
    May 13, 2018 at 22:22

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